9-12 Curriculum Maps

ELA

The study of English Language Arts in the Bedford Central School District integrates language, literature, writing, speaking, and listening in accordance with New York State’s implementation of the Common Core Learning Standards. Vital to the curriculum is students' study of and consistent practice with critical thinking, as the students sharpen their analytic and interpretive skills as they progress through each level of school.

English 1R (9th grade)

COURSE TITLE: English 9th Grade

COURSE DESCRIPTION: In order to help students successfully transition into their high school careers, English 1 is designed to build a foundation of essential literacy skills, while also providing a wide, in-depth exploration of literary themes and concepts. The content area’s work is brought together with a wide variety of writing assignments and creative projects aligned with the Common Core Learning Standards. The course aims to allow students to learn, practice and develop skills essential to high school success, including researching, speaking, listening, writing, reading, studying, organizing, and accessing modern technology. English 1 students receive an unweighted H credential for earning at least a 90 average for the year.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Short Stories The Catcher in the Rye If I Could Fly	Lord of the Flies Persepolis Night Father The Odyssey A Streetcar Named Desire	To Kill A Mockingbird Just Mercy Twelve Angry Men	Poetry Romeo and Juliet The Merchant of Venice

UNIT TITLE:
NYS Standards:
NYS English Language Arts Learning Standards
Guiding Questions/Essential Questions:
How do stories about coming of age help us understand ourselves, others, and the challenges of growing up?
Unit Topics with Learning Objectives:
Reading Skills Identifying literary devices and explaining how they serve to develop theme, character, plot Symbolism, Tone and mood, hyperbole, irony, allegory, alliteration, couplets, iambic pentameter, onomatopoeia, format of Sonnet Historical/cultural significance of setting - both within the story and the time period in which it was written - and how it affects style, theme, characters’ actions Techniques authors use to develop their characters Vocabulary: synonyms, using context clues to decode unfamiliar words, defining words, etc Writing Skills Five-paragraph essay Introduction with thesis statements Writing in the literary present Identifying and selecting specific and relevant supporting details Using transitions Logical organization of ideas Creating strong conclusions Literary analysis essay Research Skills Defining Plagiarism Note-taking skills MLA format Parenthetical and block citations Properly formatting a works cited page using a variety of sources Evaluating the credibility of sources Grammar Writing complete sentences Identifying and correcting run-ons Comma usage with compound sentences, introductory phrases and clauses, parenthetical expressions, items in a series, and equal adjectives Subject verb agreement Pronoun-antecedent agreement Colons and semicolons Apostrophes Parts of speech
Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams, essays, and class discussions Question and answer sessions, both formal and informal —planned/spontaneous Conferences between the instructor and student at various points in the semester In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Quizzes, quick writes, journal responses, and Socratic Seminars Methods of Summative Assessments: Unit Exams Unit Essays Semester Assessment Final examination Projects (project phases submitted at various completion points could be formatively assessed)
Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

English 2R (10th grade)

COURSE TITLE: English 10th Grade

COURSE DESCRIPTION: While the fundamental goals for this course are the same as those for 1R, there is a distinct and challenging difference with regard to the pacing, complexity and style of the work. As a skills-based curriculum, the course will use literature to fuel activities involving reading, writing, speaking, thinking, and researching.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
The American Dream Short Stories, Poetry, and Non-Fiction Grammar Review: Parts of Speech Of Mice and Men A Separate Peace Tennessee Williams (Streetcar or The Glass Menagerie) Synthesis Essay	The Individual vs Society Short Stories, Poetry, and Non-Fiction Grammar Review: Parts of a Sentence Fences Master Harold and the Boys Fahrenheit 451 The Secret Life of Bees The Curious Incident of the Dog in the Nigh-Time Writing to influence: Advertising	The Power of Language Short Stories, Poetry, and Non-Fiction Grammar Review: Punctuation and Usage Orwell (1984 or Animal Farm) Inherit the Wind The Secret Life of Bees The Joy Luck Club Public Speaking and Speech Writing	The Search for Identity Short Stories, Poetry, and Non-Fiction Grammar Review: Syntax and Editing Shakespeare (Othello, 12th Night, or Much Ado About Nothing) Ordinary People The Kite Runner Things Fall Apart Thesis Building and Writing for Literary Analysis

UNIT TITLE:
NYS Standards:
NYS English Language Arts Learning Standards
Guiding Questions/Essential Questions:
How does the individual interact successfully or unsuccessfully with society?
Unit Topics with Learning Objectives:
Reading Skills Identifying literary devices and explaining how they serve to develop theme, character, plot Symbolism, Tone and mood, hyperbole, irony, allegory, alliteration, couplets, iambic pentameter, onomatopoeia, format of Sonnet Historical/cultural significance of setting - both within the story and the time period in which it was written - and how it affects style, theme, characters’ actions Techniques authors use to develop their characters Vocabulary: synonyms, using context clues to decode unfamiliar words, defining words, etc Writing Skills Thesis statements Introductions and conclusions Logical organization Selecting appropriate and relevant supporting details Sophisticated transition techniques Research Skills Parenthetical and block citations Using quotations Plagiarism MLA Grammar Writing complete sentences Identifying and correcting run-ons Comma usage with compound sentences, introductory phrases and clauses, parenthetical expressions, items in a series, and equal adjectives Subject verb agreement Pronoun-antecedent agreement Colons and semicolons Apostrophes Verb tenses - identify and appropriate use Appositives Parallel structure
Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams, essays, and class discussions Question and answer sessions, both formal and informal —planned/spontaneous Conferences between the instructor and student at various points in the semester In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Quizzes, quick writes, journal responses, and Socratic Seminars Methods of Summative Assessments: Unit Exams Unit Essays Semester Assessment Final examination Projects (project phases submitted at various completion points could be formatively assessed)
Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

English 2H (Honors English 10th grade)

COURSE TITLE: Honors English 10th Grade

COURSE DESCRIPTION: While the fundamental goals for this course are the same as those for 2R, there is a distinct and challenging difference with regard to the pacing, complexity and style of the work. In that many of the students will continue into our junior and senior honors and AP courses, 2H students will work on open-ended assignments that require a greater sense of organization, collaboration, independence, and motivation to complete. Lengthy, independent reading assignments are a regular part of this course.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Analyzing Literature Short Stories, Poetry, and Non-Fiction Grammar Review	Of Mice and Men Anatomy Thematic Essay Socratic Seminar Creative Writing	Othello Animal Farm Public Speaking & Speech Writing Rhetorical Devices Argument Essay	Fences Poetry Screenwriting

UNIT TITLE:
NYS Standards:
NYS English Language Arts Learning Standards
Guiding Questions/Essential Questions:
How does the individual interact successfully or unsuccessfully with society?
Unit Topics with Learning Objectives:
Reading Skills Identifying literary devices and explaining how they serve to develop theme, character, plot Symbolism, Tone and mood, hyperbole, irony, allegory, alliteration, couplets, iambic pentameter, onomatopoeia, format of Sonnet Historical/cultural significance of setting - both within the story and the time period in which it was written - and how it affects style, theme, characters’ actions Techniques authors use to develop their characters Vocabulary: synonyms, using context clues to decode unfamiliar words, defining words, etc Writing Skills Thesis statements Introductions and conclusions Logical organization Selecting appropriate and relevant supporting details Sophisticated transition techniques Research Skills Parenthetical and block citations Using quotations Plagiarism MLA Grammar Writing complete sentences Identifying and correcting run-ons Comma usage with compound sentences, introductory phrases and clauses, parenthetical expressions, items in a series, and equal adjectives Subject verb agreement Pronoun-antecedent agreement Colons and semicolons Apostrophes Verb tenses - identify and appropriate use Appositives Parallel structure
Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams, essays, and class discussions Question and answer sessions, both formal and informal —planned/spontaneous Conferences between the instructor and student at various points in the semester In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Quizzes, quick writes, journal responses, and Socratic Seminars Methods of Summative Assessments: Unit Exams Unit Essays Semester Assessment Final examination Projects (project phases submitted at various completion points could be formatively assessed)
Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

English 3R (11th grade)

MP1 Units:

MP2 Units:

MP3 Units:

MP4 Units:

The Crucible

Short Stories

The Nickel Boys

Poetry

The Great Gatsby

Macbeth/Hamlet

The Things They Carried

UNIT TITLE:
NYS Standards:
https://www.nysed.gov/sites/default/files/programs/curriculum-instruction/nys-next-generation-ela-standards.pdf
Guiding Questions/Essential Questions:
What does the American Dream represent, and how is it portrayed in different literary works? How do American writers address issues of identity, race, and ethnicity in their work? In what ways do American authors use nature and the environment as a symbol or theme in their writing? How do American authors engage with the theme of individualism?
Content Knowledge/Vocabulary:

Unit Topics with Learning Objectives:
Introduction of various literary movements Transcendentalism Reading historical documents and connections to historical documents Close reading passages Writing Skills Parallel Structure Subordination and coordination Sentence variation Essay structures beyond the five paragraph and thesis based essay Grammar Skills Use of dashes Verb tenses Subjunctive mood Misplaced modifiers
Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams, essays, and class discussions Question and answer sessions, both formal and informal —planned/spontaneous Conferences between the instructor and student at various points in the semester In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Quizzes, quick writes, journal responses, and Socratic Seminars Methods of Summative Assessments: Unit Exams Unit Essays Semester Assessment Final examination Projects (project phases submitted at various completion points could be formatively assessed)
Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas

English 3H (Honors English 11th grade)

COURSE TITLE: Honors English 11th Grade

COURSE DESCRIPTION: Honors English in American Literature was designed to coincide with the American History being taught in social studies in the student’s junior year. It will also function as a preparatory course for the senior AP Literature course. The course will focus on the evolution of American Literature and the complexities of the social, economic, political and moral changes that took place within our country and were reflected in our literature, over time. The course will be taught in a survey style in order to facilitate understanding and provide a contextual view of current literature.

The course is rigorous and demanding. Students will be asked to read independently, write and analyze at a high level, pushing well beyond what has been previously expected of them. The goal will be to build upon the foundation they received their freshman and sophomore years; however, students will now be expected not only to analyze a particular text for meaning, but also to place that text and its literary merits within the broader understanding of the culture in which it was written and its place in the pantheon of American Literature. Students will be expected to analyze not just the literature itself but also the literature’s reflection of the American human experience. A love of literature and a curiosity about what that literature conveys and how it is constructed is necessary for an honors student. Students should be prepared to write in a variety of forms and think on a variety of levels.

Suggested Guidelines: 90+ average in English 2R or 2H and teacher recommendation.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
The Scarlet Letter Non-fiction Early American Historical documents The Crucible Puritanism Romanticism	Ethan Frome The Autobiography of Frederick Douglass Short stories Realism Naturalism Regionalism	Modernism The Great Gatsby Death of a Salesman	The Things They Carried The Other Wes Moore

UNIT TITLE:
NYS Standards:
https://www.nysed.gov/sites/default/files/programs/curriculum-instruction/nys-next-generation-ela-standards.pdf
Guiding Questions/Essential Questions:
What defines the American Dream and is it attainable for everyone? How does literature reflect the social and political issues of its time in America? What role does individualism play in American society as depicted in literature? How does American literature grapple with the concept of freedom?
Unit Topics with Learning Objectives:
Reading Skills Introduction of various literary movements Reading historical documents, secondary and primary sources Close-reading passages Cite strong and thorough textual evidence to support analysis of what the text says explicitly/implicitly and make logical inferences, including determining where the text is ambiguous; develop questions for deeper understanding and for further exploration. Determine two or more themes or central ideas in a text and analyze their development, including how they emerge and are shaped and refined by specific details; objectively and accurately summarize a complex text. In literary texts, analyze the impact of author’s choices. In informational texts, analyze a complex set of ideas or sequence of events and explain how specific individuals, ideas, or events interact and develop. Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings. Analyze the impact of specific word choices on meaning, tone, and mood, including words with multiple meanings. Analyze how an author uses and refines the meaning of technical or key term(s) over the course of a text. In informational texts, analyze the impact and evaluate the effect structure has on exposition or argument in terms of clarity, persuasive/rhetorical technique, and audience appeal. Analyze how authors employ point of view, perspective, and purpose, to shape explicit and implicit messages (e.g., persuasiveness, aesthetic quality, satire, sarcasm, irony, or understatement). In literary texts, analyze multiple adaptations of a source text as presented in different formats (e.g., works of art, graphic novels, music, film, etc.), specifically evaluating how each version interprets the source. In informational texts, integrate and evaluate sources on the same topic or argument in order to address a question, or solve a problem. Delineate and evaluate an argument in applicable texts, applying a lens (e.g. constitutional principles, logical fallacy, legal reasoning, belief systems, codes of ethics, philosophies, etc.) to assess the validity or fallacy of key arguments, determining whether the supporting evidence is relevant and sufficient. 2. Writing Skills Write arguments to support claims that analyze substantive topics or texts, using valid reasoning and relevant and sufficient evidence. Introduce precise claim(s), establish the significance of the claim(s), distinguish the claim(s) from counterclaim(s), and create an organization that logically sequences claims, counterclaims, reasons, and evidence. Develop claim(s) and counterclaim(s) thoroughly and in a balanced manner, supplying the most relevant evidence for each while pointing out the strengths and limitations of both, anticipating the audience’s knowledge level, concerns, values, and possible biases. Use precise language, content-specific vocabulary and literary techniques to express the appropriate complexity of the topic. Use appropriate and varied transitions, as well as varied syntax, to make critical connections, create cohesion, and clarify the relationships among complex ideas and concepts. Provide a concluding statement or section that explains the significance of the argument presented. Maintain a style and tone appropriate to the writing task. Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content. Write narratives to develop real or imagined experiences or events using effective techniques, well-chosen details, and well-structured event sequences. : Create a poem, story, play, artwork, or other response to a text, author, theme or personal experience; demonstrate knowledge and understanding of a variety of techniques and genres. Explain connections between the original and the created work. 3. Research Skills Conduct research through self-generated question, or solve a problem; narrow or broaden the inquiry when appropriate. Synthesize multiple sources, demonstrating understanding and analysis of the subject under investigation. Gather relevant information from multiple sources, using advanced searches effectively; assess the strengths and limitations of each source in terms of the task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas; avoid plagiarism, overreliance on one source, and follow a standard format for citation. 4. Grammar Sentence structure Parallel structure Dashes, colons, semicolons Subject-verb agreement Pronoun antecedent
Assessments:
Methods of Formative Assessment: Observations during in-class activities; Homework exercise as review of instruction, exams, essays, etc. Conferences between instrutcor and student; Socratic seminars Quizzes Quick writes/journals In-class activities (collaborate and independent work) Methods of Summative Assessments: Unit exams Essays Projects and presentation Final examination
Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly.

AP Language and Composition

COURSE TITLE: AP English Language and Composition

COURSE DESCRIPTION: The AP course in English Language and Composition engages students in becoming skilled readers of prose written in a variety of periods, disciplines, and rhetorical contexts, and in becoming skilled writers who compose for a variety of purposes. Through both reading and writing, students will gain an awareness of the interactions among a writer’s purpose, audience expectations, and subjects. In addition, students will analyze how writers use rhetorical strategies and stylistic devices to enhance the effectiveness of their writing. In addition, students will study the rhetoric of visual media (i.e., magazine advertisements, political cartoons, films, comic strips, etc.) to determine how nonverbal arguments are constructed. In concert with the College Board’s AP English Course Description, this course teaches “students to read primary and secondary sources carefully, to synthesize material from these texts in their own compositions, and to cite sources using conventions recommended by professional organizations such as the Modern Language Association (MLA).”

The AP course in English Language and Composition substitutes for the college freshman class in composition. Therefore, students will write in a variety of forms, including narrative, expository, analytical, and argumentative, with an emphasis on the types of writing they will encounter at the college level. AP English Language and Composition demands that students read challenging texts, understand the purpose of such texts, and respond clearly and effectively to those texts. As a result, students will be expected to move beyond such programmed responses as the five-paragraph essay and add other techniques to their repertoire.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Rhetorical Analysis Narrative of the Life of Frederick Douglass	Synthesis The Great Gatsby	Argument The Crucible	Exam Review AP Classroom

UNIT TITLE:
NYS Standards:
NYS English Language Arts Learning Standards
Guiding Questions/Essential Questions:
How can I use wide-ranging vocabulary appropriately and effectively? How can I use a wide variety of sentence structures, including appropriate and correct use of subordination and coordination? How can I incorporate logical organization, enhanced by specific literary and rhetorical techniques to increase coherence? What is a good balance of generalization and specific illustrative detail? How can I use rhetoric effectively, including controlling tone, establishing and maintaining voice, and achieving appropriate emphasis through diction and syntax? How can I demonstrate an understanding of the writing process, with an emphasis on brainstorming, outlining, drafting, revising, and editing?
Unit Topics with Learning Objectives:
Viewing language through a historical lenses The craft of clear and direct writing at the collegiate level Rhetorical devices and appeals Rhetorical precis writing SPACECAT for rhetorical situation DIDLS for tone Syntax and types of sentences (periodic, cumulative, etc.) Humor types and techniques Synthesizing complex texts while maintaining authorial voice Formulating complex theses MLA Citation Skills Research Skills (CRAAP test, using databases [JStor, Google Scholar, etc.)] Strategies for AP Lang Multiple Choice questions Types of Argument (Rogerian, Toulmin, Aristotelian) Debate skills Identifying fallacies of argument Issuing rebuttals/counterclaims
Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams, essays, and class discussions Question and answer sessions, both formal and informal —planned/spontaneous Conferences between the instructor and student at various points in the semester In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Quizzes, quick writes, journal responses, and Socratic Seminars Methods of Summative Assessments: Unit Exams Unit Essays AP Practice essays Semester Assessment Multiple choice practice on AP Classroom Final examination Projects (project phases submitted at various completion points could be formatively assessed)
Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

English 4: Exploring Identity

COURSE TITLE: English 4: Exploring Identity

COURSE DESCRIPTION: This full year course is geared toward mature students who need to solidify their reading, writing, and discussion skills prior to graduation. Through a diverse selection of texts, students will examine and explore the complex interactions between individual identity and societal influences. Through close reading, analysis, and discussion, students will delve into characters’ quests for self-discovery, grappling with questions of race, ethnicity, gender, sexuality, socioeconomic status, and other aspects of identity. They will examine how characters navigate personal and cultural identities amidst societal expectations, norms, and prejudices. Additionally, students will explore the ways in which language, narrative techniques, and literary devices shape representations of identity in literature and in film. Through writing assignments, projects, and presentations, students will engage in thoughtful exploration and expression of their own identities and perspectives, ultimately developing a deeper understanding of identity in literature and in life.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Short Stories Memoir Unit	The Poet X Poetry	Long Way Down The Piano Lesson	Just Mercy Resume/Job Skills Unit

UNIT TITLE:
NYS Standards:
NYS English Language Arts Learning Standards
Guiding Questions/Essential Questions:
How does who we are shape and get shaped by the world around us, and how can stories help us understand this?
Unit Topics with Learning Objectives:
Reading Skills Read closely for textual details Annotate texts to support comprehension and analysis Analyze the impact of style and content on the text Collect and organize evidence from texts to support analysis in writing Make claims about texts using specific textual evidence Trace the development of ideas over the course of the text Writing Skills Use formal style and objective tone in writing Demonstrate clarity and cohesion in writing Independently practice the writing process outside of class Paraphrase and quote relevant evidence from texts Use precise words and phrases, telling details, and sensory language Engage in constructive peer-review of narrative essays Produce writing that is appropriate to task, purpose, and audience Write an effective introduction to a narrative essay Write an effective conclusion to a narrative essay Incorporate a range of narrative techniques, such as dialogue, pacing, description, and reflection Research Skills Write effective introduction, body, and conclusion paragraphs for a research-based argument paper Use proper MLA citation methods in writing Craft claims about inquiry questions, inquiry paths, and a problem-based question using specific textual evidence from the research Develop counterclaims in opposition to claims Conduct independent searches using research processes including planning for searches, assessing sources, annotating sources, recording notes, and evaluating argument Assess sources for credibility, relevance, and accessibility Grammar Edit for a variety of language conventions, including agreement, sentence construction and variety, correct capitalization, all punctuation, and spelling.
Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Classwork exercises as review for exams, essays, and class discussions Question and answer sessions, both formal and informal —planned/spontaneous Conferences between the instructor and student at various points in the semester In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Quizzes, quick writes, journal responses, and class participation Methods of Summative Assessments: Unit Quizzes Unit Essays Final examination Projects (project phases submitted at various completion points could be formatively assessed) Oral Presentations
Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Public Speaking (Semester Course)

COURSE TITLE: Public Speaking and Speech Writing

COURSE DESCRIPTION: Students will learn to develop, write, and orate persuasive, informative and demonstrative speeches. Students will also learn to write speeches in a cohesive and organized style through the study of noteworthy speeches. Class members will learn to face an audience with confidence and to organize speeches and presentations that persuade and inform listeners with purpose. This course addresses how to conquer the fear of public speaking and its negative stresses and encourages students’ use of humor, creativity and personality in their presentations. Students should expect to deliver impromptu and prepared speeches and to identify effective techniques. Students will also be expected to set personal goals and to learn how to select and design appropriate materials and methods of delivery. There is an emphasis on writing and on preparation and practice outside of class.

MP1/MP3 Units:	MP2/MP4 Units:
Introduction to Public Speaking Nonverbal Communication Active Listening	Audience Awareness Rhetorical and Persuasive Foundations

UNIT TITLE:
NYS Standards:
NYS English Language Arts Learning Standards
Guiding Questions/Essential Questions:
How can I use my voice, body, and words to confidently and effectively communicate ideas to an audience? What makes a speech impactful, and how can I structure my writing to persuade, inform, or inspire an audience? How can I overcome fear and use my unique personality, creativity, and style to connect with an audience?
Unit Topics with Learning Objectives:
Introduction to Public Speaking Identify the key components of effective public speaking, including purpose, organization, and audience engagement. Practice and reflect on strategies to manage public speaking anxiety. Demonstrate basic speaking skills through short, low-stakes presentations (e.g., introductions or "About Me" speeches). Set personal growth goals related to public speaking confidence and communication style. Nonverbal Communication Analyze how body language, facial expressions, eye contact, gestures, and posture impact a speaker’s message. Practice aligning nonverbal cues with verbal content to enhance message clarity and credibility. Evaluate and reflect on classmates’ and public figures’ use of nonverbal communication through peer and video analysis. Active Listening Demonstrate the ability to listen attentively and respond appropriately during peer presentations and class discussions. Identify key listening barriers and apply strategies to remain focused and engaged. Reflect on how active listening enhances communication and builds speaker-audience rapport. Audience Awareness Analyze how purpose, occasion, and audience shape the tone, content, and style of a speech. Adapt a speech to meet the needs, interests, and expectations of a specific audience. Practice audience-centered techniques such as rhetorical questioning, examples, and inclusive language. Rhetorical and Persuasive Speech Foundations Define and apply rhetorical appeals (ethos, pathos, logos) in speech writing and delivery. Develop a persuasive speech with a clear claim, supporting evidence, and logical reasoning. Evaluate famous speeches to identify persuasive strategies and stylistic devices. Revise written speeches for clarity, impact, and persuasiveness based on peer and teacher feedback.
Assessments:
Methods of Formative Assessments: Impromptu Speaking Peer and Self-Evaluations Exit Tickets Speech Outlines/Graphic Organizers Individual Conferencing Methods of Summative Assessments: Unit Quizzes Prepared Speeches Written speech analysis
Differentiation/Extensions/Accommodations:
1. Choice in speaking topics 2. Scaffolded Speech Outlines 3. Flexible Grouping 4. Rehearsal support before final presentations

12th Grade SLT- Society, Literature, and Truth

COURSE TITLE: Society, Literature, and Truth (SLT)

COURSE DESCRIPTION: SLT is a course where students and teachers confront in a collaborative and multidisciplinary way the fundamental questions that define humanity. Through literature, philosophical texts, films, and discussions, we further our exploration of key topics to examine questions that have confronted humanity throughout history. Marking periods are centered around specific themes which provide opportunities for students to learn, question, and clarify their understanding of key aspects of the human experience. This course emphasizes critical thinking and participation in seminar discussions that is the foundation for success for the future.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Critical Thinking and Knowledge	Morality, Justice, and Ethical Decision Making	Freedom and living the Authentic Life	Preparing for a Future

UNIT TITLE:
NYS Standards:
NYS Standards for Reading, Writing, Speaking, Listening in Social Studies (NYS Framework, pp28-32)
Guiding Questions/Essential Questions:
1-How do we know what we know? 2-What is the purpose of life? 3-How do we think and read critically? 4-What is ‘truth’? 5-What is ethics? 6-What is the process for making decisions ethically? 7-How does society impact the individual? 8-How do young people today prepare to be responsible citizens in the future?
Unit Topics with Learning Objectives:
Over the course of the four marking periods, students will use the lens of specific marking period themes and will Analyze Key Texts: Students will critically read and analyze literature, philosophical texts, and films, identifying key themes, arguments, and historical contexts that shape human understanding. Engage in Critical Discussions: Students will actively participate in seminar-style discussions, formulating well-supported arguments, respectfully challenging ideas, and collaboratively exploring complex questions about the human experience. Apply Multidisciplinary Approaches: Students will approach the study of humanity from diverse disciplines, such as literature, philosophy, sociology, and history, integrating insights from each to develop a comprehensive understanding of the human condition. Explore Fundamental Questions: Students will examine and reflect on fundamental philosophical, ethical, and existential questions, such as the nature of truth, freedom, justice, identity, and morality, and how these have shaped human history. Develop Critical Thinking Skills: Students will refine their ability to think critically, question assumptions, and evaluate evidence and perspectives, fostering skills essential for future academic and professional success. Clarify Personal Beliefs: Students will engage in reflective writing and discussion that allows them to clarify and refine their personal beliefs and values, while also understanding diverse perspectives on the human experience. Synthesize Ideas Across Disciplines: Students will synthesize ideas and concepts from a range of texts and media, drawing connections between philosophical theories, literary works, and real-world issues to explore the relevance of these ideas in contemporary society. Foster Collaborative Learning: Students will work collaboratively with peers to examine complex issues, contributing to a learning environment that values diverse voices and promotes intellectual growth. Create Meaningful Connections: Students will relate themes from class materials to their own lives, encouraging personal growth and a deeper understanding of their place within the larger narrative of human history.
Assessments:
Formative: Exit Tickets: At the end of a lesson, students write a brief response to a prompt related to the day's topic, helping assess understanding and areas needing clarification. Think-Pair-Share: Students think about a question, discuss their thoughts with a partner, and then share insights with the class, promoting collaborative learning. Concept Mapping: Students create visual maps connecting key concepts from the lesson, demonstrating their understanding of relationships between ideas. Journals or Learning Logs: Regular entries reflecting on what they've learned, questions they have, or personal connections to the material. Role-Playing or Simulations: Students act out historical events or civic scenarios, allowing them to engage deeply with content and demonstrate comprehension. Group Projects: Collaborative assignments on specific topics, encouraging research, presentation skills, and teamwork. Quizzes with Immediate Feedback: Short quizzes that provide instant feedback to students, helping them identify areas for improvement. Debates: Organizing structured debates on relevant issues encourages critical thinking and understanding of multiple perspectives. Infographics: Students create visual representations of data or concepts, integrating technology and artistic expression to convey information effectively. Peer Teaching: Students prepare and present a lesson or topic to their classmates, reinforcing their understanding while enhancing communication skills. Summative: Research Project: Students select a historical event, figure, or cultural phenomenon to research. They create a presentation (such as a PowerPoint or poster) that includes key facts, significance, and personal reflections. Socratic Seminar: Students use their prior content knowledge and document analysis skills to connect historical issues to the present day in a whole-class text-based discussion. Unit Assessment (test or quiz): Students demonstrate their content and skill knowledge on assessments aligned with state standards for the unit or concept.
Differentiation/Extensions/Accommodations:
Flexible Grouping: Organize students into varied groups based on interests, readiness, or learning profiles. Use both homogeneous and heterogeneous groups for discussions, projects, or research. Choice Boards: Create a menu of activities that students can choose from based on their interests. This could include projects, written assignments, presentations, or artistic expressions. Tiered Assignments: Design assignments at varying levels of complexity. For instance, some students may analyze primary sources, while others may summarize information from textbooks. Use of Technology: Incorporate tools like audio books, videos, podcasts, and interactive timelines to cater to different learning preferences. Encourage students to create digital presentations or blogs. Project-Based Learning: Allow students to engage in projects that explore social studies topics in depth. They can focus on areas of personal interest or local relevance, fostering a sense of ownership. Visual Aids and Graphic Organizers: Use maps, charts, and diagrams to help visual learners. Graphic organizers can assist students in organizing their thoughts and understanding complex concepts. Scaffolding: Provide support structures, such as guided notes or sentence starters, to help students who may struggle with written assignments or analysis. Varied Assessment Methods: Offer different ways for students to demonstrate understanding, such as traditional tests, creative projects, or oral presentations. Incorporate Current Events: Connect lessons to current events that are relevant to students’ lives. This can make learning more engaging and applicable. Encourage Reflection: Use journals or reflection prompts to help students process their learning and make connections to their own lives and experiences.

Writing Intensive

COURSE TITLE: Writing Intensive

COURSE DESCRIPTION: The Writing Intensive course engages students in becoming skilled writers who compose for a variety of purposes. Through both reading and writing, students will gain an awareness of the interactions among a writer’s purpose, audience expectations, and subjects. Students will write in their journals every day throughout the entire year, building their strength as writers through this process.

Students will write in a variety of forms, including narrative, expository, analytical, and argumentative, with an emphasis on the types of writing they will encounter at the college level. Students will be expected to move beyond such programmed responses as the five-paragraph essay and add other techniques to their repertoire.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Introduction to Journal College Essay Unit Poetry Unit	Daily Journal Short Story Unit Left for Dead non fiction book unit	Daily Journal Argument and Persuasion Unit Research Paper unit	Daily Journal College and Career Unit ASPIRE - INSPIRE

UNIT TITLE:
NYS Standards:
NYS English Language Arts Learning Standards
Guiding Questions/Essential Questions:
What does being prepared for the challenge of college writing look like? How can I use wide-ranging vocabulary appropriately and effectively? How can I use a wide variety of sentence structures for effect? How can I incorporate logical organization, enhanced by specific literary and rhetorical techniques to increase coherence? What is a good balance of generalization and specific illustrative detail? How can I use rhetoric effectively, including controlling tone, establishing and maintaining voice, and achieving appropriate emphasis through diction and syntax? How can I demonstrate an understanding of the writing process, with an emphasis on brainstorming, outlining, drafting, revising, and editing?
Unit Topics with Learning Objectives:
Viewing language through a historical lenses The craft of clear and direct writing at the collegiate level Rhetorical devices and appeals Formulating clear and defensible thesis statements MLA Citation Skills Research Skills (CRAAP test, using databases [JStor, Google Scholar, etc.)]
Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams, essays, and class discussions Question and answer sessions, both formal and informal —planned/spontaneous Conferences between the instructor and student at various points in the semester In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Quizzes, quick writes, journal responses, and Socratic Seminars Methods of Summative Assessments: Journal Entries Unit Exams Unit Essays Projects
Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Math

The mathematics department strives to provide students with a strong foundation in mathematical concepts, problem-solving skills, and logical reasoning. The mathematics program aims to create a supportive and challenging learning environment where students can develop competence and confidence in their mathematical abilities. Fostering a growth mindset, learning experiences provide opportunities for students to apply their skills to real-world situations and experience mathematics as a creative and collaborative learning experience by helping students see the value of mathematics in their daily lives and future careers.

The mathematics program aligns with Bedford’s Vision, Mission, and Core Beliefs and incorporates the principles of the New York State Learning Standards: Focus, Coherence, and Rigor. This includes building conceptual understanding at each grade level, developing concepts within and across grade levels, and building procedural fluency, and the application of learning embedded in the standards. (NYSLS in Mathematics Guidance Document, 2020). All mathematics classes routinely use the Standards for Mathematical Practices. These practices encourage students to explore mathematical concepts using multiple problem-solving strategies, collaboration, and participation in mathematical discourse using mathematical vocabulary.

ESOL Math

COURSE TITLE: ESOL Pre-Algebra

COURSE DESCRIPTION:

This course is designed for students who are English Language Learners in ESOL Level 1 and Level 2 and reinforces arithmetic skills, developing the pre-algebra concepts of variable recognition, signed numbers, formulas and single variable equations. Students will be introduced to algebraic symbolism, simplifying expressions, solutions to algebraic equations, and the graphic representations associated with variables. A primary focus is on building the vocabulary essential for academic study and success in future mathematics courses.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Working with Integers Fractions & Decimals Algebraic Expressions	Solving Equations Word Problems Inequalities	Ratio, Rates, Proportions Percents Graphing Linear Equations	Writing Equations of Lines System of Equations & Inequalities

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams and class discussions Question and answer sessions, both formal and informal —planned/spontaneous In-class activities where students informally present their results Methods of Summative Assessments: Unit Exams Quizzes Final Examination
Methods of Differentiation/Extensions/Accommodations:
1. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 2. Pacing Differentiation : Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 3. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 4. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Operations With Integers

UNIT TITLE: Operations With Integers
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How do Properties of Integers Work
Unit Topics with Learning Objectives:
How to add, subtract, multiply & divide integers

Fractions & Decimals

UNIT TITLE: Fractions & Decimals
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
What are the properties of different operations with fractions
Unit Topics with Learning Objectives:
How to convert to Mixed Numbers and Improper Fractions. How to Simplify Fractions How to add, subtract, multiply & divide fractions How to convert between fractions & decimals How to order decimals on number line How to round decimals

Algebraic Expressions

UNIT TITLE: Algebraic Expressions
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to simplify algebraic expressions with various operations
Unit Topics with Learning Objectives:
How do exponents and square roots work How Order of Operations work Vocab associated with mathematical operations Evaluating operations with variables How to combine like terms

Solving Linear Equations

UNIT TITLE: Solving Linear Equations
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to solve various types of linear equations
Unit Topics with Learning Objectives:
How to identify if a value is a solution to an equation How to solve 1 step equations How to solve 2 step equations How to use the distributive property How to solve equations with fractions and decimals How to solve equations with variables on both sides

Word Problems

UNIT TITLE: Word Problems
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to solve various types of Mathematical Word Problems
Unit Topics with Learning Objectives:
How to solve word problems for 1 value How to solve word problems for 2 values How to solve Real World word problems How to solve consecutive integer word problems How to solve Money word problems How to solve Geometric word problems

Inequalities

UNIT TITLE: Inequalities
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to solve various types of inequalities
Unit Topics with Learning Objectives:
How to determine if a value is a solution to an inequality Solving one step inequalities How to graph solutions to inequalities on a number line How to solve two step inequalities How to solve multi-step inequalities Understanding when to switch inequality signs Understanding Interval Notation How to solve Compound Inequalities How to solve word problems with inequalities

Ratios, Rates & Proportions

UNIT TITLE: Ratios, Rates & Proportions
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to utilize Ratios, Rates and Proportions to solve for missing values
Unit Topics with Learning Objectives:
Understanding what a ratio means Understanding different notations for ratios How to determine if ratios are equivalent How to solve word problems with ratios Understanding how to find unit rates How to solve proportions

Percents

UNIT TITLE: Percents
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to utilize Percents to find values
Unit Topics with Learning Objectives:
How to write a percent as a fraction How to create proportions for percent problems How to find a missing percent How to use percents to find part of a whole How to convert percents to decimals How to utilize percents to calculate tips, discounts, taxes….etc How to calculate percent error

Equations of Lines

UNIT TITLE: Equations of Lines
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to graph various types of lines on a coordinate plane
Unit Topics with Learning Objectives:
How to plot points on a coordinate plane Understanding the general equation of y=mx+b Understanding how to utilize slope and y-intercepts to graph lines How to find slope and y-intercepts from already graphed lines How to graph horizontal and vertical lines How to get y by itself prior to graphing lines How to determine if lines are parallel

Writing Equations of Lines & Linear/Inequality Systems

UNIT TITLE: Writing Equations of Lines & Linear/Inequality Systems
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to write equations of line given various inputs How to graph a system of equations/inequalities
Unit Topics with Learning Objectives:
Given slope and a point, find equation of a line Given two points, write the equation of a line How to create a system of equations How to check a solution to systems of equation How to solve systems of inequalities Checking solutions to system of inequalities

Algebra 1A

COURSE TITLE: Algebra 1A

COURSE DESCRIPTION: Algebra 1A is the first year-long course in a two-year sequence leading to the administration of the Algebra 1 Regents Examination at the end of the second year. This course follows the New York State Next Generation Mathematics Standards adopted by the NYS Education Department and is designed to provide extended study of algebraic topics. The course employs an integrated problem solving approach in the study of algebraic relationships. Major emphasis will be placed on: numeracy, evaluating algebraic expressions, equations and functions, solving linear equations and inequalities, graphing linear equations and inequalities, solving systems of linear equations and inequalities. Each of these topics will include computational work as well as real-life applications. A graphing calculator is required. Students will take a local final in June. This course is followed by Algebra 1B which culminates in students taking the Common Core Algebra 1 Regents examination.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Algebraic Expressions Solving Linear Equations	Graphing Linear equations Linear inequalities Linear Functions	Systems of equations Systems of inequalities	Polynomials

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams and class discussions Question and answer sessions, both formal and informal —planned/spontaneous Conferences between the instructor and student at various points in the semester In-class activities where students informally present their results Student feedback collected by periodically answering specific questions about the instruction and their self-evaluation of performance and progress Lab reports & quizzes Methods of Summative Assessments: Unit Exams Semester Assessment Final examination (Regents) Projects (project phases submitted at various completion points could be formatively assessed) NYS Labs
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Algebraic Expressions

UNIT TITLE: Algebraic Expressions
NYS Standards:
NYS Mathematics Next Generation Learning Standards (Algebra I: Pages 108-122 )
Guiding Questions/Essential Questions:
What is an algebraic expression, and how is it different from an equation? What are like terms, and why is it important to combine them when simplifying expressions? How do you evaluate an algebraic expression for a specific value of a variable? What key words help us translate verbal phrases into algebraic expressions?
Unit Topics with Learning Objectives:
Lesson 1: Vocabulary Students will be able to: Define expressions and identify parts of an algebraic term. Lesson 2: Integer Rules Students will be able to: Apply integer rules to simplify expressions. Lesson 3: Order Of Operations Students will be able to: Simplify expressions using PEMDAS. Lesson 4: Combining Like Terms Day 1 Students will be able to: Identify like terms by recognizing common variables and exponents. Lesson 5: Combining Like Terms Day 2 Students will be able to: Simplify expressions by adding/subtracting like terms. Lesson 6: Translating Expressions Students will be able to: Translate verbal phrases into algebraic expressions.

Solving Linear Equations

UNIT TITLE: Solving Linear Equations
NYS Standards:
NYS Mathematics Next Generation Learning Standards (Algebra I: Pages 108-122 )
Guiding Questions/Essential Questions:
What are the steps to solve a one-variable linear equation? How can you check if your solution to a linear equation is correct?
Unit Topics with Learning Objectives:
Lesson 1: One-step Equations Students will be able to: Apply inverse operations to solve 1-step equations for an unknown. Lesson 2: Two-step Equations Students will be able to: Apply inverse operations to solve 2-step equations for an unknown Lesson 3: Solving Equations with Like Terms Students will be able to: Combine like terms and solve for an unknown. Lesson 4: Distributing & Combining Like Terms Students will be able to: Apply the distributive property, combine like terms, and solve for the unknown. Lesson 5: Variables on Both Sides Students will be able to: Solve equations that have variables on both sides. Lesson 6: Multistep Equations Students will be able to: Apply inverse operations to solve multi-step equations for an unknown. Lesson 7: Literal Equations Students will be able to: Solve an equation with multiple variables. Lesson 8: Word Problems Students will be able to: Write equations based on a given word problem and solve for the unknown.

Graphing Linear Equations

UNIT TITLE: Graphing Linear Equations
NYS Standards:
NYS Mathematics Next Generation Learning Standards (Algebra I: Pages 108-122 )
Guiding Questions/Essential Questions:
How can you identify the slope and intercept from a linear equation? What are the four types of slopes? What is the standard form of a linear equation?
Unit Topics with Learning Objectives:
Lesson 1: Graph Linear Equations with Table and Identify Slope and Intercepts Students will be able to: complete a table of values and graph linear equations from the points in the table. Lesson 2: Horizontal and Vertical Lines Students will be able to: Determine the slope of horizontal and vertical lines and graph the lines. Lesson 3: Graph from Slope-intercept Form Students will be able to: Graph line from slope-intercept form by identifying the slope and y-intercept. Lesson 4: Convert into slope-intercept form Students will be able to: Apply inverse operations to convert equations into slope-intercept form. Lesson 5: Slope Formula Students will be able to: Apply the slope formula to determine the slope of a line given two points. Lesson 6: Write the equation of a line in slope intercept form Students will be able to: Write the equation of a line given the slope and y-intercept or given two points. Lesson 7: Write the equation form a situation Students will be able to: Write the equation of a line given a real-world scenario.

Functions

UNIT TITLE: Functions
NYS Standards:
NYS Mathematics Next Generation Learning Standards (Algebra I: Pages 108-122 )
Guiding Questions/Essential Questions:
What makes a relation a function? What is an input/output value? What does f(x) represent?
Unit Topics with Learning Objectives:
Lesson 1: Intro to Functions Students will be able to: Define a function, domain, range, and independent/dependent variables. Lesson 2: Function Representations Students will be able to: Determine if a relation is a function or not. Lesson 3: Function Notation and evaluating Students will be able to: Evaluate functions in function notation. Lesson 4: Graphing Linear Functions Students will be able to: Graph points from a table & use the graphing calculator to graph a linear function. Lesson 5: Interval Notation Students will be able to: Express domain and range in interval notation. Lesson 6: Functions in the real world Students will be able to: Work with functions in real world examples.

Linear Inequalities

UNIT TITLE: Linear Inequalities
NYS Standards:
NYS Mathematics Next Generation Learning Standards (Algebra I: Pages 108-122 )
Guiding Questions/Essential Questions:
What vocabulary can be used to represent each inequality symbol? What is the difference between an equation and an inequality?
Unit Topics with Learning Objectives:
Lesson 1: Intro to inequalities Students will be able to: Represent inequalities on a number line. Lesson 2: Solving inequalities Students will be able to: solve one variable inequalities using inverse operations. Lesson 3: Solving more inequalities Students will be able to: solve one variable inequalities using inverse operations. Lesson 4: Translating inequalities Students will be able to: Identify key terms used in inequality word problems and match them with the appropriate symbol, creating a linear inequality. Lesson 5: Solving inequality word problems Students will be able to: Create inequalities to represent real world scenarios and use them to solve problems. Lesson 6: More inequality word problems Students will be able to: Create inequalities to represent real world scenarios and use them to solve problems.

System of Equations

UNIT TITLE: System of Equations
NYS Standards:
NYS Mathematics Next Generation Learning Standards (Algebra I: Pages 108-122 )
Guiding Questions/Essential Questions:
What does it mean to solve a system of equations? How can we determine if a system has one solution, no solution, or infinitely many solutions? What are the advantages and limitations of each method for solving systems of equations?
Unit Topics with Learning Objectives:
Lesson 1: Intro to systems- Graphing Students will be able to: Graph linear equations by determining the slope and y-intercept. Lesson 2: Graphing systems & Determining Solutions Students will be able to: Determine the solution to a system of equations using the graphing method. Lesson 3: Graphing Calculator Students will be able to: Determine the solution to the system of equations in slope-intercept form using their calculator. Lesson 4: Solving Systems using Substitution Students will be able to: Apply the substitution method to determine the solution to a given system of equations. Lesson 5: More Solving using Substitution Students will be able to: Apply the substitution method to determine the solution to a given system of equations. Lesson 6: Solving Systems using Elimination Students will be able to: Apply the elimination method to determine the solution to a given system of equations. Lesson 7: More Solving Systems using Elimination Students will be able to: Apply the elimination method to determine the solution to a given system of equations. Lesson 8: Which Method is Best? Students will be able to: determine which of the three methods they’ve learned is most appropriate for each problem.

System of Linear Inequalities

UNIT TITLE: System of Linear Inequalities
NYS Standards:
NYS Mathematics Next Generation Learning Standards (Algebra I: Pages 108-122 )
Guiding Questions/Essential Questions:
What does it mean to solve a system of inequalities? How is solving a system of inequalities different from solving a system of equations? Can a system of inequalities have no solution? How can you tell?
Unit Topics with Learning Objectives:
Lesson 1: Graphing Linear Inequalities (y by itself) Students will be able to: Graph an inequality in slope-intercept form. Lesson 2: Graphing Linear Inequalities (Getting y by itself) Students will be able to: Arrange inequalities into slope-intercept form and graph. Lesson 3: System of Linear Inequalities Students will be able to: Identify solutions to a system of inequalities after graphing both inequalities on the same axes. Lesson 4: More Systems of Linear Inequalities Students will be able to: Identify solutions to a system of inequalities after graphing both inequalities on the same axes Lesson 5: Systems of Linear Inequalities (Calculator) Students will be able to: Identify solutions to a system of inequalities using their graphing calculator. Lesson 6: Linear Inequalities Word Problems (Using x and y intercepts) Students will be able to: Graph inequalities using x and y-intercept Lesson 7: Systems of Linear Inequalities Word problems Students will be able to: Graph systems of inequalities using x and y-intercepts. Lesson 8: More Systems of Linear Inequalities Word Problems Students will be able to: Graph inequalities using x and y-intercepts to solve real world scenarios.

Polynomials

UNIT TITLE: Polynomials
NYS Standards:
NYS Mathematics Next Generation Learning Standards (Algebra I: Pages 108-122 )
Guiding Questions/Essential Questions:
What is a polynomial, and how can we identify its parts (like terms, coefficients, and exponents)? What rules help us multiply and divide powers with the same base? What happens when we raise a power to another power? How do we simplify expressions with negative or zero exponents?
Unit Topics with Learning Objectives:
Lesson 1: Adding & Subtracting Polynomials Students will be able to: Add and subtract polynomials by combining like terms. Lesson 2: Multiplying Terms & Power-to-Power Students will be able to: recognize and apply the product and power rule for exponents. Lesson 3: Mixed Review Lesson 4: Multiplying by a Monomial Students will be able to: Apply the product rule. Lesson 5: Multiplying Polynomials Students will be able to: Distribute and apply the product rule. Lesson 6: Dividing Powers Students will be able to: Apply the quotient rule. Lesson 7: Mixed Review Lesson 8: Powers with Zero & Negative Exponents Students will be able to: Apply the zero power and negative exponent rules.

Algebra 1B

Algebra 1 HS

COURSE TITLE: Algebra 1 - High School

COURSE DESCRIPTION: This course follows the Common Core Next Gen curriculum adopted by the NYS Education Department. The course employs an integrated approach that goes beyond rote learning, in order to ensure that students have a deep understanding of algebraic concepts. This course will include a major emphasis placed on the fundamental laws of Algebra, algebraic operations, linear, quadratic and exponential functions and relationships as well as descriptive statistics. This course requires the use of a graphing calculator and culminates with the Algebra 1 Regents examination in June.

Prerequisite: Math 8

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Number Systems Statistics (1 and 2 variable) Radicals	Linear Graphs, Equations, and Functions Systems of Linear Equations Systems of Inequalities	Polynomials Factoring Solving Quadratic Equations Quadratic Functions	Exponential Functions Sequences Other Functions Regents Prep

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams and class discussions Question and answer sessions, both formal and informal —planned/spontaneous In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Graded Do-Nows Methods of Summative Assessments: In-unit quizzes Unit Exams Cumulative Assessment (Mid-Year) Final examination (Regents)
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, etc.). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Number Systems

UNIT TITLE: Number Systems
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Page 109)
Guiding Questions/Essential Questions:
What are the different number systems, and how are they related to one another? (Natural, Whole, Integers, Rational, Irrational, Real) Why do we need different types of numbers in mathematics? How can you determine which number system a number belongs to? What happens when you perform operations (add, subtract, multiply, divide) with different types of numbers? What distinguishes rational numbers from irrational numbers, and how can you recognize them? How can numbers be represented in different forms (fractions, decimals, roots), and why does it matter?
Unit Topics with Learning Objectives:
Number Systems Identify and recognize several types of Real Numbers used in our world Evaluate and categorize or place on a number line Compare numbers PEMDAS & Evaluating Algebraic Expressions Evaluate expressions that involve multiple operations by using the order of operations Evaluate expressions using a calculator and round to the given value Substitute and evaluate algebraic expressions Square Roots and Irrational Numbers Use the calculator to find the square root of numbers and round appropriately when needed Apply properties of radicals to evaluate problems involving radicals Rewrite radicals in simplest radical form

Statistics

UNIT TITLE: Statistics
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 123-124)
Guiding Questions/Essential Questions:
How do mean, median, and mode each describe a data set, and when is each most useful? What does the range, interquartile range (IQR), and standard deviation tell us about the data’s variability? Why is it important to consider both the center and the spread when analyzing data? How do different types of graphs (box plots, histograms, dot plots, scatter plots) help us understand data? What patterns or trends can be discovered by visualizing data? How can we use a scatter plot and a line of best fit to make predictions? What is the difference between correlation and causation, and why does it matter in interpreting data?
Unit Topics with Learning Objectives:
Mean, Median, Mode & Range Calculate the mean, median, mode, and range for a data set. Solve for a missing score when given scores and an average. Dot Plot Create dot plots for a given data set. Use dot plots to analyze data and answer questions. Box Plot Create box plots for given data sets using the 5-number statistical summary. Use box plots to analyze data and answer questions. Interquartile Range & Standard Deviation Calculate the IQR of a data set. Use your calculator to find the standard deviation of a data set. Answer questions related to IQR, and standard deviation based on data sets. Histogram Interpret data from a histogram and answer questions. Create a histogram from given data. Scatterplots Create a scatterplot using given data. Recognize the distinct types of correlation and strength of the correlation. Use your calculator to create a linear regression equation and find the correlation coefficient. Make predictions using your equation and correlation coefficient. Linear Regression and Correlation Use your calculator to create a linear regression equation and find the correlation coefficient. Make predictions using your equation and correlation coefficient. State the meanings of the slope, y-intercept, and correlation coefficient in the context of the question.

Radicals

UNIT TITLE: Radicals
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Page 109)
Guiding Questions/Essential Questions:
What does it mean to take the square root (or other root) of a number, and why is this operation important in mathematics? How can we represent and simplify radical expressions in different forms? How do the properties of radicals help us simplify and combine radical expressions? When is it appropriate to approximate versus simplify a radical? How do we perform operations (addition, subtraction, multiplication, division) with radical expressions, and how are these similar to or different from operations with other expressions? How can we solve equations that include radical expressions, and what strategies ensure accurate solutions? What are potential pitfalls (like extraneous solutions) when solving radical equations, and how can we avoid them?
Unit Topics with Learning Objectives:
Pythagorean Theorem Identify and label parts of a right triangle. Use Pythagorean Theorem to find the missing side of a right triangle. Interpret and solve word problems involving Pythagorean Theorem. Simplest Radical Form Apply properties of radicals to evaluate problems involving radicals. Rewrite radicals in simplest radical form (including variable radicands). Operation with Radicals Combine radicals by adding or subtracting (including like and unlike radicands). Multiply radicals and express answers in simplest radical form. Rationalizing Denominators Rationalize fractions to be in simplest form by rationalizing the denominator (monomials). Radical Equations Solve equations involving radicals.

Linear Graphs, Equations, and Functions

UNIT TITLE: Linear Graphs, Equations, and Functions
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 113-115, 117-122)
Guiding Questions/Essential Questions:
What makes a function linear, and how can we recognize one? How do the slope and y-intercept of a linear equation describe its graph? How can we represent a linear relationship in different forms (graph, equation, table, verbal description), and how are these forms connected? What defines a linear function, and how can we recognize it from different representations (graph, table, equation, verbal description)? How can function notation (e.g., f(x)) help us describe and evaluate functions? How do we interpret and analyze the meaning of a function's output value given a specific input, using function notation (e.g., f(3)=12)? How can we translate between different representations of a linear function using function notation? How can linear functions be used to model and solve real-world problems? How can we write a linear equation to describe a pattern or situation? How do we determine an appropriate domain and range for a linear function in a real-world context? How can linear functions model real-world situations, and what do the domain and range represent in those situations?
Unit Topics with Learning Objectives:
Review of Solving Equations Simplify and solve One-Step, Two-Step, and Multi-Step Equations (including combining like terms and distributive property) Solve equations with the variable on both sides Solve multi-step equations involving fractions Solving Multi-Step Equations Simplify and solve multi-step equations including combining like terms, distributive property, decimals, fractions, and variable on both sides Literal Equations Understand that a literal equation has more than one variable (often, these are formulas) Use inverse operations to re-arrange a given literal equation so that the identified variable is isolated Independent and Dependent Quantities Differentiate between independent and dependent variables Understand that a function is a relation where each input has exactly one output Determine if a given relationship is a function or not (including vertical line test) Linear Functions Recognize and use function notation ( ) to write and describe linear functions Evaluate functions: algebraically, from a table, and graphically Given x or f(x) recognize and use the function notation to solve for the unknown Graphs of Functions Evaluate linear functions both algebraically and graphically Accurately use function notation when referring to inputs/outputs Fill out a table of values by calculating the appropriate outputs using the function rule Plot the points from the table of values onto a graph Use the graphing calculator to view the table/graph and evaluate various functions Domain and Range Define domain (inputs) and range (outputs) of a function Determine what is included and not included in the domain and/or range of a function Given a graph of a function, identify the domain and range and write in interval AND inequality notation Realistic Domain and Range Translate real-world situations into linear functions – identify independent & dependent variables, slope, and y-intercept Determine and write the realistic domain and range of real-world, linear scenarios Conclude which kinds of numbers make up the domain and/or range of a given real-world scenario

Systems of Linear Equations

UNIT TITLE: Systems of Linear Equations
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 116-117)
Guiding Questions/Essential Questions:
What does it mean to solve a system of equations, and what does the solution represent? How can we determine whether a system has one solution, no solution, or infinitely many solutions? How can we solve a system of linear equations graphically and algebraically (substitution and elimination)? What are the advantages and disadvantages of different methods for solving systems (graphing, substitution, elimination)? What does the point of intersection of two linear equations represent in a real-world context? How can systems of equations model real-world situations and help us make decisions or predictions? How does solving a system of equations help us compare two relationships or scenarios? What does it mean if a system of equations has no solution or infinitely many solutions in terms of the situation it models? How can we use the graphing calculator to locate the point of intersection in a system of linear inequalities?
Unit Topics with Learning Objectives:
Plotting Points and Graphing Lines Graph a point on a coordinate plane. Graph a line using a point and the slope and write the equation of a line. State the slope and y-intercept of a line give a function. Graph and distinguish between vertical and horizontal lines. Intro to Systems of Equations Graph a system of equations and find the point of intersection. Identify and recognize one, zero, or infinitely many solutions. Evaluate a point to see if it is the solution to a system of equations. System Word Problems Graphically & Use Calculator Translate systems of equations Graph each system by hand or on the calculator to find the break-even point or point of intersection. State what the break-even point means in terms of the problem. Substitution y=’s (Algebraically) Use the substitution method to determine the intersection point. Identify and recognize one, zero, or infinitely many solutions using the substitution method. State what the break-even point means in terms of the problem. Elimination (Algebraically) Use the elimination method to determine the intersection point or break-even point. State what the break-even point means in terms of the problem. Solving Systems Word Problems (Algebraically) Identify, recognize, and solve systems of equations using any method (elimination or substitution) State what the break-even point means in terms of the problem.

System of Inequalities

UNIT TITLE: System of Inequalities
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 113, 115-117)
Guiding Questions/Essential Questions:
What does an inequality represent, and how is it different from an equation? How do inequality symbols (>, <, ≥, ≤) affect the meaning of a mathematical statement? What does the solution to an inequality tell us about a situation or problem? How do we solve one-step and multi-step inequalities, and how is the process similar to solving equations? Why must we reverse the inequality symbol when multiplying or dividing by a negative number? How can we check if a number is a solution to an inequality? How can we represent the solution to an inequality on a number line? What is the difference between an open circle and a closed circle on a graph, and what do they represent? What does it mean to solve a system of inequalities, and how is it different from solving a system of equations? What does the solution to a system of inequalities represent, and how do we interpret the solution set graphically? How can we determine whether a point is a solution to a system of inequalities? How do graphs help us visualize the solutions to a system of inequalities? What do the boundary lines and shaded regions represent on a graph of a system of inequalities? How do we write and graph a system of inequalities that models a real-world situation? How do the solutions of individual inequalities relate to the solution set of the entire system? What role do domain and range play when interpreting the solution to a system of inequalities?
Unit Topics with Learning Objectives:
Intro to Inequalities Identify and recognize the vocabulary of inequalities. Use inequality symbols to compare numbers. Determine if a value is a solution to an inequality. Solve and Graph Inequalities Modeling Linear Inequalities Identify independent & dependent variables in word problems. Solve equations & inequalities and interpret the solutions. Translate and solve inequality word problems. Graphing Inequalities on the Coordinate Plane Identify the slope and y-intercept from a graph. Write the equation of a line from a graph. Graph, shade and label an inequality and the solution set. Determine if a point is in a solution set both algebraically and graphically. Use the graphing calculator to graph an inequality and determine if a point is a solution. Represent an inequality using a graph. Translating Linear Inequalities & Systems of Linear Inequalities Define variables used in word problems. Create inequalities and systems of inequalities by translating word problems. Graphing Systems of Inequalities Graph a system of inequalities and label the solution set. Determine if a point is a solution to a system of inequalities. Choose the correct graph when given a system of inequalities and multiple graphs. Use a calculator to graph a system of inequalities and determine if a point is a solution. Solving Systems of Inequalities Word Problems Define variables used in word problems. Translate word problems into systems of inequalities by translating word problems. Find the x and y-intercepts to quickly graph inequalities. Graph a system of inequalities and label the solution set. Identify a solution to a system of inequalities and justify the solution when needed.

Polynomials

UNIT TITLE: Polynomials
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 110-112)
Guiding Questions/Essential Questions:
What is a polynomial, and how can we recognize and classify different types (monomial, binomial, trinomial)? How can we use vocabulary (like degree, terms, coefficients, and exponents) to describe polynomials precisely? How do we add, subtract, and multiply polynomials, and what patterns emerge from these operations? How does multiplying a monomial by a polynomial apply the distributive property? What is double distribution (FOIL), and how do we use it to multiply two binomials? How does understanding the structure of a polynomial help us simplify or solve expressions and equations involving them?
Unit Topics with Learning Objectives:
Adding and Subtracting Polynomials Define important vocabulary related to polynomials Identify like and unlike terms Add and subtract polynomials Laws of Exponents Define the rules for multiplying and dividing like bases with exponents Use the laws of exponents for multiplication and division to simplify expressions Divide polynomials by monomials Define the exponent rules for power to a power, power of a product/quotient, zero power, and negative powers Use the laws of exponents for power to a power, power of a product/quotient, zero power, and negative powers to simplify expressions Multiplying Binomials Multiply monomials using the laws of exponents Multiply binomials using double distribution and/or the box method Find the area of a rectangle whose length and width are represented by algebraic expressions

Factoring

UNIT TITLE: Factoring
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Page 110)
Guiding Questions/Essential Questions:
What does it mean to factor an expression, and how is it related to multiplying polynomials? How can factoring be used to rewrite expressions in an equivalent form? How do we recognize and factor out the greatest common factor (GCF) from a polynomial? How do we factor a trinomial using the sum of the “b” term and the product of the “c” term? How do we factor special patterns like the difference of squares and perfect square trinomials? How can we factor trinomials completely using multiple factoring methods? What strategies help us decide which factoring method to use for a given polynomial?
Unit Topics with Learning Objectives:
Factoring with Greatest Common Factor (GCF) Factor out a GCF and write a polynomial in factored form. Factoring Polynomials (a=1) Factor trinomials where the “a” term is equal to 1. Factoring Polynomials (a>1) Factor trinomials where the “a” term is greater than 1. Difference of Perfect Squares Factor the difference of perfect squares. Factor Completely Factor completely using GCF, regular factoring, and difference of perfect squares.

Solving Quadratic Equations

UNIT TITLE: Solving Quadratic Equations
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 112, 114-116)
Guiding Questions/Essential Questions:
What makes an equation quadratic, and how can we recognize its standard form? What do the solutions of a quadratic equation represent, and how are they related to the graph of the equation? How can we determine the number and type of solutions a quadratic equation has? What are the different methods for solving quadratic equations (factoring, completing the square, using the quadratic formula, and graphing), and when is each method most useful? How can factoring be used to solve quadratic equations? What do the factored form and solutions of a polynomial equation tell us about its graph (e.g., x-intercepts)? How does factoring help us understand the relationship between the algebraic and graphical representations of a quadratic function? How are the solutions of a quadratic equation related to the x-intercepts of its graph? How can quadratic equations be used to model and solve real-world problems? How can we interpret the meaning of the solutions in the context of a real-world situation? How can we solve a quadratic-linear system graphically AND algebraically? How can we identify the solution(s) to a quadratic-linear system and write the solution(s) as point(s) (x, y)?
Unit Topics with Learning Objectives:
Solving Quadratics by Factoring ● Convert equations into standard form and identify a, b, and c terms. ● Find the x-intercepts of a quadratic written in factored form. Find the x-intercepts of a quadratic function using any method of factoring. Completing the Square ● Identify and complete perfect square trinomials. Complete the square to find answers in simplest radical form or round to a given place value. Completing the Square (a > 1) ● Complete the square when a = 1 or a >1. ● Manipulating quadratic equations to determine the best method to use to find x-intercepts. Determine the best method to find x-intercepts based on prior learning. Quadratic Formula ● Use the quadratic formula to solve for x-intercepts of a quadratic function. Write the solutions of a quadratic function in simplest radical form. Which Method is Best? ● Determine the most efficient method to use to solve a quadratic function. Distinguish between the format and criteria needed to solve quadratics based on the method used. Applications of Quadratics ● Set up and solve quadratic word problems using any method of solving quadratics. Set up and solve for a missing value using any method of solving quadratics. Solving Quadratic Linear Systems Graphically ● Solve quadratic linear systems by graphing both functions and finding the point(s) of intersection. Using the calculator to find the point(s) of intersection of a quadratic linear system. Solving Quadratic Linear Systems Algebraically ● Solve quadratic linear systems algebraically. ● Manipulating equations into y= form to solve a system algebraically. ● State the solution to a system as a point(s) of intersection.

Quadratic Functions

UNIT TITLE: Quadratic Functions
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 118-122)
Guiding Questions/Essential Questions:
What does the general form of a quadratic equation tell us about its graph? How do the coefficients of a quadratic function in standard form (y=ax2+bx+c) affect the shape and position of its graph? How can we determine whether a parabola opens upward or downward, and what does that tell us about the function? What are the key features of a parabola (vertex, axis of symmetry, direction, y-intercept, x-intercepts), and how do we find them? How can we use symmetry to help graph a quadratic function? How is the vertex related to the maximum or minimum value of the function, and why is this important? How do different forms of a quadratic equation (standard, vertex, factored) reveal different characteristics of the graph? How are the solutions of a quadratic equation related to the x-intercepts of the graph? How can we move between tables, graphs, and equations to fully understand a quadratic function? How can we describe the transformations of a parabola compared to the parent function (y=x2)? How do we write the equation of a transformed parabola given its graph or key features? What are the domain and range of a quadratic function, and how are they connected to the graph’s shape and vertex? How can we use the graph of a quadratic function to solve real-world problems?
Unit Topics with Learning Objectives:
Graphing Quadratic Functions (Parabolas) Graph a quadratic function in standard form using a table of values. Define and identify/name key components of a parabola (vertex, axis of symmetry, y-intercept, etc.) Graphing Quadratics using the Graphing Calculator Use the graphing calculator to identify the vertex (min/max), y-intercept, roots, axis of symmetry, etc. of a given parabola. Graph a quadratic function in standard form using the graphing calculator to come up with the table of values. Factored Form of a Quadratic Write a quadratic function in factored form when given the roots. Write a quadratic function in standard form when given the roots. Determine the x-intercepts of a quadratic when given a quadratic function in factored form. Factored Form using GCF Write a quadratic function in factored form by factoring out a GCF first. When given a quadratic function in standard form, solve for the roots by factoring completely first. Vertex Form of a Quadratic Given the vertex of a parabola, write the quadratic function in Vertex Form. Give a quadratic in Vertex Form, identify the vertex and axis of symmetry. Convert an equation in Vertex Form to Standard Form. Shifting Quadratic Functions Identify transformations (vertical/horizontal translations, reflections over the x-axis, and dilations) of quadratic functions when compared to the parent function y = x². Domain and Range of Quadratics Given a graph of a quadratic function, identify the x- and y-intercepts, vertex, and domain & range. Write domain and range of a quadratic in interval OR inequality notation. Identify the realistic domain and range of real-world scenarios. Quadratic Word Problems Analyze and solve real-world word problems involving quadratic functions by identifying key information and graphing the parabola to represent the scenario. Interpret the key components of the parabola (vertex, zeros, etc.) in the context of the problem and justify the reasoning behind it.

Exponential Functions

UNIT TITLE: Exponential Functions
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 113, 119-122)
Guiding Questions/Essential Questions:
What makes a function exponential, and how is it different from a linear or quadratic function? How can we recognize and write exponential functions from tables, graphs, equations, or real-world situations? What does the base of an exponential function tell us about its rate of growth or decay? How can we distinguish between exponential growth and exponential decay? How does the value of the base in f(x)=a(b)x determine whether the function is increasing or decreasing? How do exponential functions compare to linear and quadratic functions in terms of growth over time? What real-world situations are best modeled by exponential functions rather than linear ones? How can we use a table or graph to determine whether a situation represents exponential growth or decay? What are the key features of the graph of an exponential function (intercepts, asymptote, domain and range, end behavior)? What is the domain and range of an exponential function, and how are they connected to its real-world meaning?
Unit Topics with Learning Objectives:
Introduction to & Graphs of Exponential Functions Identify patterns and recognize exponential functions State if an exponential function is increasing or decreasing Identify and state the initial value and other characteristics of an exponential function Writing Exponential Functions Write an exponential function using both tables and graphs Scenarios & Exponential Functions Use exponential functions to determine population growth and decline. Recognize that growth and decay follow the same models as population. State the initial value and ratio of an exponential function and solve them using a calculator. Compound Interest Solving exponential functions using the compound interest formula Translations of Linear and Exponential Functions Recognize patterns of exponential functions. State if an exponential function is increasing or decreasing. State the initial value and other characteristics of an exponential function. Exponential Functions State Test Questions Solve exponential functions using the skills learned in the unit.

Sequences

UNIT TITLE: Sequences
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 113, 118)
Guiding Questions/Essential Questions:
What is a sequence, and how is it different from other types of functions or expressions? How do we identify and describe patterns in arithmetic and geometric sequences? How can sequences be represented in multiple ways (verbally, numerically, graphically, algebraically)? How can we recognize whether a sequence is arithmetic or geometric? How do the common difference and common ratio affect the behavior of a sequence? What are the explicit formulas for the nth term of an arithmetic and geometric sequence, and how do we use them? How can sequences be interpreted as functions with a domain of positive integers? In what ways are arithmetic sequences related to linear functions, and geometric sequences to exponential functions?
Unit Topics with Learning Objectives:
Arithmetic and Geometric Sequences Determine terms of an arithmetic or geometric sequence using the given pattern Identify if a given sequence is arithmetic, geometric, or neither Calculate the common difference (arithmetic) or common ratio (geometric) for a given sequence Determining Terms of Sequences Use the explicit formula for arithmetic and geometric sequences to determine the n^th term in a sequence Sequences as Functions Determine how an arithmetic sequence is always a linear function Determine how a geometric sequence is sometimes and exponential function Convert the explicit formula for both arithmetic and geometric sequences into function notation

Other Functions

UNIT TITLE: Other Functions
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 119-121)
Guiding Questions/Essential Questions:
How do absolute value, square root, and piecewise functions differ from linear and quadratic functions? How can we graph absolute value, square root, and piecewise functions using the equation and/or a table of values? What makes each function unique in terms of its domain, range, and overall behavior? How can we identify the rule or expression that defines a function when it changes across different intervals (as in piecewise functions)? How do transformations (shifts, reflections, stretches, and compressions) affect the graphs of these functions? How do we determine the domain and range of absolute value, square root, and piecewise functions from graphs and equations? How can we move between different representations (graph, equation, table, verbal description) for each type of function?
Unit Topics with Learning Objectives:
Absolute Value and Square Root Graph absolute value and square root functions Understand domain and range of functions State translations on functions Compare functions Piecewise Functions Graph piecewise functions Understand how to use domain values to graph functions Evaluate piecewise functions

Financial Algebra

Geometry

COURSE TITLE: Geometry

COURSE DESCRIPTION: This course is guided by the Common Core Next Gen curriculum adopted by the NYS Education Department and is designed to provide an extended study of geometric topics allowing for the reinforcement of algebraic techniques. This course employs an integrated approach to the study of geometric relationships. Through a consideration of Euclidean, transformational and coordinate approaches, students will investigate situations in order to justify geometric relationships and properties of geometric figures. Major emphasis will be placed on: quadratics, coordinate geometry, polygons, right triangles, trigonometry, similarity and congruency proofs. Work includes analytical problems involving calculations as well as Euclidean and analytic proofs, manipulation of radical and rational expressions as well as solving radical and quadratic equations. This course requires the use of a graphing calculator and culminates with the Geometry Regents examination in June.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Factoring Radicals Foundations of Geometry Parallel Lines	Properties of Triangles Introduction to Proofs Triangle Congruence Proofs and CPCTC	Similarity Similarity Proofs Right Triangle Trigonometry Circles and Equations of Circles	Coordinate Geometry Proofs Quadrilateral Proofs Transformations Solid Geometry

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams and class discussions Question and answer sessions, both formal and informal —planned/spontaneous Conferences between the instructor and student at various points in the semester In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Methods of Summative Assessments: Unit Exams Semester Assessment Final examination (Regents) Projects (project phases submitted at various completion points could be formatively assessed)
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Factoring

UNIT TITLE: Factoring
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What does it mean to factor a number or an expression? How is factoring related to multiplication and division? What is the difference between prime factorization and algebraic factoring? How can the distributive property help us understand factoring? How do we factor out the greatest common factor (GCF) from a polynomial? What patterns help us recognize special products, such as the difference of squares or perfect square trinomials? How do we factor trinomials using different methods (e.g., trial and error, grouping, the AC method)? How can we check if our factored expression is correct? How is factoring used to solve quadratic equations? Essential Questions What does it mean to factor, and why is it an important mathematical process? How is factoring related to multiplication and division? How can recognizing patterns help us factor more efficiently? How does factoring help us solve equations and understand functions? In what ways does factoring simplify mathematical expressions and problem-solving? How can we determine the best method to factor a given expression?
Unit Topics with Learning Objectives:
1. Understanding Polynomial Structure Define polynomials and identify terms, coefficients, degrees, and leading terms. Classify polynomials based on degree and number of terms (monomials, binomials, trinomials). Understand the role of exponents and how they affect polynomial expressions. 2. Representing Functions in Multiple Ways Multiply monomials using exponent rules. Apply the distributive property to multiply polynomials, including binomials and trinomials. Use the FOIL/Double Distribute method to multiply two binomials. Multiply special binomials, including perfect square binomials and conjugates.. 3. Factoring Polynomials Identify and factor out the greatest common factor (GCF) from a polynomial. Factor trinomials of the form ax²+bx+c using various methods (trial and error, AC method) Factor special binomials, including difference of squares Recognize and factor perfect square trinomials. 4. Solving Polynomial Equations Using Factoring Solve polynomial equations by factoring and using the Zero Product Property. Solve quadratic equations by factoring Solve quadratic equations by using the Quadratic Formula Solve real-world problems involving polynomial equations by factoring.

Radicals

UNIT TITLE: Radicals
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What is a radical expression, and how is it related to exponents? How do we simplify radical expressions, and why is it important to express them in their simplest form? How do we perform operations with radicals, including addition, subtraction, multiplication, and division? What are the rules for rationalizing the denominator, and why is this process necessary? What role do conjugates play in simplifying radical expressions, particularly in division? How are radicals used in solving real-world problems, such as in geometry? Essential Questions Why do we need to simplify radicals, and how does this help us better understand mathematical relationships? How do radical operations extend our understanding of number systems beyond integers and fractions? What strategies can we use to ensure accuracy when performing operations with radicals? How does rationalizing denominators improve the clarity and usefulness of mathematical expressions? Why is it important to understand radicals when working with quadratic equations, distance formulas, and geometric measurements?
Unit Topics with Learning Objectives:
1. Understanding Radical Expressions Define radical expressions and explain their relationship to exponents. Identify and classify different types of radicals, including square roots, cube roots, and higher-order roots. Recognize perfect squares and perfect cubes to simplify radical expressions efficiently. 2. Simplifying Radical Expressions Simplify square roots and other radical expressions by factoring out perfect squares, cubes, and other powers. Express radical expressions in simplest form, ensuring no perfect square factors remain under the radical sign. Apply the properties of radicals, including the product and quotient rules, to simplify expressions. 3. Performing Operations with Radicals Add and subtract radical expressions by combining like radicals. Multiply and divide radical expressions using the distributive property and the rules of exponents. Rationalize denominators in expressions involving radicals by multiplying by conjugates or appropriate factors. Apply the concept of conjugates to simplify expressions involving binomial radicals. 4. Applying Radicals in Geometry(In Future Units) Use radicals to express exact lengths in geometric problems, such as in right triangles, circles, and polygons. Apply the Pythagorean Theorem and its converse to solve for missing side lengths in right triangles, using radical simplification when necessary. Solve problems involving distance and midpoint formulas that require radical simplification.

Foundations of Geometry

UNIT TITLE: Foundations of Geometry
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What are the basic building blocks of geometry, such as points, lines, planes, and angles? How do we use geometric notation and symbols to represent objects and relationships in geometry? What are the different types of angles, and how are they measured? How do we classify different types of lines (parallel, perpendicular, skew) and their relationships? What are postulates, theorems, and definitions, and how do they form the foundation of geometric reasoning? How do we use the coordinate plane to represent and analyze geometric figures? How is geometry used to solve real-world problems in design, engineering, and architecture? Essential Questions Why is geometry important in understanding and describing the world around us? How do geometric principles help us create models, solve problems, and make predictions? In what ways does geometry provide a foundation for reasoning and proof in mathematics? How does the coordinate plane allow us to analyze and solve geometric problems algebraically?
Unit Topics with Learning Objectives:
1. Understanding Basic Geometric Concepts Define and identify fundamental geometric terms, including points, lines, planes, segments, and rays. Use appropriate geometric notation to represent and describe figures. Understand and apply concepts of collinearity, and intersection of geometric objects. 2. Measuring and Classifying Angles and Segments Identify and classify different types of angles (acute, right, obtuse, straight). Apply the Segment Addition Postulate and Angle Addition Postulate to solve problems. Identify and use properties of congruent segments and angles. 3. Understanding Geometric Reasoning and Proof Identify and apply basic postulates and theorems related to points, lines, and planes. 4. Working with Coordinate Geometry Plot and identify points, lines, and geometric figures on the coordinate plane. Calculate distances between points using the Distance Formula. Find the midpoint of a segment using the Midpoint Formula. Explore geometric relationships using algebraic representations on the coordinate plane.

Parallel Lines

UNIT TITLE: Parallel Lines
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What are parallel lines, and how do they differ from perpendicular and skew lines? How can we determine whether two lines are parallel using angle relationships? What types of angles are formed when a transversal intersects two parallel lines? How do we use postulates and theorems to prove that two lines are parallel? How do parallel lines behave in different geometric contexts, such as on the coordinate plane? How can algebraic methods, such as slope, be used to identify parallel lines Essential Questions Why are angle relationships important when analyzing and proving parallel lines? What strategies can we use to prove lines are parallel, and why is proof important in geometry? How does coordinate geometry help us analyze and understand parallel lines? How do parallel lines relate to congruence, similarity, and transformations in geometry?
Unit Topics with Learning Objectives:
1. Understanding Parallel and Perpendicular Lines Define and identify parallel, perpendicular, and skew lines in two-dimensional space. Use proper geometric notation to represent parallel and perpendicular relationships. Understand and apply the Parallel Postulate in geometric reasoning. 2. Angle Relationships with Parallel Lines and a Transversal Identify and define corresponding, alternate interior, alternate exterior, and consecutive (same-side) interior angles. Apply the properties of these angle pairs to determine angle measures. Use algebraic expressions to solve for unknown angle measures formed by parallel lines and a transversal. Prove that two lines are parallel using angle relationships. 3. Proving Lines Are Parallel Use logical reasoning, postulates, and theorems to justify whether two lines are parallel. 4. Parallel Lines in the Coordinate Plane Use the slope formula to determine whether two lines are parallel. Write equations of parallel lines given a point and a slope. Solve problems involving parallel lines and linear equations in the coordinate plane.

Properties of Triangles

UNIT TITLE: Properties of Triangles
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What defines a triangle, and how can triangles be classified based on their sides and angles? What are the different types of triangles, and how do their properties differ? How can we determine the sum of the interior and exterior angles of a triangle? How do the Triangle Inequality Theorem and properties of triangle side lengths help us determine if a triangle is possible? How do we use the Pythagorean Theorem to find missing side lengths in right triangles? How can we use properties of medians, altitudes, perpendicular bisectors, and angle bisectors to solve problems in triangles? How are triangles used in real-world applications such as architecture, engineering, and navigation? Essential Questions Why are triangles considered one of the most fundamental shapes in geometry and real-world structures? How do the properties of triangles help us make predictions and solve problems in mathematics and science? How can we use logical reasoning and proof to establish relationships between angles and sides in triangles? Why is the Pythagorean Theorem so significant, and how does it connect algebra and geometry? How can geometric properties of triangles be applied in technology, construction, and engineering?
Unit Topics with Learning Objectives:
1. Classifying Triangles Classify triangles based on their sides (scalene, isosceles, equilateral) and angles (acute, right, obtuse). Identify and describe the properties of each type of triangle, including side lengths and angle measurements. 2. Triangle Angle Sum Theorem Understand and apply the Triangle Angle Sum Theorem, which states that the sum of the interior angles of a triangle is always 180°. Use the Triangle Angle Sum Theorem to find missing angle measures in triangles. Apply the Exterior Angle Theorem to solve for unknown angles in triangles. 3. Triangle Inequality Theorem State and apply the Triangle Inequality Theorem to determine whether three given side lengths can form a triangle. Solve problems involving the Triangle Inequality Theorem, including determining the range of possible side lengths for a triangle. 4. The Pythagorean Theorem Understand and apply the Pythagorean Theorem (a² + b² = c²) to find the lengths of the sides of a right triangle. Solve real-world problems involving right triangles using the Pythagorean Theorem. Recognize and classify right triangles based on side lengths (e.g., Pythagorean triples). 5. Special Segments in Triangles Solve problems involving the special segments of a triangle, such as medians, altitudes, perpendicular bisectors, and angle bisectors. 6. Applications of Triangle Properties Use the properties of triangles to solve problems involving areas and perimeters of triangles and related geometric figures.

Introduction to Proofs

UNIT TITLE: Introduction to Proofs
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What is the difference between a postulate and a theorem in geometry, and why are both necessary in geometric reasoning? What are the basic steps involved in writing a geometric proof? How does logical reasoning play a role in proving geometric relationships and theorems? How do definitions, postulates, and previously proven theorems work together to form logical arguments in proofs? What types of geometric relationships (such as congruence, similarity, parallelism) can be proven using formal proofs? How do we organize a proof in different formats, such as two-column, paragraph, or flowchart proofs? Essential Questions Why is proof essential in geometry, and how does it ensure the validity of geometric statements and relationships? How do postulates and theorems form the foundation of logical reasoning in geometry, and why are they accepted as true without proof? How do we build logical arguments to prove geometric properties, and why is precision important in these arguments? In what ways does mathematical proof extend beyond geometry to other fields, such as algebra, number theory, and logic? How does understanding proofs and postulates help us develop critical thinking skills and apply logical reasoning in other areas of mathematics and life? How does geometry provide a framework for mathematical communication, and why is being able to explain and justify conclusions important in mathematics?
Unit Topics with Learning Objectives:
Understanding Postulates and Theorems Define and differentiate between postulates (axioms) and theorems in geometry. Understand the role of postulates and theorems in geometric reasoning and how they form the foundation for proofs. Recognize common postulates and theorems used in geometry, such as the Segment Addition Postulate, Angle Addition Postulate, Substitution, etc. Introduction to Proofs Understand the structure and purpose of geometric proofs, including logical reasoning and step-by-step justification of geometric statements. Demonstrate the ability to write a basic two-column proof that involves definitions, postulates, and previously proven theorems. Logical Reasoning in Geometry Use deductive reasoning to draw conclusions based on accepted definitions, postulates, and theorems. Apply logical reasoning to prove basic geometric properties, such as angle relationships, congruence, and parallelism. Applying Postulates and Theorems in Proofs Use theorems (e.g., Vertical Angles Theorem, Linear Pairs Postulate, Addition and Subtraction Properties of Equality) to justify steps in geometric proofs. Apply postulates such as the Segment Addition Postulate and Angle Addition Postulate to prove geometric relationships.

Triangle Congruence Proofs

UNIT TITLE: Triangle Congruence Proofs
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What does it mean for two triangles to be congruent, and how can we determine if two triangles are congruent? How do the five congruence postulates (SSS, SAS, ASA, AAS, HL) help us prove triangle congruence? How can we use congruence postulates to prove that two triangles are congruent in a variety of geometric situations? How does the concept of CPCTC apply once we have proven two triangles congruent? How does the use of congruent triangles help in solving for missing angles or sides in geometric figures? What is the role of congruence in proving other geometric properties, such as parallelism or symmetry? How can CPCTC be used in real-world applications, such as design, engineering, and architecture? What are some common mistakes or misconceptions when working with triangle congruence and CPCTC, and how can we avoid them? Essential Questions How does the concept of triangle congruence help us understand geometric relationships and solve problems in geometry? Why is CPCTC an essential tool in geometric reasoning after proving two triangles congruent? How do geometric proofs involving triangle congruence and CPCTC demonstrate the importance of logical reasoning and precision in mathematics? How can triangle congruence be applied to real-world problems, such as in construction, architecture, and navigation? In what ways does triangle congruence, when combined with CPCTC, contribute to solving complex geometric problems and proving larger geometric theorems? Why is it important to prove that two triangles are congruent before applying CPCTC to solve for missing parts? How does understanding triangle congruence and CPCTC help us develop broader problem-solving skills in geometry and beyond?
Unit Topics with Learning Objectives:
Understanding Triangle Congruence Define triangle congruence and explain when two triangles are congruent. Identify the corresponding parts of congruent triangles (sides and angles) and understand the concept of CPCTC (Corresponding Parts of Congruent Triangles are Congruent). Recognize and apply the five congruence postulates (SSS, SAS, ASA, AAS, HL) to prove triangles congruent. 2. Using Congruence Postulates to Prove Triangles Congruent Apply the Side-Side-Side (SSS) Congruence Postulate to prove two triangles are congruent. Apply the Side-Angle-Side (SAS) Congruence Postulate to prove two triangles are congruent. Apply the Angle-Side-Angle (ASA) Congruence Postulate to prove two triangles are congruent. Apply the Angle-Angle-Side (AAS) Congruence Postulate to prove two triangles are congruent. Apply the Hypotenuse-Leg (HL) Congruence Theorem to prove two right triangles are congruent. 3. Writing Triangle Congruence Proofs Develop logical reasoning and write two-column proofs to prove triangle congruence using postulates and theorems. Use theorems and postulates to justify steps in a geometric proof that involves triangle congruence. Identify and correct errors in triangle congruence proofs, including misapplication of congruence postulates or incorrect reasoning. 4. Applying CPCTC to Solve Problems Use CPCTC to prove that corresponding parts of congruent triangles are congruent (e.g., corresponding sides and angles). Solve for missing angles and sides in congruent triangles using CPCTC. Apply CPCTC to prove geometric relationships and properties in more complex geometric figures. 6. Mastering Proof Strategies and Techniques Develop skills in strategic planning for solving triangle congruence proofs. Recognize when to apply specific postulates (SSS, SAS, ASA, AAS, HL) based on the given information in a problem. Use geometric properties such as perpendicular bisectors, angle bisectors, and parallel lines to aid in solving triangle congruence proofs.

Similarity

UNIT TITLE: Similarity
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions How do we determine if two figures are similar using side lengths and angles? What properties are preserved under similarity transformations? How can scale factors be used to describe the relationship between similar figures? How can we set up and solve proportions to find missing side lengths in similar figures? How are ratios and scale factors connected? How do changes in scale factor affect area and volume? What shortcuts or theorems can we use to prove triangles are similar (AA, SSS, SAS)? How do corresponding sides and angles help us reason about triangle similarity? How can triangle similarity be used to find unknown measures indirectly (e.g., using shadows, reflections, or models)? How can dilation and rigid motions show that two figures are similar? What role does the center of dilation and scale factor play in a dilation? How does a dilation differ from a rigid motion? How can similarity be used to solve real-world measurement problems? How does similarity appear in art, architecture, and nature? How can understanding similarity support reasoning in trigonometry and coordinate geometry? Essential Questions What does it mean for two figures to be similar, and how can we prove it? How can proportional reasoning help us understand and describe geometric relationships? In what ways does similarity connect geometry to the real world? How can we use transformations to explain why two figures are similar? How does understanding similarity help us make predictions, comparisons, and solve problems in unfamiliar situations?
Unit Topics with Learning Objectives:
1. Understanding Similarity and Scale Define similarity in terms of corresponding angles and proportional sides. Identify and describe similar figures using scale factors. Compare and contrast similarity and congruence. Use proportional reasoning to determine if two figures are similar. 2. Dilation and Similarity Transformations Perform and describe dilations on the coordinate plane using a center and scale factor. Determine the effect of dilations on side lengths, angles, perimeter, and area. Explain how a sequence of transformations (including dilations) can demonstrate that two figures are similar. Represent and verify similarity transformations algebraically on the coordinate plane. 3. Ratios, Proportions, and Scale Factors Write and solve proportions related to similar figures. Use ratios and scale factors to find missing side lengths in similar shapes. Understand how scale factors affect perimeter, area, and volume. Apply scale factors to model and real-world problems (e.g., maps, blueprints, scale drawings). 4. Triangle Similarity Theorems Use the AA (Angle-Angle) Similarity Postulate to prove triangles are similar. Use the SSS (Side-Side-Side) and SAS (Side-Angle-Side) Similarity Theorems to prove triangles are similar. Identify corresponding parts of similar triangles and use them to solve for unknown measures. Justify reasoning about triangle similarity through written and visual proofs. 5. Applications of Triangle Similarity Use similar triangles to solve indirect measurement problems (e.g., heights, distances, shadows). Apply the Triangle Proportionality Theorem and its converse to find missing segment lengths. Use the properties of parallel lines and transversals to set up proportional relationships. Connect triangle similarity to trigonometric ratios and real-world modeling contexts.

Trigonometry

UNIT TITLE: Trigonometry
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions How are trigonometric ratios (sine, cosine, and tangent) defined using side lengths of a right triangle? How can we use the tangent ratio to find missing sides or angles in right triangles? Why do trigonometric ratios remain consistent for all right triangles with the same angle measures? How are trigonometric ratios related to triangle similarity? What is the relationship between complementary angles and their trigonometric ratios? How can inverse trigonometric functions help us find missing angle measures? How do we determine which trigonometric ratio to use in a given problem? How can we use right triangle trigonometry to solve problems involving elevation, depression, and indirect measurement? How does trigonometry connect to coordinate geometry (e.g., using slope or vectors)? What are common errors when setting up and solving trigonometric proportions, and how can we avoid them? How can we verify the reasonableness of a trigonometric solution? How can technology (like a graphing calculator or geometry software) help us visualize trigonometric relationships? How do trigonometric ratios lead into the study of the unit circle and periodic functions? Essential Questions How can we use triangles to model and solve real-world problems? What do trigonometric ratios represent, and how are they connected to similarity? How does understanding right triangle relationships deepen our understanding of geometry? In what ways does trigonometry help us describe and understand the world around us? How are angles, ratios, and side lengths interconnected in right triangles? How can we use technology and multiple representations to explore and apply trigonometric relationships?
Unit Topics with Learning Objectives:
Connecting Similarity to Trigonometry Recall that corresponding sides of similar right triangles are proportional. Explain how trigonometric ratios (sine, cosine, tangent) are derived from right triangle similarity. Understand that trigonometric ratios are constant for a given acute angle. Identify and label the sides of a right triangle relative to a given acute angle. Defining and Using Trigonometric Ratios Define and use the sine, cosine, and tangent ratios in right triangles. Determine which trigonometric ratio to apply to solve for missing sides or angles. Solve right triangles using trigonometric ratios and Pythagorean relationships. Verify solutions by checking the reasonableness of side lengths and angle measures. Inverse Trigonometric Functions Use inverse trigonometric functions to find missing angle measures in right triangles. Understand the domain and range of inverse sine, cosine, and tangent functions. Apply inverse trig functions to verify relationships between angles and sides. Interpret inverse trigonometric function values geometrically and contextually. Special Right Triangles and Exact Values Use properties of 45°–45°–90° and 30°–60°–90° triangles to determine side lengths. Connect exact values of sine, cosine, and tangent for special angles to triangle ratios. Compare results from special right triangles to calculator or table values. Explain how special right triangles serve as a foundation for the unit circle. Applications of Trigonometry Solve real-world and mathematical problems involving angles of elevation and depression. Model and solve indirect measurement problems using trigonometric ratios. Interpret word problems, draw diagrams, and identify appropriate trigonometric relationships. Apply trigonometry to contexts such as navigation, surveying, and architecture.

NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What are the key parts of a circle, and how are they related (radius, diameter, chord, secant, tangent)? How do you determine whether a line is tangent to a circle? How are tangent segments from a common external point related? How can we find the measure of a central angle or an intercepted arc? How are inscribed angles related to the arcs they intercept? How does the measure of an inscribed angle compare to its intercepted arc? What relationships exist between angles formed by chords, secants, and tangents? How can we use algebra to solve for unknown measures in circle relationships? How are the measures of arcs, chords, and angles connected in circles with intersecting or overlapping segments? What is the relationship between the lengths of intersecting chords, secants, and tangents? How can we write the equation of a circle using the Pythagorean Theorem? How can we use the equation of a circle to describe its geometric properties (center, radius, diameter)? How does completing the square help us rewrite the equation of a circle in standard form? How can circle geometry be applied to real-world contexts like design, motion, and engineering? How are symmetry and transformations reflected in circles and circular patterns? Essential Questions How can we describe and analyze the relationships between lines, segments, and circles? How are the measures of arcs, angles, and segments within a circle connected? In what ways can algebraic reasoning help us solve geometric problems involving circles? How does understanding the geometry of circles help us model and interpret real-world situations? What defines a circle, and how do its properties differ from other geometric figures? How are transformations and symmetry reflected in the geometry of circles?
Unit Topics with Learning Objectives:
Introduction to Circles and Vocabulary Define and identify parts of a circle (radius, diameter, chord, secant, tangent, arc, central angle). Distinguish between minor arcs, major arcs, and semicircles. Describe and analyze relationships between radii, diameters, and chords. Identify congruent chords and their relationships to the circle’s center. Tangents and Their Properties Define and identify tangent lines to circles. Determine whether a line is tangent to a circle using geometric reasoning or algebraic methods. Use properties of tangent segments from a common external point to solve problems. Understand and apply the relationship between a tangent and a radius drawn to the point of tangency. Arcs and Angles in Circles Define and measure central and inscribed angles. Determine the relationship between an inscribed angle and its intercepted arc. Identify and use the relationships among central angles, inscribed angles, and arcs. Recognize and apply the Inscribed Angle Theorem and related cases (angles formed by tangents and chords). Segments and Angle Relationships in Circles Identify and find the measures of angles formed by chords, secants, and tangents. Use the relationships between arcs and angles for intersecting chords, secants, and tangents. Apply theorems involving the products of the segments of intersecting chords, secants, and tangents. Solve problems involving circle segment relationships using algebraic reasoning. Circles in the Coordinate Plane Derive the equation of a circle using the Pythagorean Theorem. Write the equation of a circle in standard form and general form. Find the center and radius of a circle given its equation. Use completing the square to rewrite circle equations in standard form. Graph circles and interpret their geometric properties in context.

Quadrilaterals

UNIT TITLE: Quadrilaterals
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What properties define a quadrilateral How can we use side lengths, slopes, and angle measures to classify a quadrilateral? How can we prove that a figure is a parallelogram? What relationships exist between opposite sides, opposite angles, and diagonals in parallelograms? How can we use the properties of parallelograms to find missing measures or justify reasoning? What distinguishes rectangles, rhombi, and squares from other parallelograms? How are rectangles, rhombi, and squares similar and different in their defining properties? How do the diagonals behave in each type of parallelogram? How can we prove that a quadrilateral is a rectangle, rhombus, or square using coordinate geometry? What properties define trapezoids and kites, and how do they differ from parallelograms? How are the bases, legs, and angles of trapezoids related? What special relationships exist in isosceles trapezoids and kites? How can the midsegment of a trapezoid be used to find missing measures or establish relationships? How can coordinate geometry be used to verify properties of any quadrilateral (e.g., slopes, distances, midpoints)? How can understanding the hierarchy of quadrilaterals help us organize their relationships? How can we apply quadrilateral properties to solve real-world problems involving design, engineering, or architecture? How can we use reasoning, diagrams, and algebra to construct and justify geometric proofs about quadrilaterals? Essential Questions How can we classify quadrilaterals based on their properties and relationships? How do we use reasoning and proof to establish relationships among sides, angles, and diagonals in quadrilaterals? In what ways do algebraic and coordinate methods help us verify geometric properties of quadrilaterals? How can understanding quadrilaterals help us model, design, and interpret structures in the real world? How are special quadrilaterals related, and how do their defining properties connect to one another? What makes a proof convincing when reasoning about geometric relationships?
Unit Topics with Learning Objectives:
Defining and Classifying Quadrilaterals Identify and define a quadrilateral and its key components (sides, vertices, diagonals, angles). Classify quadrilaterals based on side and angle properties. Describe the hierarchy of quadrilaterals (parallelogram, rectangle, rhombus, square, trapezoid, kite). Use Venn diagrams or flowcharts to represent relationships among quadrilateral families. Recognize how changes in side or angle properties shift a figure’s classification. Properties of Parallelograms Define and identify parallelograms and their properties. Use the properties of parallelograms to find missing angles, sides, and diagonal measures. Prove that opposite sides are parallel and congruent, and opposite angles are congruent. Show that the diagonals of a parallelogram bisect each other. Apply properties of parallelograms in algebraic and geometric problem solving. Special Parallelograms — Rectangles, Rhombi, and Squares Define and identify rectangles, rhombi, and squares. Use properties of diagonals to distinguish among these special parallelograms. Prove that a parallelogram is a rectangle, rhombus, or square using side, angle, or diagonal relationships. Explore the relationships and overlap between these special quadrilaterals within the hierarchy. Solve problems involving perimeter, area, and diagonal relationships of special parallelograms. 4. Trapezoids Define and identify trapezoids, including special cases (isosceles trapezoid). Explore relationships between bases, legs, and angles in trapezoids. Apply and prove the trapezoid midsegment theorem. Identify and use symmetry properties in isosceles trapezoids. Solve for missing measures and justify reasoning using trapezoid properties. 5. Coordinate Geometry and Proofs with Quadrilaterals Use the distance formula, midpoint formula, and slope to verify properties of quadrilaterals. Prove that a quadrilateral is a parallelogram, rectangle, rhombus, square, or trapezoid using coordinate geometry. Represent geometric relationships algebraically and interpret them graphically. Write formal and informal proofs involving the properties of quadrilaterals. Explain reasoning and justify conclusions using mathematical language and evidence.

Transformations

UNIT TITLE: Transformations
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What are the four main types of transformations, and how do they affect figures on the coordinate plane? How do translations, reflections, rotations, and dilations change a figure’s position, orientation, or size? How can we describe a transformation both visually and algebraically? How do we determine whether a transformation preserves congruence or similarity? How does a sequence of transformations affect a figure’s orientation and location? How can we represent transformations using coordinate rules or function notation? How can we use rigid motions to define and explain congruence between figures? What are the effects of different centers and scale factors in dilations? How can we use transformations to show that two figures are similar? What does it mean for a figure to have symmetry, and how can symmetry be described as a transformation? How can combining transformations lead to new, equivalent transformations? How can we verify that a transformation has been applied correctly using coordinate relationships? How do transformations connect geometry to design, art, and the natural world? How can we use transformations to create and analyze geometric patterns or tessellations? Essential Questions How do geometric transformations help us understand relationships between figures? What does it mean for two figures to be congruent or similar in terms of transformations? How can we describe, represent, and predict the effects of transformations in the coordinate plane? How do transformations reveal patterns of symmetry and balance in geometry and nature? How can algebraic rules and geometric reasoning work together to describe movement and change? In what ways can transformations model real-world situations or design problems?
Unit Topics with Learning Objectives:
Introduction to Transformations Define the four main types of transformations: translation, reflection, rotation, and dilation. Identify examples of transformations in the coordinate plane, real life, and nature. Understand the difference between rigid motions (congruence-preserving) and non-rigid motions (similarity-preserving). Recognize the effects of transformations on position, orientation, and size. Translations Describe translations using vectors and coordinate rules. Determine the image of a figure after a translation on a coordinate plane. Apply translations to solve problems involving congruent figures. Understand the relationship between a figure and its translated image. Reflections Identify and describe reflections across lines of symmetry, including axes and arbitrary lines. Determine the coordinates of a reflected image on the coordinate plane. Apply reflections to prove congruence and symmetry. Explore the properties of figures under reflection, including orientation changes. Rotations Define rotations and describe rotation around a point (including the origin) using degrees and direction. Use coordinate rules to determine the image of a rotated figure. Analyze how rotations affect orientation, congruence, and symmetry. Combine rotations with other transformations to solve geometric problems. Dilations and Similarity Define dilations and identify centers of dilation and scale factors. Determine the coordinates of a dilated image. Use dilations to show similarity between figures. Apply scale factors to solve problems involving perimeter, area, and volume. Distinguish between congruence (rigid motions) and similarity (dilations). Compositions of Transformations Explore the effect of performing two or more transformations in sequence. Represent composite transformations algebraically and graphically. Determine whether the order of transformations affects the final image. Use compositions of transformations to solve problems involving congruence and similarity.

3D Geometry

UNIT TITLE: 3D Geometry
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What are the defining properties of 3D figures (polyhedra, prisms, pyramids, cylinders, cones, spheres)? How can you classify solids based on faces, edges, and vertices? How are nets used to visualize and construct three-dimensional figures? How do you calculate the surface area of prisms, pyramids, cylinders, cones, and spheres? How do you calculate the volume of prisms, pyramids, cylinders, cones, and spheres? How do cross-sections of 3D figures help reveal their properties? How can 3D figures be represented in coordinate space, and how can distance and midpoint formulas apply? How do transformations (translations, rotations, reflections, dilations) affect 3D objects? How can you compare 3D figures using surface area and volume? How can proportional reasoning and similarity be applied to 3D figures? How are real-world objects modeled as prisms, cylinders, pyramids, or other solids for measurement and design purposes? What strategies help visualize and solve problems involving hidden faces, edges, or vertices? How do changes in dimensions affect volume and surface area of 3D figures? How can you apply 3D geometry formulas to solve practical problems in science, engineering, and everyday life? Essential Questions How can we represent and analyze three-dimensional objects using two-dimensional drawings or models? How do the properties of 3D figures relate to their 2D faces, edges, and vertices? How can volume and surface area be used to measure and compare three-dimensional objects? In what ways can 3D geometry be applied to real-world contexts like architecture, engineering, and design? How do transformations and cross-sections help us understand the structure and properties of solids? How can spatial reasoning improve our understanding of position, shape, and dimension in three-dimensional space?
Unit Topics with Learning Objectives:
Introduction to 3D Figures Identify and classify three-dimensional figures based on faces, edges, and vertices. Differentiate between polyhedra and non-polyhedra (cylinders, cones, spheres). Recognize and describe real-world examples of 3D figures. Use visualizations, models, and nets to understand the structure of solids. Prisms and Pyramids Identify bases and lateral faces of prisms and pyramids. Calculate the surface area of prisms and pyramids. Calculate the volume of prisms and pyramids using appropriate formulas. Apply reasoning to relate the area of the base to the overall volume. Solve real-world problems involving prisms and pyramids. Cylinders, Cones, and Spheres Identify key parts of cylinders, cones, and spheres. Calculate surface area, including lateral and total surface area, for cylinders and cones. Calculate volume for cylinders, cones, and spheres. Compare and contrast properties of cones, cylinders, and spheres. Solve real-world problems using surface area and volume of curved solids. Nets and Cross-Sections Use nets to visualize and construct three-dimensional figures. Identify cross-sections of 3D solids and determine their shapes. Apply cross-sections to calculate surface area and solve problems. Understand how different cross-sections can reveal properties of solids. Coordinate Geometry and 3D Visualization Represent 3D objects in coordinate space. Use distance and midpoint formulas to analyze edges and segments in 3D figures. Determine dimensions, lengths, and positions of elements in three-dimensional coordinate problems. Develop strategies for visualizing hidden faces, edges, and vertices.

Geometry Honors

Calc for Business

Statistics

COURSE TITLE: Statistics

COURSE DESCRIPTION: Statistics is a full year course designed to introduce students to how data informs decision making in the real world. Students will learn how to collect, analyze, interpret, and communicate conclusions from data. This course focuses on understanding variability, making predictions using quantitative models, and using probability to measure uncertainty. Students will develop statistical reasoning through real datasets, simulations, technology, experimentation, and written communication.

Students will regularly analyze data from real contexts such as sports, social media, medicine, marketing, politics, environmental science, psychology, and education. Emphasis is placed on explaining thinking clearly, interpreting results in context, and supporting claims with evidence. By the end of the course, students will be able to confidently evaluate claims they encounter in the world—news articles, studies, graphs, polls—using valid statistical reasoning.

This course prepares students for data literacy beyond high school—college level research courses, STEM pathways, business analytics, and responsible citizenship in a data-driven world.

MP1 Units:

MP2 Units:

MP3 Units:

MP4 Units:

Foundations of Data and Data Displays

Numerical Summaries of Data.

Bivariate Data

Probability (both independence and combinatorics )

Normal Distribution

Collecting Data and Experimental Design

Sampling Distributions and CLT

Estimation and Confidence Intervals

Significance Testing

Statistics in Practice

Review for final

Independent Projects

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams and class discussions Question and answer sessions, both formal and informal —planned/spontaneous In-class activities where students informally present their results Entrance and exit tickets Methods of Summative Assessments: In-unit Quizzes Unit Exams Final examination Projects (may vary from unit to unit)
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation: Learning Centers: Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation: Flexible Grouping: Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments: Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation: Varied Assessment Methods: Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation: Flexible Seating Arrangements: Offering various seating options to cater to students' comfort and learning preferences. Use of Technology: Incorporating digital tools that can provide personalized learning experiences. 5. Interest-Based Differentiation: Thematic Units: Designing units around themes that interest students to enhance engagement. 6. Feedback Differentiation: Individualized Feedback: Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection: Encouraging students to evaluate their own work and set personal learning goals. 7. Scaffolding: Step-by-Step Instructions: Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers: Using visual aids to help students organize information and ideas.

UNIT TITLE: Statistics
NYS Standards:
Math 140 ECE (Early College Experience) from WCC
Guiding Questions/Essential Questions:
How can students connect Statistics to their everyday lives? How can we use data to describe what we see and support what we believe? When is a pattern in data meaningful, and when might it just be random chance? How does variability change how confidently we can make conclusions? How do we know if results from a sample can be trusted to represent a population? What makes a statistical study fair, unbiased, and valid? How do we decide whether a difference is real or just due to random variability?
Unit Topics with Learning Objectives:
Unit 1–2 (Describing Data) What are the most important features of a distribution? How do measures of center and spread tell different stories about the same dataset? When does “average” fail to describe the typical case? Unit 3 (Regression / Bivariate) How can we measure and describe the strength of a relationship between two variables? When is a model useful for prediction, and when should we be skeptical of using it? Unit 4 (Probability) How can randomness be structured, modeled, or simulated? When should we trust our intuition and when is probability required instead? Unit 5 (Normal Distribution) Define the normal distribution and its key properties, such as symmetry, the relationship between the mean, median, and mode, and the role of the mean and standard deviation. Define the normal distribution and its key properties, such as symmetry, the relationship between the mean, median, and mode, and the role of the mean and standard deviation. Explain why many real-world variables approximate a normal distribution. Convert a value from a normal distribution to a standard normal (z) score and vice versa. Understand the purpose and advantages of using Z-scores for comparison. Construct a normal curve and identify regions under the curve. Unit 6 (Sampling / Experiments) What makes a study reliable and fair? Why is how you collect data often more important than how much data you collect? Why do sample statistics vary, and how predictable is that variability? Why is the sampling distribution the foundation of inference? Unit 7–8 (Inference) How can we quantify how confident we are in an estimate? How do we use evidence to decide between competing claims?

AP Calculus AB

COURSE TITLE: AP Calculus AB

COURSE DESCRIPTION: AP CALCULUS AB

(1 Unit) AP Calculus AB is a highly rigorous, college level mathematics course with high expectations designed to build students’ in-depth understanding of calculus. Students enrolled in this course intend to take the nationwide AP exam. Success on this examination could potentially result in earned college credit. The course is designed for students who have a thorough and complete knowledge of Geometry, Algebra 2 & Trigonometry, and Pre-Calculus. The AP Calc AB course will call on the skills and information acquired from these prerequisite courses to complete units of study of Limits and Continuity, Differentiation, Integration and Accumulation of Change, Differential Equations, all with a major emphasis on application(s). The curriculum emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, and algebraically. The AP Calc AB course will be fast-paced and challenging and thus students should expect to work hard for the entirety of the course.

Prerequisite Course: Precalculus, Precalculus Honors and teacher recommendation

College Board course and exam description

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Prerequisites for Calculus Limits and Continuity Differentiation and Basic Derivative Rules	Differentiation: Composite, Implicit, and Inverse Functions Contextual Applications of Differentiation Analytical Applications of Differentiation	Integration and Accumulation of Change Differential Equations	Applications of Integration AP Exam Review

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities of students; nonverbal and verbal feedback during lecture Homework exercises as review for exams and class discussions Question and answer sessions, both formal and informal —planned/spontaneous In-class activities where students informally present their results Quizzes Conferences between the instructor and student at various points in the semester Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Methods of Summative Assessments: Unit Exams Semester Assessment Final examination (Regents) Projects (project phases submitted at various completion points could be formatively assessed) NYS Labs
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Limits and Continuity

UNIT TITLE: Limits and Continuity
College Board Standards: https://apcentral.collegeboard.org/media/pdf/ap-calculus-ab-and-bc-course-and-exam-description.pdf
NYS Science Learning Standards (CORE CONTENT: Pages )
Guiding Questions/Essential Questions:
What is the limit of a function, and how is it used to describe the behavior of functions near a point or as the input approaches infinity? How can limits help describe instantaneous rates of change and the behavior of functions at boundaries? What does it mean for a function to be continuous at a point and on an interval? How do discontinuities in a function affect its graph and real-world applications? Computation and Application How can you evaluate limits algebraically, graphically, and numerically? What are the key techniques for finding limits, such as direct substitution, factoring, rationalization, and applying special trigonometric limits? How are limits involving infinity and horizontal or vertical asymptotes analyzed? How does the Squeeze Theorem help evaluate limits that are difficult to compute directly? Problem Solving How do you determine whether a given function has a limit at a particular point? What are removable, jump, and infinite discontinuities, and how do they appear in graphs and equations? How do piecewise functions challenge our understanding of limits and continuity? How can you use the Intermediate Value Theorem to verify the existence of roots or solutions within an interval? Real-World Connections How can limits be used to model real-world phenomena, such as population growth or rates of change in physics? Why is the concept of continuity critical in mathematical modeling and real-world applications? These questions aim to cover a range of levels, from foundational understanding to more complex problem-solving and real-world connections. Let me know if you'd like help breaking these down further or creating practice problems!
Unit Topics with Learning Objectives:
1.1 Introducing Calculus: Can Change Occur at an Instant? 2.B Identify mathematical information from graphical, numerical, analytical, and/or verbal representations. LIM-1 1.2 Defining Limits and Using Limit Notation 2.B Identify mathematical information from graphical, numerical, analytical, and/or verbal representations. 1.3 Estimating Limit Values from Graphs 2.B Identify mathematical information from graphical, numerical, analytical, and/or verbal representations. 1.4 Estimating Limit Values from Tables 2.B Identify mathematical information from graphical, numerical, analytical, and/or verbal representations. 1.5 Determining Limits Using Algebraic Properties of Limits 1.E Apply appropriate mathematical rules or procedures, with and without technology. 1.6 Determining Limits Using Algebraic Manipulation 1.C Identify an appropriate mathematical rule or procedure based on the classification of a given expression (e.g., Use the chain rule to find the derivative of a composite function). 1.7 Selecting Procedures for Determining Limits 1.C Identify an appropriate mathematical rule or procedure based on the classification of a given expression (e.g., Use the chain rule to find the derivative of a composite function). 1.8 Determining Limits Using the Squeeze Theorem 3.C Confirm whether hypotheses or conditions of a selected definition, theorem, or test have been satisfied. 1.9 Connecting Multiple Representations of Limits 2.C Identify a re-expression of mathematical information presented in a given representation. continued on next page UNIT AT A GLANCE Return to Table of Contents © 2020 College Board AP Calculus AB and BC Course and Exam Description Course Framework V.1 \| 32 Return to Table of Contents © 2020 College Board Limits and Continuity UNIT 1 Enduring Understanding Topic Suggested Skills Class Periods ~22–23 CLASS PERIODS (AB) ~13–14 CLASS PERIODS (BC) LIM-2 1.10 Exploring Types of Discontinuities 3.B Identify an appropriate mathematical definition, theorem, or test to apply. 1.11 Defining Continuity at a Point 3.C Confirm whether hypotheses or conditions of a selected definition, theorem, or test have been satisfied. 1.12 Confirming Continuity over an Interval 1.E Apply appropriate mathematical rules or procedures, with and without technology. 1.13 Removing Discontinuities 1.E Apply appropriate mathematical rules or procedures, with and without technology. 1.14 Connecting Infinite Limits and Vertical Asymptotes 3.D Apply an appropriate mathematical definition, theorem, or test. 1.15 Connecting Limits at Infinity and Horizontal Asymptotes 2.D Identify how mathematical characteristics or properties of functions are related in different representations. FUN-1 1.16 Working with the Intermediate Value Theorem (IVT) 3.E Provide reasons or rationales for solutions or conclusions

Differentiation: Definition and Basic Derivative Rules

UNIT TITLE: Differentiation: Definition and Basic Derivative Rules
College Board Standards:
College Board Standards: https://apcentral.collegeboard.org/media/pdf/ap-calculus-ab-and-bc-course-and-exam-description.pdf
Guiding Questions/Essential Questions:

Unit Topics with Learning Objectives:
2.1 Defining Average and Instantaneous Rates of Change at a Point 2.B Identify mathematical information from graphical, numerical, analytical, and/or verbal representations. 2.2 Defining the Derivative of a Function and Using Derivative Notation 1.D Identify an appropriate mathematical rule or procedure based on the relationship between concepts (e.g., rate of change and accumulation) or processes (e.g., differentiation and its inverse process, anti-differentiation) to solve problems. 4.C Use appropriate mathematical symbols and notation (e.g., Represent a derivative using f x ′ ′ y dy dx ( ), , and ). 2.3 Estimating Derivatives of a Function at a Point 1.E Apply appropriate mathematical rules or procedures, with and without technology. FUN-2 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist 3.E Provide reasons or rationales for solutions and conclusions. FUN-3 2.5 Applying the Power Rule 1.E Apply appropriate mathematical rules or procedures, with and without technology. 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple 1.E Apply appropriate mathematical rules or procedures, with and without technology. FUN-3 LIM-3 2.7 Derivatives of cos x, sin x, e x , and ln x 1.E Apply appropriate mathematical rules or procedures, with and without technology. Return to Table of Contents © 2020 College Board AP Calculus AB and BC Course and Exam Description Course Framework V.1 \| 54 Differentiation: Definition and Fundamental Properties UNIT 2 UNIT AT A GLANCE (cont'd) Enduring Understanding Topic Suggested Skills Class Periods ~13–14 CLASS PERIODS (AB) ~9–10 CLASS PERIODS (BC) FUN-3 2.8 The Product Rule 1.E Apply appropriate mathematical rules or procedures, with and without technology. 2.9 The Quotient Rule 1.E Apply appropriate mathematical rules or procedures, with and without technology. 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions 1.D Identify an appropriate mathematical rule or procedure based on the relationship between concepts (e.g., rate of change and accumulation) or processes (e.g., differentiation and its inverse process, anti-differentiation) to solve problems.

Differentiation: Composite, Implicit, and Inverse Functions

UNIT TITLE: Differentiation: Composite, Implicit, and Inverse Functions
College Board Standards:
College Board Standards: https://apcentral.collegeboard.org/media/pdf/ap-calculus-ab-and-bc-course-and-exam-description.pdf
Guiding Questions/Essential Questions:
Essential Questions: How do you apply the Chain Rule to differentiate composite functions? How can you differentiate a function that is composed of other functions, and what does the Chain Rule tell us about the rate of change of these functions? What are the steps involved in differentiating implicit functions? How can we differentiate equations where the dependent and independent variables are mixed together, and what is the role of the derivative in such cases? How do you differentiate inverse functions, and what relationship exists between a function and its inverse in terms of derivatives? How can we use the concept of inverse functions to find their derivatives, and what is the connection between the derivative of a function and the derivative of its inverse? What is the relationship between the derivative of a composite function and its components? How can we analyze the rate of change of a function when it is built from other functions, and how do the derivatives of the components affect the overall derivative? How can we use the Chain Rule, Implicit Differentiation, and the Inverse Function Theorem to solve real-world problems? What practical applications involve composite, implicit, and inverse functions, and how can we use differentiation to solve these types of problems?
Unit Topics with Learning Objectives:
3.1 The Chain Rule 1.C Identify an appropriate mathematical rule or procedure based on the classification of a given expression (e.g., Use the chain rule to find the derivative of a composite function). 3.2 Implicit Differentiation 1.E Apply appropriate mathematical rules or procedures, with and without technology. 3.3 Differentiating Inverse Functions 3.G Confirm that solutions are accurate and appropriate. 3.4 Differentiating Inverse Trigonometric Functions 1.E Apply appropriate mathematical rules or procedures, with and without technology. 3.5 Selecting Procedures for Calculating Derivatives 1.C Identify an appropriate mathematical rule or procedure based on the classification of a given expression (e.g., Use the chain rule to find the derivative of a composite function). 3.6 Calculating Higher-Order Derivatives 1.E Apply appropriate mathematical rules or procedures, with and without technology

Contextual Applications of Differentiation

UNIT TITLE: Contextual Applications of Differentiation
College Board Standards:
College Board Standards: https://apcentral.collegeboard.org/media/pdf/ap-calculus-ab-and-bc-course-and-exam-description.pdf
Guiding Questions/Essential Questions:
Essential Questions: - How can derivatives be used to solve real-world problems involving instantaneous rates of change? - How do you use the derivative to analyze motion and other rate-based scenarios?
Unit Topics with Learning Objectives:
4.1 Interpreting the Meaning of the Derivative in Context 1.D Identify an appropriate mathematical rule or procedure based on the relationship between concepts (e.g., rate of change and accumulation) or processes (e.g., differentiation and its inverse process, anti-differentiation) to solve problems. 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration 1.E Apply appropriate mathematical rules or procedures, with and without technology. 4.3 Rates of Change in Applied Contexts Other Than Motion 2.A Identify common underlying structures in problems involving different contextual situations. 4.4 Introduction to Related Rates 1.E Apply appropriate mathematical rules or procedures, with and without technology. 4.5 Solving Related Rates Problems 3.F Explain the meaning of mathematical solutions in context. 4.6 Approximating Values of a Function Using Local Linearity and Linearization 1.F Explain how an approximated value relates to the actual value. LIM-4 4.7 Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms 3.D Apply an appropriate mathematical definition, theorem, or test.

Analytical Applications of Differentiation

UNIT TITLE: Analytical Applications of Differentiation
College Board Standards:
College Board Standards: https://apcentral.collegeboard.org/media/pdf/ap-calculus-ab-and-bc-course-and-exam-description.pdf
Guiding Questions/Essential Questions:
Essential Questions: - How can we determine maximums and minimums of functions, and what do they tell us in practical situations (optimization)? - How does the behavior of a function's derivatives reveal the function's overall shape and properties?
Unit Topics with Learning Objectives:
5.1 Using the Mean Value Theorem 3.E Provide reasons or rationales for solutions and conclusions. 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points 3.E Provide reasons or rationales for solutions and conclusions. FUN-4 5.3 Determining Intervals on Which a Function is Increasing or Decreasing 2.E Describe the relationships among different representations of functions and their derivatives. 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema 3.D Apply an appropriate mathematical definition, theorem, or test. 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema 1.E Apply appropriate mathematical rules or procedures, with and without technology. 5.6 Determining Concavity of Functions over Their Domains 2.E Describe the relationships among different representations of functions and their derivatives. 5.7 Using the Second Derivative Test to Determine Extrema 3.D Apply an appropriate mathematical definition, theorem, or test. 5.8 Sketching Graphs of Functions and Their Derivatives 2.D Identify how mathematical characteristics or properties of functions are related in different representations. 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative 2.D Identify how mathematical characteristics or properties of functions are related in different representations. 5.10 Introduction to Optimization Problems 2.A Identify common underlying structures in problems involving different contextual situations. 5.11 Solving Optimization Problems 3.F Explain the meaning of mathematical solutions in context. 5.12 Exploring Behaviors of Implicit Relations 1.E Apply appropriate mathematical rules or procedures, with and without technology. 3.E Provide reasons or rationales for solutions and conclusions.

Integration and Accumulation of Change

UNIT TITLE: Integration and Accumulation of Change
College Board Standards:
College Board Standards: https://apcentral.collegeboard.org/media/pdf/ap-calculus-ab-and-bc-course-and-exam-description.pdf
Guiding Questions/Essential Questions:
Essential Questions: - How can a limit of a sum of areas (Riemann sums) be represented by a continuous function (definite integral)? - What is the relationship between differentiation and integration, as established by the Fundamental Theorem of Calculus?
Unit Topics with Learning Objectives:
6.1 Exploring Accumulations of Change 4.B Use appropriate units of measure. LIM-5 6.2 Approximating Areas with Riemann Sums 1.F Explain how an approximated value relates to the actual value. 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation 2.C Identify a re-expression of mathematical information presented in a given representation. FUN-5 6.4 The Fundamental Theorem of Calculus and Accumulation Functions 1.D Identify an appropriate mathematical rule or procedure based on the relationship between concepts (e.g., rate of change and accumulation) or processes (e.g., differentiation and its inverse process, anti-differentiation) to solve problems. 6.5 Interpreting the Behavior of Accumulation Functions Involving Area 2.D Identify how mathematical characteristics or properties of functions are related in different representations. FUN-6 6.6 Applying Properties of Definite Integrals 3.D Apply an appropriate mathematical definition, theorem, or test. 6.7 The Fundamental Theorem of Calculus and Definite Integrals 3.D Apply an appropriate mathematical definition, theorem, or test. 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation 4.C Use appropriate mathematical symbols and notation (e.g., Represent a derivative using f x ′ ′ y dy dx ( ), , and ). 6.9 Integrating Using Substitution 1.E Apply appropriate mathematical rule or procedures, with and without technology. 6.10 Integrating Functions Using Long Division and Completing the Square 1.E Apply appropriate mathematical rules or procedures, with and without technology.

Differential Equations

UNIT TITLE: Differential Equations
College Board Standards:
College Board Standards: https://apcentral.collegeboard.org/media/pdf/ap-calculus-ab-and-bc-course-and-exam-description.pdf
Guiding Questions/Essential Questions:
Essential Questions: - How can we find unique solutions to differential equations given initial conditions? - How can slope fields be used to visually represent and understand solutions to differential equations?
Unit Topics with Learning Objectives:
7.1 Modeling Situations with Differential Equations 2.C Identify a re-expression of mathematical information presented in a given representation. 7.2 Verifying Solutions for Differential Equations 3.G Confirm that solutions are accurate and appropriate. 7.3 Sketching Slope Fields 2.C Identify a re-expression of mathematical information presented in a given representation. 7.4 Reasoning Using Slope Fields 4.D Use appropriate graphing techniques. FUN-7 7.5 Approximating Solutions Using Euler’s Method bc only 1.E Apply appropriate mathematical rules or procedures, with and without technology. 7.6 Finding General Solutions Using Separation of Variables 1.E Apply appropriate mathematical rules or procedures, with and without technology. 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables 1.E Apply appropriate mathematical rules or procedures, with and without technology. 7.8 Exponential Models with Differential Equations 3.G Confirm that solutions are accurate and appropriate. 7.9 Logistic Models with Differential Equations bc only 3.F Explain the meaning of mathematical solutions in context.

Applications of Integration

UNIT TITLE: Applications of Integration
College Board Standards:
College Board Standards: https://apcentral.collegeboard.org/media/pdf/ap-calculus-ab-and-bc-course-and-exam-description.pdf
Guiding Questions/Essential Questions:
Essential Questions: - How can integrals be used to determine accumulation of change, area, and volume in various contexts? - How does the average value of a function over an interval relate to the accumulation of change over that interval?
Unit Topics with Learning Objectives:
8.1 Finding the Average Value of a Function on an Interval 1.E Apply appropriate mathematical rules or procedures, with and without technology. -4CHA 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals 1.D Identify an appropriate mathematical rule or procedure based on the relationship between concepts (e.g., rate of change and accumulation) or processes (e.g., differentiation and its inverse process, anti-differentiation) to solve problems. 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts 3.D Apply an appropriate mathematical definition, theorem, or test. 8.4 Finding the Area Between Curves Expressed as Functions of x 4.C Use appropriate mathematical symbols and notation (e.g., Represent a derivative using f x ′ ′ y dy dx ( ), , and ). 8.5 Finding the Area Between Curves Expressed as Functions of y 1.E Apply appropriate mathematical rules or procedures, with and without technology. -5CHA 8.6 Finding the Area Between Curves That Intersect at More Than Two Points 2.B Identify mathematical information from graphical, numerical, analytical, and/or verbal representations. 8.7 Volumes with Cross Sections: Squares and Rectangles 3.D Apply an appropriate mathematical definition, theorem, or test. 8.8 Volumes with Cross Sections: Triangles and Semicircles 3.D Apply an appropriate mathematical definition, theorem, or test. 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis 3.D Apply an appropriate mathematical definition, theorem, or test. continued on next page AP Calculus AB and BC Course and Exam Description Course Framework V.1 \| 146 Return to Table of Contents © 2020 College Board Applications of Integration UNIT 8 Enduring Understanding Topic Suggested Skills Class Periods ~19–20 CLASS PERIODS (AB) ~13–14 CLASS PERIODS (BC) 8.10 Volume with Disc Method: Revolving Around Other Axes 2.D Identify how mathematical characteristics or properties of functions are related in different representations. -5CHA 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis 4.E Apply appropriate rounding procedures. 8.12 Volume with Washer Method: Revolving Around Other Axes 2.D Identify how mathematical characteristics or properties of functions are related in different representations. -6CHA 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled bc only 3.D Apply an appropriate mathematical definition, theorem, or test.

AP Statistics

COURSE TITLE: AP Statistics

COURSE DESCRIPTION: This course is a college-level mathematics course with very high expectations and level of rigor. This course will introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, planning a study, anticipating patterns, and statistical inference. All students in the course are encouraged to take the Advanced Placement Statistics Exam. Success on this exam could potentially result in earned college credit. A variety of statistical applications will be explored after the Advanced Placement Statistics Examination.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Exploring Data Normal Distribution Examining Relationships Producing Data	Probability Random Variables Binomial & Geometric Distributions	Sampling Distributions Introduction to Inference Inference for Distributions	Inference for Proportions Chi-Squared Procedures Inference for Regression

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams and class discussions Question and answer sessions, both formal and informal —planned/spontaneous In-class activities where students informally present their results Methods of Summative Assessments: Unit Exams Quizzes WebAssign Final Examination
Methods of Differentiation/Extensions/Accommodations:
1. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 2. Pacing Differentiation : Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 3. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 4. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Exploring Data

UNIT TITLE: Exploring Data
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to Exploring Data to Make Conclusions
Unit Topics with Learning Objectives:
1-1 Displaying Distributions with Graphs -Bar Graphs, Pie Charts, Displaying Quantitative Variables: Dotplots & Stemplots -Center, Shape, Spread, Outlier 1-2 Displaying Quantitative Variables -Histograms -Symmetric, Skewed Right, Skewed Left 1-3 Relative Frequency, Cumulative Frequency, Percentiles, Ogives -Time Plot 1-4 Describing Distributions with Numbers -Mean, Median 1-5 Spread -Q1 and Q3, IQR, Outliers Criterion, Five Number Summary, Modified Boxplot 1-6 Measuring Spread: Standard Deviation -Variance, Standard Deviation (Properties of Stan Dev) -Degrees of Freedom 1-7 Changing the Unit of Measurement -Linear Transformation, Effect of a Linear Transformation

The Normal Distribution

UNIT TITLE: The Normal Distribution
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to utilize the Normal Distribution to Find Probabilities
Unit Topics with Learning Objectives:
2-1 Density Curves & The Normal Distribution - Density Curve (Mean & Median of) 2-2 Normal Distributions - (68,95,99.7), 2-3 Section Summary 2-4 Standard Normal Calculations - Standardizing & z –scores, Standard Normal Table (Table A), Finding Value given Proportion 2-5 Assessing Normality - By looking at Histogram, Normal Probability Plot

Examining Relationships

UNIT TITLE: Examining Relationships
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to Examine Data between Quantitative Variables
Unit Topics with Learning Objectives:
3-1 Scatterplots -Explanatory & Response Variables -Form, Direction, & Strength, Outlier, Positively & Negatively Associated 3-2 (Same as 3-1) 3-3 Adding Categorical Variables to Scatterplots -Making Scatterplot in Calculator 3-4 Correlation - r , Using Calculator to find r - , Doesn’t change if Exp & Res change, Need to be Quantitative, Measures strength of Linear Relationship, Not Resistant 3-5 (Same as 3-4) 3-6 Least-Squares Regression -Regression Line, Least-Squares Regression Line (LSRL) (Equation = ) (, ), Using Calculator to construct LSRL, Computer Printout 3-7 The Role of in Regression -Coefficient of Determination, SST & SSE -Distinction between Exp & Res Variables essential in Regression , Connection between Correlation & Slope, LSRL goes through , is the fraction of the variation in the values of y that is explained by the least-squares regression of y on x. 3-8 Residuals (observed – predicted) -Mean of the least-squares residuals is always zero -Residual Plot (Curved Pattern = Not Linear) -Individual Points with Large Residuals vs Individual Points that are Extreme in the x direction -Influential Points vs Outlier 3-9 Using Calculator for Residual Plot

Examining More with Two-Variable Data

UNIT TITLE: Examining More with Two-Variable Data
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to Examine Non- Linear Data
Unit Topics with Learning Objectives:
4-1 Transforming Relationships -Monotonic Increasing & Decreasing Functions, Concavity of Power Functions 4-2 Exponential Growth & Logarithm Transformation - 4-3 Prediction in the Exponential Growth Model 4-4 Power Law Models -Prediction in Power Law Models, Technology Toolbox 4-5 Section Summary 4-6 Cautions about Correlation & Regression -Extrapolation, Lurking Variables -Using averaged data 4-7 Causation? Common Response & Confounding 4-8 Relations in Categorical Data -Marginal Distributions, Describing Distributions 4-9 Conditional Distributions 4-10 Simpson’s Paradox

Producing Data

UNIT TITLE: Producing Data
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to design samples and collect data
Unit Topics with Learning Objectives:
5-1 Designing Samples -Observational Study & Experiment, Population vs Sample, Sampling vs Census -Voluntary Response Sample, Convenience Sampling, Bias 5-2 Simple Random Samples -SRS, Random Digits Table & How to Read Table, Probability Sample, Stratified Random Sample (Strata), Multistage Sampling 5-3 Cautions about Sample Surveys -Undercoverage, Nonresponse, Wording of Questions -Inference about Population, Larger Samples Good yet don’t Reduce Bias 5-4 Section Summary -Systematic Random Sample 5-5 Designing Experiments -Experimental Units = Subjects (Humans ) & Treatments -Placebo -Comparative Experiments (Units -> Treatment -> Observe Response) -Placebo Effect, Control Group 5-6 Randomization -Randomization Comparative Experiments “effects of chance will average out” -Principles of Experimental Design (1. Control, 2. Randomize, 3. Replicate) -Statistically significant -Completely Randomized Design 5-7 Cautions about Experimentation -Double Blind , Lack of Realism -Matched Pairs Design, Block Designs 5-8 Section Summary 5-9 Simulating Experiments -Probability Model, Simulation -Independence 5-10 Simulations with Calculator Steps to follow performing simulation

Probability: The Study of Randomness

UNIT TITLE: Probability: The Study of Randomness
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to utilize Theoretical Probability
Unit Topics with Learning Objectives:
6-1 The Idea of Probability -Predictable Pattern in Long Run, Law of Large Numbers -Randomness & Probability -Independence 6-2 Probability Models -Sample Space, Event, Tree Diagram, Multiplication Principle -Replacement (Without Replacement) 6-3 Probability Rules - Between 0 and 1, Sum of 1, Prob of Event = 1 – Prob of Not, Can add Prob if no overlap - Union, Empty Event, Intersect, Venn Diagrams, Disjoint (Mutually Exclusive) - Probabilities in a Finite Sample Space (must add to 1) - Assigning Probabilities: Equally Likely Outcomes , Benford’s Law 6-4 Independence & Multiplication Rule -Events Independent if P(A and B) = P(A)P(B) -Disjoint events and not independent 6-5 General Probability Rules -Union ( P(A or B or C)) = P(A) + P(B) + P(C) -Uniform Distribution -General Addition Rule for Unions of Two Events (Disjoint or not) - P(A or B) = P(A) + P(B) – P(A and B) or -Joint Event, Joint Probability 6-6 Conditional Probability Definition of Conditional Probability 6-7 Intersection -Tree Diagrams Revisted -Bayes’s Rule -Independence Again -Two events A and B are independent if

Random Variables

UNIT TITLE: Random Variables
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to Find Means and Standard Deviations of Random Variables
Unit Topics with Learning Objectives:
7-1 Discrete & Continuous Random Variables -Discrete Random Variables, Probability Distribution, Probability Histograms 7-2 Continuous Random Variables -Uniform Distribution, Probability Distribution -Normal Distributions as Probability Distributions 7-3 Means & Variances of Random Variables -The Mean of a Random Variable -Mean (), Expected Value -The Variance of a Random Variable -Variance (), Standard Deviation () 7-4 Statistical Estimation & Law of Large Numbers -Law of Large Numbers, (Law of Small Numbers) 7-5 Rules for Means - (, ) Rules for Variances - Independence , (Dependent = Correlation) - (, ) Addition Rule for Variances of Independent Random Variables - () Combining Normal Random Variables - Any Linear Combination of Independent Normal Random Variables is also Normally Distributed

Binomial & Geometric Distributions

UNIT TITLE: Binomial & Geometric Distributions
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to calculate probabilities of Binomial & Geometric Distributions
Unit Topics with Learning Objectives:
8-1 The Binomial Distributions (Binomial Setting) -Success or Failure, Fixed number of observations, Independent, Probability of Success is Constant -Binomial Random Variable , Binomial Distribution (n = # of observations, p = prob of succ) -Finding Binomial Probabilities (binompdf (n,p,x) ( x = specific # of successes) - (binomcdf (n,p,x) (x = at most that many successes) 8-2 Binomial Formulas -Binomial Coefficient ( number of ways of arranging k successes in n observations) -Binomial Probability (n observations, p = prob on each, k successes) 8-3 Binomial Mean & Standard Deviation -, Standard Deviation -The Normal Approximation to Binomial Distributions () Rule of Thumb: Need to satisfy 8-4 Binomial Distribution with the Calculator -Simulating Binomial Experiments 8-5 The Geometric Distributions -Success or Failure, Prob of Success Constant, Independent, Number of Trials until First Success -Prob of Success on nth trial 8-6 Expected Value and Other Properties of the Geometric Random Variable -Mean -The probability that it takes more than n trials to see the first success is: -Simulating Geometric Experiments

Sampling Distributions

UNIT TITLE: Sampling Distributions
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How the properties of Sampling Distributions help us find probabilities of Samples
Unit Topics with Learning Objectives:
9-1 Sampling Distributions -Parameter – Statistic ( and ), -Sampling Variability , Sampling Distribution 9-2 Describing Sampling Distributions -Shape, Center, Spread, Outliers -Bias of a Statistic (Unbiased if Mean of Sampling Dist = True Value of the Parameter) -Variability of a Statistic (Spread determined by Sampling Design and Size of Sample) -Larger samples give smaller spread -Bias & Variability 9-3 Section Summary 9-4 Sampling Proportions -Sampling Distribution of a Sample Proportion (Mean = , Standard Dev = ) -Rule of Thumb 1 () for using Standard Dev -Rule of Thumb 2 () for using Normal Appoximation 9-5 Section Summary 9-6 Sample Means -Sampling Distribution of Sample Means ( Mean = , and Standard Dev is ) -Sampling Distribution of a Sample Mean from a Normal Population ( ) 9-7 Central Limit Theorem - If n is large enough, Sampling Dist of Sample Mean is close to

Introduction to Inference

UNIT TITLE: Introduction to Inference
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to come to conclusions using inference via Confidence Intervals and Tests of Significance
Unit Topics with Learning Objectives:
10-1 Estimating with Confidence -Statistical Confidence (Confidence Interval = Estimate Margin of Error) 10-2 Confidence Interval for a Population Mean -Conditions (SRS from pop or interest, Samp Dist of is approx normal) -Critical Values ( ) 10-3 How Confidence Intervals Behave -Effects of changing values on C.I. -Choosing the Sample Size needed for desired C.I. or Margin of Error ( ) 10-4 Section Summary 10-5 Tests of Significance -Significance Test, Null Hypothesis, Alternative Hypothesis, P-Value, Statistically Significant 10-6 Stating Hypotheses -Null Hypothesis (One-Sided, Two-Sided Alternative) -P-value (Smaller P-Value, the stronger the evidence against ) -Statistically Significant at level (Significance Level) 10-7 Tests for Population Mean -Inference Toolbox (Identify the Pop of Int, Choose Inference Proc, Conditions met so carry out proc (Calculate the test statistic, Find P-Value, Interpret Results in Context) -One Sample z Statistic -z Test for a Population Mean 10-8 Test with Fixed Significance Level -One Sided Alternative : -Two Sided Alternative: -Confidence Intervals & Two Sided Tests (A level two-sided significance tests rejects a hypothesis exactly when the value falls outside a level 1- confidence interval for ) 10-9 Section Summary 10-10 Making Sense of Statistical Significance -Choosing a level of significance (Statistical Significance and Practical Significance) -Statistical inference is Not valid for all sets of data. (Hawthorne Effect) -Beware of Multiple Analyses 10-11 Section Summary 10-12 Inference as Decision -Type I & Type II Errors (If we reject when in fact is true, this is a Type I Error) (If we accept when in fact is true, this is Type II Error) -Error Probabilities -Significance and Type I Error (The significance level of any fixed level test is the probability of a Type I Error) 10-13 Power -The probability that a fixed level significance test will reject when a particular alternative value of the parameter is true is called the Power of the test against the alternative. -The power of a test against any alternative is 1 minus the probability of a Type II Error for that alternative. Increasing The Power (Increase , Consider alternative that is farther away from , Increase sample size, Decrease ) 10-14 Different Views of Statistical Tests -Testing Hypotheses

Inference for Distributions

UNIT TITLE: Inference for Distributions
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How do t-Distributions work? Two Sample Confidence Intervals and Significance Tests for Means
Unit Topics with Learning Objectives:
11-1 Inference for the Mean of a Population -Conditions (SRS, Normal Distribution) -Standard Error - when we use s in place of t – distributions (Degrees of Freedom) 11-2 t Confidence Intervals & Tests -One Sample t Procedures: , where is the upper (1-C)/2 critical value for the t (n – 1) Distribution 11-3 Matched pairs t Procedures -Matched Pairs Design (Apply the one-sample t procedures to the observed differences) 11-4 Robustness of t Procedures -Robust = if the confidence level or P-value does not change very much when the assumptions of the procedure are violated (Likeprocedures are strongly influenced by outliers) -Using t Procedures (the assumption of SRS is more important than assumption of pop being normal) -Sample Size < 15 (Check specific data to see if close to normal, if so can use t Procedures) -Sample Size at least 15 (t Procedures can be used except for outliers or strong skewness) -Large Samples (t Procedures can be used even for clearly skewed distributions…..n40) -The Power of the t Test 11-5 Section Summary 11-6 Comparing Two Means -Two-Sample Problems (Compare responses to two treatments, separate sample for each treatment) -Conditions for Comparing Two Means (Two SRSs, Samples Independent (Matching violates Independence), Both Pop are Normally Dist) 11-7 The Sampling Distribution of -The mean is , Variance is , If two populations are normal, dist of is normal) -Two-Sample z Statistic: -Two-Sample t Statistic: -Two-Sample t Statistic Procedures: -Draw SRS from two normal populations; C.I. = -To test the hypothesis , compute the two-sample t statistic -Robustness Again (two-sample t procedures are more robust than one-sample t methods) 11-8 More accurate levels in the t Procedures 11-9 Pooled two-sample t Procedure

Inference for Proportions

UNIT TITLE: Inference for Proportions
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How do Confidence Intervals and Tests of Significance Tests work for Proportions
Unit Topics with Learning Objectives:
12-1 Inference for a Population Proportion Sample Proportion: Conditions for Inference: SRS from Pop of Interest, , ( is an unbiased estimator of p, Standard Dev of is ) 12-2 Confidence Interval : (where is the upper (1-C)/2 ) 12-3 Sample Size for Desired Margin of Error (The margin of error will be less than or equal to m if you take the to be 0.5 ) 12-4 Comparing Two Proportions Sampling Distribution of Mean: Stand Dev: Confidence Intervals for C.I. = 12-5 Significance Tests for -Pooled Sample Proportion -

Inference for Tables: Chi-Square Procedures

UNIT TITLE: Inference for Tables: Chi-Square Procedures
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How do Chi-Square Tests work
Unit Topics with Learning Objectives:
13-1 Test for Goodness of Fit (to determine whether a population has a certain hypothesized distribution) -Chi-Square Test for Goodness of Fit Chi-Square Statistic -Properties: Only positive values and skewed right, specified by degrees of freedom (n -1), total area under a chi-square curve = 1, as degrees of freedom increase the curve becomes more symmetrical and normal -Conditions: All expected counts are at least 1 and no more than 20% of the expected counts are < 5 13-2 Technology Toolbox 13-3 Inference for Two-Way Tables -Comparing Multiple Comparisons () -Expected Count in any cell of a two-way table when is true is: 13-4 Chi-Square Test for Homogeneity of Populations - Chi-Square Statistic (The sum is over all r x c cells in the table) -Conditions: Select independent SRSs from each of c populations. the distribution of the response variable is the same in all c populations the distribution are not all the same -Degrees of Freedom (r-1)(c-1) -P-value is the area to the right of under the curve with df 13-5 The chi-square test of Association / Independence (assesses whether an observed association is statistically significant) - There is no association between two categorical variables - There is an association between two categorical variables -Computing Conditional Distributions -Computing Expected Cell Counts Performing the test 13-6 The Chi-Square test and the Z test (same for a 2 x 2 table and a two proportion z test)

Inference for Regression

UNIT TITLE: Inference for Regression
NYS Standards:
NYS Math Learning Standards
Guiding Questions/Essential Questions:
How to do Tests of Significance for Regression
Unit Topics with Learning Objectives:
14-1 Inference About the Model -Conditions: -For any fixed value of x, the response y varies according to a normal distribution. Repeated responses y are independent of each other. -The mean response has a straight line relationship with x ; The slope and intercept are unknown parameters. -The standard deviation of y (call it ) is the same for all values of x. The value of is unknown. -The slope b of the least-squares line is an unbiased estimator of the true slope , and the interceptof the least-squares line is an unbiased estimator of the true intercept -The Standard Error about the line is: Use s to estimate the unknown in the regression model - n – 2 degrees of freedom 14-2 Confidence Intervals for the Regression Slope -The confidence interval for of the true regression line is: - In this formula, the standard error of the least-squares slope b is and is the upper (1-C) / 2 critical value from the t distribution with n-2 degrees of freedom. -Testing the Hypothesis of No Linear Relationship , compute the t statistic 14-3 Predictions & Conditions -A level C confidence interval for the mean response when x takes the value is : -The standard error is: -A level C prediction interval for a single observation on y when x takes the value is: -In both situations, is the upper (1-C) / 2 critical value from the t distribution with n-2 degrees of freedom. -Checking the Regression Conditions -The observations are independent, The True relationship is Linear, The standard deviation of the response about the true line is the same everywhere, The response varies normally about the true regression line.

Precalculus Honors

COURSE TITLE: Precalculus Honors

COURSE DESCRIPTION: This is an intensive honors college preparatory course, designed to provide students with an in-depth study in advanced skills required to be successful in a college-level Calculus course, AP Calculus AB, or AP Calculus BC. Major emphasis is placed on the study and understanding of topics at a deep and conceptual level. Topics include analytical geometry, continuous and discontinuous functions and their graphs, conics, circular and exponential functions, sequences and series, polar coordinates, and limits. Additional honors topics include, but are not limited to: matrices, parametric equations, mathematical induction, and an introduction to differential calculus. This course requires the use of a graphing calculator and culminates in a local final examination in June.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Functions Optimization	Limits Basic Derivatives Derivatives of transcendentals	Applications of Derivatives Partial Fraction Decomposition Polar Functions	Parametric Functions Infinite Series

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams and class discussions Question and answer sessions, both formal and informal —planned/spontaneous Conferences between the instructor and student at various points in the semester In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Methods of Summative Assessments: Unit Exams Semester Assessment Final examination (local) Projects (project phases submitted at various completion points could be formatively assessed)
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Functions

UNIT TITLE: Functions
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What is the difference between a relation and a function? How can you determine if a graph, equation, or table represents a function? How does the domain and range of a function relate to its graph? How do transformations (e.g., translations, reflections, stretches) affect the graph of a function? What are the key features of a function, such as intercepts, asymptotes, and end behavior? How do linear, quadratic, and exponential functions differ in their graphs and equations? What role does inverse play in understanding functions? How can functions model real-world situations and solve problems? Essential Questions How do functions help us understand and describe relationships in mathematics and the real world? Why are patterns and relationships important in mathematics? How can different representations of a function (algebraic, graphical, numerical) enhance our understanding of its behavior? What are the advantages and limitations of using functions to model real-world phenomena? How can understanding the structure of functions help solve complex problems? What is the significance of transformations in understanding and manipulating functions? How do the concepts of continuity and change manifest in the study of functions?
Unit Topics with Learning Objectives:
1. Understanding the Concept of a Function Define a function and distinguish it from a general relation. Use appropriate notation to represent functions, including function evaluation (e.g., f(x)f(x)f(x)). Identify and explain the domain and range of a function in various contexts. 2. Representing Functions in Multiple Ways Represent functions using equations, tables, graphs, and verbal descriptions. Interpret and translate between different representations of a function. Identify key features of functions (e.g., intercepts, intervals of increase and decrease, maxima and minima) from graphs and equations. 3. Types of Functions Explore and analyze linear, quadratic, polynomial, exponential, logarithmic, trigonometric, and piecewise-defined functions. Compare and contrast these functions in terms of their graphs, equations, and key features (e.g., asymptotes, end behavior). 4. Inverses of Functions Determine whether a function is one-to-one and explain why this property is necessary for an inverse to exist. Find the inverse of a function algebraically and graphically. Explore the relationship between a function and its inverse. 5. Advanced Problem-Solving and Analysis Solve equations involving functions, including systems of equations graphically and algebraically. Explore compositions of functions and their applications. Analyze the behavior of functions, including limits, continuity, and asymptotes.

Optimization

UNIT TITLE: Optimization
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What does it mean to optimize a function in a mathematical context? How can you identify critical points of a function, and how do they relate to optimization? How do you determine whether a critical point is a maximum, minimum, or neither? What is the importance of endpoints in optimization problems on closed intervals? How can constraints be incorporated into optimization problems, and how do they affect the solution? How do you interpret the solutions to optimization problems in the context of real-world scenarios? Essential Questions How can mathematical models help us make the best possible decisions in real-world situations? Why are critical points and rates of change fundamental to understanding optimization? What are the limitations of optimization methods when applied to real-world contexts? Why is it important to consider constraints in decision-making and problem-solving? How does optimization demonstrate the power of mathematics in maximizing efficiency and minimizing waste?
Unit Topics with Learning Objectives:
1. Understanding Optimization Concepts Define optimization and explain its significance in mathematical and real-world contexts. Distinguish between local extrema (minimums and maximums) and global extrema. Explain the role of constraints in optimization problems. Evaluate functions on closed intervals to identify global extrema, considering endpoints. Solve optimization problems involving one-variable functions and determine whether solutions are reasonable. 2. Modeling and Solving Optimization Problems Set up equations or functions to model real-world optimization scenarios. Translate word problems into mathematical expressions, clearly identifying the objective function and constraints. Use algebraic and graphical methods to solve constrained optimization problems. 3. Applications of Optimization Solve applied optimization problems in various fields, such as geometry (e.g., maximizing area or minimizing perimeter), economics (e.g., profit maximization or cost minimization), and physics (e.g., finding the optimal path or force). Analyze the sensitivity of optimization problems to changes in constraints or parameters. Interpret the meaning of optimal solutions within the context of real-world problems. 4. Advanced Problem-Solving Explore multivariable optimization in introductory contexts Solve non-linear optimization problems involving quadratic, polynomial, and rational functions. Examine problems with multiple objectives and evaluate trade-offs in decision-making. 5. Honors-Level Rigor and Extensions Justify optimization solutions with logical reasoning and precise mathematical language. Investigate the limitations of optimization models and explore cases where no optimal solution exists. Develop strategies for solving complex, multi-step optimization problems.

Limits

UNIT TITLE: Limits
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What does it mean for a function to "approach" a value as the input approaches a number or infinity? How can you evaluate a limit algebraically, graphically, and numerically? What are the different types of limits, such as one-sided limits, two-sided limits, and limits at infinity? What is the difference between a limit existing and a function being defined at a point? How can indeterminate forms like 0/0 be resolved using algebraic techniques? How do asymptotes relate to limits at infinity? What role do limits play in defining continuity and discontinuity of a function? How can special limit rules, such as the Squeeze Theorem, help evaluate limits? Essential Questions How do limits provide a foundation for calculus and the study of change? Why is the concept of "approaching" a value critical to understanding functions and their behavior? How can the behavior of a function near a point give us insight into its long-term behavior? What are the implications of limits for understanding continuity and discontinuity in real-world situations? How do mathematical tools like limits allow us to explore ideas of infinity and infinitesimally small quantities? How do the principles of limits connect to the broader mathematical goal of making precise predictions about dynamic systems?
Unit Topics with Learning Objectives:
1. Understanding the Concept of Limits Define a limit and explain its meaning in terms of the behavior of a function as the input approaches a specific value or infinity. Distinguish between one-sided and two-sided limits. Explain the difference between a limit existing and a function being defined at a point. 2. Evaluating Limits Evaluate limits numerically using tables of values. Estimate limits graphically by analyzing a function's behavior near a specific point. Compute limits algebraically, including limits that result in indeterminate forms (e.g., 0/0, ∞/∞). 3. Special Limit Techniques Apply algebraic techniques, such as factoring, rationalizing, and simplifying expressions, to evaluate limits. Use limit laws and properties to solve problems systematically. Use special limit definitions involving sine, cosine, and e. Apply the Squeeze Theorem to evaluate limits in specific cases. 4. Limits at Infinity and Infinite Limits Analyze and compute limits as x→∞ x→−∞. Describe the relationship between horizontal asymptotes and limits at infinity. Evaluate vertical asymptotes in terms of infinite limits. 5. Continuity and Discontinuity Define continuity at a point and over an interval using limits. Determine where a function is continuous or discontinuous, classifying discontinuities as removable, jump, or infinite. Relate the concept of limits to the Intermediate Value Theorem. 6. Honors-Level Rigor and Extensions Explore the formal definition of a limit (ϵ\epsilonϵ-δ\deltaδ definition) and use it to justify results. Solve complex, multi-step problems involving limits, including those requiring advanced algebraic manipulation. Explore the relationship between limits and the derivative as a foundational concept in calculus. 7. Applications of Limits Apply limits to real-world scenarios, such as rates of change, population models, or physics problems. Use limits to describe the behavior of dynamic systems as inputs approach critical thresholds.

Basic Derivatives

UNIT TITLE: Basic Derivatives
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What does the derivative of a function represent? How is the derivative related to the slope of a tangent line at a point? What is the difference between average rate of change and instantaneous rate of change? How can the derivative be interpreted graphically, numerically, and analytically? How is the derivative defined using limits? What are the rules for finding derivatives of basic functions, such as polynomials, constants, and power functions? What is the significance of higher-order derivatives, and how do they relate to the original function? How can the derivative help identify critical points, increasing/decreasing intervals, and points of inflection? Essential Questions How do derivatives help us model and analyze change in real-world and mathematical contexts? Why is the concept of instantaneous rate of change fundamental to understanding dynamic systems? How do derivatives provide insights into the behavior of functions and their graphs? What are the connections between the derivative, the tangent line, and the concept of a limit? How do the rules of differentiation simplify the process of analyzing complex functions? Why is the derivative considered a foundational tool in calculus and beyond?
Unit Topics with Learning Objectives:
1. Understanding the Concept of the Derivative Define the derivative as the limit of the difference quotient. Interpret the derivative as the slope of the tangent line to a curve at a point. Differentiate between average rate of change and instantaneous rate of change. Explain the connection between the derivative and the concept of a limit. 2. Computing Derivatives Compute derivatives from first principles (using the limit definition). Apply basic differentiation rules, including: The power rule. The constant rule. The constant multiple rule. The sum and difference rules. Find the derivative of polynomial and simple algebraic functions. 3. Graphical and Numerical Interpretation Approximate derivatives numerically using tables or computational tools. Interpret the graph of a derivative in relation to the original function. Analyze how the derivative relates to the slope and concavity of a function’s graph. 4. Applications of Derivatives Use derivatives to solve problems involving rates of change in real-world contexts. Apply the derivative to find the slope of tangent lines and write the equation of a tangent line at a point. Use the derivative to identify intervals where a function is increasing or decreasing. 5. Honors-Level Rigor and Connections Explore the connection between differentiability and continuity, recognizing that differentiable functions are continuous but not all continuous functions are differentiable. Solve more challenging problems requiring the interpretation of derivatives in applied settings. Begin exploring higher-order derivatives and their meaning in real-world contexts, such as acceleration.

Derivatives of Transcendental Functions

UNIT TITLE: Derivatives of Transcendental Functions
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What are transcendental functions, and how do they differ from algebraic functions? How do you find the derivatives of exponential and logarithmic functions? How are the rules for differentiating trigonometric functions applied? What is the derivative of the inverse trigonometric functions, and how can it be derived? How do the Chain Rule and other differentiation rules apply to transcendental functions? What are the key differences in interpreting the derivatives of transcendental functions compared to algebraic functions? How can derivatives of transcendental functions be used to model and analyze real-world problems? How are special limits, such as lim⁡x→0 sin⁡x/x=1, used to derive formulas for the derivatives of transcendental functions? Essential Questions How do transcendental functions expand our ability to model and analyze natural phenomena? Why are exponential, logarithmic, and trigonometric functions critical in understanding rates of change? How does understanding the derivatives of transcendental functions help us analyze dynamic systems in fields like physics, engineering, and biology? What is the significance of combining rules like the Chain Rule and the Product Rule when differentiating transcendental functions? How does the study of transcendental functions deepen our understanding of the connections between geometry, algebra, and calculus? In what ways do transcendental functions illustrate the power and elegance of calculus in solving complex problems?
Unit Topics with Learning Objectives:
1. Understanding Transcendental Functions Define transcendental functions and distinguish them from algebraic functions. Identify common transcendental functions, including exponential, logarithmic, and trigonometric functions. Explain the importance of transcendental functions in modeling real-world scenarios, such as growth/decay, oscillations, and waves. 2. Differentiating Exponential Functions Apply the derivative rules to find the derivatives of exponential functions, including f(x)=ex and f(x)=ax for a>0. Derive and apply the chain rule for differentiating composite exponential functions. Solve problems involving rates of change for exponential growth and decay. 3. Differentiating Logarithmic Functions Compute the derivatives of natural logarithmic functions f(x)=ln(x), and logarithmic functions f(x)=loga(x), Use the Chain Rule to differentiate composite logarithmic functions. Apply logarithmic differentiation in complex functions involving products, quotients, or powers. 4. Differentiating Trigonometric Functions Differentiate the basic trigonometric functions sin⁡(x), cos⁡(x), tan⁡(x), sec⁡(x), csc⁡(x), and cot⁡(x). Derive and apply the chain rule for differentiating composite trigonometric functions. Solve real-world problems involving rates of change and oscillatory motion using derivatives of trigonometric functions. 5. Differentiating Inverse Trigonometric Functions Find the derivatives of inverse trigonometric functions, such as arcsin⁡(x), arccos⁡(x), arctan⁡(x), and others. Apply the chain rule to differentiate compositions involving inverse trigonometric functions. Interpret the significance of derivatives of inverse trigonometric functions in geometric and physical contexts. 6. Application of Derivatives of Transcendental Functions Use derivatives of transcendental functions to solve optimization and related rates problems. Analyze and interpret the behavior of transcendental functions and their derivatives in various applications (e.g., population models, physics, economics). Understand the role of transcendental functions in modeling real-world phenomena, including growth, oscillation, and wave motion. 7. Honors-Level Rigor and Extensions Solve advanced problems that involve combinations of exponential, logarithmic, and trigonometric functions using appropriate differentiation rules. Explore higher-order derivatives and their interpretations for transcendental functions. Analyze and simplify complex expressions involving transcendental functions, leveraging differentiation techniques to solve real-world problems.

Applications of Derivatives

UNIT TITLE: Applications of Derivatives
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions How do derivatives help us understand the rate of change of a quantity with respect to another variable? What is the relationship between the derivative of a function and the slope of the tangent line at a point on its graph? How can derivatives be used to solve optimization problems, such as finding maximum or minimum values? How do we apply derivatives to related rates problems, where two or more quantities are changing with respect to time? What role do critical points and inflection points play in analyzing the behavior of a function in real-world contexts? How can the first and second derivatives help determine the nature of critical points (maximum, minimum, or saddle point)? In what ways can derivatives be applied to physics, economics, biology, and other fields to model dynamic systems? How do we use the second derivative to analyze concavity and understand the overall shape of a function’s graph? Essential Questions How do derivatives provide insight into the dynamic behavior of systems, allowing us to model and analyze real-world phenomena? Why are optimization techniques, based on derivatives, crucial in decision-making processes in various fields such as economics, engineering, and biology? How do related rates problems demonstrate the interconnectedness of different quantities changing over time? In what ways can the second derivative be used not only to determine concavity but also to identify significant behaviors like acceleration or deceleration in motion? How do the concepts of maxima, minima, and rates of change impact problem-solving and analysis in practical applications? What are the limitations of applying derivatives to real-world problems, and how do mathematical models approximate complex phenomena? How do derivatives facilitate the transition from descriptive to predictive models in science and engineering?
Unit Topics with Learning Objectives:
1. Understanding Rates of Change Students will interpret the derivative of a function as the rate of change of one quantity with respect to another. Students will explain how derivatives are used to model and analyze dynamic systems in various fields, such as physics, economics, and biology. Students will calculate the average and instantaneous rates of change of functions and apply them in practical situations. 2. Solving Optimization Problems Students will apply the first derivative test to find and classify critical points (local maxima, minima, or saddle points) in optimization problems. Students will solve real-world optimization problems by identifying objective functions and constraints. Students will interpret the results of optimization problems in real-world contexts, such as maximizing profit, minimizing cost, or optimizing physical quantities (area, volume, etc.). 3. Related Rates Students will apply the concept of related rates to solve problems where two or more quantities are changing over time. Students will use implicit differentiation to relate rates of change in related rates problems. Students will interpret the results of related rates problems in context and solve them algebraically and numerically. 4. Analyzing Critical and Inflection Points Students will identify critical points of a function and determine intervals where the function is increasing or decreasing. Students will apply the second derivative test to determine concavity and identify points of inflection in a function. Students will analyze the behavior of a function at critical points and points of inflection to determine its overall behavior. 5. Applications in Physics and Motion Students will use derivatives to analyze motion, including velocity, speed, and acceleration. Students will interpret the first and second derivatives of position functions to model motion in one or more dimensions. Students will apply derivatives to solve problems involving motion under constant acceleration and related real-world phenomena. 6. Real-World Problem Solving Students will apply derivatives to model and solve real-world problems in fields such as economics (e.g., marginal cost/revenue), biology (e.g., population models), and engineering (e.g., optimization of materials). Students will translate real-world problems into mathematical functions and use derivatives to analyze and solve them. Students will evaluate the reasonableness of derivative-based solutions and assess their impact in real-world scenarios.

Partial Fraction Decomposition

UNIT TITLE: Partial Fraction Decomposition
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What is partial fraction decomposition, and why is it useful in simplifying rational expressions? How do you decompose a rational function into a sum of simpler fractions? What are the different types of factors (linear, irreducible quadratic) in the denominator, and how do you handle each case in decomposition? How can you set up and solve the system of equations generated by partial fraction decomposition? How do you perform partial fraction decomposition when the numerator's degree is greater than or equal to the degree of the denominator? What role do the methods of equating coefficients and using substitution play in solving for the constants in the partial fractions? How does partial fraction decomposition help in integrating rational functions or simplifying complex algebraic expressions? How do you determine the number of fractions needed based on the factorization of the denominator? Essential Questions How does partial fraction decomposition allow us to simplify and integrate rational functions? What is the significance of understanding the different types of factors (linear vs. irreducible quadratic) when decomposing fractions? How does partial fraction decomposition illustrate the power of algebraic manipulation and solving systems of equations? In what ways can partial fraction decomposition be applied in calculus, particularly in evaluating integrals and solving differential equations? How does the process of decomposition reveal the structure of a rational function and its underlying components? Why is it important to break complex rational functions into simpler components when solving real-world problems, such as in physics or engineering? How does the decomposition of rational expressions demonstrate the connection between algebra and other areas of mathematics like calculus or number theory?
Unit Topics with Learning Objectives:
1. Understanding Partial Fraction Decomposition Students will define partial fraction decomposition and explain its purpose in simplifying rational expressions. Students will identify the different types of factors in a rational expression (linear factors, irreducible quadratic factors) and describe how to handle each case in partial fraction decomposition. Students will recognize when and why partial fraction decomposition is used in simplifying integrals and solving algebraic problems. 2. Decomposing Rational Functions Students will decompose proper rational functions into a sum of partial fractions using appropriate factorization of the denominator. Students will handle linear and irreducible quadratic factors in the denominator, determining the appropriate form of the partial fractions. Students will apply the concept of proper and improper fractions, ensuring that the degree of the numerator is less than the degree of the denominator before proceeding with decomposition. 3. Solving for Constants in Partial Fractions Students will set up and solve systems of linear equations to determine the constants in the partial fraction decomposition. Students will use the method of equating coefficients or substitution to solve for unknown constants in partial fractions. Students will apply appropriate algebraic techniques (e.g., substitution, equating coefficients) to solve for the unknowns in more complex partial fraction decompositions. 4. Algebraic Manipulation and Simplification Students will demonstrate proficiency in algebraic manipulation, including factoring and simplifying rational expressions, as part of the decomposition process. Students will correctly decompose rational expressions with complex denominators, including cases with repeated factors or irreducible quadratic factors. Students will simplify the process of solving rational functions by breaking them into simpler components using partial fraction decomposition.

Polar Functions

UNIT TITLE: Polar Functions
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What is the polar coordinate system, and how does it differ from the Cartesian coordinate system? How do you convert between polar and Cartesian coordinates, and when is this conversion useful? What is the equation of a polar function, and how does it relate to the graph of the function? How do you plot polar equations and interpret their graphs, such as circles, limaçons, and roses? How do you find the area enclosed by a polar curve? What are the key features of polar graphs, such as symmetry, intercepts, and periodicity? How do the concepts of radius and angle in polar coordinates represent real-world phenomena like wave patterns or circular motion? How does the polar form of equations relate to conic sections and other geometric shapes? Essential Questions How does the polar coordinate system enhance our understanding of circular and rotational motion, and why is it used in fields like physics and engineering? Why is it important to understand the relationship between polar and Cartesian coordinates when analyzing mathematical models in two dimensions? How do polar functions provide a more natural way to model certain phenomena, such as the motion of celestial bodies or the structure of waves and spirals? In what ways do polar graphs offer insight into symmetry, periodicity, and behavior that may not be as clear in Cartesian coordinates? How do polar equations allow us to represent and solve real-world problems involving circular or oscillatory motion, such as in mechanical engineering or acoustics? How does the study of polar functions contribute to the broader field of complex analysis and other advanced areas of mathematics? How do the geometric properties of polar curves relate to real-world shapes and patterns, such as those found in nature or architecture?
Unit Topics with Learning Objectives:
1. Understanding Polar Coordinates Define the polar coordinate system and distinguish it from the Cartesian coordinate system. Understand the meaning of the polar coordinates (r,θ), where r represents the radial distance from the origin and θ represents the angle from the positive x-axis. Convert between polar and Cartesian coordinates, and explain when and why each system is useful in solving problems. 2. Graphing Polar Equations Plot points in polar coordinates and translate them to Cartesian coordinates for graphing purposes. Graph simple polar equations such as r=a, r=asin⁡(θ), and r=acos⁡(θ), identifying key features such as intercepts and symmetry. Analyze and graph more complex polar equations, including lemniscates, roses, and limaçons, and describe their characteristics. 3. Analyzing Polar Functions Identify the symmetry of a polar graph (e.g., symmetry about the x-axis, y-axis, or the pole). Determine the periodicity of a polar function and use this information to analyze the behavior of its graph. Find the intersections and key points of a polar graph, including points where the graph intersects the pole or axes. 4. Converting Between Polar and Cartesian Coordinates Convert polar equations to Cartesian form using the relationships x=rcos⁡(θ) and y=rsin⁡(θ) Convert Cartesian equations to polar form by expressing the equation in terms of r and θ Solve problems that require the conversion of equations between polar and Cartesian systems. 5. Applications of Polar Coordinates Apply polar coordinates to model real-world problems involving rotational motion, waves, and other periodic phenomena. Solve problems in physics, engineering, and other fields where polar coordinates provide a more natural representation than Cartesian coordinates. Analyze and interpret graphs of polar functions to solve applied problems, including calculating distances, areas, and other quantities. 7. Advanced Topics and Extensions Explore advanced polar equations and curves, such as cardioids and spiral curves, and their real-world applications. Understand the role of polar coordinates in complex analysis and other higher-level mathematical fields. Solve complex problems involving the intersection of polar curves or the transformation of equations to/from polar coordinates.

Parametric Functions

UNIT TITLE: Parametric Functions
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What is a parametric equation, and how does it represent a relationship between two variables using a third variable (the parameter)? How do you graph parametric equations, and what steps are involved in plotting points for parametric curves? How do you convert parametric equations to a single Cartesian equation, and when is this conversion useful? How do you interpret parametric equations in real-world contexts, such as modeling motion or physical phenomena? How can you eliminate the parameter in parametric equations to obtain a Cartesian equation that represents the same curve? How do you calculate the derivatives of parametric equations and what is the significance of the parametric form of the derivative? How do parametric equations help model and analyze motion, such as velocity and acceleration in physics? How do you work with parametric functions involving time, such as in problems dealing with projectile motion or motion along a path? Essential Questions How does the use of parametric equations enhance our understanding of the relationship between variables, especially in dynamic or time-dependent systems? Why is it important to represent motion and curves parametrically, particularly when the relationship between variables is not easily described in Cartesian coordinates? How does the ability to eliminate the parameter from parametric equations help us analyze complex systems and simplify models? In what ways do parametric equations provide a more flexible framework for modeling real-world phenomena like motion, growth, and change? How do parametric equations and their derivatives help us understand the behavior of curves, including their slopes, tangents, and rates of change? How can parametric equations be used to model the motion of objects along paths, and what real-world applications (such as in physics or engineering) benefit from this approach? How do parametric equations extend our ability to describe curves in space and beyond two-dimensional graphs, and how is this useful in higher dimensions?
Unit Topics with Learning Objectives:
1. Understanding Parametric Equations Define parametric equations and explain how they express relationships between two variables using a third variable (the parameter). Interpret parametric equations in the context of real-world problems, such as motion, curves, or physical phenomena. Recognize the advantages of using parametric equations to describe curves that cannot easily be expressed in Cartesian form. 2. Graphing Parametric Equations Plot points and graph curves defined by parametric equations by eliminating the parameter or calculating individual points for different values of the parameter. Understand the direction of motion or progression along a parametric curve, considering the relationship between the parameter and the variables. Use technology (e.g., graphing calculators or software) to graph parametric equations and explore the behavior of the curves. 3. Converting Between Parametric and Cartesian Forms Convert parametric equations into a single Cartesian equation by eliminating the parameter (where possible). Translate Cartesian equations into parametric form, creating parametric equations that represent the same curve or system. Identify situations where parametric equations provide a more natural or useful representation than Cartesian equations. 4. Derivatives and Rates of Change for Parametric Equations Compute the derivative of a parametric equation with respect to the parameter using the chain rule. Calculate the slope of the tangent line to a curve defined by parametric equations by finding dy/dx. Use parametric derivatives to determine velocity, acceleration, and other rates of change in problems involving motion or physical systems. 5. Applications of Parametric Equations Model real-world situations involving motion, such as projectile motion, using parametric equations. Analyze and solve problems that involve time-dependent relationships between variables, such as in physics or engineering. Apply parametric equations to model and analyze curves in higher dimensions (e.g., space curves or three-dimensional motion). 6. Understanding and Analyzing Parametric Curves Analyze the shape, symmetry, and other characteristics of a parametric curve, including finding intercepts, critical points, and turning points. Interpret the geometric properties of a parametric curve, such as curvature and concavity, through derivatives. Investigate parametric curves with respect to their behavior over time, including periodicity, velocity, and acceleration. 7. Real-World Problem Solving Using Parametric Functions Solve real-world problems involving parametric functions in fields such as physics (e.g., projectile motion), engineering (e.g., robot paths), and biology (e.g., growth patterns). Use parametric equations to model and solve problems involving circular, oscillatory, or cyclical behavior. Evaluate and interpret the results of problems involving parametric equations, ensuring both mathematical accuracy and contextual relevance.

Infinite Series

UNIT TITLE: Infinite Series
NYS Standards:
NYS Mathematics Learning Standards
Guiding Questions/Essential Questions:
Guiding Questions What is an infinite series, and how does it differ from a finite series or sum? How do we determine whether an infinite series converges or diverges? What are the different types of infinite series, such as geometric series, p-series, and power series? How do we find the sum of a convergent infinite series, and what methods are used to calculate this sum? How do the tests for convergence, such as the ratio test, root test, and integral test, help determine whether a series converges? How can we apply the concepts of partial sums and limits to understand the behavior of an infinite series? How are power series and Taylor series used to represent functions, and how do they provide approximations for functions? How does the concept of radius and interval of convergence apply to power series and affect their validity? Essential Questions How do infinite series help us model real-world phenomena that involve summing an infinite number of terms, such as in physics, engineering, and economics? Why is it important to understand the convergence of infinite series, and what does the convergence or divergence of a series tell us about the behavior of a system or function? How can the concept of a limit be used to define the sum of an infinite series, and why is this important in understanding functions and sequences? How do different methods for determining the convergence of a series relate to one another, and why do we need multiple tools (like the ratio test, root test, etc.) for convergence? How do power series, and particularly Taylor series, extend our ability to approximate functions, and how do they contribute to fields like numerical analysis and computational methods? In what ways do infinite series provide insight into the behavior of functions, including continuity, differentiability, and integrability? How do infinite series play a role in the broader context of calculus and analysis, particularly in the development of more advanced mathematical theories?
Unit Topics with Learning Objectives:
1. Understanding Infinite Series Define an infinite series and distinguish between convergent and divergent series. Recognize the difference between a sequence and a series, and understand how partial sums are used to approximate the sum of an infinite series. Explore various types of infinite series, including geometric series, p-series, alternating series, and power series. 2. Convergence Tests for Infinite Series Apply the nth-term test for divergence to determine whether a series diverges. Use the geometric series test to determine the convergence or divergence of geometric series. Apply the p-series test to determine the convergence of series of the form 1np. Use the ratio test and root test to determine the convergence or divergence of series, particularly when factorials or exponential functions are involved. Determine the comparison test and limit comparison test for series that involve rational expressions. Use the alternating series test (Leibniz’s test) to analyze alternating series for convergence. 3. Summing Convergent Series Find the sum of a convergent geometric series using the formula , S=a1-rwhere a is the first term and r is the common ratio. Calculate the sum of other specific convergent series (e.g., telescoping series, some power series) when appropriate methods are available. 4. Power Series and Taylor Series Define a power series and determine the radius and interval of convergence. Determine the Taylor series and Maclaurin series for common functions (e.g., exponential, sine, cosine, and logarithmic functions). Use power series to approximate functions and represent functions as infinite sums. Understand and apply binomial series to approximate functions such as 1+xr. 5. Applications of Infinite Series Apply infinite series to approximate real-world functions, such as physical models in engineering or economics. Use Taylor series to approximate values of functions at points other than x=0. Model real-world phenomena involving infinite sums, such as calculating the present value of an infinite series in finance. 6. Interpretation and Problem Solving Interpret the results of convergence tests to solve problems involving series and determine their behavior. Solve word problems involving infinite series, applying the appropriate tests and formulas. Communicate mathematical reasoning clearly when analyzing series, including justifying convergence or divergence and calculating sums.

Quantitative Geometry

COURSE TITLE: Quantitative Geometry

COURSE DESCRIPTION: Quantitative Geometry is a year-long course that is aligned with the New York Common Core Learning Standards and includes a focus on topics such as constructions and congruence proofs, trigonometry and similarity proofs, coordinate geometry, circles, 3-D shapes and applications in probability with a lessened emphasis on reasoning and proof. Students registering for this course should have successfully completed Algebra 1 or Algebra 1B and have passed the Algebra 1 Regents Examination. The course requires the use of a graphing calculator and culminates with the administration of a local final exam in June. (1 unit)

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Foundations of Geometry Coordinate Geometry	Properties of Triangles Similarity Proofs Similarity Congruence	Constructions Transformations Right Triangle Trigonometry	Circles 2D & 3D Measurements Coordinate Geometry Proofs

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams and class discussions Question and answer sessions, both formal and informal —planned/spontaneous In-class activities where students informally present their results Methods of Summative Assessments: In-unit Quizzes Unit Exams Final examination Projects (may vary from unit to unit)
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation: Learning Centers: Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation: Flexible Grouping: Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments: Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation: Varied Assessment Methods: Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation: Flexible Seating Arrangements: Offering various seating options to cater to students' comfort and learning preferences. Use of Technology: Incorporating digital tools that can provide personalized learning experiences. 5. Interest-Based Differentiation: Thematic Units: Designing units around themes that interest students to enhance engagement. 6. Feedback Differentiation: Individualized Feedback: Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection: Encouraging students to evaluate their own work and set personal learning goals. 7. Scaffolding: Step-by-Step Instructions: Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers: Using visual aids to help students organize information and ideas.

Units

Foundations of Geometry

UNIT TITLE: Foundations of Geometry
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 125-138)
Guiding Questions/Essential Questions:
How are words, symbols, and notations used to communicate Geometric concepts? How do angles and segments relate to each other in Geometric figures?
Unit Topics with Learning Objectives:
01-01 Geometry Terms I Identify and name basic geometric figures Use symbolic notation to describe geometric figures 01-02 Geometry Terms II Identify and name basic geometric figures Use symbolic notation to describe geometric figures 01-03 Midpoint and Bisector Use the properties of a bisector to identify congruent segments and angles 01-04 Angle Relationships Calculate the complement and supplement of an angle Find the measure of congruent angles 01-05 Parallel Lines Identify angle relationships created when parallel lines are intersected by a transversal Determine angle measures using the parallel line theorems 01-06 Parallel Lines II Identify angle relationships created when parallel lines are intersected by a transversal Determine angle measures using the parallel line theorems

Coordinate Geometry

UNIT TITLE: Coordinate Geometry
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 125-138)
Guiding Questions/Essential Questions:
How can Geometric figures be displayed on the coordinate grid? How do the Algebraic properties of lines relate to Geometry?
Unit Topics with Learning Objectives:
02-01 Slope Define the slope of a line. Calculate the slope of a line on a graph. Calculate the slope of a line given two points. 02-02 Slope-Intercept Form Write an equation in slope intercept form. Graph a line in slope intercept form. 02-03 Point-Slope Form Write an equation in point slope form. Graph a line in point slope form. 02-04 Write the equation of a line Write an equation of a vertical or horizontal line. Use the x and y intercepts to graph a line. 02-05 Writing the equation of parallel or perpendicular lines Use slope to determine if two lines are parallel, perpendicular, or neither. 02-06 Midpoint Find the midpoint of a line segment graphically and using the midpoint formula. 02-07 Distance Calculate the distance between two points graphically and using the distance formula.

Constructions and Measurement

UNIT TITLE: Constructions and Measurement
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 125-138)
Guiding Questions/Essential Questions:
What tools are used in Geometry? How are the tools of Geometry used to construct Geometric Figures?
Unit Topics with Learning Objectives:
03-01 Ruler Measure the length of a segment Bisect a segment Copy a segment onto a line Double a segment Perform segment addition Verify the length of a segment using the distance formula 03-02 Protractor Measure an angle Bisect an angle Copy an angle Double an angle Verify angle pair relationships 03-03 Copy a Segment Construct a copy of a segment Construct a triangle given 3 sides (SSS) Construct an equilateral triangle 03-04 Copy an Angle Construct a copy of an angle Construct a triangle given two sides and an included angle (SAS) Construct a triangle given two angles and an included side (ASA) 03-05 Bisect a Segment Construct the perpendicular bisector of a segment Find the midpoint of a segment using a construction 03-06 Bisect an Angle Construct an angle bisector Construct a 45-45-90 triangle Construct a 30-60-90 triangle 03-07 Perpendicular Lines Construct the perpendicular bisector of a segment Construct a perpendicular line through a given point 03-08 Parallel Lines Construct a parallel line through a point Construct a rectangle 03-09 Polygons in a circle Construct a parallel line through a point Construct a rectangle

Properties of Triangles

UNIT TITLE: Properties of Triangles
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 125-138)
Guiding Questions/Essential Questions:
How do the properties of triangles help us understand and classify different types of triangles? What relationships exist between the angles and sides of a triangle, and how can they be applied? How can the properties of triangles be used to solve real-world problems? What methods can we use to determine whether three given side lengths or angles can form a triangle?
Unit Topics with Learning Objectives:
04-01a Classifying Triangles Classify triangles by sides and angles. Use the distance formula, Pythagorean Theorem, and slope to identify segment and angle relationships. 04-01b Practice with Classifying Triangles Classify triangles by sides and angles. Use the distance formula, Pythagorean Theorem, and slope to identify segment and angle relationships. 04-02a Triangle Angle Theorems Find the measure of angles in a triangle using the Triangle Angle Sum Theorem. Find the measure of angles in a triangle using the Exterior Angle Theorem. 04-02b Extra Practice with Angles Find the measure of angles in a triangle using the Triangle Angle Sum Theorem. Find the measure of angles in a triangle using the Exterior Angle Theorem. 04-03a Triangle Side Theorems Explore the relationship between angle measures and side lengths of a triangle. Compare side lengths of a triangle using the Triangle Inequality Theorem. 04-03b Practice with Sides Explore the relationship between angle measures and side lengths of a triangle. Compare side lengths of a triangle using the Triangle Inequality Theorem.

Similarity

UNIT TITLE: Similarity
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 125-138)
Guiding Questions/Essential Questions:
What does it mean for two triangles to be similar, and how is similarity different from congruence? What are the criteria for determining if two triangles are similar? How do proportions and ratios help us describe the relationship between similar triangles? How do corresponding angles and sides of similar triangles relate to one another? What role does scale factor play in understanding similar triangles? How can we use similar triangles to solve real-world problems involving indirect measurement? How do geometric theorems, such as the AA (Angle-Angle) Criterion, help us prove triangle similarity?
Unit Topics with Learning Objectives:
05-01 Similarity, Proportions, Correspondence Solve linear proportions. Define similarity. Identify corresponding parts of similar triangles. Set up a proportion and solve for the unknown given a real-world scenario. 05-02 Dilation / Scale Factor Define Pre-Image and Image. Use the scale factor to determine if the image will be larger or smaller than the pre-image. Use the scale factor to find the length of corresponding sides of figures. 05-03 Scale Factor on the Coordinate Plane Graph dilated images on the coordinate plane. Determine the coordinates of the image after applying a dilation to the pre-image. Calculate the scale factor between a pre-image and image. 05-04 Similar Triangles Identify vertical and reflexive angles within similar triangles to show congruent angles. Set up proportions to show that corresponding sides in similar triangles are in proportion. Use AA~, SAS~, and SSS~ to prove similar triangles. 05-05 Angle Bisector Theorem Apply the Angle Bisector Theorem to set up a proportion. Solve for a missing side by solving a linear proportion. 05-06 Overlapping Triangles & Mid-Segment Theorem Set up and solve proportions involving corresponding sides of similar triangles to find the length of missing segments. Apply the midsegment theorem to find the measure of missing segments. 05-07 Applications of Similar Triangles Translate real-world scenarios into diagrams involving similar triangles. Apply knowledge of similar triangles to find missing lengths.

Similar Triangle Proofs

UNIT TITLE: Similar Triangle Proofs
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 125-138)
Guiding Questions/Essential Questions:
What does it mean for two triangles to be similar? What are the criteria (AA, SAS, SSS) for proving triangles are similar, and why do they work? How can constructing logical arguments and proofs about triangle similarity develop problem-solving and reasoning skills?
Unit Topics with Learning Objectives:
06-01 Introduction to Proofs and Theorems Create and mark diagrams with given information Write statements and reasons for given Geometric relationships 06-02 Intro to Proof Drawing Conclusions Create and mark diagrams with given information Write statements and reasons for given Geometric relationships 06-03 Methods of Proving Triangles Similar Identify the methods of proving similar triangles 06-04 Proofs with Reflexive & Vertical Angles Prove triangles are similar that contain reflexive angles Prove triangles are similar that contain vertical angles 06-05 Proofs with Parallel Lines Prove triangles are similar that contain alternate interior angles Prove triangles are similar that contain corresponding angles 06-06 Similar Triangle Proofs Prove triangles are similar that contain right angles

Transformations

UNIT TITLE: Transformations
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 125-138)
Guiding Questions/Essential Questions:
What are transformations, and how do they change the position or size of a shape on the coordinate plane? What distinguishes rigid motions (translations, rotations, and reflections) from non-rigid transformations (dilations)? What properties remain unchanged during a transformation, and why are these properties significant? What is the relationship between a pre-image and its image after a sequence of transformations?
Unit Topics with Learning Objectives:
07-01 The Coordinate Plane & Transformations To identify the four quadrants on the coordinate plane. To plot points on the coordinate plane using the x- and y-axis. 07-02 Translations To translate shapes on the coordinate plane by applying a given translation rule and verify the congruence of the pre-image and image after translation. 07-03 Reflections To reflect shapes on the coordinate plane across a given line of reflection (e.g., the x-axis, y-axis, or other lines such as y=x and y=-x), determine the coordinates of the reflected shape, and explain how reflection preserves congruence while changing orientation. 07-04 Rotations To rotate shapes on the coordinate plane around a given point (including the origin) by specified angles (90°, 180°, 270°, or 360°), determine the coordinates of the rotated shape, and explain how rotation affects the orientation and congruence of the shape. 07-05 Dilations To perform dilations of shapes on the coordinate plane with a given center of dilation and scale factor, determine the coordinates of the dilated shape, and analyze how dilations affect the size, position, and proportional relationships of the shape while preserving its similarity. 07-06 Symmetry Use reflections to identify line symmetry of shapes. Use rotations to identify rotational symmetry of shapes. 07-07 Composition of Transformations To perform and describe a sequence of rigid motions (translations, rotations, and reflections) to map one figure onto another, verify congruence between the figures, and explain how rigid motions preserve distance and angle measures.

Right Triangle Trigonometry

UNIT TITLE: Right Triangle Trigonometry
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 125-138)
Guiding Questions/Essential Questions:
What are the primary trigonometric ratios, and how are they defined in a right triangle? How do you determine which trigonometric ratio to use when solving for a missing side or angle? How can you use inverse trigonometric functions to find missing angles? How can trigonometry be applied to real-world problems involving right triangles (e.g., navigation, construction, physics)?
Unit Topics with Learning Objectives:
09-01 Introduction to Trigonometry To label the opposite, adjacent, and hypotenuse sides of a right triangle. To define the big three trig functions: sine, cosine, & tangent. To write ratios for sine, cosine, & tangent given a right triangle. To use the graphing calculator to evaluate trig functions for a given angle. 09-02 Solve for Missing Sides To find missing side lengths of right triangles using trig ratios. 09-03 Solve for Missing Angles To find missing angle measures of right triangles using inverse trig ratios. 09-04 Trig Applications Day 1 To use trig and inverse trig functions to solve right triangle trig word problems. 09-05 Trig Applications Day 2 To use trig and inverse trig functions to solve right triangle trig word problems.

Circles

UNIT TITLE: Circles
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 125-138)
Guiding Questions/Essential Questions:
What are the key properties and components of a circle (e.g., radius, diameter, chord, tangent, secant)? How are angles formed by chords, tangents, and secants related to arcs in a circle? How do the properties of circles help us understand relationships between angles, lengths, and areas? How can we use inscribed and central angles to solve problems involving circles?
Unit Topics with Learning Objectives:
10-01 Circles Vocabulary To define and understand important vocabulary related to circles. 10-02 Central, Inscribed, & Floating Angles To determine the degree measure of central, inscribed & floating angles and their intercepted arcs. 10-03 Exterior Angles To determine the degree measure of exterior (outside) angles and arcs. 10-04 Angle-Arc Shortcuts To determine the degree measure of angles and arcs within special cases (inscribed angles to same arc, tangent-radius, inscribed angles to semicircle, & inscribed quadrilaterals). 10-05 Lengths of Chord and Secant Segments To determine the segment lengths of chords and secants. 10-06 Lengths of Secants and Tangents To determine the segment lengths of secants and tangents. 10-07 Arc and Chord Relationships To determine the measure of chords and/or arcs when given congruent chords or parallel chords in a circle. 10-08 Radius-Chord Relationships To determine the length of segments using the Radius-Chord Theorem. To determine the measure of angles using the Radius-Chord Converse Theorem.

Coordinate Geometry Proofs

UNIT TITLE: Coordinate Geometry Proofs
NYS Standards:
NYS Math Learning Standards (CORE CONTENT: Pages 125-138)
Guiding Questions/Essential Questions:
How can the coordinate plane be used to prove geometric properties of quadrilaterals and/or triangles? What role do distance, midpoint, and slope formulas play in coordinate geometry proofs? How can algebra and geometry work together to justify relationships between points, lines, and shapes?
Unit Topics with Learning Objectives:
12-01 Properties of Quadrilaterals To identify and understand properties of different quadrilaterals (ex. parallelogram, rectangle, etc.). 12-02 Proving Parallelograms and Rectangles To prove a quadrilateral is a parallelogram and/or a rectangle on the coordinate plane. 12-03 Proving Rhombi and Squares To prove a quadrilateral is a rhombus and/or a square on the coordinate plane. 12-04 Proving Trapezoids To prove a quadrilateral is a trapezoid on the coordinate plane. 12-05 Proving Triangles To prove a triangle is right or not right using the coordinate plane. To prove a triangle is equilateral, isosceles, or scalene on the coordinate plane.

Precalculus

Algebra 2 & Trigonometry

Algebra 2 and Trigonometry Honors

Science & Technology

The Science and Technology Department believes that by fostering an understanding of STEM concepts and skills we will enable our students to hold the key to the future. Our program challenges students to build a strong foundation in science and engineering through our middle school program while our high school program offers an impressive suite of courses to continue their learning through core and elective courses, advanced courses, and college credit-bearing 4-course Engineering program.

We are committed to designing student experiences in science and engineering that leverage a student's own innate curiosity and fascination with the world around them and draws on their individual interests, strengths, and learning styles. Students need to understand science not only to open up doors to potential careers but to navigate the world in which we live.

Accelerated Physics

COURSE DESCRIPTION: This Physics course follows a demanding curriculum that will move at a rapid pace and requires a commitment to study at home on the part of the student. This course is for students who have a keen interest in studying science/engineering and may be thinking about pursuing those endeavors in college and who plan to enroll concurrently in an AP Science this year, and possibly enrolling in AP Physics the following year. This course will help students acquire factual knowledge and analytical skills within a conceptual and thematic framework, practice experimental design and interpretation, work collaboratively with other students in challenging labs, class activities and projects, and develop critical thinking skills. This course culminates with a demanding local final.

*This course follows a similar sequence to the Physics course, however, it does not have a lab period. Also, several of the topics are covered in greater depth and detail than in our traditional Physics course.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Motion Parametric Equations Free-Fall and Vertically Fired Objects	Motion in Two Dimensions: Projectiles Fired Horizontally and At An Angle Newton’s Laws Friction Circular Motion	Energy, Work and Power Impulse and Momentum Static Electricity	Electrical Current and Circuits Magnetism Waves Light

Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams and class discussions Question and answer sessions, both formal and informal —planned/spontaneous Conferences between the instructor and student at various points in the semester In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Lab reports & quizzes Methods of Summative Assessments: Unit Exams Semester Assessment Final examination Projects (project phases submitted at various completion points could be formatively assessed) NYS Labs
Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Motion in One Direction

UNIT TITLE: Motion in One Direction
NYS Standards:
NYS Science Learning Standards (Pages 58-63 )
Guiding Questions/Essential Questions:
Foundational Concepts How do displacement, velocity, and acceleration relate to each other? How can we differentiate between average and instantaneous velocity or acceleration? Motion Analysis How can position-time and velocity-time graphs be used to describe motion? How does the slope of a position-time graph represent velocity? What does the area under a velocity-time graph represent? Equations of Motion How do the kinematic equations describe the motion of an object in one dimension? How can we predict the future motion of an object given its initial conditions and acceleration? How can we determine the time of flight, maximum height, or range for an object moving in one direction?
Unit Topics with Learning Objectives:
Average Velocity Objectives: Define average velocity and differentiate it from average speed. Calculate average velocity using displacement and time. Solve real-world problems involving average velocity. Skills: Analyze displacement and time data to compute average velocity. Interpret units of velocity in context (e.g., meters per second, kilometers per hour). Apply the formula vavg=Δd/Δt in various scenarios. Instantaneous Velocity Objectives: Define instantaneous velocity and explain how it differs from average velocity. Relate instantaneous velocity to the slope of a position-time graph. Determine instantaneous velocity using equations of motion or graphical methods. Skills: Estimate instantaneous velocity from a position-time graph by determining the slope of the tangent line. Apply the concept of instantaneous velocity in solving motion problems. Graphical Analysis of Motion Graphs Objectives: Identify and interpret position-time, velocity-time, and acceleration-time graphs. Understand the relationship between slope and area in motion graphs (e.g., slope of a position-time graph represents velocity). Use motion graphs to describe an object’s motion qualitatively and quantitatively. Skills: Draw and interpret motion graphs based on given scenarios or data. Calculate displacement, velocity, or acceleration from graphs. Identify intervals of constant velocity, acceleration, or rest from motion graphs. Recognize graphical trends (e.g., linear, parabolic) to understand motion behavior. Motion Equations Objectives: Derive and use the kinematic equations for uniformly accelerated motion. Solve problems involving one-dimensional motion using kinematic equations. Skills: Use the following equations appropriately: vf=vi+at d=vit+1/2at^2 vf^2=vi^2+2ad Analyze and solve problems involving initial velocity, final velocity, time, acceleration, and displacement. Incorporate vector quantities in problem-solving when applicable. Connect equations to graphical representations (e.g., matching motion graphs to kinematic scenarios).

Parametric Equations

UNIT TITLE: Parametric Equations
NYS Standards:
NYS Science Learning Standards (Pages 58-63 )
Guiding Questions/Essential Questions:
Foundational Concepts What are parametric equations, and why are they useful in describing motion in physics? How do they represent motion in two dimensions simultaneously? What advantages do they offer over traditional equations? How can we use parametric equations to predict key characteristics of motion? How do we determine the time up a ramp, maximum distance away from the starting point, and total time a lab cart is on a ramp. How can we determine the time to any point on the ramp, and the corresponding displacement? What real-world applications rely on this understanding? What is the connection between parametric equations and the paths of moving objects? How can we visualize motion graphically using parametric equations? How does this representation help in solving physics problems
Unit Topics with Learning Objectives:
Objectives: Understand and apply parametric equations to describe motion in two. Break down projectile motion into horizontal and vertical components. Analyze the motion of objects under the influence of gravity, considering initial velocity and launch angle. Solve problems involving time, displacement, velocity, and acceleration in a parametric context. Skills: Writing and interpreting parametric equations for position and velocity: d=vit+1/2at^2 and vf=vi+at Calculating time a cart gets to its maximum displacement, its maximum displacement, total time back to the starting point, and the time and position of the cart anywhere in its path. Graphing motion described by parametric equations. Connecting parametric solutions to real-world problems, such as projectile paths.

Free-Fall and Vertically Fired Objects

UNIT TITLE: Free-Fall and Vertically Fired Objects
NYS Standards:
NYS Science Learning Standards (Pages 58-63 )
Guiding Questions/Essential Questions:
Foundational Concepts What are the key differences between free fall and vertically fired objects? How does gravity affect the motion of objects in free fall and vertically fired scenarios? What assumptions are made about air resistance when analyzing free fall and vertical motion? Free Fall How does the acceleration due to gravity influence the velocity and position of an object in free fall? How can we use kinematic equations to predict the motion of an object in free fall? How do mass and initial conditions (e.g., dropped vs. thrown) impact the motion of objects in free fall? Vertically Fired Objects How does the initial velocity of a vertically fired object affect its maximum height and time of flight? What happens to an object's velocity and acceleration at the peak of its motion? How do symmetry and time apply to vertically fired motion when the object returns to its starting point? Graphical Representation How can position-time, velocity-time, and acceleration-time graphs be used to describe free fall and vertical motion? How do we interpret the slope of velocity-time graphs for free fall and vertically fired objects? Real-World Applications How does analyzing free fall help us understand real-world scenarios like skydiving, bungee jumping, or objects dropped from a height? How are vertically fired objects relevant to engineering and design, such as rocket launches or projectile motion experiments?
Unit Topics with Learning Objectives:
Free Fall Objectives: Understand the concept of free fall as motion under the influence of gravity alone (neglecting air resistance). Recognize the acceleration due to gravity (g) as a constant (9.81 m/s^2) downward near the Earth's surface. Solve problems involving free-falling objects, including displacement, velocity, and time. Skills: Apply kinematic equations for free fall, such as: vf=vi+at dy=vit+1/2at^2 vf^2=vi^2+2ad Analyze motion where vi=0 for objects dropped from rest. Calculate the time to fall and impact velocity for objects dropped from a specific height. Interpret motion graphs (velocity-time and position-time) for free-falling objects. Vertically Fired Objects Objectives: Analyze the motion of objects fired vertically upward, considering gravity’s acceleration during ascent and descent. Calculate the maximum height, time to reach the maximum height, and total time of flight. Understand the symmetry of vertical motion (e.g., time up = time down). Skills: Resolve vertical motion using the following equations: vf=vi+at dy=vit+1/2at^2 vf^2=vi^2+2ad Calculate the maximum height using vy=0 at the peak of the motion. Determine the total time of flight as twice the time to reach the maximum height. Combine upward and downward motion to solve for displacement, velocity, and time. Interpret velocity-time and position-time graphs for vertically fired objects. General Skills for Free Fall and Vertically Fired Objects Identify the direction and magnitude of velocity and acceleration at different points in motion. Recognize that at the peak of vertical motion, velocity is zero but acceleration remains constant. Solve real-world problems (e.g., calculating how long it takes a ball to hit the ground after being thrown upward). Conduct experiments to measure free-fall acceleration and verify theoretical predictions.

Motion in Two Dimensions: Free Fall and Vertically Fired Objects

UNIT TITLE: Motion in Two Dimensions: Free Fall and Vertically Fired Objects
NYS Standards:
NYS Science Learning Standards (Pages 58-63)
Guiding Questions/Essential Questions:
General Principles of Projectile Motion What is projectile motion, and how is it characterized by motion in two independent directions? How do horizontal and vertical components of motion relate to each other in projectile motion? Why is the horizontal velocity of a projectile constant, while its vertical velocity changes over time? Horizontally Launched Projectiles How does the height of launch affect the range and time of flight for a horizontally launched projectile? How does the initial speed of a horizontally launched projectile influence its motion? Projectiles Launched at an Angle How can the initial velocity of a projectile launched at an angle be resolved into horizontal and vertical components? How do the angle of launch and initial velocity impact the range, maximum height, and time of flight of a projectile? What is the significance of symmetry in the motion of a projectile launched at an angle? How do we calculate the range, maximum height, and total time of flight for a projectile launched at an angle? Graphical Representations How can position-time, velocity-time, and acceleration-time graphs represent two-dimensional motion? What does the shape of a projectile's trajectory reveal about its motion? Projectiles Launched at an Angle using Parametric Equations How do parametric equations represent motion in two dimensions simultaneously? What advantages do they offer over traditional equations? Why is it important to analyze horizontal and vertical components separately? How do we determine the time of flight, maximum height, and range of a projectile with parametric equations? What real-world applications rely on this understanding? Real-World Applications How can understanding projectile motion help us solve real-world problems, such as calculating the trajectory of a ball? How do air resistance and other external factors affect the idealized models of projectile motion?
Unit Topics with Learning Objectives:
Motion in Two Directions: Horizontally Launched Projectiles Objectives: Understand the independence of horizontal and vertical motion in projectile motion. Skills: Analyze projectile paths to determine key quantities like time, range, and final velocity. Sketch and interpret trajectory diagrams. Motion in Two Directions: Projectiles Launched at an Angle Objectives: Analyze projectiles launched at an angle using horizontal and vertical components of motion. Derive and calculate the range, maximum height, and time of flight for angled projectiles. Explore the effects of launch angle, initial velocity, and gravity on projectile motion. Skills: Resolve the initial velocity into horizontal (vx=vcos⁡θ) and vertical (vy=vsinθ) components. Use vertical motion equations to calculate maximum height and time of flight. Use horizontal motion equations to determine range (dx=vxt). Calculate the total time of flight by doubling the time to reach the maximum height. Interpret trajectories and the parabolic path of a projectile. Solve problems using symmetry principles (e.g., equal time up and down for symmetrical paths). General Skills for Motion in Two Directions Apply kinematic equations to two-dimensional motion scenarios. Use vector addition to combine horizontal and vertical velocities to find resultant velocity at any point in the motion. Recognize the effects of gravity as the sole vertical force acting on projectiles (assuming air resistance is negligible). Compare theoretical and experimental data in lab activities involving projectile motion. Motion in Two Directions: Using Parametric Equations Understand and apply parametric equations to describe motion in two dimensions. Break down projectile motion into horizontal and vertical components. Analyze the motion of objects under the influence of gravity, considering initial velocity and launch angle. Solve problems involving time, displacement, velocity, and acceleration in a parametric context. Skills: Writing and interpreting parametric equations for x(t)x(t)x(t) (horizontal position) and y(t)y(t)y(t) (vertical position): x(t)=vxt y(t)=vyt+1/2at^2 Using trigonometric functions to resolve initial velocity into components: vx=vcos⁡(θ) vy=vsin⁡(θ) Calculating total flight time, maximum height, and range of a projectile. Graphing motion described by parametric equations. Connecting parametric solutions to real-world problems, such as projectile paths or orbital trajectories.

Newton’s Laws

UNIT TITLE: Newton’s Laws
NYS Standards:
NYS Science Learning Standards (Pages 58-63)
Guiding Questions/Essential Questions:
Newton's First Law (Law of Inertia) What is inertia, and how does it relate to the motion of an object? How can we distinguish between balanced and unbalanced forces? How does Newton's First Law explain the motion of an object at rest or moving at a constant velocity? Newton's Second Law (F = ma) How do force, mass, and acceleration interact to determine the motion of an object? How can Newton’s Second Law be applied to solve real-world problems involving force and motion? How do changes in mass or force affect an object’s acceleration? Newton's Third Law (Action and Reaction) What does it mean that every action has an equal and opposite reaction? How do action-reaction pairs apply to interactions between objects? How can we identify and analyze the forces in action-reaction pairs in everyday scenarios? Forces and Free-Body Diagrams How can we represent and analyze forces acting on an object using free-body diagrams? How do different types of forces (e.g., friction, tension, normal force, gravity) affect motion? How can net force be determined and used to predict an object’s motion? Solving Pull At An Angle and Multi Block System Problems How can we solve for blocks pulled at an angle? How can we solve for multiple blocks pulled horizontally? How can we solve for multiple blocks being pulled at an angle? Solving Lifting Problems How can we solve for blocks being lifted up? Applications of Newton’s Laws How do Newton’s Laws explain real-world phenomena like car crashes, rocket launches, or sports movements? How do friction and air resistance influence the application of Newton's Laws? How can understanding Newton’s Laws help in designing systems or structures that manage forces effectively?
Unit Topics with Learning Objectives:
Newton's First Law (Law of Inertia) Objectives: Understand and state Newton's First Law: An object remains at rest or in uniform motion unless acted upon by a net external force. Define inertia and explain its relationship to mass. Recognize real-world examples of inertia in action. Skills: Identify forces acting on an object and determine if the net force is zero. Predict motion based on the presence or absence of net external forces. Relate mass to the amount of inertia an object has. Analyze examples such as objects in motion in a vehicle and their tendency to resist changes in motion. Newton's Second Law (F = ma) Objectives: Understand and state Newton's Second Law: The net force acting on an object is equal to its mass times its acceleration. Solve problems involving force, mass, and acceleration using Fnet=ma. Explore the relationship between force, mass, and acceleration qualitatively and quantitatively. Skills: Calculate net force when multiple forces act on an object. Solve problems for unknowns (e.g., force, mass, or acceleration) using Fnet=ma. Analyze motion scenarios with friction, tension, and normal forces. Draw and interpret free-body diagrams to visualize forces. Newton's Second Law (F = ma) for Multiple Blocks and Lifting Problems Objectives: Solve problems involving force, mass, and acceleration using Fnet=ma for: A block being pulled at an angle. Multiple blocks being pulled. Multiple blocks being pulled at an angle. Objects being lifted up. Skills: Calculate net force when multiple blocks are being pulled. Solve problems for unknowns (e.g., force, mass, or acceleration) using Fnet=ma. Draw and interpret free-body diagrams to visualize forces. Newton's Third Law (Action-Reaction) Objectives: Understand and state Newton's Third Law: For every action, there is an equal and opposite reaction. Recognize that forces always occur in pairs acting on different objects. Explain action-reaction pairs in real-world contexts. Skills: Identify action-reaction force pairs in various scenarios (e.g., a rocket launch, walking, pushing a wall). Analyze interactions between objects and differentiate the effects of action-reaction pairs on objects of different masses. Relate Newton's Third Law to momentum and collisions (as a foundational concept). General Skills for Newton's Laws Construct and interpret free-body diagrams for complex force systems. Relate Newton's Laws to practical applications (e.g., seat belts, sports, and machinery). Predict motion or equilibrium conditions for objects in various physical situations. Analyze laboratory experiments demonstrating the laws (e.g., using dynamics carts, pulleys, or inclined planes).

Friction

UNIT TITLE: Friction
NYS Standards:
NYS Science Learning Standards (Pages 58-63)
Guiding Questions/Essential Questions:
Friction What is friction, and what factors determine its magnitude and direction? How do static friction and kinetic friction differ, and when do they apply? How does the coefficient of friction relate to the types of surfaces in contact? How does friction enable or restrict motion in real-world scenarios? What role does friction play in the motion of objects on inclined planes or in stopping moving objects? Connections Between Friction and Circular Motion How does friction contribute to maintaining circular motion, such as in a car turning a corner or a spinning object? How can the lack of sufficient friction affect circular motion (e.g., skidding or slipping)? What is the relationship between the coefficient of friction, speed, and radius in curved path scenarios? Graphical and Mathematical Analysis How can force diagrams be used to analyze forces in circular motion? How do we calculate the maximum speed of an object moving in a circular path based on frictional force? How does centripetal acceleration relate to the velocity and radius of circular motion? Real-World Applications How does friction apply to scenarios such as driving on curves?
Unit Topics with Learning Objectives:
Friction Objectives: Define friction and differentiate between static and kinetic friction. Understand the factors that affect frictional force, including the normal force and the coefficient of friction (μ). Solve problems involving frictional forces in various contexts, such as motion on flat surfaces or inclined planes. Skills: Apply the equations for friction: fs≤μsFN (static friction) fk=μkFN (kinetic friction) Distinguish between maximum static friction and kinetic friction in problem-solving. Analyze scenarios where friction is the primary force (e.g., braking cars, objects sliding down inclines). Incorporate free-body diagrams to visualize forces and solve problems involving friction. Relate friction to energy concepts (e.g., work done by friction causing energy dissipation). General Skills for Friction Conduct experiments to measure coefficients of friction and analyze frictional forces.

Circular Motion

UNIT TITLE: Circular Motion
NYS Standards:
NYS Science Learning Standards (Pages 58-63)
Guiding Questions/Essential Questions:
Circular Motion What is centripetal force, and how does it maintain an object’s circular motion? How do velocity, radius, and mass affect the centripetal force required for circular motion? Why is there no outward force (centrifugal force) acting on an object in circular motion? Connections Between Friction and Circular Motion How does friction contribute to maintaining circular motion, such as in a car turning a corner or a spinning object? How can the lack of sufficient friction affect circular motion (e.g., skidding or slipping)? What is the relationship between the coefficient of friction, speed, and radius in curved path scenarios? Graphical and Mathematical Analysis How can force diagrams be used to analyze forces in circular motion? How do we calculate the maximum speed of an object moving in a circular path based on frictional force? How does centripetal acceleration relate to the velocity and radius of circular motion? Real-World Applications How do friction and circular motion apply to scenarios such as driving on curves, roller coasters, or planetary orbits? What are the challenges of maintaining circular motion in low-friction environments like icy roads or space?
Unit Topics with Learning Objectives:
Circular Motion Objectives: Understand uniform circular motion and the concept of centripetal force as the net force directed toward the center of the circular path. Explain the relationship between centripetal force, mass, velocity, and radius (Fc=mv^2/r). Explore real-world examples of circular motion, such as orbits, car turns, and amusement park rides. Skills: Solve problems using the centripetal force equation Fc=mv^2/r. Analyze forces acting on objects in circular motion, including tension, friction, and gravitational forces. Calculate acceleration in circular motion using ac=v^2/r.. Interpret and create free-body diagrams for circular motion scenarios (e.g., objects on a string). Relate circular motion to Newton’s Laws (e.g., centripetal force being the net force causing acceleration). General Skills for Circular Motion Relate circular motion concepts to real-world contexts (e.g., roller coasters, satellites).

Energy, Work, and Power

UNIT TITLE: Energy, Work, and Power
NYS Standards:
NYS Science Learning Standards (Pages 58-63 )
Guiding Questions/Essential Questions:
Energy What is energy, and how does it relate to the ability to do work? How do kinetic energy and potential energy differ, and how are they calculated? What is the principle of conservation of energy, and how does it apply to closed systems? How do different types of energy (e.g., mechanical, thermal, chemical) transform in real-world scenarios? Work What is work, and how is it calculated in physics? How does the angle between the force and displacement affect the amount of work done? Power What is power, and how does it relate to work and time? How can we compare the power output of different systems or machines? Work-Energy Theorem How does the work-energy theorem relate the work done on an object to its change in kinetic energy? How can the work-energy theorem be applied to solve problems involving forces and motion? Graphical and Mathematical Analysis How can work be determined from force-displacement graphs? How does gravitational potential energy change with height, and how does kinetic energy change with velocity? How are energy, work, and power related mathematically, and how can they be used to solve problems? Real-World Applications How does energy conservation explain the motion of objects like pendulums or roller coasters? How does friction affect the conversion of mechanical energy into other forms, such as heat?
Unit Topics with Learning Objectives:
Energy Objectives: Define and differentiate between kinetic energy (KE) and potential energy (PE). Understand the principle of conservation of energy and its applications in closed systems. Solve problems involving mechanical energy (kinetic and potential energy) in systems with and without external forces. Skills: Calculate kinetic energy: KE=1/2mv^2. Calculate gravitational potential energy: PE=mgh. Apply the law of conservation of energy: KEi+PEi=KEf+PEf. Recognize and analyze energy transformations (e.g., pendulums, roller coasters). Extend concepts to elastic potential energy: PEelastic=1/2kx^2 (for springs). Work Objectives: Define work as the transfer of energy by a force acting over a distance. Calculate work done by constant and variable forces. Understand the relationship between work, force, displacement, and the angle between them. Connect work to changes in energy using the work-energy theorem: W=ΔE. Skills: Use the work equation: W=Fdcos⁡θ. Solve problems involving work done by multiple forces, including friction and gravity. Analyze work-energy diagrams and relate them to mechanical energy changes. Interpret graphical representations, such as force-displacement graphs, to calculate work. Power Objectives: Define power as the rate at which work is done or energy is transferred. Distinguish between average power and instantaneous power. Solve problems involving power in various contexts, such as engines, machines, or human effort. Skills: Calculate power: P=W/t=Fd/t=Fv. Analyze power requirements for different scenarios, including lifting objects and moving vehicles. Solve problems involving units of power (watts, horsepower). Conduct experiments to measure work and power.

Impulse and Momentum

UNIT TITLE: Impulse and Momentum
NYS Standards:
NYS Science Learning Standards (Pages 58-63 )
Guiding Questions/Essential Questions:
Momentum What is momentum, and how is it calculated for an object in motion? How do mass and velocity influence an object's momentum? What does it mean for momentum to be a vector quantity? Impulse What is impulse, and how is it related to the change in momentum? How can impulse be calculated using force and time? How do real-world examples, like airbags or padding, demonstrate the concept of impulse? Impulse-Momentum Theorem How does the impulse-momentum theorem explain the relationship between force, time, and momentum change? How can increasing the time of impact reduce the force experienced in collisions? What role does impulse play in sports, transportation safety, and other everyday scenarios? Conservation of Momentum What is the law of conservation of momentum, and how does it apply to isolated systems? How does momentum behave in elastic and inelastic collisions? How can we calculate the velocities of objects after a collision using momentum conservation? Graphical and Mathematical Analysis How can force-time graphs be used to determine impulse? How does the area under a force-time graph relate to the change in momentum? How can momentum conservation equations be applied to solve real-world problems? Real-World Applications How do impulse and momentum explain the safety features in vehicles, such as seat belts and crumple zones? How can the conservation of momentum be observed in activities like billiards, rocket propulsion, or sports? How does the concept of recoil demonstrate momentum conservation?
Unit Topics with Learning Objectives:
Momentum Objectives: Define momentum as the product of mass and velocity (p=mv). Understand momentum as a vector quantity and analyze its direction and magnitude. Solve problems involving momentum in various scenarios. Skills: Calculate momentum for moving objects. Analyze changes in momentum when mass, velocity, or both change. Impulse Objectives: Define impulse as the change in momentum caused by a force acting over a period of time. Understand the impulse-momentum theorem: J=Δp. Solve problems involving impulse and changes in momentum. Skills: Calculate impulse using J=FΔt. Relate impulse to force-time graphs and calculate impulse from the area under the graph. Interpret the effect of increasing or decreasing time of impact on the force (e.g., airbag functionality). Conservation of Momentum Objectives: State and apply the law of conservation of momentum in isolated systems. Analyze momentum in collisions (elastic and inelastic) and explosions. Skills: Solve one-dimensional collision problems using: m1v1 +m2v2 =m1v1f + m2v2f. Differentiate between elastic collisions (where kinetic energy is conserved) and inelastic collisions (where it is not). Combined Topics: Impulse, Momentum, and Collisions Objectives: Connect impulse to momentum changes during collisions. Explore real-world applications such as car crashes and sports. Relate the force-time relationship in collisions to safety designs (e.g., helmets, crumple zones). Skills: Use momentum and impulse concepts to explain collision outcomes qualitatively and quantitatively. Conduct experiments to measure and analyze momentum changes in collision scenarios (e.g., using dynamics carts). General Skills for Impulse and Momentum Interpret graphs of force vs. time to identify impulse.

Static Electricity

UNIT TITLE: Static Electricity
NYS Standards:
NYS Science Learning Standards (Pages 58-63 )
Guiding Questions/Essential Questions:
Charge and Interaction What is electric charge, and how do protons, electrons, and neutrons contribute to the charge of an object? How do charged objects interact, and how do the laws of attraction and repulsion govern these interactions? How is charge conserved during interactions between objects? Charging Methods How do objects become charged through friction, conduction, and induction? How does grounding help neutralize charged objects? How can polarization occur without a transfer of charge? Electric Force and Coulomb’s Law What is Coulomb’s Law, and how does it describe the force between two point charges? How do the magnitude of charges and distance between them affect the electric force? How is Coulomb’s Law similar to and different from gravitational force? Electric Fields What is an electric field, and how does it influence charged particles? How are electric field lines used to visualize the strength and direction of an electric field? How do electric fields differ around point charges, dipoles, and uniformly charged plates? Electric Potential Energy What is electric potential, and how does it relate to potential energy in an electric field? How does the concept of voltage relate to electric potential difference? How can we calculate the work done on a charge moving through an electric field? Applications and Phenomena How does electrostatics explain natural phenomena like lightning and static cling? How can we protect electronic devices from damage caused by electrostatic discharge? Connections and Problem-Solving How can free-body diagrams and vector addition be used to analyze forces on charged objects?
Unit Topics with Learning Objectives:
Charge and Properties of Matter Objectives: Understand the basic properties of electric charge: positive, negative, and neutrality. Explain charge conservation and quantization. Differentiate between conductors and insulators based on charge movement. Skills: Identify charge interactions (like charges repel, unlike charges attract). Explain charge transfer processes such as friction, conduction, and induction. Solve problems involving the distribution of charges in objects (e.g., grounding and polarization). Coulomb's Law Objectives: Understand and apply Coulomb's Law to calculate the force between two point charges: F=kq1q2/r^2. Explore the similarities and differences between gravitational and electrostatic forces. Skills: Calculate electrostatic forces between charges given their magnitudes, signs, and distances. Analyze the vector nature of electrostatic forces in one- and two-dimensional setups. Solve problems involving multiple charges using the principle of superposition. Electric Fields Objectives: Define the electric field E=F/q as the force per unit charge at a point in space. Explore the relationship between electric field lines and the distribution of charges. Understand the concept of a test charge and how it interacts with an electric field. Skills: Calculate the electric field created by a single charge or a system of charges. Draw and interpret electric field lines for point charges and dipoles. . Analyze forces on charges placed in external electric fields. General Skills for Electrostatics Conduct experiments to demonstrate charge interactions (e.g., using an electroscope or Van de Graaff generator). Explain electrostatic phenomena in daily life (e.g., lightning, static cling).

Electrical Current and Circuits

UNIT TITLE: Electrical Current and Circuits
NYS Standards:
NYS Science Learning Standards (Pages 58-63 )
Guiding Questions/Essential Questions:
Basic Circuit Concepts What is an electrical circuit, and what components are typically found in a simple circuit? How do current, voltage, and resistance interact in a circuit? What are the key differences between a series and a parallel circuit in terms of current, voltage, and resistance? Types of Circuits How does current behave in a series circuit versus a parallel circuit? How do the total resistance and current change in a series circuit compared to a parallel circuit? How does the total voltage behave across components in series and parallel circuits? Ohm’s Law What is Ohm’s Law, and how can it be used to calculate the current, voltage, or resistance in a circuit? How can Ohm’s Law be applied to solve problems in both series and parallel circuits? How does resistance affect the current in a circuit, and how can resistors be used to control the current? Power and Energy in Circuits How is electrical power calculated, and what factors determine the power consumption of a circuit? What are the factors that determine the efficiency of electrical devices and circuits? Kirchhoff’s Laws What are Kirchhoff’s current and voltage laws, and how are they applied to circuits? How can Kirchhoff’s laws help us analyze circuits with multiple components and branches? Components of Circuits What are the functions of key components in a circuit, such as resistors, switches, batteries, and light bulbs? How do different types of resistors (fixed/variable) impact the overall resistance in a circuit? Circuit Design and Troubleshooting How do we design a circuit to meet a specific purpose, such as a lighting circuit or a motor circuit? How can we troubleshoot a malfunctioning circuit to identify and correct issues like an open circuit or short circuit? Safety in Electrical Circuits What are the common electrical hazards in circuits, and how can they be prevented (e.g., short circuits, overheating)? How do circuit protection devices (fuses, circuit breakers) work to prevent damage to circuits? Why is grounding important in electrical circuits, and how does it prevent electrical shocks?
Unit Topics with Learning Objectives:
Basic Concepts in Electrical Circuits Objectives: Understand the basic components of an electrical circuit: power sources (batteries), conductors (wires), resistors, and switches. Define current (I), voltage (V), and resistance (R) and understand their relationships. Understand and apply Ohm's Law: V=IR and the concept of electric potential difference. Skills: Calculate current, voltage, and resistance in simple circuits using Ohm's Law. Identify and describe the role of each component in a circuit. Interpret circuit diagrams and identify components like resistors, power sources, and capacitors. Series and Parallel Circuits Objectives: Understand the differences between series and parallel circuits. Learn how to calculate total resistance, current, and voltage in both types of circuits. Understand how the total current and voltage behave in series and parallel circuits. Skills: Solve problems involving series and parallel resistors: Series: Rtotal=R1+R2+⋯ Parallel: 1/Rtotal=1/R1+1/R2+⋯ Calculate total current and voltage in circuits with multiple resistors. Analyze circuits with both series and parallel components. Understand how current is shared between branches in parallel circuits and how voltage remains constant across components in parallel. Power in Circuits Objectives: Define electric power and understand its relationship with current and voltage: P=VI Solve problems involving electrical power in both simple and complex circuits. Understand the concept of energy consumption and efficiency in electrical devices. Skills: Calculate electrical power and energy consumption using P=VI=I^2R=V^2/R. Analyze the power consumed by resistors and electrical devices in a circuit. Solve real-world problems involving energy use in appliances. Kirchhoff's Laws Objectives: Understand and apply Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law (KVL) to solve more complex circuits. KCL: The sum of currents entering a junction is equal to the sum of currents leaving. KVL: The sum of the voltages around any closed loop in a circuit is zero. General Skills for Electrical Circuits Build and troubleshoot simple circuits using resistors, switches, and batteries. Measure current, voltage, and resistance in a circuit using a multimeter. Conduct experiments to verify Ohm’s Law and analyze the characteristics of series and parallel circuits. Apply electrical concepts to real-world devices (e.g., household circuits, electronics).

Magnetism

UNIT TITLE: Magnetism
NYS Standards:
NYS Science Learning Standards (Pages 58-63 )
Guiding Questions/Essential Questions:
Basic Concepts of Magnetism What is magnetism, and how are magnetic fields generated? How do magnetic poles interact with each other, and why do like poles repel while opposite poles attract? What are magnetic domains, and how do they explain the behavior of magnets? How does the Earth’s magnetic field affect compasses and navigation? Magnetic Fields What is a magnetic field, and how is it represented in terms of field lines? How do magnetic field lines behave around a magnet or a current-carrying wire? How can the strength and direction of a magnetic field be determined and measured? How does the shape and configuration of a magnetic field change when magnets interact with each other? Electromagnetism How does an electric current create a magnetic field, and how can this principle be applied in devices like electromagnets? What factors affect the strength of an electromagnet, such as the number of coils, the current, and the core material? How do electromagnets differ from permanent magnets in terms of their properties and uses? How does the concept of electromagnetism relate to everyday devices like motors, generators, and transformers? Magnetic Forces on Charges and Currents How does the motion of charged particles interact with a magnetic field to produce a force? How is the force on a moving charge in a magnetic field calculated (using the Lorentz force law)? How does a magnetic field affect the motion of current-carrying wires, and how is this applied in devices like motors and solenoids? Applications of Magnetism How is magnetism used in real-world applications such as electric motors, MRI machines, and magnetic storage devices? How do magnetic fields contribute to the operation of transformers and electrical power generation? What role does magnetism play in transportation technologies, such as maglev trains or electric cars? Magnetic Materials What are the different types of magnetic materials (ferromagnetic, paramagnetic, diamagnetic), and how do their properties differ? How can materials be magnetized, and how do they lose or retain their magnetization over time? Magnetic Induction What is electromagnetic induction, and how does it lead to the generation of electric current? What is Lenz's Law, and how does it relate to the direction of induced currents in a changing magnetic field? Safety and Environmental Considerations How does the Earth's magnetic field protect life on Earth from harmful solar radiation?
Unit Topics with Learning Objectives:
Magnetic Fields Objectives: Define a magnetic field and describe how it is represented by field lines. Understand the sources of magnetic fields, such as magnetic dipoles (bar magnets) and moving charges. Explore the concept of magnetic force and the relationship between magnetic field strength and distance from the source. Skills: Draw and interpret magnetic field lines for bar magnets. Understand the right-hand rule for determining the direction of the magnetic force on a moving charge and the direction of the magnetic field around a current-carrying wire. Magnetic Force on Moving Charges Objectives: Explore how moving charges interact with magnetic fields. Understand the concept of the Lorentz force, which combines the electric and magnetic forces on a charge. Skills: Use the right-hand rule to determine the direction of the magnetic force on a moving charge or current-carrying wire. Electromagnetism Objectives: Define electromagnetism and understand how electric currents create magnetic fields. Understand the factors that affect the strength of the magnetic field around a wire or solenoid. Skills: Design and analyze electromagnets and understand their applications in motors and speakers. Faraday’s Law of Induction Objectives: Understand the concept of electromagnetic induction and how a changing magnetic field induces an electric current. Magnetic Properties of Matter Objectives: Understand ferromagnetic materials. Explore the concept of magnetic domains and how they influence the behavior of materials. Skills: Classify materials based on their magnetic properties. Understand the process of magnetization and how it occurs in ferromagnetic materials. Explain how Earth's magnetic field affects compasses and navigation. General Skills for Magnetism Conduct experiments to visualize magnetic fields (e.g., using iron filings or magnetic field sensors). Use the right-hand rule to analyze the force on moving charges and current-carrying wires in magnetic fields. Solve real-world problems involving electromagnets, motors, and generators.

Waves

UNIT TITLE: Waves
NYS Standards:
NYS Science Learning Standards (Pages 58-63 )
Guiding Questions/Essential Questions:
Basic Concepts of Waves What is a wave, and how is it different from a particle? What are the main types of waves (mechanical, electromagnetic, transverse, longitudinal), and how do they differ? How are wave properties like wavelength, frequency, amplitude, and speed related? How do waves transfer energy without transferring matter? Wave Properties and Behavior What is the relationship between wavelength, frequency, and wave speed? How does the amplitude of a wave affect its energy? How do waves interact with each other through interference (constructive and destructive interference)? How do waves reflect, refract, and diffract when they encounter different materials or boundaries? What is the Doppler Effect, and how does it explain changes in the frequency of waves as the source or observer moves? Mechanical Waves What are the differences between transverse and longitudinal waves in terms of particle motion and energy transfer? How do sound waves, which are longitudinal mechanical waves, propagate and interact with materials? Wave Behavior and Applications How are wave properties like frequency and amplitude used in musical instruments and sound production? Energy and Power in Waves How does the energy of a wave relate to its amplitude, frequency, and wavelength? World Applications of Waves How do waves help us understand and manage natural phenomena, such as earthquakes or ocean waves?
Unit Topics with Learning Objectives:
Basic Wave Properties Objectives: Define waves and understand the difference between mechanical and electromagnetic waves. Identify the key properties of waves: wavelength, frequency, amplitude, period, and speed. Understand the concept of wave motion, including the transfer of energy without the transfer of matter. Skills: Define and calculate wave speed using v=fλ, where v is wave speed, f is frequency, and λ is wavelength. Describe and measure the amplitude, frequency, and period of waves. Differentiate between transverse and longitudinal waves. Wave Behavior Objectives: Understand and explain the phenomena of wave reflection, refraction, diffraction, and interference. Skills: Predict and explain the behavior of waves when they encounter barriers or different media. Analyze the effects of interference (constructive and destructive) on wave patterns. Solve problems involving the reflection of waves. Sound Waves Objectives: Understand the properties of sound waves, including speed, frequency, wavelength, and amplitude. Explore how sound waves travel through different media and how they are affected by factors such as temperature and medium properties. Understand the Doppler effect and its applications. Skills: Calculate the speed of sound in various media based on given conditions. Explain how sound waves are produced, propagate, and perceived. Solve problems related to the Doppler effect, predicting changes in frequency and wavelength due to relative motion. Wave Interference and Superposition Objectives: Understand the principle of superposition and how waves can interfere with each other. Investigate constructive and destructive interference patterns in both light and sound waves. Skills: Apply the principle of superposition to solve problems involving the interaction of multiple waves. Analyze standing waves in strings and air columns, including the formation of nodes and antinodes. Standing Waves Objectives: Define standing waves and understand how they form in confined media (e.g., strings, air columns). Explore the relationship between frequency, wavelength, and the physical properties of the medium (e.g., length, tension, mass density). Skills: Calculate the fundamental frequency and harmonics of standing waves in strings and air columns. Identify and label nodes and antinodes in standing wave patterns. Solve problems involving resonance in musical instruments, pipes, and strings. Wave Energy and Power Objectives: Understand how waves carry energy and how energy is related to wave amplitude and frequency. Explore the concept of wave power and intensity in mechanical and electromagnetic waves. General Skills for Waves Conduct experiments to demonstrate the properties of waves, including reflection and refraction Use mathematical models to solve problems involving wave motion and energy. Understand real-world applications of wave phenomena, such as in musical instruments. Analyze wave interference patterns and their practical uses in technology (e.g., noise-canceling headphones).

Light

UNIT TITLE: Light
NYS Standards:
NYS Science Learning Standards (Pages 58-63 )
Guiding Questions/Essential Questions:
Nature of Light How does the speed of light in different mediums compare, and how does this affect its behavior? Wave Properties of Light What are the key properties of light waves, including wavelength, frequency, and amplitude? How is the color of light related to its wavelength or frequency? How do light waves interact with matter, and how does this lead to phenomena like reflection, refraction, and diffraction? What is the electromagnetic spectrum, and where does visible light fit within it? How does the intensity of light relate to the amplitude of the light wave? Reflection and Refraction What is the law of reflection, and how does it explain how light bounces off surfaces? How does light refract (bend) when it passes from one medium to another, and how does Snell's Law describe this behavior? How does the refractive index of a material affect the speed and direction of light? How are lenses and mirrors used to manipulate light, and what are their applications in optical devices like microscopes, telescopes, and cameras? Diffraction and Interference What is diffraction, and how does it occur when light passes through narrow openings or around obstacles? How does interference (constructive and destructive) affect the behavior of light waves? How do diffraction patterns demonstrate the wave nature of light? Optical Phenomena What causes the colors we see in a rainbow, and how does dispersion work in a prism? How does total internal reflection occur, and how is it used in fiber optics and other technologies? How does the phenomenon of polarization relate to the orientation of light waves? Applications of Light How is light used in communication technologies like fiber optics?
Unit Topics with Learning Objectives:
Nature of Light Objectives: Understand light as an electromagnetic wave and its relationship to the electromagnetic spectrum. Investigate the speed of light in a vacuum (c=3×10^8 m/sec) and in various media. Skills: Understand the concept of the electromagnetic spectrum and categorize different types of electromagnetic waves based on their wavelengths and frequencies. Explain the phenomena of reflection, refraction, diffraction, and interference as related to light waves. Reflection and Refraction Objectives: Understand the laws of reflection and refraction. Explore the behavior of light when it encounters different surfaces and media. Apply Snell’s Law to predict how light refracts when transitioning between different media. Skills: Apply the law of reflection: the angle of incidence equals the angle of reflection (θi=θr). Use Snell’s Law to solve problems involving refraction of light across different media: n1sin⁡θ1=n2sin⁡θ2, where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively. Solve problems involving critical angle and total internal reflection. Dispersion of Light Objectives: Explore the dispersion of light through a prism and the formation of a spectrum. Understand how different wavelengths of light refract by different amounts, leading to the separation of colors. Skills: Analyze how a prism disperses light into its constituent colors. Use the concept of dispersion to explain phenomena like rainbows and the separation of light into colors. Solve problems involving the dispersion of light, including the use of prisms in spectrometers. Interference and Diffraction of Light Objectives: Understand the concepts of interference and diffraction as applied to light. Explore the conditions for constructive and destructive interference, particularly in double-slit and multi-slit experiments. Skills: Apply the interference formula for a double-slit experiment: λ/d=x/L, where λ is the wavelength, d is the slit separation, x is the distance between the fringes, and L is the distance away from the diffraction grating. Analyze diffraction patterns produced by multi-slit diffraction. Polarization of Light Objectives: Understand the concept of light polarization and its relationship to wave motion. Explore the phenomenon of polarization by reflection and through polarizing filters. Skills: Explain the process of light polarization and the difference between unpolarized and polarized light. Demonstrate the effects of polarization using polarizing filters. Practical Applications of Light Objectives: Explore the practical applications of light and optical principles in everyday life and technology. Investigate the use of fiber optics. Skills: Analyze the working principles of fiber optics and explain how light is transmitted through total internal reflection. General Skills for Light Conduct experiments to observe reflection, refraction, and diffraction. Use ray diagrams and mathematical models to solve problems involving light behavior. Apply the principles of light to real-world technologies, from cameras to fiber optics. Explain the scientific principles behind everyday phenomena such as rainbows, sunsets, and the blue sky.

Anatomy and Physiology (half year course)

COURSE TITLE: Anatomy and Physiology

COURSE DESCRIPTION: Anatomy and Physiology is a comprehensive high school course that introduces students to the structure and function of the human body. The course covers key systems such as the skeletal, muscular, circulatory, respiratory, digestive, nervous, and endocrine systems, focusing on how each system contributes to overall health and homeostasis. Students will explore the relationships between anatomy (the study of body structures) and physiology (the study of their functions), learning about the complexities of organs, tissues, and cells. Through lectures, lab experiments, and hands-on activities, students will gain a deeper understanding of human biology and the interdependence of body systems. The course is designed to provide foundational knowledge for students interested in pursuing careers in healthcare, biology, and other science-related fields.

MP1 Units:	MP2 Units:
Introduction to Anatomy and Physiology The Integumentary System The Muscular System The Skeletal System The Digestive System The Respiratory System	The Urinary System The Cardiovascular System The Nervous System The Endocrine System The Immune System The Reproductive System

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams and class discussions Question and answer sessions, both formal and informal —planned/spontaneous Conferences between the instructor and student at various points in the semester In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Lab reports & quizzes Methods of Summative Assessments: Unit Exams Semester Assessment Projects (project phases submitted at various completion points could be formatively assessed)
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Introduction to Anatomy and Physiology

UNIT TITLE: Introduction to Anatomy and Physiology
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages )
Guiding Questions/Essential Questions:
What is the difference between anatomy and physiology? How are structure and function related in the human body? What are the basic principles of homeostasis?
Unit Topics with Learning Objectives:
Define anatomy and physiology. Identify major levels of organization in the human body (cells, tissues, organs, systems). Understand the concept of homeostasis and how it regulates the body's internal environment. Describe the major body systems and their primary functions.

Integumentary System

UNIT TITLE: Integumentary System
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages )
Guiding Questions/Essential Questions:
How does the skin protect the body from environmental threats? What is the role of the integumentary system in homeostasis? How does the body heal itself after an injury to the skin?
Unit Topics with Learning Objectives:
Describe the structure and function of the skin, including its layers and appendages (hair, nails, glands). Explain how the integumentary system regulates temperature and prevents dehydration. Understand the processes of skin repair and regeneration.

Skeletal System

UNIT TITLE: Skeletal System
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages )
Guiding Questions/Essential Questions:
What is the structure of bones, and how do they grow and repair? How do bones and joints contribute to movement? How do muscles and bones work together to produce movement?
Unit Topics with Learning Objectives:
Identify the major bones of the human body and their functions. Understand the different types of bone cells (osteoblasts, osteoclasts) and the process of bone remodeling. Explain the functions of ligaments, tendons, and cartilage in the skeletal system.

Muscular System

UNIT TITLE: Muscular System
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages )
Guiding Questions/Essential Questions:
How do muscles produce movement in the body? What is the role of the nervous system in muscle contraction? How does the muscular system interact with the skeletal system?
Unit Topics with Learning Objectives:
Describe the three types of muscle tissue (skeletal, smooth, cardiac) and their functions. Understand the process of muscle contraction (sliding filament theory). Explain how muscles work in antagonistic pairs and the concept of muscle contraction.

Nervous System

UNIT TITLE: Nervous System
NYS Standards:
NYS Science Learning Standards (Page 64 )
Guiding Questions/Essential Questions:
How does the nervous system coordinate body functions? What is the role of neurons in transmitting signals? How do reflexes and voluntary movements differ in the nervous system?
Unit Topics with Learning Objectives:
Describe the structure and function of the central and peripheral nervous systems. Explain the structure and function of neurons, including action potentials and synaptic transmission. Identify and describe the different divisions of the nervous system and their roles in body control.

Endocrine System

UNIT TITLE: Endocrine System
NYS Standards:
NYS Science Learning Standards (Page 64 )
Guiding Questions/Essential Questions:
How do hormones regulate body functions? What are the major glands of the endocrine system? How does the endocrine system interact with the nervous system?
Unit Topics with Learning Objectives:
Understand the role of hormones in regulating growth, metabolism, and reproduction. Identify and describe the major endocrine glands and their hormones (e.g., thyroid, adrenal, pituitary). Explain feedback mechanisms (positive and negative) in regulating hormonal levels.

Cardiovascular System

UNIT TITLE: Cardiovascular System
NYS Standards:
NYS Science Learning Standards (Page 64 )
Guiding Questions/Essential Questions:
How does the heart pump blood throughout the body? How do blood vessels regulate blood flow to different organs? How does the cardiovascular system maintain homeostasis?
Unit Topics with Learning Objectives:
Describe the structure and function of the heart, including its chambers, valves, and blood flow cycle. Identify the major blood vessels (arteries, veins, capillaries) and their roles in circulation. Explain how the cardiovascular system responds to exercise, stress, and changes in body temperature.

Respiratory System

UNIT TITLE: Respiratory System
NYS Standards:
NYS Science Learning Standards (Page 64 )
Guiding Questions/Essential Questions:
How does the respiratory system facilitate gas exchange? What is the process of breathing and how is it regulated? How does the body regulate oxygen and carbon dioxide levels?
Unit Topics with Learning Objectives:
Describe the structure of the respiratory system, including the lungs, alveoli, and bronchi. Understand the mechanics of breathing, including inspiration and expiration. Explain how the respiratory and cardiovascular systems work together to transport gases.

Digestive System

UNIT TITLE: Digestive System
NYS Standards:
NYS Science Learning Standards (Page 64 )
Guiding Questions/Essential Questions:
How does the body process and absorb nutrients from food? How are enzymes involved in digestion? How does the digestive system maintain homeostasis?
Unit Topics with Learning Objectives:
Describe the structure and function of the major organs in the digestive system (mouth, stomach, intestines). Understand the role of enzymes in breaking down macromolecules (proteins, lipids, carbohydrates). Explain the processes of nutrient absorption and waste elimination.

Urinary System

UNIT TITLE: Urinary System
NYS Standards:
NYS Science Learning Standards (Page 64 )
Guiding Questions/Essential Questions:
How does the body maintain fluid and electrolyte balance? How does the urinary system contribute to homeostasis? How do the kidneys interact with other systems in the body?
Unit Topics with Learning Objectives:
Describe the structure and function of the kidneys, including the process of filtration and urine formation. Explain how the kidneys regulate blood pressure, pH balance, and waste elimination. Understand the role of the urinary system in detoxification and metabolic waste removal.

Reproductive System

UNIT TITLE: Reproductive System
NYS Standards:
NYS Science Learning Standards (Page 64 )
Guiding Questions/Essential Questions:
What is the role of the reproductive system in human development? How does fertilization and development occur? How do hormones regulate the menstrual cycle and pregnancy?
Unit Topics with Learning Objectives:
Describe the structure and function of male and female reproductive organs. Explain the processes of sperm production, ovulation, fertilization, and early embryonic development. Understand the role of hormones (e.g., estrogen, progesterone, testosterone) in reproduction.

Immune System

UNIT TITLE: Immune System
NYS Standards:
NYS Science Learning Standards (Page 64 )
Guiding Questions/Essential Questions:
How does the immune system defend the body from pathogens? What is the role of white blood cells in fighting infection? How do vaccines help the immune system?
Unit Topics with Learning Objectives:
Describe the structure and function of the immune system, including innate and adaptive immunity. Identify key components of the immune response, such as antibodies and antigens. Understand the concepts of immunity, vaccination, and the role of memory cells in disease prevention.

Human Development and Aging

UNIT TITLE: Human Development and Aging
NYS Standards:
NYS Science Learning Standards (Page 64 )
Guiding Questions/Essential Questions:
How does the human body change over the course of a lifetime? What factors affect aging and health in the later stages of life?
Unit Topics with Learning Objectives:
Explain the stages of human development from conception to adulthood. Describe the physiological changes that occur with aging and how lifestyle factors can impact aging.

Animal Behavior (half year course)

COURSE TITLE: Animal Behavior

COURSE DESCRIPTION: Animal Behavior is a high school course that explores the fascinating ways animals interact with their environment, each other, and humans. Students will study the biological, psychological, and environmental factors that influence animal behavior, including instinct, learning, communication, mating, social structures, and survival strategies. The course covers a range of species, from domesticated animals to wildlife, and investigates behaviors in both natural and controlled settings. Students will learn about the methods used by scientists to observe, record, and interpret animal behavior, including field studies and laboratory experiments. The course also delves into the ethical considerations involved in studying and interacting with animals. Through discussions, case studies, and hands-on activities, students will develop an understanding of how animal behavior contributes to the survival and adaptation of species, while also gaining insights into how humans influence and are influenced by the behavior of animals.

MP1 Units:	MP2 Units:
Introduction to Animal Behavior Genetics and Evolution of Behavior Instincts and Innate Behaviors Learning and Conditioning in Animals Animal Communication: Signals and Cues Feeding Behavior and Foraging Strategies Mating Systems and Reproductive Behavior	Social Structures and Group Dynamics Territoriality and Aggression Parental Care and Offspring Development Predator-Prey Interactions and Survival Strategies Animal Cognition and Problem Solving Behavioral Ecology: Adapting to the Environment Human-Animal Interactions Ethical Considerations in Animal Behavior Research

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams and class discussions Question and answer sessions, both formal and informal —planned/spontaneous Conferences between the instructor and student at various points in the semester In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Lab reports & quizzes Methods of Summative Assessments: Unit Exams Semester Assessment Projects (project phases submitted at various completion points could be formatively assessed)
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Introduction to Animal Behavior

UNIT TITLE: Introduction to Animal Behavior
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
What is animal behavior, and why is it important to study? How do scientists observe and measure animal behavior? What methods do researchers use to categorize and interpret animal actions?
Unit Topics with Learning Objectives:
Define animal behavior and explain its significance in understanding species survival. Identify key research methods in animal behavior, including observation, experimentation, and data collection. Differentiate between behavioral ecology and comparative psychology.

Genetics and Evolution of Behavior

UNIT TITLE: Genetics and Evolution of Behavior
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
How do genetics and evolution influence animal behavior? In what ways does natural selection shape behavior across generations? How are behavioral traits inherited and passed on to offspring?
Unit Topics with Learning Objectives:
Understand the role of genetics in determining animal behavior. Explain how natural selection drives the evolution of behavior. Examine examples of behavioral traits that have evolved to increase survival and reproduction.

Instincts and Innate Behaviors

UNIT TITLE: Instincts and Innate Behaviors
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
What are instincts, and how do they differ from learned behaviors? How do innate behaviors contribute to survival and reproduction? Can instinctual behaviors be modified or overridden by experience?
Unit Topics with Learning Objectives:
Define instinct and innate behavior, and identify examples in animals. Analyze the role of innate behaviors in species survival, particularly in newborns or young animals. Examine how instincts relate to genetics and evolutionary pressures.

Learning and Conditioning in Animals

UNIT TITLE: Learning and Conditioning in Animals
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
How do animals learn, and what types of learning exist? What are the key differences between classical and operant conditioning? How does learning affect survival and adaptation in the wild?
Unit Topics with Learning Objectives:
Understand and explain different types of learning: classical conditioning, operant conditioning, and observational learning. Investigate how animals use learning to adapt to their environment and improve their chances of survival. Identify examples of learned behaviors in different species.

Animal Communication: Signals and Cues

UNIT TITLE: Animal Communication: Signals and Cues
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
How do animals communicate with each other and their environment? What are the different forms of animal communication (visual, auditory, chemical, tactile)? How do communication signals benefit animals in terms of survival and reproduction?
Unit Topics with Learning Objectives:
Explore various communication methods in animals, including visual signals, vocalizations, chemical cues (pheromones), and touch. Analyze the function and purpose of communication in social structures, mating rituals, and territory defense. Investigate how animals interpret and respond to different signals.

Feeding Behavior and Foraging Strategies

UNIT TITLE: Feeding Behavior and Foraging Strategies
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
What factors influence an animal's feeding behavior? How do animals maximize energy intake and minimize energy expenditure while foraging? How do ecological factors shape the foraging strategies of different species?
Unit Topics with Learning Objectives:
Examine the different types of foraging behaviors, such as solitary vs. group foraging. Analyze the balance between energy gained and energy spent during feeding. Study various foraging strategies, including optimal foraging theory, and their role in animal survival.

Mating Systems and Reproductive Behavior

UNIT TITLE: Mating Systems and Reproductive Behavior
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
How do animals choose mates, and what factors influence mate selection? What are the different types of mating systems, and how do they vary among species? How does reproductive behavior ensure the survival of offspring?
Unit Topics with Learning Objectives:
Investigate the different types of mating systems: monogamy, polygamy, promiscuity, and cooperative breeding. Explore the role of sexual selection in mate choice and reproductive success. Understand the importance of parental investment in offspring survival.

Social Structures and Group Dynamics

UNIT TITLE: Social Structures and Group Dynamics
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
How do social structures in animal groups benefit individuals and the group as a whole? What are the different types of social structures (e.g., hierarchies, cooperative groups)? How do group dynamics influence the behavior of individual animals?
Unit Topics with Learning Objectives:
Understand the concept of social organization in animal groups, including dominance hierarchies and cooperative groups. Analyze the benefits and challenges of living in a group, such as protection, resource sharing, and cooperation. Explore the influence of social structure on individual roles and behaviors within the group.

Territoriality and Aggression

UNIT TITLE: Territoriality and Aggression
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
Why do animals defend territories, and how does territoriality relate to survival and reproduction? What causes aggression in animals, and how does it affect group dynamics and individual success? How do animals resolve conflicts over resources?
Unit Topics with Learning Objectives:
Investigate the role of territoriality in resource allocation and mate protection. Examine different forms of aggression in animals, including predation, competition, and dominance fights. Analyze the strategies animals use to minimize conflict and maintain order within territories.

Parental Care and Offspring Development

UNIT TITLE: Parental Care and Offspring Development
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
What types of parental care exist in the animal kingdom, and how do they vary by species? How does parental care increase the survival rate of offspring? What factors influence the duration and intensity of parental investment?
Unit Topics with Learning Objectives:
Explore the different strategies of parental care, including provisioning, protection, and teaching. Understand the role of parental investment in offspring survival and development. Analyze the trade-offs involved in different forms of care, from intensive parental involvement to minimal care.

Predator-Prey Interactions and Survival Strategies

UNIT TITLE: Predator-Prey Interactions and Survival Strategies
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
How do predator-prey interactions shape animal behavior and evolution? What are some common survival strategies employed by predators and prey? How do animals adapt to changing predator-prey dynamics?
Unit Topics with Learning Objectives:
Investigate predator strategies such as stalking, hunting, and ambush. Examine prey strategies such as camouflage, mimicry, and escape behaviors. Study co-evolution between predators and prey, and how they influence each other's behavior.

Animal Cognition and Problem Solving

UNIT TITLE: Animal Cognition and Problem Solving
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
How do animals perceive their environment and solve problems? What is the role of intelligence and learning in animal survival? How do different species demonstrate cognitive abilities, such as tool use or planning?
Unit Topics with Learning Objectives:
Define animal cognition and explore examples of problem-solving behaviors across different species. Study the cognitive abilities of animals, such as memory, learning, and decision-making. Examine how tool use, planning, and communication contribute to an animal's ability to adapt to its environment.

Behavioral Ecology: Adapting to the Environment

UNIT TITLE: Behavioral Ecology: Adapting to the Environment
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
How do animals adapt their behavior to meet environmental challenges? What is the relationship between an animal's behavior and its ecological niche? How do behavioral adaptations influence survival and reproduction?
Unit Topics with Learning Objectives:
Understand how animals' behaviors are shaped by their environment, including habitat, climate, and availability of resources. Investigate how behavior contributes to an animal's ecological role or niche. Analyze case studies of behavioral adaptations in response to environmental pressures.

Human-Animal Interactions

UNIT TITLE: Human-Animal Interactions
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
How do human activities affect animal behavior, and vice versa? What ethical considerations arise from human interaction with animals in various settings (e.g., domestication, zoos, research)? How can humans improve their relationships with animals for mutual benefit?
Unit Topics with Learning Objectives:
Explore the effects of domestication, captivity, and human influence on animal behavior. Investigate ethical issues surrounding animal use in research, entertainment, and agriculture. Discuss how humans can promote animal welfare and foster better human-animal relationships.

Ethical Considerations in Animal Behavior Research

UNIT TITLE: Ethical Considerations in Animal Behavior Research
NYS Standards:
NYS Science Learning Standards (Pages 64-72)
Guiding Questions/Essential Questions:
What ethical concerns arise in the study of animal behavior? How do researchers ensure the humane treatment of animals in behavioral studies? What is the role of animal welfare in scientific research?
Unit Topics with Learning Objectives:
Identify ethical principles guiding animal behavior research, including animal rights and welfare considerations. Study the role of Institutional Animal Care and Use Committees (IACUC) and ethical guidelines for experimentation. Analyze case studies that highlight ethical dilemmas in animal behavior research and their resolutions.

AP Biology

COURSE TITLE: AP Biology

COURSE DESCRIPTION:

AP Biology has undergone two major revisions that have moved the course from a traditional “content coverage” model of instruction to one that focuses on enduring, conceptual understandings. Students spend less time on factual recall and more time learning essential biological concepts. Students develop inquiry and reasoning skills through laboratory experiences and the use of authentic data sets. They collect and analyze data, and apply mathematical routines for statistical data analysis. Students practice modeling of biological phenomena as a means of understanding their complexities. The course sequence follows the evolutionary progression of life on earth. Study begins at the molecular level with the organic molecules necessary for life through to cells all the way to species interactions in ecology. The course culminates in a dissection lab practicum investigating mammal anatomy and physiology, which is no longer covered in the revised (summer 2019) AP Biology Curriculum.

Learn more about the course, the individual units and the exam.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Chemistry of Life Cell Structure and Function Cellular Energetics	Cellular Communication and Cell Cycle Heredity	Gene Expression and Regulation Natural Selection	Ecology

Forms of Assessments:
Formative Assessments In August 2019, a dedicated platform designed to support students was released by the College Board. PERSONAL PROGRESS CHECKS provide formative AP questions for every unit to provide feedback to students and the teacher on the areas where students need to focus. Evaluation of BioZone Workbooks that students use to individually practice the following: Analyze data sets Model biological concepts Perform statistical tests and mathematical calculations Design and analyze scientific experiments Evaluation of students’ written response to questions based on textbook readings. Question and answer sessions, which take place, formally and informally, throughout all instructions. Small lab group question and answer sessions are especially helpful in assessing students’ understanding of procedures and key concepts. In-class activities where students informally present their ideas, questions and results. For example: Laboratory Investigations are collaborative enterprises in which lots of small group discussions take place between students and teachers allowing for formative assessment. Observations of students’ nonverbal feedback during lectures, labs, & group activities. Student feedback about the effectiveness of teaching strategies. Methods of Summative Assessments Lab reports and quizzes Unit Exams Final exam experience where students, individually, demonstrate their understanding.
Differentiation/Extensions/Accommodations:
Many of the instructional strategies used in this course to support diverse learners are collaborative in nature, and other strategies are designed for students to work by themselves. Instructional Strategies For Collaborative Learning: Modeling biological processes Concept Mapping & Venn Diagrams Sharing of lab group data for statistical analysis and graphing Word-pair Activity (Pairing of vocabulary words with an explanation of the relationship between them) Use of Manipulatives (Manually create three dimensional structures to demonstrate biological events) Modeling Activities (Create and analyze visual representations of biological concepts and processes) “B, M, & E Activity: Beginning, Middle, and End” (Students break down complex multi-step processes into components of what is happening at the beginning, middle and end of the process) Instructional Strategies For Individual Learning: Cornell Note-taking Strategy Self-Assessment Strategies (use of answer keys for online quizzes, tests, textbook , and workbook homework)

AP Chemistry

COURSE TITLE: AP Chemistry

COURSE DESCRIPTION: AP Chemistry is offered as a second-year college-level chemistry course. The majority of students will have taken Regents or Honors chemistry prior to taking AP chemistry. AP chemistry uses a double period weekly for laboratory investigations. The course is very dependent on solving equations. Students who are hard-working that feel an intrinsic satisfaction for learning difficult concepts will appreciate the rigor of this course. This is a college level, general chemistry course. Topics include chemical bonding, stoichiometry, states of matter, principles of thermodynamics, chemical kinetics, equilibrium, electrochemistry, qualitative and quantitative analysis, nuclear structure and radioactivity. The course culminates with a demanding final exam and the AP Chemistry test in May.

Learn more about the course, the individual units and the exam.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Unit #1 Atomic Structure and Properties Unit #2 Compound Structure and Properties	Unit #3 Properties of Substances and Mixtures Unit #4 Chemical Reactions Unit #5 Kinetics	Unit #6 Thermochemistry Unit #7 Equilibrium Unit #8 Acids and Bases	Unit #9 Thermodynamics and Electrochemistry

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Question and answer sessions, both formal—planned and informal—spontaneous In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Methods of Summative Assessments: Projects (project phases submitted at various completion points could be formatively assessed) Unified Arts Folder / Portfolio Presentations Student evaluation / Conclusion Questions
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

AP Computer Science A

COURSE TITLE: AP Computer Science A

COURSE DESCRIPTION: This is a rigorous course in coding and is equivalent to a one semester college level introductory course in computer science. Students learn to code using the Java programming language. Students will be prepared to take the AP Computer Science A exam in May. While not a requirement, it is strongly recommended that students complete a prior course in computer science. If a prior course is not completed, department approval is required. Topics include problem solving, design strategies and methodologies, organization of data (data structures), approaches to processing data (algorithms), analysis of potential solutions, and the ethical and social implications of computing.

Learn more about the course, the individual units and the exam.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Object-Oriented Programming Class Structure and Design	Arrays and Algorithms Conditions and Logic Two-Dimensional Arrays	ArrayLists and String Methods Method Decomposition and Recursion Searching and Sorting	Searching and Sorting (cont.)

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Question and answer sessions, both formal—planned and informal—spontaneous In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Methods of Summative Assessments: Projects (project phases submitted at various completion points could be formatively assessed) Unified Arts Folder / Portfolio Presentations Student evaluation / Conclusion Questions
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

AP Computer Science Principles

COURSE TITLE: AP Computer Science Principles

COURSE DESCRIPTION:This is a college level course that offers students the opportunity to gain exposure to computing and study its effects and integration into the real world. Students learn how computers work and function as a part of the internet, creative aspects of programming, abstractions, algorithms, large data sets, the Internet, cybersecurity concerns, and computing impacts. This course will help students develop a thorough grasp of the computing foundations and concepts relevant to college and careers that involve every field today. Multidisciplinary in nature, the course teaches students to analyze problems, use creative thinking, and collaborate to investigate solutions to real-world issues using computing. Students need to have strong communication and writing skills to be successful in the course. Students will be prepared to take the AP Computer Science Principles Exam in May which also includes a portfolio of projects submitted beforehand.

Learn more about the course, the individual units and the exam.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Creative Development	Data	Algorithms and Programming	Computer Systems & Networks

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Question and answer sessions, both formal—planned and informal—spontaneous In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Methods of Summative Assessments: Projects (project phases submitted at various completion points could be formatively assessed) Unified Arts Folder / Portfolio Presentations Student evaluation / Conclusion Questions
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

AP Environmental Science

COURSE TITLE: AP Environmental Science

COURSE DESCRIPTION:

Environmental concerns plague our growing population, but knowledge is the key to living healthy, productive and sustainable lives. If you want to understand the complex science behind the environmental challenges facing our world and investigate new and evolving solutions, AP Environmental Science may be the course for you. The AP Environmental Science course is an integrated multidisciplinary capstone course for students interested in understanding the complex nature of environmental problems. Topics of study include a broad range of integrated disciplines ranging from environmental ethics, politics, economics, and law to forestry, ecology, evolution, agriculture, pollution, toxicology, and energy. The course is designed with a strong laboratory component including several opportunities for field investigations and trips throughout the year. Opportunities for open-minded discussion and a respectful exchange of ideas permeate an evidence-based approach to evaluating the scientific principles and concepts of environmental science. The course culminates with a cumulative final exam and the AP Examination in May.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
The Living World: Ecosystems	The Living World: Biodiversity Populations Earth Systems & Resources	Land & Water Use Energy Resources and Consumption	Atmospheric Pollution/Global Change Aquatic and Terrestrial Pollution

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Question and answer sessions, both formal—planned and informal—spontaneous In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Methods of Summative Assessments: Projects (project phases submitted at various completion points could be formatively assessed) Unified Arts Folder / Portfolio Presentations Student evaluation / Conclusion Questions
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

The Living World: Ecosystems

UNIT TITLE: Unit 1 - The Living World: Ecosystems
NYS Standards:
College Board Standards (CORE CONTENT: Pages )
Guiding Questions/Essential Questions/AP College Board Enduring Understanding:
ERT-1: Ecosystems are the result of biotic and abiotic interactions. ENG-1: Energy can be converted from one form to another.
Unit Topics with Learning Objectives:
Topic 1.1: Introduction to Ecosystems ERT-1.A: Explain how the availability of resources influences species interactions. ERT-1.A.1: In a predator-prey relationship, the predator is an organism that eats another organism (the prey). ERT-1.A.2: Symbiosis is a close and long-term interaction between two species in an ecosystem. Types of symbiosis include mutualism, commensalism, and parasitism. ERT-1.A.3: Competition can occur within or between species in an ecosystem where there are limited resources. Resource partitioning -using the resources in different ways, places, or at different times- can reduce the negative impact of competition on survival. Topic 1.2: Terrestrial Biomes ERT-1.B: Describe the global distribution and principal environmental aspects of terrestrial biomes. ERT-1.B.1: A biome contains characteristic communities of plants and animals that result from, and are adapted to, its climate. ERT-1.B.2: Major terrestrial biomes include taiga, temperate rainforests, temperate seasonal forests, tropical rainforests, shrubland, temperate grassland, savanna, desert, and tundra. ERT-1.B.3: The global distribution of mineral terrestrial natural resources, such as water and trees for lumber, varies because of some combination of climate, geography, latitude and altitude, nutrient availability, and soil. ERT-1.B.4: The worldwide distribution of biomes is dynamic; the distribution has changed in the past and may again shift as a result of global climate changes. Topic 1.3: Aquatic Biomes ERT-1.C: Describe the global distribution and principal environmental aspects of aquatic biomes. ERT-1.C.1: Freshwater biomes include streams, rivers, ponds, and lakes. These freshwater biomes are a vital resource for drinking water. ERT-1.C.2: Marine biomes include oceans, coral reefs, marshlands, and estuaries. Algae in marine biomes supply a large portion of the Earth’s oxygen, and also take in carbon dioxide from the atmosphere. ERT-1.C.3: The global distribution of nonmineral marine natural resources, such as different types of fish, varies because of some combination of salinity, depth, turbidity, nutrient availability, and temperature. Topic 1.4: The Carbon Cycle ERT-1.D: Explain the steps and reservoir interactions in the carbon cycle. ERT-1.D.1: The carbon cycle is the movement of atoms and molecules containing the element carbon between sources and sinks. ERT-1.D.2: Some of the reservoirs in which carbon compounds occur in the carbon cycle hold those compounds for long periods of time, while some hold them for relatively short periods of time. ERT-1.D.3: Carbon cycles between photosynthesis and cellular respiration in living things. ERT-1.D.4: Plant and animal decomposition have led to the storage of carbon over millions of years. The burning of fossil fuels quickly moves that stored carbon into atmospheric carbon, the form of carbon dioxide. Topic 1.5: The Nitrogen Cycle ERT-1: Explain the steps and reserved interactions in the nitrogen cycle. ERT-1.E.1: The nitrogen cycle is the movement of atoms and molecules containing the element nitrogen between sources and sinks. ERT-1.E.2: Most of the reservoirs in which nitrogen compounds occur in the nitrogen cycle hold those compounds for relatively short periods of time. ERT-1.E.3: Nitrogen fixation is the process in which atmospheric nitrogen is converted into a form of nitrogen (primarily ammonia) that is available for uptake by plants and that can be synthesized into plant tissue. ERT-1.E.4: The atmosphere is the major reservoir of nitrogen. Topic 1.6: The Phosphorus Cycle ERT-1.F: Explain the steps and reservoir interactions in the phosphorus cycle. ERT-1.F.1: The phosphorus cycle is the movement of atoms and molecules containing the element phosphorus between sources and sinks. ERT-1.F.2: The major reservoirs of phosphorus in the phosphorus cycle are rock and sediments that contain phosphorus-bearing minerals. ERT-1.F.3: There is no atmospheric component in the phosphorus cycle, and the limitations this imposes on the return of phosphorus from the ocean to land make phosphorus naturally scarce in aquatic and many terrestrial ecosystems. In undisturbed ecosystems, phosphorus is the limiting factor in biological systems. Topic 1.7: The Hydrologic (Water) Cycle ERT-1.G: Explain the steps and reservoir interactions in the hydrologic cycle. ERT-1.G.1: The hydrologic cycle, which is powered by the sun, is the movement of water in its vars solid liquid, and gaseous phases between sources and sinks. ERT-1.G.2: The oceans are the primary reservoir of water at the Earth;s surface, with ice caps and groundwater acting as much smaller reservoirs. Topic 1.8: Primary Productivity ENG-1.A: Explain how solar energy is acquired and transferred by living organisms. ENG-1.A.1: Primary productivity is the rate at which solar energy (sunlight) is converted into organic compounds via photosynthesis over a unit of time. ENG-1.A.2: Gross primary productivity is the total rate of photosynthesis in a given area. ENG-1.A.3: Net primary productivity is the rate of energy storage by photosynthesizers in a given area, after subtracting the energy lost to respiration. ENG-1.A.4: Productivity is measured in units of energy per unit area per unit time (e.g., kcal/m²/yr). ENG-1.A.5: Most red light is absorbed in the upper 1m of water, and blue light only penetrates deeper than 100m in the clearest water. This affects photosynthesis in aquatic ecosystems, whose photosynthesizers have adapted mechanisms to address the lack of visible light. Topic 1.9: Trophic Levels ENG-1.B: Explain how energy flows and matter cycles through trophic levels. ENG-1.B.1: All ecosystems depend on a continuous inflow of high-quality energy in order to maintain their structure and function of transferring matter between the environment and organisms via biogeochemical cycles. ENG-1.B.2: Biogeochemical cycles are essential for life and each cycle demonstrates the conservation of matter. ENG-1.B.3: In terrestrial and near-surface marine communities, energy flows from the sun to producers in the lowest trophic level and then upward to higher trophic levels. Topic 1.10: Energy Flow and the 10% Rule ENG-1.C: Determine how the energy decreases as it flows through ecosystems. ENG-1.C.1: The 10% rule approximates that in the transfer of energy from one trophic level to the next, only about 10% of the energy is passed on. ENG-1.C.2: The loss of energy that occurs when energy moves from lower to higher trophic levels can be explained through the laws of thermodynamics. Topic 1.11: Food Chains and Food Webs ENG-1.D: Describe food chains and food webs, and their constituent members by trophic level. ENG-1.D.1: A food web is a model of an interlocking pattern of food chains that depicts the flow of energy and nutrients in two or more food chains. ENG-1.D.2: Positive and negative feedback loops can each play a role in food webs. When one species is removed from or added to a specific food web, the rest of the food web can be affected.

The Living World: Biodiversity

UNIT TITLE: Unit 2 - The Living World: Biodiversity
NYS Standards:
College Board Standards (CORE CONTENT: Pages 47-58)
Guiding Questions/Essential Questions/AP College Board Enduring Understanding:
ERT-2: Ecosystems have structure and diversity that change over time.
Unit Topics with Learning Objectives:
Topic 2.1: Introduction to Biodiversity ERT.2.A: Explain levels of biodiversity and their importance to ecosystems. ERT.2.A.1: Biodiversity in an ecosystem includes genetic, species, and habitat diversity. ERT.2.A,2: The more genetically diverse a population is, the better it can respond to environmental stressors. Additionally, a population bottleneck can lead to a loss of genetic diversity. ERT.2.A.3: Ecosystems that have a larger number of species are more likely to recover from disruptions. ERT.2.A.4: Loss of habitat leads to a loss of specialist species, followed by a loss of generalist species. It also leads to reduced numbers of species that have large territorial requirements. ERT.2.A.5: Species richness refers to the number of different species found in an ecosystem. Topic 2.2: Ecosystem Services ERT-2.B: Describe ecosystem services. ERT-2.B.1: There are four categories of ecosystem services: provisioning, regulating, cultural, and supporting. ERT-2.C: Describe the results of human disruptions to ecosystem services. ERT-2.C.1: Anthropogenic activities can disrupt ecosystem services, potentially resulting in economic and ecological consequences. Topic 2.3: Island Biogeography ERT-2.D: Describe island biodiversity. ERT-2.D.1: Island biogeography is the study of the ecological relationships and distribution of organisms on islands, and of these organisms’ community structures. ERT-2.D.2: Islands have been colonized in the past by new species arriving from elsewhere. ERT-2.E: Describe the role of island biogeography in evolution. ERT-2.E.1: Many island species have evolved to be specialists versus generalists because of the limited resources, such as food and territory, on most islands. The long-term survival of specialists may be jeopardized if and when invasive species, typically generalists, are introduced and outcompete the specialists. Topic 2.4: Ecological Tolerance ERT-2.F: Describe ecological tolerance. ERT-2.F.1: Ecological tolerance refers to the range of conditions, such as temperature, salinity, flow rate, and sunlight that an organism can endure before injury or death results. ERT-2.F.2: Ecological tolerance can apply to individuals and to species. Topic 2.5: Natural Disruptions to Ecosystems ERT-2.G: Explain how natural disruptions, both short-and-long-term, impact an ecosystem. ERT-2.G.1: Natural disruptions to ecosystems have environmental consequences that may, for a given occurrence, be as great as, or greater than, many human-made disruptions. ERT-2.G.2: Earth system processes operate on a range of scales in terms of time. Processes can be periodic, episodic, or random. ERT-2.G.3: Earth’s climate has changed over geological time for many reasons. ERT-2.G.4: Sea level has varied significantly as a result of changes in the amount of glacial ice on Earth over geological time. ERT-2.G.5: Major environmental change or upheaval commonly result in large swathes of habitat changes. ERT-2..6: GWildlife engages in both short - and long-term migration for a variety of reasons, including natural disruptions. Topic 2.6: Adaptations ERT-2.H: Describe how organisms adapt to their environment. ERT-2.H.1: Organisms adapt to their environment over time, noth in short-and long-term scales, via incremental changes at the genetic level. ERT-2.H.2: Environmental changes, either sudden or gradual, may threaten a species’ survival, requiring individuals to alter behaviors, move, or perish. Topic 2.7: Ecological Succession ERT-2.I: Describe ecological succession. ERT-2.I.1: There are two main types of ecological succession: primary and secondary succession. ERT-2.I.2: A keystone species in an ecosystem is a species whose activities have a particularly significant role in determining community structure. ERT-2.I.3: An indicator species is a plant or animal that, by its presence, abundance, scarcity, or chemical composition, demonstrates that some distinctive aspect of the character or quality of an ecosystem is present. ERT-2.J: Describe the effect of ecological succession on ecosystems. ERT-2.J.1: Pioneer members of an early successional species commonly o,ve into unoccupied habitat and over time adapt to its particular conditions, which may result in the origin of new species. ERT-2.J.2: Succession in a disturbed ecosystem will affect the total biomass, species richness, and net productivity over time.

Populations

UNIT TITLE: Unit 3 - Populations
NYS Standards:
College Board Standards (CORE CONTENT: Pages 59-73)
Guiding Questions/Essential Questions/AP College Board Enduring Understanding:
ERT-3: Populations change over time in reaction to a variety of factors. EIN-1: Human Populations change in reaction to a variety of factors, including social and cultural factors.
Unit Topics with Learning Objectives:
Topic 3.1: Generalist and Specialist Species ERT-3.A: Identify the differences between generalist and specialist species. ERT-3.A.1: Specialist species tend to be advantaged in habitats that remain constant, while generalist species tend to be advantaged in habitats that are changing. Topic 3.2: K-Selected & r-Selected Species ERT-3.B: Identify differences between K- and r-selected species. ERT-3.B.1: K-selected species tend to be large, have few offspring per reproduction events live in stable environments, expend significant energy for each offspring, mature after many years of extended youth and parental care, have long life spans/life expectancy, and reproduce more than once in their lifetime. Competition for resources in K-selected species’ habitats is usually relatively high. ERT-3.B.2: r- selected species tend to be small, have many offspring, expend or invest minimal energy for each offspring, mature early, have short life spans, and may reproduce only once in their lifetime. Competition for resources in r-selected species’ habitats is typically relatively low. ERT-3.B.3: Biotic potential refers to the maximum reproductive rate of a population in ideal conditions. ERT-3.B.4: Many species have reproductive strategies that are not uniquely r-selected or K-selected, or they change in different conditions at different times. ERT-3.B.5: K-selected species are typically more adversely affected by invasive species. Most invasive species are r-selected species. Topic 3.3: Survivorship Curves ERT-3-C: Explain survivorship curves. ERT-3.C.1: A survivorship curve is a line that displays the relative survival rates of a cohort - a group of individuals of the same age - in a population, from birth to the maximum age reached by any one cohort member. There are Type I, Type II, and Type III curves. Survivorship curves differ from K-selected and r-selected species, with K-selected species typically following a Type I or Type II curve and r-selected species following a Type III curve. Topic 3.4: Carrying Capacity ERT-3.D: Describe carrying capacity. ERT-3.D.1: When a population exceeds its carrying capacity (carrying capacity can be denoted as K), overshoot occurs. There are environmental impacts of population overshoot, including resource depletion. ERT-3.E: Describe the impact of carrying capacity on ecosystems. ERT-3.E.1: A major ecological effect of population overshoot is dieback of the population (often severe to catastrophic) because the lack of available resources leads to famine, disease, and/or conflict. Topic 3.5: Population Growth and Resource Availability ERT-3.F: Explain how resource availability affects population growth. ERT-3.F.1: Population growth is limited by environmental factors, especially by the available resources and space. ERT-3.F.2: Resource availability and the total resource base are limited and finite over all scales of time. ERT-3.F.3: When the resources needed by a population for growth are abundant, population growth usually accelerates. ERt-3.F.5: When the resource base of the population shrinks, the increased potential for unequal distribution of resources will ultimately result in increased mortality, decreased fecundity, or both, resulting in population growth declining to, or below, carrying capacity. Topic 3.6: Age Structure Diagrams EIN-1.A: Explain age structure diagrams. EIN-1.A.1: Population growth rates can be interpreted from age structure diagrams by the shape of the structure. EIN-1.A.2: A rapidly growing population will, as a rule, have a higher proportion of younger people compared to stable or declining populations. Topic 3.7: Total Fertility Rate EIN-1.B: Explain factors that affect total fertility rate in human populations. EIN-1.B.1: Total fertility rate (TFR) is affected by the age at which females have their first child, educational opportunities for females, access to family planing, and government acts and policies. EIN-1.B.2: If fertility rate is at replacement levels, a population is considered relatively stable. EIN-1.B.3: Factors associated with infant mortality rates include whether mothers have access to good healthcare and nutrition. Changes in these factors can lead to changes in infant mortality rates over time. Topic 3.8: Human Population Dynamics EIN-1.C: Explain how human populations experience growth and decline. EIN-1.C.1: Birth rates, infant mortality rates, and overall death rates, access to family planning, access to good nutrition, access to education, and postponement of marriage all affect whether a human population is growing or declining. EIN-1.C.2: Factors limiting global human population include the Earth’s carrying capacity and the basic factors that limit human population growth as set forth by Malthusian theory. EIN-1.C.3: Population growth can be affected by both density-independent factors, such as major storms, fires, heat waves, or droughts, and density-dependent factors, such as access to clean water and air, fod availability, disease transmission, or territory size. EIN-1.C.4: The rule of 70 states that dividing the number 70 by the percentage population’s doubling time. Topic 3.9: Demographic Transition EIN-1.D: Define the demographic transition. EIN-1.D.1: The demographic transition refers to the transition from high to lower birth and death rates in a country or region as development occurs and that country moves from a pre-industrial to an industrialized economic system. This transition is typically demonstrated through a four-stage demographic transition model (DTM). EIN-1.D.2: Characteristics of developing countries include higher infant mortality rates and more children in the workforce than developed countries.

Earth Systems and Resources

UNIT TITLE: Unit 4 - Earth Systems and Resources
NYS Standards:
College Board Standards (CORE CONTENT: Pages 75-88)
Guiding Questions/Essential Questions/AP College Board Enduring Understanding:
ERT-4: Earth’s systems interact, resulting in a state of balance over time. ENG-2: Most of the Earth’s atmospheric processes are driven by input of energy from the sun.
Unit Topics with Learning Objectives:
Topic 4.1: Plate Tectonics ERT-4.A: Describe the geological changes and events that occur at convergent, divergent, and transform plate boundaries. ERT-4.A.1: Convergent boundaries can result in the creation of mountains, island arcs, earthquakes, and volcanoes. ERT-4.A.2: Divergent boundaries can result in seafloor spreading, rift valleys, volcanoes, and earthquakes. ERT-4.A.3: Transform boundaries can result in earthquakes. ERT-4.A.4: Maps that show the global distribution of plate boundaries can be used to determine the location of volcanoes, island arcs, earthquakes, hot spots, and faults. ERT-4.A.5: An earthquake occurs when stress overcomes a locked fault, releasing stored energy. Topic 4.2: Soil Formation and Erosion ERT-4.B: Describe the characteristics and formation of soil. ERT-4.B.1: Soils are formed when parent material is weathered, transported, and deposited. ERT-4.B.2: Soils are generally categorized by horizons based on their composition and organic material. ERT-4.B.3: Soils can be eroded by winds or water. Protecting solid can protect water quality as soils effectively filter and clean water that moves through them. Topic 4.3: Soil Composition and Properties ERT-4.C: Describe similarities and differences between properties of different solid types. ERT-4.C.1: Water holding capacity - the total amount of water soil can hold - varies with different solid types. Water retention contributes to land productivity and fertility of soils. ERT-4.C.2: The particle size and composition of each soil horizon cna affect the porosity. Permeability, and fertility of the soil. ERT-4.C.3: There are a variety of methods to test the chemical, physical, and biological properties of soil that can aid in a variety of decisions, such as irrigation and fertilizer requirements. ERT-4.C.4: A soil texture triangle is a diagram that allows for the identification and comparison of soil types based on their percentage of clay, silt, and sand. Topic 4.4: Earth’s Atmosphere ERT-4.D: Describe the structure and composition of the Earth’s Atmosphere. ERT-4.D.1: The atmosphere is made up of major gasses, each with its own relative abundance. ERT-4.D.2: The layers of the atmosphere are based on temperature gradients and include the troposphere, stratosphere, mesosphere, thermosphere, and exosphere. Topic 4.5: Global Wind Patterns ERT-4.E: Explain how environmental factors can result in atmospheric circulation. ERT-4.E.1: Global wind patterns primarily result from the most intense solar radiation arriving at the equator, resulting in density differences and the Coriolis effect. Topic 4.6: Watersheds ERT-4.F: Describe the characteristics of a watershed. ERT-4.F.1: Characteristics of a given watershed include its area, length, slope, soil, vegetation types, and divides with adjoining watersheds. Topic 4.7: Solar Radiation and Earth’s Seasons ENG-2.A: Explain how the sun’s energy affects the Earth’s surface. ENG-2.A.1: Incoming solar radiation (insolation) is the Earth’s main source of energy and is dependent on season and latitude. ENG-2.A.2: The angle of the sun’s rays determines the intensity of solar radiation. Due to the shape of the Earth, the latitude that is directly horizontal to the solar radiation receives the most intensity. ENG-2.A.3: The highest solar radiation per unit area is received at the equator and decreases toward the poles. ENG-2.A.4: The solar radiation received at a location on the Earth’s surface varies seasonally, with the most radiation received during the location’s longest summer day and the least on the shortest winter day. ENG-2.A.5: The tilt of Earth’s axis of rotation causes the Earth’s season and the number of hours of daylight in a particular location on the Earth’s surface. Topic 4.8: Earth’s Geography and Climate ENG-2.B: Describe how the Earth’s geography affects weather and climate. ENG-2.B.1: Weather and climate are affected not only by the sun’s energy but by geologic and geographic factors, such as mountains and ocean temperatures. ENG-2.B.2: A rain shadow is a region of land that has become drier because a higher elevation area blocks precipitation from reaching the land. Topic 4.9: El Nino and La Nina ENG-2.C: Describe the environmental changes and effects that result from El Nino or La Nina events (ENSO - El Nino Southern Oscillation). ENG-2.C.1: El Nino and La Nina are phenomena associated with changing ocean surface temperatures in the Pacific Ocean. These phenomena can cause global changes to rainfall, wind, and ocean circulation patterns. ENG-2.C.2: El Nino and La Nina are influenced by geological and geographic factors and can affect different locations in different ways.

Land and Water Use

UNIT TITLE: Unit 5 - Land and Water Use
NYS Standards:
College Board Standards (CORE CONTENT: Pages 89-113)
Guiding Questions/Essential Questions/AP College Board Enduring Understanding:
EIN-2: When humans use natural resources, they alter natural systems. STB-1: Humans can mitigate their impact on land and water resources through sustainable use.
Unit Topics with Learning Objectives:
Topic 5.1: The Tragedy of the Commons EIN-2.A: Explain the concept of the tragedy of the commons. EIN-2.A.1: The tragedy of the commons suggests that individuals will use shared resources in their own self-interest rather than in keeping with the common good, thereby depleting the resources. Topic 5.2: Clearcutting EIN-2.B: Describe the effect of clearcutting on forests. EIN-2.B.1: Clearcutting can be economically advantageous but leads to soil erosion, increased soil and stream temperatures, and flooding. EIN-2.B.2: Forests contain trees that absorb pollutants and store carbon dioxide. The cutting and burning of trees releases carbon dioxide and contributes to climate change. Topic 5.3: The Green Revolution EIN-2.C: Describe changes in agricultural practices. EIN-2.C.1: The Green Revolution started a shift to new agricultural strategies and practices in order to increase food production, with both positive and negative results. Some of these strategies and methods are mechanization, genetically modified organisms (GMOs), fertilization, irrigation, and the use of pesticides. EIN-2.C.2:Mechanization of farming can increase profits and efficiency for farms. It can also increase reliance on fossil fuels. Topic 5.4: Impact of Agricultural Practices EIN-2.D: Describe agricultural practices that cause environmental damage. LOR-2.D.1: Agricultural practices that can cause environmental damage include tilling, slash-and-burn farming, and the use of fertilizers. Topic 5.5: Irrigation Methods EIN-2.E: Describe different methods of irrigation. EIN-2.E.1: The largest human use of freshwater is for irrigation (70%). EIN-2.E.2: Types of irrigation include drip irrigation, flood irrigation, furrow irrigation, and spray irrigation. EIN-2.F: Describe the benefits and drawbacks of different methods of irrigation. EIN-2.F.1: Waterlogging occurs when too much water is left to sit in the soil, which raises the water table of ground water and inhibits plants’ ability to absorb oxygen through their roots. EIN-2.F.2: Furrow irrigation involves cutting furrows between crop rows and filling them with water. This system is inexpensive, but about ⅓ of the water is lost to evaporation and runoff. EIN-2.F.3: Flood irrigation involves flooding an agricultural field with water. This system sees about 20% of the water lost to evaporation and runoff. THis can also lead to waterlogging of the soil. EIN-2.F.4: Spray irrigation involves pumping groundwater into spray nozzles across an agricultural field. This system is more efficient than flood and furrow irrigation, with ¼ or less of the water lost to evaporation or runoff. However, spray systems are more expensive than flood and furrow irrigation, and also require energy to run. EIN-2.F.5: Drip irrigation uses perforated hoses to release small amounts of water to plant roots. This system is the most efficient, with only about 5% water lost to evaporation and runoff. However, this system is expensive and so is not often used. EIN-2.F.6: Salinization occurs when the salts in groundwater remain in the soil after the water evaporates. Over time, salinization can make soil toxic to plants. EIN-2.F.7: Aquifers can be severely depleted if overused for agricultural irrigation, as has happened to the Ogallala Aquifer in the central United States. Topic 5.6: Pest Control Methods EIN-2.G: Describe the benefits and drawbacks of different methods of pest control. EIN-2.G.1: One consequence of using common pest-control methods such as pesticides, herbicides, fungicides, rodenticides, and insecticides is that organisms can become resistant to them through artificial selection. Pest control decreases crop damage by pests and increase crop yield. EIN-2.G.2: Crops can be genetically engineered to increase their resistance to pests and diseases. However, using genetically engineered crops in planting or other ways can lead to loss of genetic diversity of that particular crop. Topic 5.7: Meat Production Methods EIN-2.H: Identify different methods of meat production. EIN-2.H.1: Methods of meat production include concentrated animal feeding operations (CAFOs), also called feedlots, and free-range grazing. EIN-2.I: Describe the benefits and drawbacks of different methods of meat production. EIN-2.I.1: Meat production is less efficient than agriculture; it takes approximately 20 times more land to produce the same amount of calories from meat as it does plants. EIN-2.I.2: Concentrated animal feeding operations (CAFOs) are used as a way to quickly get livestock ready for slaughter. They tend to be crowded, and animals are fed grains or feed that are not as suitable as grass. Additionally, feedlots generate a large amount of organic waste, which can contaminate ground and surface water. The use of feedlots are less expensive than other methods, which can keep costs to consumers down. EIN-2.I.3: Free range grazing allowed animals to graze on grass during their entire lifecycle. Meat from free range animals tends to be free from antibiotics and other chemicals used in feedlots. Organic waste from these animals acts as fertilizer. Free range grazing requires large areas of land and the meat produced is more expensive for consumers. EIN-2.I.4: Overgrazing occurs when too many animals feed on a particular area of land. Overgrazing causes loss of vegetation, which leads to soil erosion. EIN-2.I.5: Overgrazing can cause desertification. Desertification is the degradation of low precipitation regions toward being increasingly arid until they become deserts. EIN-2.I.6: Less consumption of meat could reduce CO2, methane, and N2O emissions; conserve water; reduce the use of antibiotics and growth hormones; and improve topsoil. Topic 5.8: Impacts of Overfishing EIN-2.J: Describe causes of and problems related to overfishing. EIN-2.J.1: Overfishing has led to the extreme scarcity of some fish species, which can lessen biodiversity in aquatic systems and harm people who depend on fishing for food and commerce. Topic 5.9: Impacts of Mining EIN-2.K: Describe natural resource extraction through mining. EIN-2.K.1: As the more accessible ores are mined to depletion, mining operations are forced to access lower grade ores. Accessing these ores requires increased use of resources that can cause increased waste and pollution. EIN-2.K.2: Surface mining is the removal of large portions of soil and rock, called overburden, in order to access the ore underneath. An example is strip mining, which removed the vegetation from an area, making the area more susceptible to erosion. EIN-2.L: Describe ecological and economic impacts of natural resource extraction through mining. EIN-2.L.1:Mining wastes include the soil and rocks that are moved to gain access to the ore and the waste, called slag and tailings that remain when the minerals have been removed from the ore. Mining helps to provide low cost energy and material can destroy habitats, contaminate groundwater, and release dust particles and methane. EIN-2.L.2:As coal reserves get smaller, due to a lack of easily accessible reserves, it becomes necessary to access coal through subsurface mining, which is very expensive. Topic 5.10: Impacts of Urbanization EIN-2.M: Describe the effects of urbanization on the environment. EIN-2.M.1: Urbanization can lead to depletion of resources and saltwater intrusion in the hydrologic cycle. EIN-2.M.2: Urbanization, though the burning of fossil fuels and landfills, affects the carbon cycle by increasing the amount of carbon dioxide in the atmosphere. EIN-2.M.3: Impervious surfaces are human-made structures - such as roads, buildings, sidewalks, and parking lots - that do not allow water to reach the soil, leading to flooding. EIN-2.M.4: Urban sprawl is the change in population distribution from high population density to low population density suburbs that spread into rural lands, leading to potential environmental problems. Topic 5.11: Ecological Footprints EIN-2.N: Explain the variables measured in an ecological footprint. EIN-2.N.1: Ecological footprints compare resource demands and waste production required for an individual or a society. Topic 5.12: Introduction to Sustainability STB-1.A: Explain the concept of sustainability. STB-1.A.1: Sustainability refers to humans living on Earth and their use of resources without depletion of the resources for future generations. Environmental indicators that can guide humans to sustainability include biological diversity, food production, average global surface temperature and CO2 concentrations, human population, and resource depletion. STB-1.A.2: Sustainable yield is the amount of a renewable resource that can be taken without reducing the available supply. Topic 5.13: Methods to Reduce Urban Runoff STB-1.B: Describe methods for mitigating problems related to urban runoff. STB-1.B.1: Methods to increase water infiltration include replacing traditional pavement with permeable pavement, planting trees, increased use of public transportation, and building up, not out. Topic 5.14: Integrated Pest Management STB-1.C: Describe integrated pest management. STB-1.C.1: Integrated pest management (IPM) is a combination of methods used to effectively control pest species while minimizing the distribution to the environment. These methods include biological, physical, and limited chemical methods such as biocontrol, intercropping, crop rotation, and natural predators of the pests. STB-1.D: Describe the benefits and drawbacks of integrated pest management (IPM). STB-1.D.1: The use of integrated pest management (IPM) reduced the risk that pesticides pose to wildlife, water supplies, and human health. STB-1.D.2: Integrated pest management (IPM) minimizes distributions to the environment and threats to human health but can be complex and expensive. Topic 5.15: Sustainable Agriculture STB-1.E: Describe sustainable agricultural and food production practices. STB-1.E.1: The goal of soil conservation is to prevent soil erosion. Different methods of soil conservation include contour plowing, windbreaks, perennial crops, terracing, no-till agriculture, and strip cropping. STB-1.E.2: Strategies to improve soil fertility include crop rotation and the addition of green manure and limestone. STB-1.E.3: Rotational grazing is the regular rotation of livestock between different pastures in order to avoid overgrazing in a particular area. Topic 5.16: Aquaculture STB-1.F: Describe the benefits and drawbacks and aquaculture. STB-1.F.1: Aquaculture has expanded because it is highly efficient, requires only small areas of water, and requires little fuel. STB-1.F.2: Aquaculture can contaminate wastewater, and fish that escape may compete or breed with wild fish. The density of fish in aquaculture can lead to increase in disease incidences, which can be transmitted to wild fish. Topic 5.17: Sustainable Forestry STB-1.G: Describe methods for mitigating human impact on forests. STB-1.G.1: Some of the methods for mitigating deforestation include reforestation, using and buying wood harvested by ecologically sustainable forestry techniques, and reusing wood. STB-1.G.2: Methods to protect forests from pathogens and insects include integrated pest management (IPM) and the removal of affected trees. STB-1.G.3: Prescribed burn is a method by which forests are set on fire under controlled conditions in order to reduce the occurrence of natural fires.

Energy Resources and Consumption

UNIT TITLE: Unit 6 - Energy Resources and Consumption
NYS Standards:
College Board Standards (CORE CONTENT: Pages 115-133)
Guiding Questions/Essential Questions/AP College Board Enduring Understanding:
ENG-3: Humans use energy from a variety of sources, resulting in positive and negative consequences.
Unit Topics with Learning Objectives:
Topic 6.1: Renewable and Nonrenewable Resources ENG-3.A: Identify differences between nonrenewable and renewable energy sources. ENG-3.A.1: Nonrenewable energy sources are those that exist in a fixed amount and involve energy transformation that cannot be easily replaced. ENG-3.A.2: Renewable energy sources are those that can be replenished naturally, at or near the rate of consumption, asn reused. Topic 6.2: Global Energy Consumption ENG-3.B: Describe trends in energy consumption. ENG-3.B.1: The use of energy resources is not evenly distributed between developed and developing countries. ENG-3.B.2: The most widely used sources of energy globally are fossil fuels. ENG-3.B.3: As developing countries become more developed, their reliance on fossil fuels for energy increases. ENG-3.B.4: As the world becomes more industrialized, the demand for energy increases. ENG-3.B.5: Availability, price, and governmental regulations influence which energy sources people use and how they use them. Topic 6.3: Fuel Types and Uses ENG-3.C: Identify types of fuels and their uses. ENG-3.C.1: Wood is commonly used as fuel in the forms of firewood and charcoal. It is often used in developing countries because it is easily accessible. ENG-3.C.2: Peat is partially decomposed organic material that can be burned for fuel. ENG-3.C.3: Three types of coal used for fuel are lignite, bituminous, and anthracite. Heat, pressure, and depth of burial contribute to the development of various coal types and their qualities. ENG-3.C.4: Natural gas, the cleanest of the fossil fuels, is mostly methane. ENG-3.C.5: Crude oil can be recovered from tar sands, which are a combination of clay, sand , water, and bitumen. ENG-3.C.6: Fossil fuels can be made into specific fuel types for specialized uses (e.g. in motor vehicles). ENG-3.C.7: Cogeneration occurs when a fuel source is used to generate both useful heat and electricity. Topic 6.4: Distribution ofNatural Energy Resources ENG-3.D: Identify where natural energy resources occur. ENG-3.D.1: The global distribution of natural energy resources, such as ores, coal, crude oil, and gas, is not uniform and depends on regions’ geologic history. Topic 6.5: Fossil Fuels ENG-3.E: Describe the use and methods of fossil fuels in power generation. ENG-3.E.1: The combustion of fossil fuels is a chemical reaction between the fuel and oxygen that yields carbon dioxide and water and releases energy. ENG-3.E.2: Energy from fossil fuels is produced by burning those fuels to generate heat, which then turns water into steam. That stream turns a turbine, which generates electricity. ENG-3.E.3: Humans use a variety of methods to extract fossil fuels from the earth for energy generation. ENG-3.F: Describe the effects of fossil fuels on the environment. ENG-3.F.1: Hydrological fracturing (fracking) can cause groundwater contamination and the release of volatile organic compounds. Topic 6.6: Nuclear Power ENG-3.G: Describe the use of nuclear energy in power generation. ENG-3.G.1: Nuclear power is generated through fission, where atoms of Uranium,-235, which are stored in fuel rods, are split into smaller parts after being struck by a neutron. Nuclear fission releases a large amount of heat, which is used to generates electricity. ENG-3.G.2: Radioactivity occurs when the nucleus of a radioactive isotopes loses energy by emitting radiation. ENG-3.G.3: Uranium-235 remains radioactive for a long time, which leads to the problems associated with the disposal of nuclear waste. ENG-3.G.4: Nuclear power generation is a nonrenewable energy source. Nuclear power is considered a cleaner energy source because it does not produce air pollutants, but it does release thermal pollution and hazardous solid waste. ENG-3.H: Describe the effects of the use of nuclear energy in the environment. ENG-3.H.1: Three mile island, Chernobyl, and Fukushima are three cases where accidents or natural disasters led to the release of radiation. These releases have had short-and long-term impacts on the environment. ENG-3.H.2: A radioactive element’s half-life can be used to calculate a variety of things, including the rate of decay and the radioactivity level at specific points in time. Topic 6.7: Energy from Biomass ENG-3.I: Describe the effects of the use of biomass in power generation on the environment. ENG-3.I.1: Burning of biomass produces heat for energy at a relatively low cost, but it also produces carbon dioxide, carbon monoxide, nitrogen oxides, particulates, and volatile organic compounds. The overharvesting of trees for fuel also causes deforestation. ENG-3.I.2: Ethanol can be used as a substitute for gasoline. Burning ethanol does not introduce additional carbon into the atmosphere via combustion, but the energy return on energy investment for ethanol is low. Topic 6.8: Solar Energy ENG-3.J: Describe the use of solar energy in power generation. ENG-3.J.1: Photovoltaic solar cells capture light energy from the sun and transform it directly into electrical energy. Their use is limited by the availability of sunlight. ENG-3.J.2: Active solar energy systems use solar energy to heat a liquid through mechanical and electric equipment to collect and store the energy captured from the sun. ENG-3.J.3: Passive solar energy systems absorb heat directly from the sun without the use of mechanical and electric equipment, and energy cannot be collected or stored. ENG-3.K: Describe the effects of the use of solar energy in power generation on the environment. ENG-3.K.1: Solar energy systems have low environmental impact and produce clean energy, but they can be expensive. Large solar energy farms may negatively impact desert ecosystems. Topic 6.9: Hydroelectric Power ENG-3.L: Describe the use of hydroelectricity in power generation. ENG-3.L.1: Hydroelectric power can be generated in generation. several ways. Dams built across rivers collect water in reservoirs. The moving water can be used to spin a turbine. Turbines can also be placed in small rivers, where the flowing water spins the turbine. ENG-3.L.2: Tidal energy uses the energy produced by tidal flows to turn a turbine. ENG-3.M: Describe the effects of the use of hydroelectricity in power generation on the environment. ENG-3.M.1: Hydroelectric power does not generate air pollution or waste, but construction of the power plants can be expensive, and there may be a loss of or change in habitats following the construction of dams. Topic 6.10: Geothermal Energy ENG-3.N: Describe the use of geothermal energy in power generation. ENG-3.N.1: Geothermal energy is obtained by using the heat stored in the Earth’s interior to heat up water, which is brought back to the surface as steam. The steam is used to drive an electric generator. ENG-3-O: Describe the effects of the use of geothermal energy in power generation on the environment. ENG-3-O.1: The cost of accessing geothermal energy can be prohibitively expensive, as is not easily accessible in many parts of the world. In addition, it can cause the release of hydrogen sulfide. Topic 6.11: Hydrogen Fuel Cell ENG-3.P: Describe the use of hydrogen fuel cells in power generation. ENG-3.P.1: Hydrogen fuel cells are an alternate to non renewable fuel sources. They use hydrogen as fuel, combining the hydrogen and oxygen in the air to form water and release energy (electricity) in the process. Water is the product (emission) of a fuel cell. ENG-3.Q: Describe the effects of the use of hydrogen fuel cells in power generation on the environment. ENG-3.Q.1: Hydrogen fuel cells have low environmental impact and produce no carbon dioxide when the hydrogen is produced from water. However, the technology is expensive and energy is still needed to create the hydrogen gas used in the fuel cell. Topic 6.12: Wind Energy ENG-3.R: Describe the use of wind energy in power generation. ENG-3.R.1: Wind turbines use the kinetic energy of moving air to spin a turbine, which in turn converts the mechanical energy of the turbine into electricity. ENG-3.S: Describe the effects of the use of wind energy in power generation on the environment. ENG-3.S.1: Wind energy is a renewable, clean source of energy. However, birds and bats may be killed if they fly into the spinning turbine blades. Topic 6.13: Energy Conservation ENG-3.T: Describe methods for conserving energy. ENG-3.T.1: Some of the methods for conserving energy around a home include adjusting the thermostat to reduce the use of heat and air conditioning, conserving water, use of energy-efficient appliances, and conservation landscaping. ENG-3.T.2: Some of the methods for conserving energy around a home include adjusting the thermostat to reduce the use of heat and air conditioning, conserving water, use of energy-efficient appliances, and conservation landscaping.

Atmospheric Pollution

UNIT TITLE: Unit 7 - Atmospheric Pollution
NYS Standards:
College Board Standards (CORE CONTENT: Pages 135-149)
Guiding Questions/Essential Questions/AP College Board Enduring Understanding:
STB-2: Human activities have physical, chemical, and biological consequences for the atmosphere.
Unit Topics with Learning Objectives:
Topic 7.1: Introduction to Air Pollution STB-2.A: Identify the sources and effects of air pollutants. STB-2.A.1: Coal combustion releases air pollutants including carbon dioxide, sulfur dioxide, toxic metals, and particulates. STB-2.A.2: The combustion of fossil fuels releases nitrogen oxides into the atmosphere. They lead to the production of ozone, formation of photochemical smog, and convert to nitric acid in the atmosphere, causing acid rain. Other pollutants produced by fossil fuel combustion include carbon monoxide, hydrocarbons, and particulate matter. STB-2.A.3: Air quality can be affected through the release of sulfur dioxide during the burning of fossil fuels, mainly diesel fuels. STB-2.A.4: Through the Clean Air Act, the Environmental Protection Agency (EPA) regulated the use of lead, particularly in fuels, which dramatically decreased the amount of lead in the atmosphere. STB-2.A.5: Air pollutants can be primary or secondary pollutants. Topic 7.2: Photochemical Smog STB-2.B: Explain the causes and effects of photochemical smog and methods to reduce it. STB-2.B.1: Photochemical smog is formed when nitrogen oxides and volatile organic hydrocarbons react with heat and sunlight to produce a variety of pollutants. STB-2.B.2: Many environmental factors affect the formation of photochemical smog. STB-2.B.3: Nitrogen oxide is produced early in the day. Ozone concentrations peak in the afternoon and are higher in the summer because ozone is produced by chemical reactions between oxygen and sunlight. STB-2.B.4: Volatile Organic Compounds (VOCs), such as formaldehyde and gasoline, evaporate or sublimate at room temperature. Trees are a natural source of VOCs. STB-2.B.5: Photochemical smog often forms in urban areas because of the large number of motor vehicles there. STB-2.B.6: Photochemical smog can be reduced through the reduction of nitrogen oxide and VOCs. STB-2.B.7: Photochemical smog can harm human health in several ways, including causing respiratory problems and eye irritation. Topic 7.3: Thermal Inversion STB-2.C: Describe thermal inversion and its relationship with pollution. STB-2.C.1: During a thermal inversion, the normal temperature gradient in the atmosphere is altered as the air temperature at the Earth’s surface is cooler than the air at higher altitudes. STB-2.C.2: Thermal inversion traps pollution close to the ground, especially smog and particulates. Topic 7.4: Atmospheric CO2 and Particulates STB-2.D: Describe natural sources of CO2 and particulates. STB-2.D.1: CO2 appears naturally in the atmosphere from sources such as respiration, decomposition, and volcanic eruptions. STB-2.D.2: There are a variety of natural sources of particulate matter. Topic 7.5: Indoor Air Pollutants STB-2.E: Identify indoor air pollutants. STB-2.E.1: Carbon monoxide is an indoor air pollutant that is classified as an asphyxiant. STB-2.E.2: Indoor air pollutants that are classified as particulates include asbestos, dust, and smoke. STB-2.E.3: Indoor air pollutants can come from natural sources, human-made sources, and combustion. STB-2.E.4: Common natural source indoor air pollutants include radon, mold, and dust. STB-2.E.5: Common human-made indoor air pollutants include insulation, Volatile Organic Compounds (VOCs) from furniture, paneling and carpets; formaldehyde from building materials, furniture, upholstery, and carpeting; and lead from paints. STB-2.E.6: Common combustion air pollutants include carbon monoxide, nitrogen oxides, sulfur dioxide, particulates, and tobacco smoke. STB-2.E.7: Radon-222 is a naturally occurring radioactive gas that is produced by the decay of uranium found in some rocks and soils. STB-2.F: Describe the effects of indoor air pollutants. STB-2.F.1: Radon gas can infiltrate homes as it moves up through the soil and enters homes via the basement or cracks in the walls or foundation. It is also dissolved in groundwater that enters homes through a well. STB-2.F.2: Exposure to radon gas can lead to radon induced lung cancer, which is the second leading cause of lung cancer in America. Topic 7.6: Reduction of Air Pollutants STB-2.G: Explain how air pollutants can be reduced at the source. STB-2.G.1: Methods to reduce air pollutants include regulatory practices, conservation practices, and alternative fuels. STB-2.G.2: A vapor recovery nozzle is an air pollution control device on a gasoline pump that prevents fumes from escaping into the atmosphere when fueling a motor vehicle. STB-2.G.3: A catalytic converter is an air pollution control device for internal combustion engines that converts pollutants (CO, NOx, and hydrocarbons) in exhaust into less harmful molecules (CO2 , N2 , O2 , and H2O). STB-2.G.4: Wet and dry scrubbers are air pollution control devices that remove particulates and/or gases from industrial exhaust streams. STB-2.G.5: Methods to reduce air pollution from coal burning power plants include scrubbers and electrostatic precipitators. Topic 7.7: Acid Rain STB-2.H: Describe acid deposition. STB-2.H.1: Acid rain and deposition is due to nitrogen oxides and sulfur oxides from anthropogenic and natural sources in the atmosphere. STB-2.H.2: Nitric oxides that cause acid deposition come from motor vehicles and coal-burning power plants. Sulfur dioxides that cause acid deposition come from coal-burning power plants. STB-2.I: Describe the effects of acid deposition on the environment. STB-2.I.1: Acid deposition mainly affects communities that are downwind from coal-burning power plants. STB-2.I.2: Acid rain and deposition can lead to the acidification of soils and bodies of water and corrosion of human-made structures. STB-2.I.3: Regional differences in soils and bedrock affect the impact that acid deposition has on the region—such as limestone bedrock’s ability to neutralize the effect of acid rain on lakes and ponds. Topic 7.8: Noise Pollution STB-2.J: Describe human activities that result in noise pollution and its effects. STB-2.J.1: Noise pollution is sound at levels high enough to cause physiological stress and hearing loss. STB-2.J.2: Sources of noise pollution in urban areas include transportation, construction, and domestic and industrial activity. STB-2.J.3: Some effects of noise pollution on animals in ecological systems include stress, the masking of sounds used to communicate or hunt, damaged hearing, and causing changes to migratory routes.

Aquatic and Terrestrial Pollution

UNIT TITLE: Unit 8 - Aquatic and Terrestrial Pollution
NYS Standards:
College Board Standards (CORE CONTENT: Pages 151-175)
Guiding Questions/Essential Questions/AP College Board Enduring Understanding:
STB-3: Human activities, including the use of resources, have physical, chemical and biological consequences for ecosystems. EIN-3: Pollutants can have both direct and indirect impacts on the health of organisms, including humans.
Unit Topics with Learning Objectives:
Topic 8.1: Sources of Pollution STB-3.A: Identify differences between point and nonpoint sources of pollution. STB-3.A.1: A point source refers to a single, identifiable source of a pollutant, such as a smokestack or waste discharge pipe. STB-3.A.2: Nonpoint sources of pollution are diffused and can therefore be difficult to identify, such as pesticide spraying or urban runoff. Topic 8.2: Human Impacts on Ecosystems STB-3.B: Describe the impacts of human activities on aquatic ecosystems. STB-3.B.1: Organisms have a range of tolerance for various pollutants. Organisms have an optimum range for each factor where they can maintain homeostasis. Outside of this range, organisms may experience physiological stress, limited growth, reduced reproduction, and in extreme cases, death. STB-3.B.2: Coral reefs have been suffering damage due to a variety of factors, including increasing ocean temperature, sediment runoff, and destructive fishing practices. STB-3.B.3: Oil spills in marine waters cause organisms to die from the hydrocarbons in oil. Oil that floats on the surface of water can coat the feathers of birds and fur of marine mammals. Some components of oil sink to the ocean floor, killing some bottom-dwelling organisms. STB-3.B.4: Oil that washes up on the beach can have economic consequences on the fishing and tourism industries. STB-3.B.5: Oceanic dead zones are areas of low oxygen in the world’s oceans caused by increased nutrient pollution. STB-3.B.6: An oxygen sag curve is a plot of dissolved oxygen levels versus the distance from a source of pollution, usually excess nutrients and biological refuse. STB-3.B.7: Heavy metals used for industry, especially mining and burning of fossil fuels, can reach the groundwater, impacting the drinking water supply. STB-3.B.8: Litter that reaches aquatic ecosystems, besides being unsightly, can create intestinal blockage and choking hazards for wildlife and introduce toxic substances to the food chain. STB-3.B.9: Increased sediment in waterways can reduce light infiltration, which can affect primary producers and visual predators. Sediment can also settle, disrupting habitats. STB-3.B.10: When elemental sources of mercury enter aquatic environments, bacteria in the water convert it to highly toxic methylmercury. Topic 8.3: Endocrine Disruptors STB-3.C: Describe endocrine disruptors. STB-3.C.1: Endocrine disruptors are chemicals that can interfere with the endocrine system of animals. STB-3.D: Describe the effects of endocrine disruptors on ecosystems. STB-3.D.1: Endocrine disruptors can lead to birth defects, developmental disorders, and gender imbalances in fish and other species. Topic 8.4: Human Impacts on Wetlands and Mangroves STB-3.E: Describe the impacts of human activity on wetlands and mangroves. STB-3.E.1: Wetlands are areas where water covers the soil, either part or all of the time. STB-3.E.2: Wetlands provide a variety of ecological services, including water purification, flood protection, water filtration, and habitat. STB-3.E.3: Threats to wetlands and mangroves include commercial development, dam construction, overfishing, and pollutants from agriculture and industrial waste. Topic 8.5: Eutrophication STB-3.F: Explain the environmental effects of excessive use of fertilizers and detergents on aquatic ecosystems. STB-3.F.1: Eutrophication occurs when a body of water is enriched in nutrients. STB-3.F.2: The increase in nutrients in eutrophic aquatic environments causes an algal bloom. When the algal bloom dies, microbes digest the algae, along with the oxygen in the water, leading to a decrease in the dissolved oxygen levels in the water. The lack of dissolved oxygen can result in large die-offs of fish and other aquatic organisms. STB-3.F.3: Hypoxic waterways are those bodies of water that are low in dissolved oxygen. STB-3.F.4: Compared to eutrophic waterways, oligotrophic waterways have very low amounts of nutrients, stable algae populations, and high dissolved oxygen. STB-3.F.5: Anthropogenic causes of eutrophication are agricultural runoff and wastewater release. Topic 8.6: Thermal Pollution STB-3.G: Describe the effects of thermal pollution on aquatic ecosystems. STB-3.G.1: Thermal pollution occurs when heat released into the water produces negative effects to the organisms in that ecosystem. STB-3.G.2: Variations in water temperature affect the concentration of dissolved oxygen because warm water does not contain as much oxygen as cold water. Topic 8.7: Persistent Organic Pollutants (POPs) STB-3.H: Describe the effect of persistent organic pollutants (POPs) on ecosystems. STB-3.H.1: Persistent organic pollutants (POPs) do not easily break down in the environment because they are synthetic, carbon-based molecules (such as DDT and PCBs). STB-3.H.2: Persistent organic pollutants (POPs) can be toxic to organisms because they are soluble in fat, which allows them to accumulate in organisms’ fatty tissues. STB-3.H.3: Persistent organic pollutants (POPs) can travel over long distances via wind and water before being redeposited. Topic 8.8: Bioaccumulation and Biomagnification STB-3.I: Describe bioaccumulation and biomagnification. STB-3.I.1: Bioaccumulation is the selective absorption and concentration of elements or compounds by cells in a living organism, most commonly fat-soluble compounds. STB-3.I.2: Biomagnification is the increase in concentration of substances per unit of body tissue that occurs in successively higher trophic levels of a food chain or in a food web. STB-3.J: Describe the effects of bioaccumulation and biomagnification. STB-3.J.1: Some effects that can occur in an ecosystem when a persistent substance is biomagnified in a food chain include eggshell thinning and developmental deformities in top carnivores of the higher trophic levels. STB-3.J.2: Humans also experience harmful effects from biomagnification, including issues with the reproductive, nervous, and circulatory systems. STB-3.J.3: DDT, mercury, and PCBs are substances that bioaccumulate and have significant environmental impacts. Topic 8.9: Solid Waste Disposal STB-3.K: Describe solid waste disposal methods. STB-3.K.1: Solid waste is any discarded material that is not a liquid or gas. It is generated in domestic, industrial, business, and agricultural sectors. STB-3.K.2: Solid waste is most often disposed of in landfills. Landfills can contaminate groundwater and release harmful gases. STB-3.K.3: Electronic waste, or e-waste, is composed of discarded electronic devices including televisions, cell phones, and computers. STB-3.K.4: A sanitary municipal landfill consists of a bottom liner (plastic or clay), a storm water collection system, a leachate collection system, a cap, and a methane collection system. STB-3.L: Describe the effects of solid waste disposal methods. STB-3.L.1: Factors in landfill decomposition include the composition of the trash and conditions needed for microbial decomposition of the waste. STB-3.L.2: Solid waste can also be disposed of through incineration, where waste is burned at high temperatures. This method significantly reduces the volume of solid waste but releases air pollutants. STB-3.L.3: Some items are not accepted in sanitary landfills and may be disposed of illegally, leading to environmental problems. One example is used rubber tires, which when left in piles can become breeding grounds for mosquitoes that can spread disease. STB-3.L.4: Some countries dispose of their waste by dumping it in the ocean. This practice, along with other sources of plastic, has led to large floating islands of trash in the oceans. Additionally, wildlife can become entangled in the waste, as well as ingest it. Topic 8.10: Waste Reduction Methods STB-3.M: Describe changes to current practices that could reduce the amount of generated waste and their associated benefits and drawbacks. STB-3.M.1: Recycling is a process by which certain solid waste materials are processed and converted into new products. STB-3.M.2: Recycling is one way to reduce the current global demand on minerals, but this process is energy-intensive and can be costly. STB-3.M.3: Composting is the process of organic matter such as food scraps, paper, and yard waste decomposing. The product of this decomposition can be used as fertilizer. Drawbacks to composting include odor and rodents. STB-3.M.4: E-waste can be reduced by recycling and reuse. E-wastes may contain hazardous chemicals, including heavy metals such as lead and mercury, which can leach from landfills into groundwater if they are not disposed of properly. STB-3.M.5: Landfill mitigation strategies range from burning waste for energy to restoring habitat on former landfills for use as parks. STB-3.M.6: The combustion of gases produced from decomposition of organic material in landfills can be used to turn turbines and generate electricity. This process reduces landfill volume. Topic 8.11: Sewage Treatment STB-3.N: Describe best practices in sewage treatment. STB-3.N.1: Primary treatment of sewage is the physical removal of large objects, often through the use of screens and grates, followed by the settling of solid waste in the bottom of a tank. STB-3.N.2: Secondary treatment is a biological process in which bacteria break down organic matter into carbon dioxide and inorganic sludge, which settles in the bottom of a tank. The tank is aerated to increase the rate at which the bacteria break down the organic matter. STB-3.N.3: Tertiary treatment is the use of ecological or chemical processes to remove any pollutants left in the water after primary and secondary treatment. STB-3.N.4: Prior to discharge, the treated water is exposed to one or more disinfectants (usually, chlorine, ozone, or UV light) to kill bacteria. Topic 8.12: Lethal Dose 50% (LD50) EIN-3.A: Define lethal dose 50% (LD50). EIN-3.A.1: Lethal dose 50% (LD50) is the dose of a chemical that is lethal to 50% of the population of a particular species. Topic 8.13: Dose Response Curve EIN-3.B: Evaluate dose response curves. EIN-3.B.1: A dose response curve describes the effect on an organism or mortality rate in a population based on the dose of a particular toxin or drug. Topic 8.14: Pollution and Human Health EIN-3.C: Identify sources of human health issues that are linked to pollution. EIN-3.C.1: It can be difficult to establish a cause and effect between pollutants and human health issues because humans experience exposure to a variety of chemicals and pollutants. EIN-3.C.2: Dysentery is caused by untreated sewage in streams and rivers. EIN-3.C.3: Mesothelioma is a type of cancer caused mainly by exposure to asbestos. EIN-3.C.4: Respiratory problems and overall lung function can be impacted by elevated levels of tropospheric ozone. Topic 8.15: Pathogens and Infectious Diseases EIN-3.D: Explain human pathogens and their cycling through the environment. EIN-3.D.1: Pathogens adapt to take advantage of new opportunities to infect and spread through human populations. EIN-3.D.2: Specific pathogens can occur in many environments regardless of the appearance of sanitary conditions. EIN-3.D.3: As equatorial-type climate zones spread north and south into what are currently subtropical and temperate climate zones, pathogens, infectious diseases, and any associated vectors are spreading into these areas where the disease has not previously been known to occur. EIN-3.D.4: Poverty-stricken, low-income areas often lack sanitary waste disposal and have contaminated drinking water supplies, leading to havens and opportunities for the spread of infectious diseases. EIN-3.D.5: Plague is a disease carried by organisms infected with the plague bacteria. It is transferred to humans via the bite of an infected organism or through contact with contaminated fluids or tissues. EIN-3.D.6: Tuberculosis is a bacterial infection that typically attacks the lungs. It is spread by breathing in the bacteria from the bodily fluids of an infected person. EIN-3.D.7: Malaria is a parasitic disease caused by bites from infected mosquitoes. It is most often found in sub-Saharan Africa. EIN-3.D.8: West Nile virus is transmitted to humans via bites from infected mosquitoes. EIN-3.D.9: Severe acute respiratory syndrome (SARS) is a form of pneumonia. It is transferred by inhaling or touching infected fluids. EIN-3.D.10: Middle East Respiratory Syndrome (MERS) is a viral respiratory illness that is transferred from animals to humans. EIN-3.D.11: Zika is a virus caused by bites from infected mosquitoes. It can be transmitted through sexual contact. EIN-3.D.12: Cholera is a bacterial disease that is contracted from infected water.

Global Change

NYS Standards: Unit 9 - Global Change
College Board Standards (CORE CONTENT: Pages 177-193)
Guiding Questions/Essential Questions/AP College Board Enduring Understanding:
STB-4: Local and regional human activities can have impacts at the global level. EIN-4: THe health of a species is closely tied to its ecosystem, and minor environmental changes can have a large impact.
Unit Topics with Learning Objectives:
Topic 9.1: Stratospheric Ozone Depletion STB-4.A: Explain the importance of stratospheric ozone to life on Earth. STB-4.A.1: The stratospheric ozone layer is important to the evolution of life on Earth and the continued health and survival of life on Earth. STB-4.A.2: Stratospheric ozone depletion is caused by anthropogenic factors, such as chlorofluorocarbons (CFCs), and natural factors, such as the melting of ice crystals in the atmosphere at the beginning of the Antarctic spring. STB-4.A.3: A decrease in stratospheric ozone increases the UV rays that reach the Earth’s surface. Exposure to UV rays can lead to skin cancer and cataracts in humans. Topic 9.2: Reducing Ozone Depletion STB-4.B: Describe chemicals used to substitute for chlorofluorocarbons (CFCs). STB-4.B.1: Ozone depletion can be mitigated by replacing ozone-depleting chemicals with substitutes that do not deplete the ozone layer. Hydrofluorocarbons (HFCs) are one such replacement, but some are strong greenhouse gases. Topic 9.3: The Greenhouse Effect STB-4.C: Identify the greenhouse gases. STB-4.C.1: The principal greenhouse gases are carbon dioxide, methane, water vapor, nitrous oxide, and chlorofluorocarbons (CFCs). STB-4.C.2: While water vapor is a greenhouse gas, it doesn’t contribute significantly to global climate change because it has a short residence time in the atmosphere. STB-4.C.3: The greenhouse effect results in the surface temperature necessary for life on Earth to exist. STB-4.D: Identify the sources and potency of the greenhouse gases. STB-4.D.1: Carbon dioxide, which has a global warming potential (GWP) of 1, is used as a reference point for the comparison of different greenhouse gases and their impacts on global climate change. Chlorofluorocarbons (CFCs) have the highest GWP, followed by nitrous oxide, then methane. Topic 9.4: Increases in the Greenhouse Gases STB-4.E: Identify the threats to human health and the environment posed by an increase in greenhouse gases. STB-4.E.1: Global climate change, caused by excess greenhouse gases in the atmosphere, can lead to a variety of environmental problems including rising sea levels resulting from melting ice sheets and ocean water expansion, and disease vectors spreading from the tropics toward the poles. These problems can lead to changes in population dynamics and population movements in response. Topic 9.5: Global Climate Change STB-4.F: Explain how changes in climate, both short- and long term, impact ecosystems. STB-4.F.1: The Earth has undergone climate change throughout geologic time, with major shifts in global temperatures causing periods of warming and cooling as recorded with CO2 data and ice cores. STB-4.F.2: Effects of climate change include rising temperatures, melting permafrost and sea ice, rising sea levels, and displacement of coastal populations. STB-4.F.3: Marine ecosystems are affected by changes in sea level, some positively, such as in newly created habitats on now-flooded continental shelves, and some negatively, such as deeper communities that may no longer be in the photic zone of seawater. STB-4.F.4: Winds generated by atmospheric circulation help transport heat throughout the Earth. Climate change may change circulation patterns, as temperature changes may impact Hadley cells and the jet stream. STB-4.F.5: Oceanic currents, or the ocean conveyor belt, carry heat throughout the world. When these currents change, it can have a big impact on global climate, especially in coastal regions. STB-4.F.6: Climate change can affect soil through changes in temperature and rainfall, which can impact soil’s viability and potentially increase erosion. STB-4.F.7: Earth’s polar regions are showing faster response times to global climate change because ice and snow in these regions reflect the most energy back out to space, leading to a positive feedback loop. STB-4.F.8: As the Earth warms, this ice and snow melts, meaning less solar energy is radiated back into space and instead is absorbed by the Earth’s surface. This in turn causes more warming of the polar regions. STB-4.F.9: Global climate change response time in the Arctic is due to positive feedback loops involving melting sea ice and thawing tundra, and the subsequent release of greenhouse gases like methane. STB-4.F.10: One consequence of the loss of ice and snow in polar regions is the effect on species that depend on the ice for habitat and food. Topic 9.6: Ocean Warming STB-4.G: Explain the causes and effects of ocean warming. STB-4.G.1: Ocean warming is caused by the increase in greenhouse gases in the atmosphere. STB-4.G.2: Ocean warming can affect marine species in a variety of ways, including loss of habitat, and metabolic and reproductive changes. STB-4.G.3: Ocean warming is causing coral bleaching, which occurs when the loss of algae within corals cause the corals to bleach white. Some corals recover and some die. Topic 9.7: Ocean Acidification STB-4.H: Explain the causes and effects of ocean acidification. STB-4.H.1: Ocean acidification is the decrease in pH of the oceans, primarily due to increased CO2 concentrations in the atmosphere, and can be expressed as chemical equations. STB-4.H.2: As more CO2 is released into the atmosphere, the oceans, which absorb a large part of that CO2 , become more acidic. STB-4.H.3: Anthropogenic activities that contribute to ocean acidification are those that lead to increased CO2 concentrations in the atmosphere: burning of fossil fuels, vehicle emissions, and deforestation. STB-4.H.4: Ocean acidification damages coral because acidification makes it difficult for them to form shells, due to the loss of calcium carbonate. Topic 9.8: Invasive Species EIN-4.A: Explain the environmental problems associated with invasive species and strategies to control them. EIN-4.A.1: Invasive species are species that can live, and sometimes thrive, outside of their normal habitat. Invasive species can sometimes be beneficial, but they are considered invasive when they threaten native species. EIN-4.A.2: Invasive species are often generalist, r-selected species and therefore may outcompete native species for resources. EIN-4.A.3: Invasive species can be controlled through a variety of human interventions. Topic 9.9: Endangered Species EIN-4.B: Explain how species become endangered and strategies to combat the problem. EIN-4.B.1: A variety of factors can lead to a species becoming threatened with extinction, such as being extensively hunted, having limited diet, being outcompeted by invasive species, or having specific and limited habitat requirements. EIN-4.B.2: Not all species will be in danger of extinction when exposed to the same changes in their ecosystem. Species that are able to adapt to changes in their environment or that are able to move to a new environment are less likely to face extinction. EIN-4.B.3: Selective pressures are any factors that change the behaviors and fitness of organisms within an environment. EIN-4.B.4: Species in a given ecosystem compete for resources like territory, food, mates, and habitat, and this competition may lead to endangerment or extinction. EIN-4.B.5: Strategies to protect animal populations include criminalizing poaching, protecting animal habitats, and legislation. Topic 9.10: Human Impacts on Biodiversity EIN-4.C: Explain how human activities affect biodiversity and strategies to combat the problem. EIN-4.C.1: HIPPCO (habitat destruction, invasive species, population growth, pollution, climate change, and over exploitation) describes the main factors leading to a decrease in biodiversity. EIN-4.C.2: Habitat fragmentation occurs when large habitats are broken into smaller, isolated areas. Causes of habitat fragmentation include the construction of roads and pipelines, clearing for agriculture or development, and logging. EIN-4.C.3: The scale of habitat fragmentation that has an adverse effect on the inhabitants of a given ecosystem will vary from species to species within that ecosystem. EIN-4.C.4: Global climate change can cause habitat loss via changes in temperature, precipitation, and sea level rise. EIN-4.C.5: Some organisms have been somewhat or completely domesticated and are now managed for economic returns, such as honeybee colonies and domestic livestock. This domestication can have a negative impact on the biodiversity of that organism. EIN-4.C.6: Some ways humans can mitigate the impact of loss of biodiversity include creating protected areas, use of habitat corridors, promoting sustainable land use practices, and restoring lost habitats.

AP Physics

COURSE TITLE: AP Physics C - Mechanics

COURSE DESCRIPTION: AP Physics at Fox Lane is a demanding course matching a college level study of Physics with emphasis on Mechanics using experimental and mathematical modeling including the use of differential and integral calculus. Here at Fox Lane, AP Physics students develop a deep understanding of the foundation principles of classical mechanics. In addition, they will apply these foundation principles to complex labs and other thoughtful hands-on and minds-on scenarios that combine multiple aspects of physics rather than present concepts in isolation. AP Physics has the demands expected in a college course; however, it is enveloped with the support you expect at Fox Lane: quality instruction aware of diverse learning styles, support in class and after school, and communication with students and their parents. Students will culminate their experience by sitting for the AP Physics C test in Mechanics and an in-school final exam in May.

Learn more about the course, the individual units and the exam.

MP1 Units:

MP2 Units:

MP3 Units:

MP4 Units:

Unit #1 Kinematics

Unit #2 Force and Translational Dynamics

Unit #3 Work/Energy/Powers

Unit #4 Linear Momentum

Unit #5 Torque and Rotational Dynamics

Unit #6 Energy and Momentum of Rotating Systems

Unit #7 Oscillations

Review and Preparation for AP Exam

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Question and answer sessions, both formal—planned and informal—spontaneous In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Methods of Summative Assessments: Projects (project phases submitted at various completion points could be formatively assessed) Unified Arts Folder / Portfolio Presentations Student evaluation / Conclusion Questions
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Applied Physics

COURSE TITLE: Applied Physics

COURSE DESCRIPTION: Students taking this course will develop an appreciation and understanding of physics and the scientific method by engaging in highly relevant problem-based learning. Units focus on a variety of topics including: the physics of driving, aerodynamics, and rocketry. Students will learn to solve problems using critical thinking skills they will need in the ‘real world’ beyond high school and they will come to recognize the benefits, as well as the limitations, of science and technology.

MP1 Units:

MP2 Units:

MP3 Units:

MP4 Units:

Measuring & Problem Solving

Catapults/Projectiles
Project Crash

Bridges

Grand Prix

Paper Planes
Rockets

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Question and answer sessions, both formal—planned and informal—spontaneous In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Methods of Summative Assessments: Projects (project phases submitted at various completion points could be formatively assessed) Unified Arts Folder / Portfolio Presentations Student evaluation / Conclusion Questions
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Measuring and Problem Solving

UNIT TITLE: Measuring and Problem Solving
NYS Standards:
NYS Science Learning Standards (Pages 58-63)
Guiding Questions/Essential Questions:
How do accurate measurements and effective problem-solving strategies contribute to our understanding of physical phenomena, and how can we apply these skills to predict and explain the behavior of systems in the real world? This question encourages students to: Reflect on the importance of measurement – recognizing that precision and accuracy in measurements are crucial to making reliable predictions and understanding the physical world. Develop problem-solving skills – understanding that physical problems often require not just knowledge of concepts, but also the ability to apply these concepts to real-world scenarios through reasoning, calculation, and critical thinking. Understand the connection between theory and practice – recognizing how measurements and problem-solving tools bridge the gap between theoretical models and the actual behavior of physical systems.
Unit Topics with Learning Objectives:
PHYSICS TOOLKIT State the fundamental SI units for time, length, and mass. Identify, use, and convert common metric prefixes. Recognize that all measured quantities have uncertainties. Distinguish between dependent and independent variables. Be able to graph data points. Understand how smooth curves drawn through data points represent the relationship between independent and dependent variables. Recognize linear and direct relationships and be able to find and interpret the slope of the curve. Show patience and persistence in problem solving. Measure weight and mass using a spring scale. Properly calibrate a spring scale. Recognize patterns in incomplete data.

Catapults/Projectiles

UNIT TITLE: Catapults/Projectiles
NYS Standards:
NYS Science Learning Standards (Pages 58-63)
Guiding Questions/Essential Questions:
How do the principles of projectile motion and the forces involved in launching a catapult help us predict the trajectory and behavior of objects in motion, and how can we optimize these factors to achieve desired outcomes? This question encourages students to: Explore the physics of projectile motion – understanding key concepts like velocity, acceleration, gravity, and angle of launch, and how these factors influence the path of an object. Investigate the forces involved – examining the role of tension, elasticity, and friction in the launching mechanism of a catapult and how these forces contribute to the object's motion. Apply mathematical models – using equations of motion (e.g., kinematic equations) to predict the range, height, and time of flight of projectiles based on various launch parameters. Consider optimization strategies – thinking critically about how to adjust variables (such as launch angle, force, and object mass) to optimize the performance of a catapult for specific goals (e.g., maximum distance, highest height, or precision targeting).
Unit Topics with Learning Objectives:
PROJECTILES Determine the angle that produces optimal horizontal displacement. Using only the materials specified, design and build a device to launch a cotton ball from a student desk and send it as far as possible in a specified direction. Improve their launcher to launch a cotton ball from a student desk and send it as accurately as possible towards a target.

Project CRASH

UNIT TITLE: Project CRASH
NYS Standards:
NYS Science Learning Standards (Pages 58-63)
Guiding Questions/Essential Questions:
How do the principles of momentum and energy conservation explain the outcomes of collisions, and how can we use these principles to predict and analyze the behavior of objects before, during, and after a collision? This question encourages students to: Understand the laws of conservation of momentum – recognizing that in isolated systems, momentum is conserved during collisions, and how this principle applies to both elastic and inelastic collisions. Explore the conservation of energy – examining how kinetic energy is conserved in elastic collisions but not in inelastic collisions, and understanding the relationship between energy transformations (e.g., into heat, sound, deformation). Analyze different types of collisions – differentiating between elastic, inelastic, and perfectly inelastic collisions, and predicting the motion and velocities of objects based on their type of interaction. Apply mathematical models – using equations of motion and conservation laws to calculate final velocities, impact forces, and changes in momentum for colliding objects. Connect to real-world applications – considering how these principles apply in everyday situations, from car crashes to sports, and how understanding collisions can improve safety, efficiency, and design.
Unit Topics with Learning Objectives:
IMPULSE & MOMENTUM Create a free-standing structure that when placed on the floor will capture and contain an unprotected, large, raw, chicken egg completing an approx. 6’ free-fall. Write a single paragraph explaining how the concepts of impulse and change in momentum were used in their design. List at least twenty safety devices found on or in an automobile. Identify if the devices are used to prevent an accident or protect a passenger during an accident. Use the internet to research a safety device and present their findings. How does the device make the car safer? Who invented the safety device? When was the safety device invented? Is the safety device standard on cars? If the safety device is standard, when did it become standard? If it is not standard, which vehicles offer it? Test different materials to see which makes for the safest seatbelt and understand why they are safer. Define Inertia and how it related to Newton’s 1st law Calculate Pressure given force and area. Utilize the concepts of impulse to explain why an airbag works. Create a vehicle utilizing limited resources that will safely carry an egg through a barrage of collisions. Write a daily log of their construction progression.

Bridges

UNIT TITLE: Bridges
NYS Standards:
NYS Science Learning Standards (Pages 58-63)
Guiding Questions/Essential Questions:
How do the forces acting on a bridge—such as tension, compression, and shear—affect its design and stability, and how can we use these principles to create safe and efficient structures that meet specific functional and environmental needs? This question encourages students to: Explore the forces on a bridge – understanding how different forces (tension, compression, shear, and torsion) act on various parts of a bridge and how engineers account for these forces in the design. Understand structural design – examining the different types of bridges (e.g., beam, arch, suspension, truss) and how their design helps to distribute forces effectively to ensure stability and strength. Consider material properties – discussing the role of materials (such as steel, concrete, wood, and composite materials) in bridge construction, and how their strength, durability, and flexibility contribute to a bridge’s overall performance. Apply engineering principles – using concepts of load-bearing capacity, stress, and strain to predict how a bridge will perform under different conditions, including weight loads, weather, and environmental factors. Connect to real-world challenges – considering how factors like cost, environmental impact, and location influence bridge design and construction, and how innovations in technology and materials can lead to safer, more sustainable bridges.
Unit Topics with Learning Objectives:
BRIDGES Research different types of bridges Internet video Work with a partner and create a bridge made of file folders and staples that can hold 2 kg for 2 minutes Use craft sticks and glue to make a bridge that is the lightest yet holds the most weight possible. The bridge must span a gap of 25 cm across, and be no longer than 50 cm long. A loading block: 5 cm wide, 5 cm tall, and 10 cm long, will be placed on the center of the bridge to test it.

Grand Prix

UNIT TITLE: Grand Prix
NYS Standards:
NYS Science Learning Standards (Pages 58-63)
Guiding Questions/Essential Questions:
How do potential and kinetic energy interact and transform between each other in a system, and how can we apply the principle of energy conservation to predict the behavior of objects in motion or at rest? This question prompts students to: Understand energy transformation – recognizing how potential energy (such as gravitational potential energy) converts to kinetic energy (such as when an object falls) and vice versa (e.g., an object moving upward converts kinetic energy into potential energy). Explore conservation of mechanical energy – understanding how, in an ideal system with no external forces like friction, the total mechanical energy (kinetic + potential) is conserved. Apply mathematical principles – using equations for kinetic energy (KE=12mv2KE = \frac{1}{2}mv^2KE=21mv2) and potential energy (PE=mghPE = mghPE=mgh) to calculate energy changes in real-world situations, such as in a roller coaster, a pendulum, or free-falling objects. Analyze real-world examples – connecting these energy concepts to everyday phenomena, such as the motion of a car, the swing of a pendulum, or the operation of engines, and exploring how energy efficiency is maximized or lost due to friction, air resistance, etc. Explore energy conservation in different systems – considering how energy is transferred between objects and how external forces (like friction or air resistance) affect the total energy in a system, and how these concepts apply to practical scenarios in engineering, technology, and natural processes.
Unit Topics with Learning Objectives:
MOTION Use a stopwatch to measure time. Use a meter stick to measure distances. Calculate average velocity Mathematically Graphically Construct a vehicle powered by a rubber band given limited resources. Safely use a glue gun Safely use a utility knife Measure physical properties of their vehicle. Mass Weight Length Width Drive Wheel Radius ENERGY Calculate average kinetic energy of their rubber band powered vehicles. Calculate average Elastic Potential Energy of the rubber band used to power their vehicles. Compare the amount of KE & PE in their vehicle and speculate why they are not equal.

Paper Planes

UNIT TITLE: Paper Planes
NYS Standards:
NYS Science Learning Standards (Pages 58-63)
Guiding Questions/Essential Questions:
How do the four fundamental forces of flight—lift, weight, thrust, and drag—interact to allow an object to achieve and maintain flight, and how can we optimize these forces for different types of flight, from airplanes to birds to rockets? This question prompts students to: Explore the four forces of flight – understanding how lift (generated by air pressure differences), weight (gravitational force), thrust (force from engines or wings), and drag (resistance from air) work together to enable flight. Analyze aerodynamics – examining how the shape and design of an object (like an airplane wing or bird’s wing) affect the flow of air and contribute to the generation of lift and reduction of drag. Investigate the role of propulsion – exploring how engines or natural forces (e.g., flapping wings or jet propulsion) generate thrust to counteract drag and move an object forward. Consider the physics of different flight types – comparing the flight of various objects, such as airplanes, helicopters, birds, and rockets, and understanding how the same forces operate differently based on the specific conditions and mechanics of each type of flight. Apply principles of flight to real-world applications – thinking about how these forces are used in engineering designs to create efficient aircraft, improve safety, reduce fuel consumption, and achieve controlled flight in various conditions.
Unit Topics with Learning Objectives:
Build paper airplanes and see how the following attributes affect the distance and time of flight: • Drag • Weight distribution

Rockets

UNIT TITLE: Rockets
NYS Standards:
NYS Science Learning Standards (Pages 58-63)
Guiding Questions/Essential Questions:
How do the principles of Newton's Third Law of Motion and the conservation of momentum enable a rocket to launch and travel through space, and how can we design rockets to overcome the challenges of gravity, air resistance, and fuel efficiency? This question prompts students to: Understand rocket propulsion – exploring how rockets generate thrust through the expulsion of gases (action) and how this leads to the rocket's motion (reaction) in accordance with Newton's Third Law. Apply the conservation of momentum – examining how the mass of the rocket and the speed of exhaust gases determine the rocket's velocity and trajectory, and how momentum is conserved in the process. Analyze the forces acting on a rocket – understanding the roles of gravity (pulling the rocket down), air resistance (slowing the rocket), and thrust (propelling the rocket forward), and how these forces change as the rocket ascends through different layers of the atmosphere. Explore the challenges of space travel – considering the impact of factors like fuel efficiency, the vacuum of space, atmospheric pressure, and the need for precise control in rocket design. Design and optimize rockets – applying principles of physics and engineering to think about how rocket designs can be improved for specific goals, such as reaching orbit, exploring other planets, or ensuring the safety and efficiency of space travel.
Unit Topics with Learning Objectives:
Identify the forces acting on a rocket in flight. Construct a test rocket from a soda bottle Identify rocket specifications such as Center of Mass and Center of Pressure Perform a successful launch of their rocket Upkeep a daily log of project progression

Biology Regents

COURSE TITLE: Biology Regents

COURSE DESCRIPTION:

Biology Regents at Fox Lane High School is a full year course open to 9th-12th graders interested in life and the environment. The course follows the New York State P-12 science learning standards, while offering a comprehensive study of how organisms’ function and interact with each other and their environment. The course has a mandatory laboratory component that includes data collection and in-depth analysis. Content is presented in a variety of ways, including relevant, problem-based learning units. This format lends itself to active and worthwhile classroom discussions and promotes highly developed student work. Successful completion of the Living Environment course is a requirement for a NYS high school Regents diploma and a prerequisite for many other courses in Science and Technology.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Life Processes And Scientific Method Biochemistry	Cytology Homeostasis in the Body	Reproduction Genetics	Evolution Ecology Human Impact

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Homework exercises as review for exams and class discussions Question and answer sessions, both formal and informal —planned/spontaneous Conferences between the instructor and student at various points in the semester In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Lab reports & quizzes Methods of Summative Assessments: Unit Exams Semester Assessment Final examination (Regents) Projects (project phases submitted at various completion points could be formatively assessed) NYS Labs
Methods of Differentiation/Extensions/Accommodations:
Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Life Processes And Scientific Method

UNIT TITLE: Life Processes And Scientific Method
NYS Standards:
NYS Science Learning Standards (Biology: Pages 64-72)
Guiding Questions/Essential Questions:
How do scientists use technology to differentiate living from non-living?
Unit Topics with Learning Objectives:
Characteristics of Life/ Life Processes Compare living things and explain how they are both similar to and different from each other and from nonliving things. Identify functions common to all living things. Explain that living things are similar in that they rely on many of the same processes to stay alive, yet are different in the adaptations they possess to carry out these processes to maintain homeostasis. Tools of the Biologist Use Compound Light Microscope to: Prepare slides to observe specimen while centered in field of view Calculate microscopic measurements for quantitative comparisons of specimens. Use staining techniques to identify organelles in the cell. Diagram, label, and identify relevant structures of microscopic organisms. Calculate total magnification. Scientific Method and Experimental Design Design a controlled experiment that allows students to Make observations Create a testable hypothesis. Distinguish between the independent and dependent variable. Distinguish between the experimental and control group. Organize data into data tables Visualize data in graphs for analysis Demonstrate graphing skills. Evaluate validity of results and draw conclusions.

Biochemistry

UNIT TITLE: Biochemistry
NYS Standards:
NYS Science Learning Standards (Biology: Pages 64-72)
Guiding Questions/Essential Questions:
How does the structure of a molecule affect the types of substances made?
Unit Topics with Learning Objectives:
Basic Chemistry Basic Atomic Structure Model atomic structure for elements essential to living things. Explain the characteristics of subatomic particles. Explain how atomic structure is reflected in the Periodic Table. Identify what makes an atom an isotope and explain examples of their uses in medicine. Identify how positive and negative ions are formed. Chemical Bonding and Intermolecular Forces Distinguish between ionic and covalent bonds and explain how they are formed. Differentiate between compounds and molecules. Model the atomic structure of the water molecule. Explain how water is polar and how that connects to the properties of water in relation to living systems. Illustrate how the polarity of water results in hydrogen bonding. Acids and Bases Explain the importance of acids and bases in biological reactions. Distinguish between acids and bases. Use indicators to measure pH. Organic Compounds (Chemical Composition of Life) Understand the difference between organic and inorganic compounds. Describe the relationship between structure and function in organic compounds and their importance to living things. Identify the elements that make up each of the organic compounds. Differentiate between monomers and polymers. Model dehydration synthesis and hydrolysis in macromolecule formation. Proteins and the Role of Enzymes Understand how proteins obtain their three dimensional shape and relationship to function as biological catalysts. Demonstrate knowledge of enzyme specificity. Explain how environmental factors (pH and Temperature) influence the rate of metabolic reactions. Explain what is meant by denaturation.

Cytology

UNIT TITLE: Cytology
NYS Standards:
NYS Science Learning Standards (Biology: Pages 64-72)
Guiding Questions/Essential Questions:
How do cells and unicellular organisms carry out life’s functions?
Unit Topics with Learning Objectives:
Organization of Life Describe the organization of life from a cell → multicellular organism. Prokaryote vs Eukaryote Differentiate between prokaryotes and eukaryotes. Structure and Function Explain how a one-celled organism is able to function despite lacking the levels of organization present in more complex organisms. Organelles Understand that cells have particular structures that perform specific jobs. These structures perform the actual work of the cell. Differentiate between animal and plant cell structures and functions. Cellular Transport Cell Membrane Structure Illustrate the components of the cell membrane and their relationship to cell processes. Explain the difference between active and passive transport. Model a cell using dialysis tubing to represent the permeability of the cell membrane. Draw conclusions about cellular transport based on experimental evidence collected from a model cell in a solution. Explain the impact of molecular size. Observe color changes using indicators to determine movement of molecules across the artificial cell membrane (dialysis tubing) Observe how water diffuses into and out of red onion cells after the addition of salt solutions and distilled water. Cells and Energy Photosynthesis Use chromatography to demonstrate differences in solubility and molecular size. Use chromatography techniques to identify various pigments in plant leaves and their role in photosynthesis. Explain why leaves turn color in the fall. Analyze how environmental factors (light, precipitation) affect the rate of photosynthesis. Understand how photosynthesis provides a vital connection between the sun and the energy needs of living systems. Understand how plant cells and some unicellular organisms contain chloroplasts, the site of photosynthesis. Use a model to illustrate how the process of photosynthesis uses solar energy to combine the inorganic molecules carbon dioxide and water into energy-rich organic compounds (e.g., glucose) and release oxygen to the environment. Identify plant adaptations required to obtain raw materials for and release products from photosynthesis. Use a microscope to view and compare the density of guard cells. Model a feedback mechanism that maintains homeostasis using the changes in stomata size by guard cells to regulate water loss and gas exchange. Cellular Respiration Use a model to illustrate that aerobic cellular respiration is a chemical process whereby the bonds of food molecules and oxygen molecules are broken and the bonds in new compounds are formed resulting in a net transfer of energy. Explain how, in many organisms, the process of cellular respiration is concluded in mitochondria, in which ATP is produced more efficiently, oxygen is used, and carbon dioxide and water are released as wastes. Observe cellular respiration in yeast cells. Use the indicator bromothymol blue to identify carbon dioxide as a byproduct of cellular respiration. Use indicators to test for the presence of alcohol as a product of fermentation. Compare and contrast aerobic and anaerobic respiration in their reactants, products, and location.

Homeostasis in the Body

UNIT TITLE: Homeostasis in the Body
NYS Standards:
NYS Science Learning Standards (Biology: Pages 64-72)
Guiding Questions/Essential Questions:
How do multicellular organisms use body systems to maintain homeostasis?
Unit Topics with Learning Objectives:
Body Systems Describe how body systems interact and respond to internal and external (environmental) changes Provide examples of how body systems interact to maintain dynamic equilibrium Design and experiment to investigate the impact of exercise on maintaining homeostasis Analyze data that results from the interactions of body systems Immunity Explain how the body protects itself from the pathogens it encounters. Describe fever and inflammation as immune responses. Describe how the body protects itself against specific pathogens. Explain how vaccines work against specific infections. Explain why a human would only need one polio vaccine (lifetime) but would require an annual flu shot. Disruption of Homeostasis Explain how factors such as genetics, diet and risk behaviors play a role in the development of diabetes and cancer. Explain how the HIV virus infects the body and its relationship to developing AIDS. Explain treatments that have been used to dramatically increase the survival rate of people with HIV. Describe how cancer's uncontrolled cell division impacts the body on both a local and systemic level. Identify and describe both traditional and developing treatments used to treat cancer. Explain how the Lyme pathogen is transmitted to the body and explain treatments used to treat the effects of the disease.

Genetics

UNIT TITLE: Genetics
NYS Standards:
NYS Science Learning Standards(Biology: Pages 64-72)
Guiding Questions/Essential Questions:
How has inheritance affected life’s present and future biodiversity?
Unit Topics with Learning Objectives:
Structure of DNA Explain how the coded instructions for specifying the characteristics of the organism are carried in DNA. Illustrate how the chemical and structural properties of DNA are the basis for how the genetic information that underlies heredity is both encoded in genes (as a string of molecular “bases”) and replicated by means of a template. Ask questions to clarify relationships about the role of DNA and chromosomes in coding the instructions for characteristic traits passed from parents to offspring. Protein Synthesis Construct an explanation based on evidence for how the structure of DNA determines the structure of proteins which carry out the essential functions of life through systems of specialized cells. Explain how the work of the cell is carried out by the many different types of molecules it assembles, mostly proteins. Illustrate protein molecules as long, usually folded chains made from 20 different kinds of amino acids in a specific sequence. Describe how the sequence of amino acids influences the shape of the protein. The shape of the protein, in turn, determines its function. Translate the genetic code given a specific nitrogenous base sequence to form a polypeptide. Identify when a mutation has occurred in the original sequence of nitrogenous bases and explain how the impact of the change influences the final protein synthesized. Variation Make and defend a claim based on evidence that inheritable genetic variations may result from: new genetic combinations through meiosis. viable errors occurring during replication. mutations caused by environmental factors and/or genetic engineering. Apply concepts of statistics and probability to explain the variation and distribution of expressed traits in a population. Genetic Engineering and Lab Techniques Describe how new varieties of farm plants and animals have been engineered by manipulating their genetic instructions to produce new characteristics. Recombinant DNA Illustrate how different enzymes can be used to cut, copy, and move segments of DNA. Model the insertion, deletion, or substitution of DNA segments, which alter genes. Explain how an altered gene may be passed on to every cell that develops from it. Describe the process by which new characteristics produced by segments of DNA may be expressed when these segments are inserted into new organisms, such as bacteria. Cloning Model the process of cloning to create an organism that is genetically identical to the donor. Gel Electrophoresis Model the process of gel electrophoresis to separate DNA fragments. Describe how DNA fragments travel through gel on the basis of molecular size and charge.

Reproduction

UNIT TITLE: Reproduction
NYS Standards:
NYS Science Learning Standards (Biology: Pages 64-72)
Guiding Questions/Essential Questions:
How does reproduction affect the development of an individual and a species?
Unit Topics with Learning Objectives:
Asexual vs Sexual Reproduction Discuss the similarities and differences between asexual and sexual reproduction in terms of variation and chromosome number. Explain the advantages and disadvantages of the types of reproduction and their influence on variation and rate of evolution. Illustrate the processes of binary fission, budding, regeneration, and vegetative propagation. Mitosis Use a model to illustrate cellular division (mitosis). Describe the differences in the reproduction of a cancer cell vs a normal cell Meiosis Compare the process of mitosis and meiosis. Explain the importance of meiosis in terms of variation. Fertilization and Development Explain what is meant by restoration of chromosome number. Define specialization and differentiation. Compare and contrast adaptations for internal and external fertilization and development. Human Reproduction and Development Use models to illustrate how human reproduction and development maintains continuity of life. Describe how humans are uniquely suited for the reproductive demands of our species Plot and analyze data for hormone levels to explain how the female menstrual cycle is an example of a feedback mechanism. Describe medical procedures used in genetic testing such as karyotyping, ultrasound, and amniocentesis. Connect results from genetic testing to disorders.

Evolution

UNIT TITLE: Evolution
NYS Standards:
NYS Science Learning Standards (Biology: Pages 64-72)
Guiding Questions/Essential Questions:
How did evolution contribute to Earth’s biodiversity?
Unit Topics with Learning Objectives:
Construct an explanation based on evidence that the process of evolution primarily results from four factors: the potential for a species to increase in number the heritable genetic variation of individuals in a species due to mutation and sexual reproduction competition for limited resources the proliferation of those organisms that are better able to survive and reproduce in the environment. Darwin and Natural Selection Process of Natural Selection Construct an explanation based on evidence for how some characteristics give individuals an advantage over others in surviving and reproducing, and the advantaged offspring, in turn, are more likely than others to survive and reproduce. The proportion of individuals that have advantageous characteristics will increase. Evaluate the evidence for the role of group behavior on individual and species’ chances to survive and reproduce. Model the process of natural selection using a variety of tools to represent the beak diversity in finches. Analyze data to explain the adaptive value of variations of organisms within a species to increase the likelihood that at least some members of the species will survive under changed environmental conditions. Predict the likelihood of survival based on food availability. Interpret cladograms to depict the emergence of new species. Apply concepts of statistics and probability to support explanations that organisms with an advantageous heritable trait tend to increase in proportion to organisms lacking this trait. Evaluate the evidence supporting claims that changes in environmental conditions may result in: increases in the number of individuals of some species. the emergence of new species over time. the extinction of other species. Extinction of species Use of the fossil record to indicate that many organisms that lived long ago are extinct. Recognize that extinction of species is common and that most of the species that have lived on Earth no longer exist. Explain how the process of extinction of a species occurs when the environment changes and the adaptive characteristics of a species are insufficient to allow its survival. Selective Breeding/Artificial Selection Describe how new varieties of cultivated plants and domestic animals resulted from selective breeding for particular traits. Evidence of Evolution Communicate scientific information that common ancestry and biological evolution are supported by multiple lines of empirical evidence such as the fossil record, comparative anatomy, embryology, cytology and biochemistry. Pace and Patterns of Evolution Explain how the process of evolution does not necessitate long-term progress in some set direction. Recognize that patterns of evolutionary changes appear to be like the growth of a bush: Some branches survive from the beginning with little or no change, many die out altogether, and others branch repeatedly, sometimes giving rise to more complex organisms. Distinguish between evolutionary patterns of gradualism and punctuated equilibrium. Endosymbiotic Theory Model the process of endosymbiosis to explain the emergence of chloroplasts and mitochondria in the evolution of eukaryotic cells. Classification and Taxonomy Analyze a dichotomous key to infer similarities in organism adaptations. Create a dichotomous key to properly illustrate similarities between organisms. First Life on Earth Explain the process by which life on Earth is thought by many scientists to have begun as simple, single-celled organisms. About a billion years ago, increasingly complex multicellular organisms began to evolve.

Ecology

UNIT TITLE: Ecology
NYS Standards:
NYS Science Learning Standards (Biology: Pages 64-72)
Guiding Questions/Essential Questions:
How does biodiversity contribute to a sustainable environment?
Unit Topics with Learning Objectives:
Introduction to Ecology Abiotic and Biotic Relationships Differentiate between abiotic and biotic factors Explain how the number of organisms any habitat can support is limited by the available energy, water, oxygen, & minerals. Symbiotic Relationships Identify the characteristics that distinguish a biotic relationship as mutualism, commensalism, or parasitism. Levels of Ecological Organization Identify the characteristics of each of the levels of ecological organization from species → biosphere. Differentiate between habitat and niche. Energy Flow in the Ecosystem Food Chains and Food Webs Construct a Food Chain/Food Web. Identify and describe the roles of producers and consumers at each trophic level. Discuss issues related to the loss/depletion of organisms at any trophic level. Construct and revise an explanation based on evidence for the flow of energy in ecosystems. Model energy flow through an ecosystem with the use of an energy pyramid. Use mathematical representations to support claims for the flow of energy among organisms in an ecosystem. Nutrient Cycling Construct and revise an explanation based on evidence for the cycling of matter among the living and nonliving components of the biosphere. Use mathematical representations to support claims for the cycling of matter among organisms in an ecosystem. Develop a model to illustrate the role of various processes in the cycling of carbon among the biosphere, atmosphere, hydrosphere, and geosphere. Develop a model to illustrate the role of various processes in the cycling of nitrogen among the biosphere, atmosphere, hydrosphere, and geosphere. Develop a model to illustrate the role of various processes in the cycling of water among the biosphere, atmosphere, hydrosphere, and geosphere. Ecosystem Stability Define biodiversity Explain how diversity of populations within ecosystems relates to the stability of ecosystems. Evaluate the claims, evidence, and reasoning that the complex interactions in ecosystems maintain relatively consistent numbers and types of organisms in stable conditions, but changing conditions may result in a new ecosystem. Explain natural and human forces that influence both primary and secondary ecological succession. Carrying Capacity Use mathematical and/or computational representations to support explanations of biotic and abiotic factors that affect carrying capacity of ecosystems at different scales. Population Dynamics Define what is meant by a limiting factor. Identify density-dependent and density-independent factors that limit population size. Use mathematical representations to support and revise explanations based on evidence about factors affecting biodiversity and populations in ecosystems of different scales.

Human Impact

UNIT TITLE: Human Impact
NYS Standards:
NYS Science Learning Standards (Biology: Pages 64-72)
Guiding Questions/Essential Questions:
How are humans affecting the local and global environments?
Unit Topics with Learning Objectives:
Describe the range of interrelationships of humans with the living and nonliving environment. Explain how the impact of increasing human consumption of resources places stress on the depletion of renewable and non-renewable resources. Identify what is meant by renewable and nonrenewable energy. Provide examples of renewable and nonrenewable energy. Describe how natural ecosystems provide an array of basic processes that affect humans: maintenance of the quality of the atmosphere, generation of soils, control of the water cycle, removal of wastes, energy flow, recycling of nutrients. Explain how humans are damaging many of the basic processes of natural ecosystems. Design, evaluate, and refine a solution for reducing the impacts of human activities on the environment and biodiversity.* Human Population Dynamics Describe how industrialization brings an increased demand for and use of energy and other resources including fossil and nuclear fuels. Explain how the usage of fossil and nuclear fuels can have positive and negative effects on humans and ecosystems. Biological Magnification Explain how the presence of a harmful substance is increased as it makes its way up the food chain. Deforestation Discuss the impact of deforestation on the environment in relation to both organisms in that environment and the human population. Invasive Species Describe the impact of invasive species on an ecosystem. Maintenance Biodiversity Design, evaluate and refine a solution for reducing the impacts of human activities on the environment and biodiversity. Use mathematical representations to support and revise explanations on evidence about factors affecting biodiversity. Explain how the maintenance of biodiversity increases the stability of an ecosystem. Describe the advantages of biodiversity. Biological Controls Use a cost-benefit analysis to evaluate benefits of biological controls. Humans Alter Ecosystems Describe the serious consequences of either the addition or removal of specific organisms. For example, planting large expanses of one crop reduces the biodiversity of the area. Explain how Climate Change can impact individuals and populations Describe the causes and potential impacts of climate change Explain how climate change can impact biodiversity Describe how depletion of the ozone layer is hazardous to human health. Trade Offs Explains how societies must decide on proposals which involve the introduction of new technologies. Describe the role of Individuals in decision making which will assess risks, costs, benefits, and trade-offs.

Chemistry Honors

COURSE TITLE: Chemistry Regents Honors

COURSE DESCRIPTION:

Why do you use soap to clean your hands? Why do you feel cold when you get out of a pool? How do fireworks produce such great colors? These are some of the many questions that we will explore in Honors Chemistry. Honors Chemistry is the study of the atoms and molecules that are the building blocks of our universe. Understanding how molecules form and how they interact with one another will help us understand and explain many of the observations in our daily lives. Chemistry is a lab based science. While we will be exploring similar topics to those covered in Regents Chemistry, we will be doing so in more depth and at a faster pace. This will require you to be self-motivated and committed. This class is meant for students with a strong science and math background and interest.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Matter & Numbers Atomic Structure Nuclear Chemistry	Periodic Table Bonding Organic Chemistry	Energy Gas Laws Chemical Formulas, Reactions & Stoichiometry	Solutions Thermodynamics, Kinetics & equilibrium Acids and Bases Redox

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Question and answer sessions, both formal—planned and informal—spontaneous In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Methods of Summative Assessments: Projects (project phases submitted at various completion points could be formatively assessed) Presentations Student evaluation / Conclusion Questions
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Matter & Numbers

NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages 54-57 )
Guiding Questions/Essential Questions:
What is chemistry?
Unit Topics with Learning Objectives:
SWBAT: Measure Matter: Define and Identify Precision vs. Accuracy Calculate Significant figures. Read scientific instruments with the correct precision. Relate scientific figures to the precision of the scientific instrument used to measure the data. Make calculations with data that reflects the correct number of significant figures. Define and Draw: Matter Substance Elements Compounds Mixtures The student will be able to understand that everything is made up of these two types of matter. The student will be able to understand a chemical formula as identifying the different atoms that make up that substance. The student will be able to identify, classify and separate different substances based on intensive properties. The student will be exposed to and be responsible for separating the components of a mixture using different separation techniques such as: chromatography, distillation, filtration and use of a centrifuge. Measure Pure Substances such as: Moles Molecules Molar Mass/Gram Formula Mass: Understand that in chemistry substances are measured using moles, mass and molecules. Convert between the three units. Calculate the percent by mass of a substance in a compound or a mixture. Understand that compounds have fixed ratios. Understand that mixtures have variable ratios.

Atomic Structure

UNIT TITLE: Atomic Structure
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages 54-57 )
Guiding Questions/Essential Questions:
Is an atom living?
Unit Topics with Learning Objectives:
SWBAT: Define Atoms Introduction to atomic structure Describe the major atomic theories that led to the modern atomic theory. Understand the importance of developing a theory over time with many contributors. Explain the important contributors and their respective models: Dalton, Thompson, Rutherford, Bohr, Wave Mechanical Model. Define and describe Important subatomic particle Electrons Nucleons Protons Neutrons Identify the mass, charge and location of each subatomic particle. Understand how to determine the number of each subatomic particle in an atom. Understand that each element has a specific number of protons. Understand that altering the number of electrons creates ions. Understand the location importance of Valence shell electrons. Apply Pauli Exclusion Principle, Hund’s Rule of Multiplicity, and Aufbau Principle, to determine the electron configuration of an element: Shell method Spectroscopic notation Orbital diagrams Lewis Dot structure Use excited state ground state to: Identify an element from brightline spectroscopic data. Understand the difference in energy levels within an atom. Understand how fireworks, flares and neon lights work. Explain the structure of atoms “Empty space” concept Nucleus Atomic Number Understand that the Atomic Number defines the element Be able to determine the atomic number for an element. Isotopes Be able to understand that an element will have several naturally occurring isotopes. Different isotopes have different mass numbers, due to differing numbers of neutrons. Mass number Be able to use mass number to determine the number of neutrons in an atom. Average Atomic mass Be able to understand the difference between mass number and average atomic mass. Be able to calculate the average atomic mass based on abundance of isotopes. Be able to understand that the aam depends on the abundance of each isotope. Be able to calculate the abundance given the aam.

Nuclear Energy

UNIT TITLE: Nuclear Energy
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages 54-57 )
Guiding Questions/Essential Questions:
Is nuclear energy more beneficial or detrimental to society?
Unit Topics with Learning Objectives:
SWBAT: Define Nuclear Chemistry: Define Radiation Using Table O, identify the different types of radiations. Alpha Beta Positron Gamma Define Radioactive Decay Predict the stability of a nucleus knowing the proper ratios of protons to neutrons. Write the natural transmutation reaction for both alpha and beta decay. Calculate Half-Life Read and interpret the half-life and decay mode of common nuclides found on Table N Calculate the total time, half life or mass of unstable nuclei Explain Nuclear Reactors Compare and contrast the amount of energy produced in nuclear reactions and chemical reactions. Account for the differences using mass defect or bonds. State benefits and drawbacks of nuclear energy Classify Types of Nuclear Reactions Provide the missing reactant or product for all nuclear reactions. Natural Transmutation Artificial Transmutation Fission Fusion Identify the types of nuclear reactions and their applications.

The Periodic Table

UNIT TITLE: The Periodic Table
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages 54-57 )
Guiding Questions/Essential Questions:
How do we know the periodic table is done being developed?
Unit Topics with Learning Objectives:
SWBAT: Identify elements on the periodic table: Students should be able to locate specific elements by their symbol and atomic number. Understand the organization of the periodic table: Recognizing the concept of periods (horizontal rows) and groups (vertical columns) and how they relate to element properties. Interpret trends on the periodic table: Analyzing patterns in atomic radius, ionization energy, electronegativity, and reactivity across the periodic table. Predict element properties based on position: Using the periodic table to make predictions about the chemical behavior of an element based on its position relative to other elements. Apply the periodic table to chemical reactions: Understanding how the position of elements on the table can influence their reactivity in chemical reactions

Bonding

UNIT TITLE: Bonding
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages 54-57 )
Guiding Questions/Essential Questions:
Why do elements bond? How can bonds affect our health?
Unit Topics with Learning Objectives:
SWBAT: Explain Bonding Must know the 3 main types of chemical bonds, and the properties associated with each. Explain how, why, and when ionic bonding occurs. Describe when and why covalent bonding takes place as well as coordinate covalent bonding. Draw electron dot structures (Lewis) for simple molecules. Use this information to describe how the octet rule has been satisfied. Determine the shape of a simple molecule. Determine if a covalent bond is polar or nonpolar. Determine if a molecule is polar or nonpolar. Explain the importance of hydrogen bonding and how it is created. Also understand molecule-ion attraction. Describe molecules and understand the van der Waals' forces that attract molecules together. Describe a network solid, know common examples, and their properties. Describe the energy associated with chemical bonding and the strength of the different bonds.

Organic Chemistry

UNIT TITLE: Organic Chemistry
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages 54-57 )
Guiding Questions/Essential Questions:
Where is organic chemistry used in the real world?
Unit Topics with Learning Objectives:
SWBAT: Define Organic Chemistry Name and Draw Hydrocarbons Alkanes, Alkenes, and Alkynes General Formulas Saturated and Unsaturated Classify, Draw and Name Other Organic Compounds Alcohols Primary, Secondary, Tertiary Monohydroxy, Dihydroxy, Trihydroxy Nomenclature Functional Group Structural Formula Condensed Structural Formula Aldehydes Nomenclature Functional Group Structural Formula Condensed Structural Formula Ketone Nomenclature Functional Group Structural Formula Condensed Structural Formula Ether Nomenclature Functional Group Structural Formula Condensed Structural Formula Organic Acid Nomenclature Functional Group Structural Formula Condensed Structural Formula Esters Nomenclature Functional Group Structural Formula Condensed Structural Formula Amines Nomenclature Functional Group Structural Formula Condensed Structural Formula Amides Nomenclature Functional Group Structural Formula Condensed Structural Formula Isomers Definition Different Structural Formula and Different Properties Classify Organic Reactions Addition Substitution Combustion Fermentation Esterifications Saponification Polymerization Classify Physical and Chemical Properties of Organic Compounds Melting Point and Boiling Point Volatility Combustion Conductivity

Energy

UNIT TITLE: Energy
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages 54-57 )
Guiding Questions/Essential Questions:
What are the different forms of energy and how are they used?
Unit Topics with Learning Objectives:
SWBAT: Classify Energy and Phases Classify Forms of energy Explain Measurement of Energy Joules Thermochemistry Fixed points on a thermometer Explain Energy Change during Physical and Chemical changes Exothermic change Endothermic change Liquids Use Vapor Pressure Classify Boiling Point Calculate Heat of vaporization Solids Calculate Melting point Calculate Heat of Fusion Define Sublimation

Gas Laws

UNIT TITLE: Gas Laws
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages 54-57 )
Guiding Questions/Essential Questions:
How are the gas laws related?
Unit Topics with Learning Objectives:
SWBAT: Gasses Explain and Calculate using Boyle's Law Charles Law Combined Gas Law Understand Standard temperature and pressure Explain Partial Pressures Explain Kinetic Theory Explain Deviations from the gas laws Use Avogadro’s hypothesis

Chemical Formulas, Reactions & Stoichiometry

UNIT TITLE: Chemical Formulas, Reactions & Stoichiometry
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages 54-57 )
Guiding Questions/Essential Questions:
How does the law of conservation apply to chemical reactions and stoichiometry?
Unit Topics with Learning Objectives:
SWBAT: Stoichiometry Understand the Mole Concept: Define and calculate the number of moles of a substance. Convert between moles, mass, and number of particles (atoms, molecules, ions) using appropriate conversion factors (Avogadro's number, molar mass). Use Molar Ratios: Interpret and use molar ratios from a balanced chemical equation to convert between amounts of reactants and products. Solve stoichiometric problems involving moles, mass, and volume. Perform Stoichiometric Calculations: Calculate the amount of reactants required to produce a given amount of product. Determine the mass of product formed from a known mass of reactant. Solve problems involving the calculation of limiting reactants and percent yield. Apply the Ideal Gas Law (if applicable): Understand the relationship between moles of gas, volume, temperature, and pressure (for gases under standard conditions). Use stoichiometry to calculate volumes of gases involved in reactions under ideal conditions (using the ideal gas law: PV = nRT). Percent Yield and Theoretical Yield: Calculate the theoretical yield of a reaction from a stoichiometric calculation. Determine the percent yield by comparing the actual yield with the theoretical yield. Use Dimensional Analysis in Stoichiometry: Apply dimensional analysis techniques to convert units in stoichiometric calculations, ensuring correct units are used in every step of the calculation.

Solutions

UNIT TITLE: Solutions
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages 54-57 )
Guiding Questions/Essential Questions:
How are solutions prevalent in your daily life?
Unit Topics with Learning Objectives:
SWBAT: Solutions Identify the solute and solvent in a solution. Differentiate between soluble and insoluble. Net ionic equations with precipitate reactions. Stoichiometry. Use Table G, determine the amount of solute that will dissolve in a solution at a given temperature. Using Table G, calculate the change in solute with a change in temperature. Using Table G, predict the state of the solute dissolving. Write the products in double replacement reactions. Using Table F, predict the solubility of a solute in water. Determine if a reaction will form a precipitate. Calculate solution concentration using molarity, molality, ppm,ppb, mole fraction. Explain Freezing point depression Boiling point elevation.

Thermo, Kinetics and Equilibrium

UNIT TITLE: Thermo, Kinetics and Equilibrium
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages 54-57 )
Guiding Questions/Essential Questions:
What factors affect the rate of reaction
Unit Topics with Learning Objectives:
SWBAT: Define Kinetics Describe the rate of a reaction Compare exothermic and endothermic reactions to heat released and gained given a written reaction. Compare exothermic and endothermic reactions to heat released and gained given a chemical reaction. Compare exothermic and endothermic reactions to heat released and gained given changes in state. Define enthalpy. Draw Potential Energy Diagrams for both exothermic and endothermic chemical reactions Label the drawing with PE of Reactants, PE of Products, Activation Energy, Heats of Reaction. Interpret the diagrams as exothermic and endothermic and be able to associate the diagram with the stability of the reactants and products. Interpret diagrams for reverse reactions. Draw the diagram with a catalyst. Interpret the reason the diagram changes with a catalyst. List the factors that affect the rate of a reaction. Explain why the factors change the rate of a reaction. Entropy Describe entropy. Predict whether entropy increases or decreases in chemical reactions. Predict whether entropy increases or decreases in physical changes. Using enthalpy and entropy, predict whether a reaction will spontaneously occur. Define Equilibrium Describe and explain phase equilibrium. Describe and explain solution equilibrium. Describe and explain chemical equilibrium. Define Le Chatelier’s Principle Apply Le Chatelier’s Principle to changes in concentration. Apply Le Chatelier’s Principle to changes in pressure. Apply Le Chatelier’s Principle to changes in temperature. Apply Le Chatelier’s Principle to changes in catalyst.

Acids and Bases

UNIT TITLE: Acids and Bases
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages 54-57 )
Guiding Questions/Essential Questions:
What happens in your stomach when you have too much acid, and how can you combat this?
Unit Topics with Learning Objectives:
SWBAT: Explain Acids and Bases Define Arrhenius definition. Define Bronsted-Lowry definition. Apply Arrhenius and Bronsted-Lowry to the ionization of acids. Apply Arrhenius and Bronsted-Lowry to the ionization of base. Using Table K, be able to name common acids. Using Table L, be able to name common bases. Describe properties of acids and bases. Identify common acids and bases. Compare the pH Scale to concentrations of hydrogen ions and hydroxide ions. Use indicators, justify the degree to which a substance is an acid or base. Identify a neutralization reaction. Identify a hydrolysis reaction. Perform titrations using a buret and calculate for unknown concentrations.

Redox

UNIT TITLE: Redox
NYS Standards:
NYS Science Learning Standards (CORE CONTENT: Pages 54-57 )
Guiding Questions/Essential Questions:
How do batteries work?
Unit Topics with Learning Objectives:
SWBAT: Explain Redox and Electrochemistry Using the rules for finding oxidation numbers, calculate the oxidation number for elements, compound and polyatomic ions. Reduction/Oxidation Define oxidation and reduction and realize that REDOX is an abbreviation for these two words. Form a complete reaction, write balanced half reactions for both oxidation and reduction. Identify the species oxidizing and the species reducing in a redox reaction. Identify the oxidizing agent and the reducing agent in a redox reaction. Using Table J, predict the the spontaneity of a reaction Using Table J, compare the activity of metals and nonmetals. Voltaic Cells Define a voltaic cell and state applications Label the voltaic cell Be able to show the flow of electrons due to reduction and oxidation of each electrode. Electrolytic Cells Define an electrolytic cell and state applications. Label the electrolytic cell. Be able to show the flow of electrons due to reduction and oxidation of each electrode.

Chemistry Regents

COURSE TITLE: Regents Chemistry

COURSE DESCRIPTION: Everything you can touch, taste, or smell is a chemical. The study of Chemistry helps us understand the natural world and has allowed the human race to achieve unbelievable feats. Chemistry is the explanation for everyday things like why laundry detergent works better in hot water or why simple ingredients can radically alter texture and flavors of your favorite foods. Even our existence is the result of a delicate balance of chemical reactions. Throughout the duration of this course, instruction will focus on the development of scientific ideas, the nature of science and the direct implications of chemistry on our lives. The topics covered include: matter and energy, atomic structure, bonding, the periodic table, mathematics of chemistry, kinetics and equilibrium, acids and bases, reduction oxidation reactions, nuclear chemistry and organic chemistry.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Matter & Numbers Atomic Structure Nuclear Chemistry	Periodic Table Bonding Organic Chemistry	Energy Gas Laws Chemical Formulas and Math of Chemistry Chemical Reactions and Stoichiometry	Solutions Thermo, Kinetics, Equilibrium Acids/Bases Redox

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Question and answer sessions, both formal—planned and informal—spontaneous In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Methods of Summative Assessments: Projects (project phases submitted at various completion points could be formatively assessed) Unified Arts Folder / Portfolio Presentations Student evaluation / Conclusion Questions
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Matter and Numbers

UNIT TITLE: Matter and Numbers
NYS Standards:
NYS Science Learning Standards (Pages 54-57)
Guiding Questions/Essential Questions:
How are compounds formed, and how do their properties differ from the elements they are made of? This question encourages exploration of elements and compounds having distinct properties, and understanding this distinction is critical. For instance, sodium (Na) is a highly reactive metal, while sodium chloride (NaCl), the compound formed by sodium and chlorine, is a stable, non-reactive salt. This difference illustrates how the arrangement of atoms and the type of bonding determine a substance’s physical and chemical properties.
Unit Topics with Learning Objectives:
Substances: Identify a substance as being made up of a single composition defined by specific intensive properties. Identify a substance as being homogeneous. Identify Elements and compounds as a pure substance Distinguish between an element and a compound. Elements are made up of only one type of atom Compounds are made up of two or more different atoms chemically bound together.

Atomic Structure

UNIT TITLE: Atomic Structure
NYS Standards:
NYS Science Learning Standards (Pages 54-57)
Guiding Questions/Essential Questions:
How do the structure and behavior of atoms determine the properties and interactions of matter? This question encourages exploration of the atom's composition (protons, neutrons, and electrons) and how these subatomic particles influence an element's chemical behavior, bonding, and physical properties. It also invites investigation into atomic models and how advancements in atomic theory have shaped our understanding of the material world.
Unit Topics with Learning Objectives:
Understand the Basic Structure of an Atom Objective : Identify and describe the three main subatomic particles (protons, neutrons, and electrons) and their respective charges, locations, and relative masses. Skills : Define the roles of protons, neutrons, and electrons in the atom. Understand how atomic number and mass number are related to protons and neutrons. Distinguish between isotopes and ions. Explore the Concept of Atomic Number and Mass Number Objective : Understand the significance of atomic number and mass number in determining an element's identity and isotopic variations. Skills : Define and calculate atomic number and mass number. Explain how the atomic number determines the element, and the mass number indicates the number of protons and neutrons. Identify isotopes based on the number of neutrons. Understand Electron Configuration and Energy Levels Objective : Explain the arrangement of electrons in an atom, including electron shells, orbitals, and energy levels. Skills : Describe the electron cloud model and its significance in atomic structure. Apply the Aufbau principle, Pauli exclusion principle, and Hund’s rule to write electron configurations for atoms. Determine the number of valence electrons in an atom and relate this to its chemical behavior. Understand the Bohr Model and Quantum Mechanical Model Objective : Compare and contrast the Bohr model and the quantum mechanical model of the atom. Skills : Describe the Bohr model’s concept of discrete energy levels for electrons. Explain the limitations of the Bohr model and the development of the quantum mechanical model. Understand the concept of orbitals and probability clouds in the quantum mechanical model of the atom. Analyze Atomic Spectra and Energy Transitions Objective : Explain the relationship between electron transitions and the emission or absorption of light in atomic spectra. Skills : Define and describe the emission and absorption spectra of elements. Understand how electron transitions between energy levels produce light (e.g., the visible spectrum in hydrogen). Relate the frequency and wavelength of emitted or absorbed light to energy changes in atoms. Relate Atomic Structure to the Periodic Table Objective : Use the periodic table to predict the atomic structure and properties of elements. Skills : Relate the number of protons, electrons, and neutrons to the position of an element in the periodic table. Understand periodic trends such as atomic radius, ionization energy, and electronegativity. Predict the electron configuration of elements based on their position in the periodic table. Understand the Concept of Ions and Isotopes Objective : Understand how atoms gain or lose electrons to form ions and how variations in the number of neutrons create isotopes. Skills : Define ions and explain the process of ionization (cation vs. anion). Explain the concept of isotopes and how they affect atomic mass. Calculate the average atomic mass of an element based on its isotopes. Apply the Concept of Atomic Structure to Chemical Bonding Objective : Relate atomic structure and electron configuration to the formation of chemical bonds. Skills : Explain how electron configurations influence an element's reactivity and bonding behavior. Differentiate between ionic, covalent, and metallic bonds in terms of electron transfer or sharing. Use atomic structure to predict the types of bonds and the properties of compounds formed. Explore Nuclear Reactions and Radioactivity Objective : Understand the basics of nuclear reactions, including types of radiation and their relationship to atomic structure. Skills : Define and describe types of radiation (alpha, beta, gamma) and their effects on atomic structure. Understand the concept of nuclear decay and half-life. Relate the stability of an atom to the ratio of protons to neutrons. Develop Proficiency in Drawing Atomic Models Objective : Draw and label accurate models of atoms and ions based on their subatomic particles and electron configurations. Skills : Draw Bohr models and Lewis dot structures for atoms and ions. Represent the electron configuration of atoms in different energy levels and orbitals. Illustrate the changes that occur when an atom gains or loses electrons (ions) or undergoes nuclear decay. Investigate the Historical Development of Atomic Theory Objective : Examine the historical progression of atomic theory and the contributions of key scientists. Skills : Summarize the contributions of early scientists like Dalton, Thomson, Rutherford, and Bohr in developing the atomic model. Explain the shift from classical to quantum mechanics in describing atomic structure.

Nuclear Chemistry

UNIT TITLE: Nuclear Chemistry
NYS Standards:
NYS Science Learning Standards (Pages 54-57)
Guiding Questions/Essential Questions:
How do nuclear reactions, such as fission and fusion, transform matter and release energy, and what are the implications for science, technology, and society? This question connects the study of nuclear processes to both the transformation of elements and the release of energy, encouraging exploration of concepts like radioactive decay, nuclear reactions, and the practical applications (and challenges) of nuclear chemistry in energy production, medicine, and environmental concerns.
Unit Topics with Learning Objectives:
Radiation Using Table O, identify the different types of radiations. Alpha Beta Positron Gamma Radioactive Decay Predict the stability of a nucleus knowing the proper ratios of protons to neutrons. Write the natural transmutation reaction for both alpha and beta decay. Half-Life Read and interpret the half-life and decay mode of common nuclides found on Table N Calculate the total time, half life or mass of unstable nuclei Nuclear Reactors Compare and contrast the amount of energy produced in nuclear reactions and chemical reactions. Account for the differences using mass defects or bonds. Label the parts of a nuclear reactor and function of each part. State benefits and drawbacks of nuclear energy Types of Nuclear Reactions Provide the missing reactant or product for all nuclear reactions. Natural Transmutation Artificial Transmutation Fission Fusion Identify the types of nuclear reactions and their applications.

Periodic Table

UNIT TITLE: Periodic Table
NYS Standards:
NYS Science Learning Standards (Pages 54-57)
Guiding Questions/Essential Questions:
How does the organization of elements in the periodic table reflect their properties, and how can this knowledge be used to predict chemical behavior? This question prompts exploration of the periodic trends (such as atomic size, electronegativity, and ionization energy) and how the arrangement of elements into groups and periods allows scientists to predict and explain the chemical behavior of elements, the formation of compounds, and trends in reactivity.
Unit Topics with Learning Objectives:
Identifying elements on the periodic table: Students should be able to locate specific elements by their symbol and atomic number. Understanding the organization of the periodic table: Recognizing the concept of periods (horizontal rows) and groups (vertical columns) and how they relate to element properties. Interpreting trends on the periodic table: Analyzing patterns in atomic radius, ionization energy, electronegativity, and reactivity across the periodic table. Predicting element properties based on position: Using the periodic table to make predictions about the chemical behavior of an element based on its position relative to other elements. Applying the periodic table to chemical reactions: Understanding how the position of elements on the table can influence their reactivity in chemical reactions

Bonding

UNIT TITLE: Bonding
NYS Standards:
NYS Science Learning Standards (Pages 54-57)
Guiding Questions/Essential Questions:
How do different types of chemical bonds (ionic, covalent, and metallic) influence the properties and behaviors of substances? This question encourages exploration of how atoms interact to form compounds, how bond type affects properties like melting point, conductivity, and solubility, and why understanding bonding is key to predicting the structure and function of molecules in various chemical reactions and real-world applications.
Unit Topics with Learning Objectives:
Must know the 3 main types of chemical bonds, and the properties associated with each. Explain how, why, and when ionic bonding occurs. Describe when and why covalent bonding takes place as well as coordinate covalent bonding. Draw electron dot structures (Lewis) for simple molecules. Use this information to describe how the octet rule has been satisfied. Determine the shape of a simple molecule. Determine if a covalent bond is polar or nonpolar. Determine if a molecule is polar or nonpolar. Explain the importance of hydrogen bonding and how it is created. Also understand molecule-ion attraction. Describe molecules and understand the van der Waals' forces that attract molecules together. Describe a network solid, know common examples, and their properties. Describe the energy associated with chemical bonding and the strength of the different bonds.

Organic Chemistry

UNIT TITLE: Organic Chemistry
NYS Standards:
NYS Science Learning Standards (Pages 54-57)
Guiding Questions/Essential Questions:
How do the structure and functional groups of organic molecules determine their reactivity, properties, and role in biological and industrial processes? This question invites exploration of the vast diversity of organic compounds, how molecular structure influences chemical behavior, and the significance of organic chemistry in fields like medicine, biochemistry, environmental science, and materials engineering. It encourages an understanding of the relationships between molecular structure, function, and the ways organic compounds are synthesized and utilized in various contexts.
Unit Topics with Learning Objectives:
Define and identify hydrocarbons using molecular formulas or structural formulas. Distinguish between alkanes, alkenes, and alkynes. Predict the homologous series of hydrocarbons using general formulas or saturated and unsaturated. Identify other organic compounds besides hydrocarbons. Alcohols Identify primary, secondary, tertiary using structural formulas. Identify monohydroxy, dihydroxy, trihydroxy alcohols using structural formulas. Using the IUPAC System, name the molecules of alcohol. Identify the class of compounds using the functional group. Draw structural formula of alcohols. Write condensed structural formula for alcohols. Aldehydes Using the IUPAC System, name molecules of aldehydes. Identify the class of compounds using the functional group. Draw structural formula of aldehydes. Write condensed structural formula for aldehydes. Ketone Using the IUPAC System, name molecules of ketones. Identify the class of compounds using the functional group. Draw structural formula of ketones. Write condensed structural formula for ketones Ether Using the IUPAC System, name molecules of ether. Identify the class of compounds using the functional group. Draw the structural formula of ether. Write condensed structural formula for ether. Organic Acid Using the IUPAC System, name molecules of organic acid. Identify the class of compounds using the functional group. Draw the structural formula of organic acids. Write condensed structural formulas for organic acids. Esters Using the IUPAC System, name molecules of esters. Identify the class of compounds using the functional group. Draw the structural formula of esters. Write condensed structural formulas for esters. Amines Using the IUPAC System, name molecules of amines. Identify the class of compounds using the functional group. Draw structural formula of amines. Write condensed structural formulas for amines. Amides Using the IUPAC System, name molecules of amides. Identify the class of compounds using the functional group. Draw structural formula of amides. Write condensed structural formula for amides Isomers Define isomers. Identify isomers from structural formulas, condensed molecular formulas or names. Express that different structural formulas always have different properties. Organic Reactions Recognize the organic reactions written as an equation. Add missing reactants or products to any of the organic reactions listed. Addition Substitution Combustion Fermentation Esterifications Saponification Polymerization Physical and Chemical Properties of Organic Compounds Compare relative properties of organic compounds to ionic and metallic bonds Melting Point Boiling Point Volatility Combustion Conductivity

Energy

UNIT TITLE: Energy
NYS Standards:
NYS Science Learning Standards (Pages 54-57)
Guiding Questions/Essential Questions:
How is energy transferred and transformed during chemical reactions, and how do these energy changes influence the behavior and properties of substances? This question prompts exploration of concepts like exothermic and endothermic reactions, activation energy, thermodynamics, and the role of energy in processes like combustion, metabolism, and industrial applications. It encourages students to understand how energy changes are central to chemical reactions and to predict how energy flows through systems in both natural and engineered processes.
Unit Topics with Learning Objectives:
Forms of energy The student will be able to understand that bonds and IMF’s are potential energy. The student will be able to understand that temperature is a measure of average kinetic energy. Understand the difference between temperature and heat. Measurement of energy Joules Understand that joules and kilojoules are the units of measure energy. Thermochemistry Be able to calculate energy changes during a phase change or temperature change. Be able to understand the importance of a closed system to measure energy changes. Fixed points on a thermometer Energy Change during Physical and Chemical changes Apply the concept of conservation of energy during a phase or temperature change. Describe the energy exchange during phase changes and chemical changes. Exothermic change Identify and explain that a change is exothermic. Endothermic change Identify and explain that a change is endothermic. Heating and Cooling Curves Be able to map the potential and kinetic energy changes during a temperature and phase change. Liquids Vapor Pressure Understand that vapor pressure is a measure of the number of molecules in the gas phase above a solid or liquid. Explain how temperature and IMF’s affect the vapor pressure of a substance. Boiling Point Understand that boiling point is pressure dependent. Understand that BP is the temperature at which the atmospheric pressure equals the vapor pressure. Heat of vaporization Be able to calculate the energy involved with a phase change both in the lab and on problems. Solids Melting point Understand that melting point and freezing point occur at the same temperature. Understand that MP is an intensive property. Heat of Fusion Be able to calculate the energy involved with a phase change both in the lab and on problems Sublimation Understand the phase change between solid and liquid phase. Understand that this occurs with substances with weak IMF’s.

Gas Laws

UNIT TITLE: Gas Laws
NYS Standards:
NYS Science Learning Standards (Pages 54-57
Guiding Questions/Essential Questions:
How do the relationships between pressure, volume, temperature, and the amount of gas help us predict and explain the behavior of gases in different conditions? This question invites exploration of the fundamental gas laws (Boyle's Law, Charles's Law, Avogadro's Law, and the Ideal Gas Law), and how they describe and predict how gases respond to changes in pressure, volume, and temperature. It encourages understanding of the molecular behavior of gases and the practical applications of gas laws in fields like engineering, meteorology, and medicine.
Unit Topics with Learning Objectives:
Understand the Basic Concepts of Gases Objective: Identify the characteristics of gases and explain how they differ from solids and liquids. Skills: Describe the physical properties of gases, such as expandability, compressibility, low density, and fluidity. Understand that gases consist of particles in constant random motion, and their behavior is influenced by pressure, volume, temperature, and the number of molecules. Learn the Gas Laws and their Relationships Objective: Understand the individual gas laws and how they describe the relationships between pressure, volume, temperature, and the amount of gas. Skills: Apply Boyle’s Law to relate pressure and volume at constant temperature (P₁V₁ = P₂V₂). Apply Charles’s Law to relate temperature and volume at constant pressure (V₁/T₁ = V₂/T₂). Apply Gay-Lussac’s Law to relate pressure and temperature at constant volume (P₁/T₁ = P₂/T₂). Understand Avogadro’s Law and the relationship between volume and the number of gas molecules at constant temperature and pressure (V₁/n₁ = V₂/n₂). Derive and Use the Ideal Gas Law Objective: Understand the Ideal Gas Law and how it combines the previous gas laws. Skills: Define the Ideal Gas Law equation (PV = nRT) and explain the meaning of each variable (P = pressure, V = volume, n = number of moles, R = ideal gas constant, T = temperature). Use the Ideal Gas Law to solve for unknown variables (P, V, n, T) in problems involving ideal gases. Explain the assumptions behind the Ideal Gas Law and its limitations. Understand Dalton’s Law of Partial Pressures Objective: Learn how to apply Dalton’s Law of Partial Pressures to determine the total pressure exerted by a mixture of gases. Skills: State Dalton’s Law: The total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the individual gases (P_total = P₁ + P₂ + P₃ + ...). Use Dalton’s Law to calculate partial pressures in gas mixtures. Understand the concept of mole fractions and how they relate to partial pressures. Explore Graham’s Law of Diffusion and Effusion Objective: Understand the relationship between the rate of diffusion or effusion of a gas and its molar mass. Skills: State Graham’s Law: The rate of diffusion of a gas is inversely proportional to the square root of its molar mass (rate₁/rate₂ = √(M₂/M₁)). Use Graham’s Law to compare the rates of diffusion of two gases. Apply the concept of effusion to understand how gases pass through small holes. Relate Gas Behavior to Kinetic Molecular Theory Objective: Explain the molecular basis of gas laws using the kinetic molecular theory. Skills: Understand that gas pressure results from collisions of gas molecules with the walls of a container. Relate temperature to the kinetic energy of gas particles. Describe the assumptions of the kinetic molecular theory, including the ideal behavior of gases, the idea that gas molecules are in constant motion, and the lack of attractive forces between gas molecules. Apply Gas Laws to Real-World Problems Objective: Use gas laws to solve practical problems in chemistry and physics. Skills: Solve problems involving gas behavior in situations such as changing temperatures, pressures, or volumes in confined spaces (e.g., weather balloons, scuba diving, tire inflation). Apply gas laws to calculate conditions of gases in chemical reactions, such as the collection of gas over water or the stoichiometry of gas reactions. Investigate the Deviations from Ideal Gas Behavior Objective: Understand when and why real gases deviate from ideal gas behavior. Skills: Identify conditions (such as high pressure or low temperature) where real gases do not behave ideally. Explain the factors contributing to deviations from ideal behavior, such as intermolecular forces and the volume occupied by gas molecules. Use the Van der Waals equation to account for real gas behavior. Relate Temperature and Kinetic Energy in Gas Behavior Objective: Understand the relationship between temperature and the kinetic energy of gas molecules. Skills: Explain that the average kinetic energy of gas molecules is directly proportional to temperature (in Kelvin). Understand the concept of absolute zero and its implications for gas behavior. Relate temperature changes to changes in the speed and energy of gas molecules. Understand the Concept of Standard Temperature and Pressure (STP) Objective: Learn the definition of standard temperature and pressure and how it relates to the behavior of gases. Skills: Define standard temperature (0°C or 273.15 K) and standard pressure (1 atm) and explain their significance. Use STP conditions to solve problems involving gas volumes (e.g., the molar volume of an ideal gas at STP is 22.4 L/mol). Understand the relationship between STP and the Ideal Gas Law in calculations

Chemical Formulas and Math of Chemistry

UNIT TITLE: Chemical Formulas and Math of Chemistry
NYS Standards:
NYS Science Learning Standards (Pages 54-57)
Guiding Questions/Essential Questions:
How do chemical formulas and mathematical relationships help us quantify, predict, and understand the composition and behavior of substances in chemical reactions? This question encourages exploration of how chemical formulas represent the composition of molecules and compounds, how stoichiometry uses mathematical calculations to predict the outcomes of reactions, and how concepts like molar mass, concentration, and reaction yields are essential for solving real-world chemical problems. It also ties together the importance of math in determining proportions, balancing reactions, and calculating energy changes in chemistry.
Unit Topics with Learning Objectives:
Understand the Types of Chemical Formulas: Differentiate between empirical formulas (simplest whole-number ratio of elements) and molecular formulas (actual number of atoms of each element in a molecule). Be able to convert between empirical and molecular formulas when given the molecular weight or the molar mass of the compound. Write and Interpret Chemical Formulas: Write the chemical formulas for simple ionic and covalent compounds using correct chemical symbols and subscripts (e.g., NaCl, H₂O, CO₂). Understand and apply the naming conventions for ionic compounds (e.g., sodium chloride) and covalent compounds (e.g., carbon dioxide). Recognize the role of oxidation states (or valence charges) in determining the formula of ionic compounds. Identify the Components of a Chemical Formula: Identify elements in a chemical formula and use the periodic table to determine the atomic masses. Understand the significance of subscripts (e.g., in H₂O, the "2" means two hydrogen atoms are bonded to one oxygen atom). Determine the Percent Composition of a Compound: Calculate the percent composition of each element in a compound from the formula. Example: Determine the percent composition of water (H₂O) or glucose (C₆H₁₂O₆). Use the atomic masses of elements to calculate the total mass of each element in a given sample. Apply the Law of Definite Proportions: Explain how a compound always contains the same elements in the same proportion by mass, regardless of its source or amount. Math of Chemistry Understand the Mole Concept: Define the mole and understand its relationship to Avogadro’s number Perform conversions between moles, mass, and number of particles (atoms, molecules, ions) using the mole concept. Example: Convert grams of a substance to moles or vice versa using molar mass. Calculate Molar Mass (Molar Weight): Calculate the molar mass of a compound by adding the atomic masses of its constituent elements (using the periodic table). Example: Determine the molar mass of water (H₂O) or calcium carbonate (CaCO₃). Calculate and Use Concentration (Molarity): Understand and apply the concept of molarity (M), which is the concentration of a solution expressed as moles of solute per liter of solution. Solve problems involving dilution and concentration, such as calculating the volume needed to prepare a certain molarity solution or determining the final concentration after dilution. Calculate Percent Yield and Theoretical Yield: Understand the difference between theoretical yield (calculated from stoichiometry) and actual yield (measured experimentally). Calculate percent yield using the formula

Chemical Reaction and Stoichiometry

UNIT TITLE: Chemical Reaction and Stoichiometry
NYS Standards:
NYS Science Learning Standards (Pages 54-57)
Guiding Questions/Essential Questions:
How can we use stoichiometry to predict the amounts of products and reactants in a chemical reaction, and how does this help us understand the conservation of mass and energy? This question encourages exploration of the principles of stoichiometry, including balancing chemical equations, mole-to-mole conversions, limiting reagents, and yield calculations. It emphasizes how stoichiometry connects with the law of conservation of mass and energy, helping to predict the quantities of substances involved in reactions and making sense of how chemical reactions occur in both laboratory and real-world contexts.
Unit Topics with Learning Objectives:
Classify Chemical Reactions: Identify and describe the different types of chemical reactions, including: Synthesis (combination) reactions Decomposition reactions Single replacement (single displacement) reactions Double replacement (double displacement) reactions Combustion reactions Recognize common examples of each type of reaction. Balance Chemical Equations: Apply the law of conservation of mass to balance chemical equations. Ensure that the number of atoms of each element is the same on both sides of the reaction. Write balanced chemical equations for given reactions, including states of matter (solid, liquid, gas, aqueous). Understand Reaction Mechanisms: Identify the reactants and products in a chemical reaction. Explain how energy is absorbed or released in different types of reactions (endothermic vs. exothermic). Predict Products of Reactions: Use the reactivity series, solubility rules, and other guidelines to predict the products of reactions. For double replacement reactions, determine if a precipitate, gas, or water will form. Understand the Mole Concept: Define and calculate the number of moles of a substance. Convert between moles, mass, and number of particles (atoms, molecules, ions) using appropriate conversion factors (Avogadro's number, molar mass). Use Molar Ratios: Interpret and use molar ratios from a balanced chemical equation to convert between amounts of reactants and products. Solve stoichiometric problems involving moles, mass, and volume. Perform Stoichiometric Calculations: Calculate the amount of reactants required to produce a given amount of product. Determine the mass of product formed from a known mass of reactant. Solve problems involving the calculation of limiting reactants and percent yield. Use Dimensional Analysis in Stoichiometry: Apply dimensional analysis techniques to convert units in stoichiometric calculations, ensuring correct units are used in every step of the calculation.

Solutions

UNIT TITLE: Solutions
NYS Standards:
NYS Science Learning Standards (Pages 54-57)
Guiding Questions/Essential Questions:
How do the properties of solutions, such as concentration, solubility, and behavior of solutes, influence chemical reactions and processes in different environments? This question encourages exploration of how factors like temperature, pressure, and the nature of solutes and solvents affect the formation and characteristics of solutions. It also invites investigation into the mathematical calculations of concentration (molarity, molality), the factors that affect solubility, and how understanding solutions is essential in fields like chemistry, biology, medicine, and environmental science.
Unit Topics with Learning Objectives:
Understanding the Nature of Solutions Objective: Explain the process of solution formation, including the roles of solute, solvent, and the interactions between them. Key Concepts: Solubility, dissolving process, and factors affecting solubility (temperature, pressure, and nature of solute/solvent). Concentration of Solutions Objective: Calculate the concentration of a solution using different units, such as molarity (M), molality (m), and percent composition. Key Concepts: Molarity, molality, parts per million (ppm), and percent by mass/volume. Factors Affecting Solubility Objective: Investigate and describe how temperature, pressure, and the chemical nature of solute and solvent affect solubility. Key Concepts: Solubility curves, Henry’s Law (for gases), temperature's effect on solids and gases, and the principle of like dissolves like. Colligative Properties Objective: Understand and apply the concept of colligative properties and how the presence of solute particles affects properties like boiling point elevation and freezing point depression. Key Concepts: Boiling point elevation, freezing point depression, osmotic pressure, and vapor pressure lowering. Solution Stoichiometry Objective: Apply stoichiometry to solve problems involving solutions, such as determining the amount of solute needed to prepare a solution of a given concentration or the amount of product formed in a reaction involving solutions. Key Concepts: Mole-to-mole conversions, dilution, and using concentration to find moles or volume in reactions. Preparing Solutions Objective: Accurately prepare solutions of known concentration by diluting more concentrated solutions and calculating the amount of solute required for a specific molarity or mass percent. Key Concepts: Serial dilutions, mass-to-volume calculations, and practical lab skills. Solubility Equilibria Objective: Understand and explain the concept of solubility equilibrium, including the use of the solubility product constant (Ksp) for sparingly soluble salts. Key Concepts: Saturated solutions, Ksp, dynamic equilibrium, and Le Chatelier's principle applied to solubility. Collaboration of Solutions in Chemical Reactions Objective: Analyze how solutions behave in chemical reactions, including acid-base reactions, precipitation reactions, and redox reactions. Key Concepts: Identifying strong and weak electrolytes, predicting products of reactions in solutions, and understanding the role of ions in solution. Conductivity of Solutions Objective: Compare the conductivity of various solutions (electrolytes vs. nonelectrolytes) and predict the conductivity based on the concentration and type of solute. Key Concepts: Conductivity, strong electrolytes, weak electrolytes, and nonelectrolytes. Applications of Solutions Objective: Recognize real-world applications of solutions, including in biological systems, medicine, environmental science, and industry. Key Concepts: Blood plasma concentration, water treatment, pharmaceuticals, and food industry solutions.

Thermo, Kinetics and Equilibrium

UNIT TITLE: Thermo, Kinetics and Equilibrium
NYS Standards:
NYS Science Learning Standards (Pages 54-57)
Guiding Questions/Essential Questions:
How do energy changes, reaction rates, and dynamic equilibria influence the direction and extent of chemical reactions, and how can this knowledge be applied to control and predict chemical processes? This question encourages exploration of: Thermodynamics: How energy changes (enthalpy, entropy, and Gibbs free energy) determine whether a reaction is spontaneous and how heat and work are transferred. Kinetics: The factors that affect the speed of reactions, including temperature, concentration, catalysts, and activation energy. Equilibrium: How reversible reactions reach a state of equilibrium, where the rates of the forward and reverse reactions are equal, and how Le Chatelier's principle can predict shifts in equilibrium due to changes in conditions.
Unit Topics with Learning Objectives:
Kinetics Describe the rate of a reaction Compare exothermic and endothermic reactions to heat released and gained given a written reaction. Compare exothermic and endothermic reactions to heat released and gained given a chemical reaction. Compare exothermic and endothermic reactions to heat released and gained given changes in state. Define enthalpy. Draw Potential Energy Diagrams for both exothermic and endothermic chemical reactions Label the drawing with PE of Reactants, PE of Products, Activation Energy, Heats of Reaction. Interpret the diagrams as exothermic and endothermic and be able to associate the diagram with the stability of the reactants and products. Interpret diagrams for reverse reactions. Draw the diagram with a catalyst. Interpret the reason the diagram changes with a catalyst. List the factors that affect the rate of a reaction. Explain why the factors change the rate of a reaction. Entropy Describe entropy. Predict whether entropy increases or decreases in chemical reactions. Predict whether entropy increases or decreases in physical changes. Using enthalpy and entropy, predict whether a reaction will spontaneously occur. Equilibrium Describe and explain phase equilibrium. Describe and explain solution equilibrium. Describe and explain chemical equilibrium. Define Le Chatelier’s Principle Apply Le Chatelier’s Principle to changes in concentration. Apply Le Chatelier’s Principle to changes in pressure. Apply Le Chatelier’s Principle to changes in temperature. Apply Le Chatelier’s Principle to changes in catalyst.

Acids/Bases

UNIT TITLE: Acids/Bases
NYS Standards:
NYS Science Learning Standards (Pages 54-57)
Guiding Questions/Essential Questions:
How do acids and bases interact with each other and with other substances, and how can their properties be used to predict chemical behavior and solve real-world problems?" This question invites exploration of: Theories of Acids and Bases: How different models (Arrhenius, Bronsted-Lowry, and Lewis) describe acids and bases, and how they help explain acid-base behavior in various contexts. Properties and Behavior: The distinctive properties of acids and bases, such as pH, conductivity, and reactivity with metals, carbonates, and indicators. Neutralization and Reactions: How acids and bases react to form salts and water, and the concept of titration for determining concentrations. Real-World Applications: How understanding acids and bases is essential in areas such as medicine (e.g., antacids, blood pH regulation), environmental science (e.g., acid rain), and industrial processes (e.g., manufacturing, food production).
Unit Topics with Learning Objectives:
Understanding Acid-Base Theories Objective: Describe the three major acid-base theories: Arrhenius, Bronsted-Lowry, and Lewis, and explain how they define acids and bases. Key Concepts: Arrhenius acids and bases, Bronsted-Lowry acids and bases (proton donors and acceptors), Lewis acids and bases (electron pair donors and acceptors). Properties of Acids and Bases Objective: Identify and compare the characteristic properties of acids and bases, including their effect on pH, taste, texture, and reaction with metals, carbonates, and indicators. Key Concepts: Sour taste, ability to conduct electricity, reactions with metals (acid), slippery feel, bitter taste, reactions with carbonates (base), and the use of pH indicators (e.g., litmus paper, phenolphthalein). pH Scale and Acid-Base Strength Objective: Understand and apply the pH scale to classify substances as acidic, neutral, or basic, and distinguish between strong and weak acids and bases. Key Concepts: pH scale (0–14), strong vs. weak acids and bases, dissociation in water, and the relationship between the concentration of hydrogen ions (H⁺) and pH. Acid-Base Neutralization Reactions Objective: Predict and write the products of acid-base neutralization reactions and explain how they result in the formation of water and a salt. Key Concepts: Neutralization reaction, salt formation, and balancing chemical equations for acid-base reactions. Titration and Calculations Objective: Perform and analyze acid-base titrations to determine the concentration of an unknown acid or base using a suitable indicator. Key Concepts: Titration process, equivalence point, molarity calculations, and using a burette, pipette, and indicator to perform titrations. Buffer Solutions Objective: Explain the concept of a buffer solution and how buffers resist changes in pH when small amounts of acid or base are added. Key Concepts: Buffer action, the role of weak acids and their conjugate bases in maintaining pH, and applications of buffers in biological systems (e.g., blood pH regulation). Bronsted-Lowry Acid-Base Equilibria Objective: Understand and apply the principles of Bronsted-Lowry acid-base equilibria, including conjugate acid-base pairs. Key Concepts: Conjugate acids and bases, equilibrium constant (Kₐ), and the relationship between acid strength and the equilibrium position. Le Chatelier's Principle and Acid-Base Equilibria Objective: Apply Le Chatelier’s principle to predict shifts in the position of equilibrium in acid-base reactions when concentrations, pressure, or temperature are changed. Key Concepts: Le Chatelier’s principle, shifting equilibrium in weak acid-base systems, and how adding more acid or base affects pH. Real-World Applications of Acids and Bases Objective: Identify real-world applications of acids and bases in various fields, such as medicine (antacids), environmental science (acid rain), food chemistry (cooking, fermentation), and industry (cleaning, manufacturing). Key Concepts: Acid rain, antacids and their role in neutralizing stomach acid, the role of acids and bases in digestion, and the use of acids and bases in industrial processes like soap making and cleaning. Acid-Base Indicators and Color Changes Objective: Understand the role of acid-base indicators in detecting the presence of acids and bases, and explain how the color change of an indicator corresponds to changes in pH. Key Concepts: Acid-base indicators (e.g., phenolphthalein, bromothymol blue), pH range for each indicator, and how indicators work to visually signal the acidity or basicity of a solution.

REDOX

UNIT TITLE: REDOX
NYS Standards:
NYS Science Learning Standards (Pages 54-57)
Guiding Questions/Essential Questions:
How do the transfer of electrons in redox reactions drive chemical changes, and how can understanding these processes be used to explain and control energy transfer in biological, industrial, and environmental systems? This question encourages exploration of: Electron Transfer: How oxidation (loss of electrons) and reduction (gain of electrons) occur in chemical reactions. Redox Couples: The relationship between oxidizing and reducing agents, and how these couples influence the direction of the reaction. Energy and Power: The role of redox reactions in energy transfer, such as in batteries, metabolism (cellular respiration), and combustion. Applications: How redox reactions are applied in real-world contexts, from electrochemical cells and corrosion to the processes in living organisms and industrial processes (e.g., metal extraction, hydrogen fuel cells).
Unit Topics with Learning Objectives:
Using the rules for finding oxidation numbers, calculate the oxidation number for elements, compound and polyatomic ions. Reduction/Oxidation Define oxidation and reduction and realize that REDOX is an abbreviation for these two words. Form a complete reaction, write balanced half reactions for both oxidation and reduction. Identify the species oxidizing and the species reducing in a redox reaction. Identify the oxidizing agent and the reducing agent in a redox reaction. Using Table J, predict the the spontaneity of a reaction Using Table J, compare the activity of metals and nonmetals. Voltaic Cells Define a voltaic cell and state applications Label the voltaic cell Be able to show the flow of electrons due to reduction and oxidation of each electrode. Electrolytic Cells Define an electrolytic cell and state applications. Label the electrolytic cell. Be able to show the flow of electrons due to reduction and oxidation of each electrode.

Computer Integrated Manufacturing

Computer Science

COURSE TITLE: Computer Science

COURSE DESCRIPTION: This is an introductory computer science class geared toward students that may have had some experience with coding in the past and are interested in learning how to develop and write their own code. Students are exposed to a variety of topics and programming languages including: hardware and software, coding games in JavaScript, the RobotBASIC programming language and the Python programming language. At the conclusion of this course students will be prepared to take either AP Computer Science or AP Computer Science Principles.

MP1 Units:	MP2 Units:	MP3 Units:	MP4 Units:
Intro JS Interactive Animations and Games	Interactive Animations and Games (cont.)	Intro JS - JavaScript Basics The Canvas and Graphics Control Structures	Functions Animations and Games

Forms of Assessments:
Methods of Formative Assessments: Observations during in-class activities; of students nonverbal feedback during lecture Question and answer sessions, both formal—planned and informal—spontaneous In-class activities where students informally present their results Student feedback collected by periodically answering specific question about the instruction and their self-evaluation of performance and progress Methods of Summative Assessments: Projects (project phases submitted at various completion points could be formatively assessed) Unified Arts Folder / Portfolio Presentations Student evaluation / Conclusion Questions
Methods of Differentiation/Extensions/Accommodations:
1. Content Differentiation : Varied Reading Materials : Providing texts at different reading levels or with varying complexity. Learning Centers : Creating stations with different activities or materials that cater to various learning preferences. 2. Process Differentiation : Flexible Grouping : Organizing students into groups based on their skill levels, interests, or learning styles. Tiered Assignments : Designing assignments with varying levels of difficulty or complexity to challenge students appropriately. 3. Product Differentiation : Choice Boards : Allowing students to choose how they demonstrate their understanding (e.g., presentation, poster, essay). Varied Assessment Methods : Using different forms of assessment (quizzes, projects, oral presentations) to gauge understanding. 4. Learning Environment Differentiation : Flexible Seating Arrangements : Offering various seating options to cater to students' comfort and learning preferences. Use of Technology : Incorporating digital tools that can provide personalized learning experiences. 5. Pacing Differentiation : Individualized Learning Plans : Setting personalized goals and timelines for students based on their readiness. Acceleration Opportunities : Providing advanced materials or tasks for students who grasp concepts quickly. 6. Interest-Based Differentiation : Thematic Units : Designing units around themes that interest students to enhance engagement. Independent Study Projects : Allowing students to explore topics of interest in greater depth. 7. Feedback Differentiation : Individualized Feedback : Offering tailored feedback that addresses specific student needs and strengths. Self-Assessment and Reflection : Encouraging students to evaluate their own work and set personal learning goals. 8. Scaffolding : Step-by-Step Instructions : Breaking tasks into manageable parts and providing guidance as needed. Graphic Organizers : Using visual aids to help students organize information and ideas.

Units

Introduction to Programming in JavaScript

UNIT TITLE: Introduction to Programming in JavaScript
NYS Standards:
NYS K-12 Computer Science and Digital Fluency Standards (9-12) (COMPUTATIONAL THINKING)
Guiding Questions/Essential Questions:
How can understanding the fundamentals of JavaScript help you create interactive applications and solve real-world problems? What is the difference between defining a function and calling a function, and how does this distinction impact how a program is structured? How does breaking down a complex problem into smaller, simpler problems help in designing more efficient programs? How do control structures like if statements, loops, and switches change the flow of a program, and why are they essential for decision-making in code? What is the purpose of using loops in programming, and how does a 'for' loop allow you to repeat a task efficiently?
Unit Topics with Learning Objectives:
Students learn the basics of programming and write their first program by typing out all commands with proper syntax. Commands: Explain how giving commands to a computer is like giving commands to a dog. Defining vs. Calling Methods: Explain the difference between defining and calling a function. Designing methods: Break a large problem down into smaller, simpler problems. Explain the functionality of the main function Control flow: Identify the different control structures we can use to modify the flow of control through a program. Looping : Create for loops to repeat code a fixed number of times. Conditionals: Create if statements that only execute code if a certain condition is true. Explain the purpose of an If/Else statement. Commenting code : Learn how to style their programs by including comments.

JavaScript Basics

UNIT TITLE: JavaScript Basics
NYS Standards:
NYS K-12 Computer Science and Digital Fluency Standards (9-12) (COMPUTATIONAL THINKING)
Guiding Questions/Essential Questions:
What is the role of variables in programming, and how do they help store and manipulate data in JavaScript? How can we use user input to make a program interactive, and why is it important to get data from users in real-world applications? How can JavaScript perform mathematical operations, and how do these operations help solve real-life problems? What is the purpose of functions in JavaScript, and how do they allow us to organize and reuse code effectively?
Unit Topics with Learning Objectives:
Students learn the basics of JavaScript including variables, user input, mathematics, and functions. Students will learn how to print messages out onto the console using the Javascript command. Students learn how to assign values to variables, manipulate those variable values, and use them in program statements. Explain what variables are and what they are used for. Create programs that ask the user for input. Describe the different mathematical operators we can use in programs and create programs that use basic math to compute useful things. Explain why random numbers are a useful part of computer programs. Learn how to create basic functions using JavaScript and use them to improve the organization, readability, and flow of their programs.

JavaScript: The Canvas and Graphics

JavaScript : The Canvas and Graphics
NYS Standards:
NYS K-12 Computer Science and Digital Fluency Standards (9-12) (COMPUTATIONAL THINKING)
Guiding Questions/Essential Questions:
How does the coordinate system on a canvas work, and why is it important to understand how to position shapes using x and y coordinates? How do you create basic shapes like circles and rectangles on the canvas, and how do these shapes serve as building blocks for more complex designs? How can you control the placement of shapes on the canvas using coordinates, and why is it important to know where each shape is positioned in relation to others? How can you add color to shapes on the canvas, and how does color affect the visual appeal and readability of your design?
Unit Topics with Learning Objectives:
Students learn how to add graphics objects and position them on the canvas. Students will explore how to create and position shapes anywhere on the canvas. Understand the coordinate system of the canvas Create basic shapes like circles and rectangles Position shapes in specific locations on the canvas Learn how to add color to shapes

Control Structures - JavaScript

UNIT TITLE: Control Structures - JavaScript
NYS Standards:
NYS K-12 Computer Science and Digital Fluency Standards (9-12) (COMPUTATIONAL THINKING)
Guiding Questions/Essential Questions:
How do control structures, such as if/else statements and loops, allow a program to make decisions and repeat actions, and why are they essential for solving complex problems? What are boolean values, and how can they be used to represent meaningful yes/no or true/false conditions in a program? What is the purpose of if/else statements, and how do they allow a program to make decisions and take different actions based on conditions? How do logical operators (AND, OR, NOT) allow you to combine conditions, and why are they important for writing more complex decision-making logic? What do comparison operators (like ==, >, <=) do, and how do they help compare values to make decisions in a program? How can you combine conditionals with graphics to create dynamic visual elements that change based on specific conditions? What is the purpose of a while loop, and how does it allow a program to repeat actions until a condition is met? How does the break statement work within a loop, and why is it important for stopping a loop prematurely or breaking out of nested loops? How can you use while loops to create dynamic graphics that change continuously or update in response to certain conditions? What is the purpose of a for loop, and how does it help efficiently repeat actions a specific number of times? How can you use for loops to create repeating patterns or animations in graphics, and how does the for loop help you control the number of iterations?
Unit Topics with Learning Objectives:
Students learn how to use control structures such as if/else statements and loops to make advanced programs in JavaScript. Booleans: Create boolean variables to represent meaningful yes/no values. If/Else Statements: Explain the purpose of if statements. Logical Operators: Describe the meaning and usage of each logical operator: OR (\|\|), AND (&&), and NOT (!). Comparison Operators: Explain the meaning of each of the comparison operators (<, <=, >, >=, ==, !=). Graphics and Conditionals: Write graphics programs with conditionals. While Loops: Explain the purpose of a while loop and utilize while loops to solve new types of problems. The Break Statement: Explain how the loop-and-a-half structure is different from a traditional while loop and explain what an infinite loop is. While Loops and Graphics: Write graphics programs that use while loops. For Loops: Create for loops in JavaScript and explain the purpose of for loops. For Loops and Graphics: Create graphics programs with for loops.

Functions - JavaScript

UNIT TITLE: Functions - JavaScript
NYS Standards:
NYS K-12 Computer Science and Digital Fluency Standards (9-12) (COMPUTATIONAL THINKING)
Guiding Questions/Essential Questions:
What is a function, and how does it help make programming more organized, efficient, and reusable? What are parameters in functions, and how do they allow a program to be more flexible and reusable by passing different values into a function? What is the purpose of returning a value from a function, and how does returning a value allow the program to produce meaningful results and pass information between different parts of the code? How do default parameter values work in a function, and why are they useful for handling cases where no argument is passed for a parameter? What is variable scope, and how does it affect which variables are accessible in different parts of a program?
Unit Topics with Learning Objectives:
Students learn to write reusable code with functions, parameters, and return values, and explore the impact of variable scopes. Parameters: Explain the use of parameters and arguments. Return Values: Explain the purpose of returning a value from a function. Default Parameter Values: Understand the role default values can have in a function. Variable Scopes: Identify the scope of a variable and which variables are in scope at a given point in a program

Introduction to Programming - Python

UNIT TITLE: Introduction to Programming - Python
NYS Standards:
NYS K-12 Computer Science and Digital Fluency Standards (9-12) (COMPUTATIONAL THINKING)
Guiding Questions/Essential Questions:
What are variables in programming, and why are they essential for storing and manipulating data in a program? How can we use the input() function in Python to ask users for information, and why is user input important for creating interactive programs? What mathematical operators are available in Python, and how can we use them to solve problems or perform calculations? How can breaking a program into smaller functions and using clear variable names improve the organization and flow of our code?
Unit Topics with Learning Objectives:
Students are introduced to a set of instructions to perform simple tasks in Python, building foundational programming skills. Objectives are similar to the introduction to programming concepts in JavaScript, now being implemented with Python.

Basic Python and Console Interaction

UNIT TITLE: Basic Python and Console Interaction
NYS Standards:
NYS K-12 Computer Science and Digital Fluency Standards (9-12) (COMPUTATIONAL THINKING)
Guiding Questions/Essential Questions:
How do you use the print() function in Python to display messages or results, and why is output important for understanding and debugging a program? What are variables in Python, and how do different data types (such as strings, integers, and floats) help store and manipulate data? How can you collect user input in Python using the input() function, and why is it important to convert input between variable types? What mathematical operators are available in Python, and how do they help perform calculations to solve problems or manipulate data? How can mathematical operators be used with strings in Python, and how do these operations affect text-based data? Why are comments important in Python, and how can they make your code more readable and easier to understand for others (and yourself)? What is the history of programming languages, and how did Python evolve to become one of the most popular languages today?
Unit Topics with Learning Objectives:
Students learn the basics of programming by writing programs that interact with users through the keyboard. Printing in Python: Print text in Python. Variables and Types: Define Python variables and types. User Input: Incorporate user input into their programs and convert between variable types. Mathematical Operators: Describe the different mathematical operators that can be used in their programs. String Operators: Use mathematical operators with strings. Comments: Incorporate comments into their programs in order to make them more readable. Programming Languages: Explain the origins and history of programming languages, with a focus on Python.

Conditionals - Python

UNIT TITLE: Conditionals - Python
NYS Standards:
NYS K-12 Computer Science and Digital Fluency Standards (9-12) (COMPUTATIONAL THINKING)
Guiding Questions/Essential Questions:
What are boolean values, and how can they be used to represent yes/no or true/false conditions in a program? How do if statements allow a program to make decisions, and why is it important to control the flow of execution based on conditions? What do the comparison operators (<, <=, >, >=, ==, !=) do, and how do they help a program compare values and make decisions? How do logical operators (or, and, not) combine multiple conditions, and why are they important for creating more complex decision-making logic? How do floating point numbers work in Python, and why is it important to round values in certain situations, such as when working with currency or measurements?
Unit Topics with Learning Objectives:
Students teach their programs to make decisions based on the information it receives. Booleans: Create boolean variables to represent meaningful yes/no values. If Statements: Use if statements for control flow in their programs. Comparison Operators: Explain the meaning of each of the comparison operators (<, <=, >, >=, ==, !=). Logical Operators: Describe the meaning and usage of each logical operator: or, and, and NOT (!). Floating Point Numbers and Rounding: Use floating point numbers and round values in their programs.

Looping - Python

UNIT TITLE: Looping - Python
NYS Standards:
NYS K-12 Computer Science and Digital Fluency Standards (9-12) (COMPUTATIONAL THINKING)
Guiding Questions/Essential Questions:
How do while loops work, and when should they be used to repeat a block of code while a certain condition is true? How do for loops allow us to repeat code a specific number of times, and why is the loop variable i often used as a counter in such loops? What is the difference between the break and continue statements in loops, and how can they control the flow of a loop's execution? What are nested control structures, and how do we use combinations of loops and conditionals to solve complex problems and control program flow?
Unit Topics with Learning Objectives:
Students learn how to write more efficient code by using loops as shortcuts. While Loops: Effectively use while loops in their programs. For Loops: Implement for loops and use the variable i as a counter. Break and Continue: Explain the critical difference between break and continue. Nested Control Structures: Identify the different control structures that can be used to modify the flow of control through a program.

Roles in a Software Development Team

UNIT TITLE: Roles in a Software Development Team
NYS Standards:
NYS K-12 Computer Science and Digital Fluency Standards (9-12) (NETWORKS & SYSTEM DESIGN)
Guiding Questions/Essential Questions:
What is the role of a software engineer in a development team, and how do they contribute to building, testing, and maintaining software? How do Quality Assurance engineers ensure the software is reliable and free from defects, and why is their work critical to the success of a software project? What role do designers play in the software development process, and how do they influence the user experience (UX) and visual design of the software? How do project managers facilitate the development process, and why is effective communication and collaboration essential for keeping the team on track and delivering a successful project?