SECTION I:  List of Topics
SECTION II:  List of HSCE's
SECTION I
ENGLISH/LANGUAGE ARTS:
Writing, Speaking, and Visual Expression
Pre-writing
Revising and Editing
Paragraph Organization
Transitions
Persuasive Writing
Citations
 
Reading, Listening, and Viewing
Predictions
Purpose and Audience
Inferences and Conclusions
Print Features
Context Clues
Word Roots and Affixes
Organizational Patterns
Fact and Opinion
Main Idea and Significant Details
Summarization
Persuasive Strategies
Instructions and Work-place Texts
 
Literary and Culture
Literary Language
Characterization
Plot
Analyze Text Characteristics
Author's Perspective and Beliefs
Compare Texts
Theme
Literary Genres
Poetry
Dramatic Literature
Historical and Cultural Context
 
Language
Sentence Structures
Appropriate Language
Dictionary, Thesaurus, and Glossary
Adverbs
Conjunctions
Prepositions
Interjections
Pronouns
Verb Usage
Spelling
Capitalization
Punctuation
 
MATH:
Algebra I
Properties of Arithmetic
Absolute Value
Exponents
Algebraic Expressions
Symbolize Problems Solutions
Inequalities
Linear Functions and Equations
Systems of Equations
Functions
Graphs of Functions
Inverses of Functions
Real World Functions
Quadratic Functions and Equations
Radical and Power Functions and Equations
Scatterplots
 
Geometry
Vectors
Convert Units
Mathematical Reasoning and Logic
Angles
Distance and Midpoint
Triangles
Trigonometry
Polygons
Circles
Surface Area and Volume
Drawing Objects
Similar and Congruent Triangles
Change in Dimensions
Object Transformations
 
Algebra II
Counting Techniques
Complex Numbers
Sequences and Series
Accuracy, Estimation, and Error
Polynomials and Rational Expressions
Polynomial and Rational Functions
Exponential and Logarithmic Functions
Trigonometric Functions and Equations
Graphs of Trigonometric Functions
Conic Sections
Interpret Graphs
Box Plots
Central Tendency and Distributions
Sampling Analysis
Probablility Theory
 
SCIENCE:
Biology
Inquiry, Reflection, and Social Implications
 
Earth Science
Inquiry, Reflection, and Social Implications
 
Chemistry
Inquiry, Reflection, and Social Implications
 
Physics
Inquiry, Reflection, and Social Implications
 
SECTION II
ENGLISH:
Prewriting
HSCE
MI Grade 11, English/L.A. HSCE
CE 1.1.1
Demonstrate flexibility in using independent and collaborative strategies for planning, drafting, revising, and editing complex texts.
 
MI Grade 11, English/L.A. HSCE
CE 1.1.2
Know and use a variety of prewriting strategies to generate, focus, and organize ideas (e.g., free writing, clustering/mapping, talking with others, brainstorming, outlining, developing graphic organizers, taking notes, summarizing, paraphrasing).
 
MI Grade 11, English/L.A. HSCE
CE 1.4.1
Identify, explore, and refine topics and questions appropriate for research.
 
MI Grade 11, English/L.A. HSCE
CE 1.4.2
Develop a system for gathering, organizing, paraphrasing, and summarizing information; select, evaluate, synthesize, and use multiple primary and secondary (print and electronic) resources.
 
MI Grade 11, English/L.A. HSCE
CE 1.4.3
Develop and refine a position, claim, thesis, or hypothesis that will be explored and supported by analyzing different perspectives, resolving inconsistencies, and writing about those differences in a structure appropriate for the audience (e.g., argumentative essay that avoids inconsistencies in logic and develops a single thesis; exploratory essay that explains differences and similarities and raises additional questions).
 
Revising and Editing
HSCE
MI Grade 11, English/L.A. HSCE
CE 1.1.1
Demonstrate flexibility in using independent and collaborative strategies for planning, drafting, revising, and editing complex texts.
 
MI Grade 11, English/L.A. HSCE
CE 1.1.5
Revise drafts to more fully and/or precisely convey meaning—drawing on response from others, self-reflection, and reading one’s own work with the eye of a reader; then refine the text—deleting and/or reorganizing ideas, and addressing potential readers’ questions.
 
MI Grade 11, English/L.A. HSCE
CE 1.1.6
Reorganize sentence elements as needed and choose grammatical and stylistic options that provide sentence variety, fluency, and flow.
 
MI Grade 11, English/L.A. HSCE
CE 1.1.7
Edit for style, tone, and word choice (specificity, variety, accuracy, appropriateness, conciseness) and for conventions of grammar, usage and mechanics that are appropriate for audience.
 
MI Grade 11, English/L.A. HSCE
CE 1.1.8
Proofread to check spelling, layout, and font; and prepare selected pieces for a public audience.
 
Paragraph Organization
HSCE
MI Grade 11, English/L.A. HSCE
CE 1.3.2
Compose written and spoken essays or work-related text that demonstrate logical thinking and the development of ideas for academic, creative, and personal purposes: essays that convey the author’s message by using an engaging introduction (with a clear thesis as appropriate), well-constructed paragraphs, transition sentences, and a powerful conclusion.
 
MI Grade 11, English/L.A. HSCE
CE 1.4.3
Develop and refine a position, claim, thesis, or hypothesis that will be explored and supported by analyzing different perspectives, resolving inconsistencies, and writing about those differences in a structure appropriate for the audience (e.g., argumentative essay that avoids inconsistencies in logic and develops a single thesis; exploratory essay that explains differences and similarities and raises additional questions).
 
MI Grade 11, English/L.A. HSCE
CE 1.4.5
Develop organizational structures appropriate to the purpose and message, and use transitions that produce a sequential or logical flow of ideas.
 
MI Grade 11, English/L.A. HSCE
CE 1.5.3
Select format and tone based on the desired effect and audience, using effective written and spoken language, sound, and/or visual representations (e.g., focus, transitions, facts, detail and evidence to support judgments, skillful use of rhetorical devices, and a coherent conclusion).
 
Transitions
HSCE
MI Grade 11, English/L.A. HSCE
CE 1.3.2
Compose written and spoken essays or work-related text that demonstrate logical thinking and the development of ideas for academic, creative, and personal purposes: essays that convey the author’s message by using an engaging introduction (with a clear thesis as appropriate), well-constructed paragraphs, transition sentences, and a powerful conclusion.
 
MI Grade 11, English/L.A. HSCE
CE 1.4.5
Develop organizational structures appropriate to the purpose and message, and use transitions that produce a sequential or logical flow of ideas.
 
MI Grade 11, English/L.A. HSCE
CE 1.5.3
Select format and tone based on the desired effect and audience, using effective written and spoken language, sound, and/or visual representations (e.g., focus, transitions, facts, detail and evidence to support judgments, skillful use of rhetorical devices, and a coherent conclusion).
 
Persuasive Writing
HSCE
MI Grade 11, English/L.A. HSCE
CE 1.3.4
Develop and extend a thesis, argument, or exploration of a topic by analyzing differing perspectives and employing a structure that effectively conveys the ideas in writing (e.g. resolve inconsistencies in logic; use a range of strategies to persuade, clarify, and defend a position with precise and relevant evidence; anticipate and address concerns and counterclaims; provide a clear and effective conclusion).
 
MI Grade 11, English/L.A. HSCE
CE 1.4.3
Develop and refine a position, claim, thesis, or hypothesis that will be explored and supported by analyzing different perspectives, resolving inconsistencies, and writing about those differences in a structure appropriate for the audience (e.g., argumentative essay that avoids inconsistencies in logic and develops a single thesis; exploratory essay that explains differences and similarities and raises additional questions).
 
MI Grade 11, English/L.A. HSCE
CE 1.5.3
Select format and tone based on the desired effect and audience, using effective written and spoken language, sound, and/or visual representations (e.g., focus, transitions, facts, detail and evidence to support judgments, skillful use of rhetorical devices, and a coherent conclusion).
 
Citations
HSCE
MI Grade 11, English/L.A. HSCE
CE 1.4.6
Use appropriate conventions of textual citation in different contexts (e.g., different academic disciplines and workplace writing situations).
 
Predictions
HSCE
MI Grade 11, English/L.A. HSCE
CE 2.1.1
Use a variety of pre-reading and previewing strategies (e.g., acknowledge own prior knowledge, make connections, generate questions, make predictions, scan a text for a particular purpose or audience, analyze text structure and features) to make conscious choices about how to approach the reading based on purpose, genre, level of difficulty, text demands and features.
 
Purpose and Audience
HSCE
MI Grade 11, English/L.A. HSCE
CE 2.1.1
Use a variety of pre-reading and previewing strategies (e.g., acknowledge own prior knowledge, make connections, generate questions, make predictions, scan a text for a particular purpose or audience, analyze text structure and features) to make conscious choices about how to approach the reading based on purpose, genre, level of difficulty, text demands and features.
 
MI Grade 11, English/L.A. HSCE
CE 3.1.4
Analyze characteristics of specific works and authors (e.g., voice, mood, time sequence, author vs. narrator, stated vs. implied author, intended audience and purpose, irony, parody, satire, propaganda, use of archetypes and symbols) and identify basic beliefs, perspectives, and philosophical assumptions underlying an author’s work.
 
MI Grade 11, English/L.A. HSCE
CE 1.1.3
Select and use language that is appropriate (e.g., formal, informal, literary, or technical) for the purpose, audience, and context of the text, speech, or visual representation (e.g., letter to editor, proposal, poem, or digital story).
 
MI Grade 11, English/L.A. HSCE
CE 1.3.5
From the outset, identify and assess audience expectations and needs; consider the rhetorical effects of style, form, and content based on that assessment; and adapt communication strategies appropriately and effectively.
 
Inferences and Conclusions
HSCE
MI Grade 11, English/L.A. HSCE
CE 2.1.2
Make supported inferences and draw conclusions based on informational print and multimedia features (e.g., prefaces, appendices, marginal notes, illustrations, bibliographies, author’s pages, footnotes, diagrams, tables, charts, maps, timelines, graphs, and other visual and special effects) and explain how authors and speakers use them to infer the organization of text and enhance understanding, convey meaning, and inspire or mislead audiences.
 
MI Grade 11, English/L.A. HSCE
CE 1.4.4
Interpret, synthesize, and evaluate information/findings in various print sources and media (e.g., fact and opinion, comprehensiveness of the evidence, bias, varied perspectives, motives and credibility of the author, date of publication) to draw conclusions and implications.
 
Print Features
HSCE
MI Grade 11, English/L.A. HSCE
CE 2.1.1
Use a variety of pre-reading and previewing strategies (e.g., acknowledge own prior knowledge, make connections, generate questions, make predictions, scan a text for a particular purpose or audience, analyze text structure and features) to make conscious choices about how to approach the reading based on purpose, genre, level of difficulty, text demands and features.
 
MI Grade 11, English/L.A. HSCE
CE 2.1.2
Make supported inferences and draw conclusions based on informational print and multimedia features (e.g., prefaces, appendices, marginal notes, illustrations, bibliographies, author’s pages, footnotes, diagrams, tables, charts, maps, timelines, graphs, and other visual and special effects) and explain how authors and speakers use them to infer the organization of text and enhance understanding, convey meaning, and inspire or mislead audiences.
 
MI Grade 11, English/L.A. HSCE
CE 2.1.9
Examine the intersections and distinctions between visual (media images, painting, film, and graphic arts) and verbal communication.
 
MI Grade 11, English/L.A. HSCE
CE 1.2.1
Write, speak, and use images and graphs to understand and discover complex ideas.
 
Context Clues
HSCE
MI Grade 11, English/L.A. HSCE
CE 4.1.2
Use resources to determine word meanings, pronunciations, and word etymologies (e.g., context, print and electronic dictionaries, thesauruses, glossaries, and others).
 
MI Grade 11, English/L.A. HSCE
CE 2.1.3
Determine the meaning of unfamiliar words, specialized vocabulary, figurative language, idiomatic expressions, and technical meanings of terms through context clues, word roots and affixes, and the use of appropriate resource materials such as print and electronic dictionaries.
 
Word Roots and Affixes
MI Grade 11, English/L.A. HSCE
CE 2.1.3
Determine the meaning of unfamiliar words, specialized vocabulary, figurative language, idiomatic expressions, and technical meanings of terms through context clues, word roots and affixes, and the use of appropriate resource materials such as print and electronic dictionaries.
 
Organizational Patterns
HSCE
MI Grade 11, English/L.A. HSCE
CE 2.1.5
Analyze and evaluate the components of multiple organizational patterns (e.g., compare/contrast, cause/effect, problem/solution, fact/opinion, theory/evidence).
 
MI Grade 11, English/L.A. HSCE
CE 2.1.1
Use a variety of pre-reading and previewing strategies (e.g., acknowledge own prior knowledge, make connections, generate questions, make predictions, scan a text for a particular purpose or audience, analyze text structure and features) to make conscious choices about how to approach the reading based on purpose, genre, level of difficulty, text demands and features.
 
MI Grade 11, English/L.A. HSCE
CE 2.1.4
Identify and evaluate the primary focus, logical argument, structure, and style of a text or speech and the ways in which these elements support or confound meaning or purpose.
 
MI Grade 11, English/L.A. HSCE
CE 1.4.5
Develop organizational structures appropriate to the purpose and message, and use transitions that produce a sequential or logical flow of ideas.
 
MI Grade 11, English/L.A. HSCE
CE 2.1.10
Listen to and view speeches, presentations, and multimedia works to identify and respond thoughtfully to key ideas, significant details, logical organization, fact and opinion, and propaganda.
 
Fact and Opinion
HSCE
MI Grade 11, English/L.A. HSCE
CE 2.1.5
Analyze and evaluate the components of multiple organizational patterns (e.g., compare/contrast, cause/effect, problem/solution, fact/opinion, theory/evidence).
 
MI Grade 11, English/L.A. HSCE
CE 2.1.10
Listen to and view speeches, presentations, and multimedia works to identify and respond thoughtfully to key ideas, significant details, logical organization, fact and opinion, and propaganda.
 
MI Grade 11, English/L.A. HSCE
CE 1.4.4
Interpret, synthesize, and evaluate information/findings in various print sources and media (e.g., fact and opinion, comprehensiveness of the evidence, bias, varied perspectives, motives and credibility of the author, date of publication) to draw conclusions and implications.
 
Main Idea and Significant Details
HSCE
MI Grade 11, English/L.A. HSCE
CE 2.1.6
Recognize the defining characteristics of informational texts, speeches, and multimedia presentations (e.g., documentaries and research presentations) and elements of expository texts (e.g., thesis, supporting ideas, and statistical evidence); critically examine the argumentation and conclusions of multiple informational texts.
 
Summarization
HSCE
MI Grade 11, English/L.A. HSCE
CE 2.1.7
Demonstrate understanding of written, spoken, or visual information by restating, paraphrasing, summarizing, critiquing, or composing a personal response; distinguish between a summary and a critique.
 
MI Grade 11, English/L.A. HSCE
CE 1.4.2
Develop a system for gathering, organizing, paraphrasing, and summarizing information; select, evaluate, synthesize, and use multiple primary and secondary (print and electronic) resources.
 
Persuasive Strategies
HSCE
MI Grade 11, English/L.A. HSCE
CE 1.4.4
Interpret, synthesize, and evaluate information/findings in various print sources and media (e.g., fact and opinion, comprehensiveness of the evidence, bias, varied perspectives, motives and credibility of the author, date of publication) to draw conclusions and implications.
 
MI Grade 11, English/L.A. HSCE
CE 2.2.1
Recognize literary and persuasive strategies as ways by which authors convey ideas and readers make meaning (e.g., imagery, irony, satire, parody, propaganda, overstatement/understatement, omission, and multiple points of view).
 
MI Grade 11, English/L.A. HSCE
CE 4.2.4
Understand the appropriate uses and implications of casual or informal versus professional language; understand, as well, the implications of language designed to control others and the detrimental effects of its use on targeted individuals or groups (e.g., propaganda, homophobic language, and racial, ethnic, or gender epithets).
 
MI Grade 11, English/L.A. HSCE
CE 3.1.4
Analyze characteristics of specific works and authors (e.g., voice, mood, time sequence, author vs. narrator, stated vs. implied author, intended audience and purpose, irony, parody, satire, propaganda, use of archetypes and symbols) and identify basic beliefs, perspectives, and philosophical assumptions underlying an author’s work.
 
Instructions and Workplace Texts
HSCE
MI Grade 11, English/L.A. HSCE
CE 2.3.1
Read, listen to, and view diverse texts for multiple purposes such as learning complex procedures, making work-place decisions, or pursuing in-depth studies.
 
MI Grade 11, English/L.A. HSCE
CE 2.3.3
Critically read and interpret instructions for a variety of tasks (e.g., completing assignments, using software, writing college and job applications).
 
Literary Language
HSCE
MI Grade 11, English/L.A. HSCE
CE 3.1.1
Interpret literary language (e.g., imagery, allusions, symbolism, metaphor) while reading literary and expository works.
 
MI Grade 11, English/L.A. HSCE
CE 2.1.3
Determine the meaning of unfamiliar words, specialized vocabulary, figurative language, idiomatic expressions, and technical meanings of terms through context clues, word roots and affixes, and the use of appropriate resource materials such as print and electronic dictionaries.
 
MI Grade 11, English/L.A. HSCE
CE 2.2.1
Recognize literary and persuasive strategies as ways by which authors convey ideas and readers make meaning (e.g., imagery, irony, satire, parody, propaganda, overstatement/understatement, omission, and multiple points of view).
 
Characterization
HSCE
MI Grade 11, English/L.A. HSCE
CE 3.1.2
Demonstrate an understanding of literary characterization, character development, the function of major and minor characters, motives and causes for action, and moral dilemmas that characters encounter by describing their function in specific works.
 
Plot
HSCE
MI Grade 11, English/L.A. HSCE
CE 3.1.3
Recognize a variety of plot structures and elements (e.g., story within a story, rising action, foreshadowing, flash backs, cause-and-effect relationships, conflicts, resolutions) and describe their impact on the reader in specific literary works.
 
Analyze Text Characteristics
HSCE
MI Grade 11, English/L.A. HSCE
CE 3.1.4
Analyze characteristics of specific works and authors (e.g., voice, mood, time sequence, author vs. narrator, stated vs. implied author, intended audience and purpose, irony, parody, satire, propaganda, use of archetypes and symbols) and identify basic beliefs, perspectives, and philosophical assumptions underlying an author’s work.
 
MI Grade 11, English/L.A. HSCE
CE 1.4.4
Interpret, synthesize, and evaluate information/findings in various print sources and media (e.g., fact and opinion, comprehensiveness of the evidence, bias, varied perspectives, motives and credibility of the author, date of publication) to draw conclusions and implications.
 
Compare Texts
HSCE
MI Grade 11, English/L.A. HSCE
CE 3.1.5
Comparatively analyze two or more literary or expository texts, comparing how and why similar themes are treated differently, by different authors, in different types of text, in different historical periods, and/or from different cultural perspectives.
 
Theme
HSCE
MI Grade 11, English/L.A. HSCE
CE 3.1.8
Demonstrate an understanding of historical, political, cultural, and philosophical themes and questions raised by literary and expository works.
 
Literary Genres
HSCE
MI Grade 11, English/L.A. HSCE
CE 2.1.6
Recognize the defining characteristics of informational texts, speeches, and multimedia presentations (e.g., documentaries and research presentations) and elements of expository texts (e.g., thesis, supporting ideas, and statistical evidence); critically examine the argumentation and conclusions of multiple informational texts.
 
MI Grade 11, English/L.A. HSCE
CE 2.3.4
Critically interpret primary and secondary research-related documents (e.g., historical and government documents, newspapers, critical and technical articles, and subject-specific books).
 
MI Grade 11, English/L.A. HSCE
CE 3.2.1
Recognize a variety of literary genres and forms (e.g., poetry, drama, novels, short stories, autobiographies, biographies, multi-genre texts, satire, parody, allegory) and demonstrate an understanding of the way in which genre and form influence meaning.
 
Historical and Cultural Context
HSCE
MI Grade 11, English/L.A. HSCE
CE 3.1.8
Demonstrate an understanding of historical, political, cultural, and philosophical themes and questions raised by literary and expository works.
 
Sentence Structures
HSCE
MI Grade 11, English/L.A. HSCE
CE 4.1.1
Use sentence structures and vocabulary effectively within different modes (oral and written, formal and informal) and for various rhetorical purposes.
 
MI Grade 11, English/L.A. HSCE
CE 4.1.5
Demonstrate use of conventions of grammar, usage, and mechanics in written texts, including parts of speech, sentence structure and variety, spelling, capitalization, and punctuation.
 
Appropriate Language
HSCE
MI Grade 11, English/L.A. HSCE
CE 4.1.4
Control standard English structures in a variety of contexts (e.g., formal speaking, academic prose, business, and public writing) using language carefully and precisely.
 
MI Grade 11, English/L.A. HSCE
CE 4.2.4
Understand the appropriate uses and implications of casual or informal versus professional language; understand, as well, the implications of language designed to control others and the detrimental effects of its use on targeted individuals or groups (e.g., propaganda, homophobic language, and racial, ethnic, or gender epithets).
 
MI Grade 11, English/L.A. HSCE
CE 4.1.1
Use sentence structures and vocabulary effectively within different modes (oral and written, formal and informal) and for various rhetorical purposes.
 
MI Grade 11, English/L.A. HSCE
CE 1.1.3
Select and use language that is appropriate (e.g., formal, informal, literary, or technical) for the purpose, audience, and context of the text, speech, or visual representation (e.g., letter to editor, proposal, poem, or digital story).
 
Dictionary, Thesaurus, and Glossary
HSCE
MI Grade 11, English/L.A. HSCE
CE 4.1.2
Use resources to determine word meanings, pronunciations, and word etymologies (e.g., context, print and electronic dictionaries, thesauruses, glossaries, and others).
 
MI Grade 11, English/L.A. HSCE
CE 2.1.3
Determine the meaning of unfamiliar words, specialized vocabulary, figurative language, idiomatic expressions, and technical meanings of terms through context clues, word roots and affixes, and the use of appropriate resource materials such as print and electronic dictionaries.
 
Adverbs
HSCE
MI Grade 11, English/L.A. HSCE
CE 4.1.5
Demonstrate use of conventions of grammar, usage, and mechanics in written texts, including parts of speech, sentence structure and variety, spelling, capitalization, and punctuation.
 
Conjunctions
HSCE
MI Grade 11, English/L.A. HSCE
CE 4.1.5
Demonstrate use of conventions of grammar, usage, and mechanics in written texts, including parts of speech, sentence structure and variety, spelling, capitalization, and punctuation.
 
Prepositions
HSCE
MI Grade 11, English/L.A. HSCE
CE 4.1.5
Demonstrate use of conventions of grammar, usage, and mechanics in written texts, including parts of speech, sentence structure and variety, spelling, capitalization, and punctuation.
 
Interjections
HSCE
MI Grade 11, English/L.A. HSCE
CE 4.1.5
Demonstrate use of conventions of grammar, usage, and mechanics in written texts, including parts of speech, sentence structure and variety, spelling, capitalization, and punctuation.
 
Pronouns
HSCE
MI Grade 11, English/L.A. HSCE
CE 4.1.5
Demonstrate use of conventions of grammar, usage, and mechanics in written texts, including parts of speech, sentence structure and variety, spelling, capitalization, and punctuation.
 
Verb Usage
HSCE
MI Grade 11, English/L.A. HSCE
CE 4.1.5
Demonstrate use of conventions of grammar, usage, and mechanics in written texts, including parts of speech, sentence structure and variety, spelling, capitalization, and punctuation.
 
Spelling
HSCE
MI Grade 11, English/L.A. HSCE
CE 4.1.5
Demonstrate use of conventions of grammar, usage, and mechanics in written texts, including parts of speech, sentence structure and variety, spelling, capitalization, and punctuation.
 
MI Grade 11, English/L.A. HSCE
CE 1.1.8
Proofread to check spelling, layout, and font; and prepare selected pieces for a public audience.
 
Capitalization
HSCE
MI Grade 11, English/L.A. HSCE
CE 4.1.5
Demonstrate use of conventions of grammar, usage, and mechanics in written texts, including parts of speech, sentence structure and variety, spelling, capitalization, and punctuation.
 
Punctuation
HSCE
MI Grade 11, English/L.A. HSCE
CE 4.1.5
Demonstrate use of conventions of grammar, usage, and mechanics in written texts, including parts of speech, sentence structure and variety, spelling, capitalization, and punctuation.
 
MATH:
Properties of Arithmetic
HSCE
MI Grade 11, Math HSCE
L1.1.1
Know the different properties that hold in different number systems and recognize that the applicable properties change in the transition from the positive integers to all integers, to the rational numbers, and to the real numbers.
 
MI Grade 11, Math HSCE
L1.1.2
Explain why the multiplicative inverse of a number has the same sign as the number, while the additive inverse of a number has the opposite sign.
 
MI Grade 11, Math HSCE
L1.1.3
Explain how the properties of associativity, commutativity, and distributivity, as well as identity and inverse elements, are used in arithmetic and algebraic calculations.
 
MI Grade 11, Math HSCE
L1.1.4
Describe the reasons for the different effects of multiplication by, or exponentiation of, a positive number by a number less than 0, a number between 0 and 1, and a number greater than 1.
 
MI Grade 11, Math HSCE
L1.1.5
Justify numerical relationships
 
Absolute Value
HSCE
MI Grade 11, Math HSCE
L1.2.2
Interpret representations that reflect absolute value relationships in such contexts as error tolerance.
 
MI Grade 11, Math HSCE
A1.2.4
Solve absolute value equations and inequalities, and justify steps in the solution.
 
Exponents
HSCE
MI Grade 11, Math HSCE
L2.1.2
Calculate fluently with numerical expressions involving exponents; use the rules of exponents; evaluate numerical expressions involving rational and negative exponents; transition easily between roots and exponents.
 
Algebraic Expressions
HSCE
MI Grade 11, Math HSCE
A1.1.1
Give a verbal description of an expression that is presented in symbolic form, write an algebraic expression from a verbal description, and evaluate expressions given values of the variables.
 
MI Grade 11, Math HSCE
A1.1.2
Know the definitions and properties of exponents and roots transition fluently between them, and apply them in algebraic expressions.
 
Symbolize Problems Solutions
HSCE
MI Grade 11, Math HSCE
A1.2.1
Write equations and inequalities with one or two variables to represent mathematical or applied situations, and solve.
 
Inequalities
HSCE
MI Grade 11, Math HSCE
A1.2.3
Solve linear and quadratic equations and inequalities including systems of up to three linear equations with three unknowns. Justify steps in the solution, and apply the quadratic formula appropriately.
 
MI Grade 11, Math HSCE
A1.2.4
Solve absolute value equations and inequalities, and justify steps in the solution.
 
Linear Functions and Equations
HSCE
MI Grade 11, Math HSCE
A1.2.3
Solve linear and quadratic equations and inequalities including systems of up to three linear equations with three unknowns. Justify steps in the solution, and apply the quadratic formula appropriately.
 
MI Grade 11, Math HSCE
A3.1.1
Write the symbolic forms of linear functions (standard, point-slope, and slope-intercept) given appropriate information, and convert between forms.
 
MI Grade 11, Math HSCE
A3.1.2
Graph lines (including those of the form x = h and y = k) given appropriate information.
 
MI Grade 11, Math HSCE
A3.1.3
Relate the coefficients in a linear function to the slope and x- and y-intercepts of its graph.
 
MI Grade 11, Math HSCE
A3.1.4
Find an equation of the line parallel or perpendicular to given line, through a given point; understand and use the facts that non-vertical parallel lines have equal slopes, and that non-vertical perpendicular lines have slopes that multiply to give -1.
 
Systems of Equations
HSCE
MI Grade 11, Math HSCE
A1.2.3
Solve linear and quadratic equations and inequalities including systems of up to three linear equations with three unknowns. Justify steps in the solution, and apply the quadratic formula appropriately.
 
Functions
HSCE
MI Grade 11, Math HSCE
A1.2.2
Associate a given equation with a function whose zeros are the solutions of the equation.
 
MI Grade 11, Math HSCE
A1.2.8
Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable. Justify steps in the solution.
 
MI Grade 11, Math HSCE
A2.1.1
Determine whether a relationship (given in contextual, symbolic, tabular, or graphical form) is a function and identify its domain and range.
 
MI Grade 11, Math HSCE
A2.1.2
Read, interpret, and use function notation and evaluate a function at a value in its domain.
 
MI Grade 11, Math HSCE
A2.1.3
Represent functions in symbols, graphs, tables, diagrams, or words and translate among representations.
 
MI Grade 11, Math HSCE
A2.1.4
Recognize that functions may be defined by different expressions over different intervals of their domains; such functions are piecewise-defined.
 
MI Grade 11, Math HSCE
A2.1.5
Recognize that functions may be defined recursively. Compute values of and graph simple recursively defined functions.
 
MI Grade 11, Math HSCE
A2.1.6
Identify the zeros of a function, the intervals where the values of a function are positive or negative, and describe the behavior of a function as x approaches positive or negative infinity, given the symbolic and graphical representations.
 
MI Grade 11, Math HSCE
A2.1.7
Identify and interpret the key features of a function from its graph or its formula(e).
 
MI Grade 11, Math HSCE
A2.2.1
Combine functions by addition, subtraction, multiplication, and division.
 
Graphs of Functions
HSCE
MI Grade 11, Math HSCE
A2.2.2
Apply given transformations to basic functions and represent symbolically.
 
Inverses of Functions
HSCE
MI Grade 11, Math HSCE
A2.2.3
Recognize whether a function (given in tabular or graphical form) has an inverse and recognize simple inverse pairs.
 
Real World Functions
HSCE
MI Grade 11, Math HSCE
A2.3.2
Describe the tabular pattern associated with functions having constant rate of change (linear); or variable rates of change.
 
MI Grade 11, Math HSCE
A2.4.1
Identify the family of function best suited for modeling a given real-world situation.
 
MI Grade 11, Math HSCE
A2.4.2
Adapt the general symbolic form of a function to one that fits the specification of a given situation by using the information to replace arbitrary constants with numbers.
 
MI Grade 11, Math HSCE
A2.4.3
Using the adapted general symbolic form, draw reasonable conclusions about the situation being modeled.
 
Quadratic Functions and Equations
HSCE
MI Grade 11, Math HSCE
A1.2.3
Solve linear and quadratic equations and inequalities including systems of up to three linear equations with three unknowns. Justify steps in the solution, and apply the quadratic formula appropriately.
 
MI Grade 11, Math HSCE
A3.3.1
Write the symbolic form and sketch the graph of a quadratic function given appropriate information.
 
MI Grade 11, Math HSCE
A3.3.2
Identify the elements of a parabola (vertex, axis of symmetry, direction of opening) given its symbolic form or its graph, and relate these elements to the coefficient(s) of the symbolic form of the function.
 
MI Grade 11, Math HSCE
A3.3.3
Convert quadratic functions from standard to vertex form by completing the square.
 
MI Grade 11, Math HSCE
A3.3.4
Relate the number of real solutions of a quadratic equation to the graph of the associated quadratic function.
 
MI Grade 11, Math HSCE
A3.3.5
Express quadratic functions in vertex form to identify their maxima or minima, and in factored form to identify their zeros.
 
Radical and Power Functions and Equations
HSCE
MI Grade 11, Math HSCE
A1.2.6
Solve power equations and equations including radical expressions, justify steps in the solution, and explain how extraneous solutions may arise.
 
MI Grade 11, Math HSCE
A3.4.1
Write the symbolic form and sketch the graph of power functions.
 
MI Grade 11, Math HSCE
A3.4.2
Express direct and inverse relationships as functions and recognize their characteristics.
 
MI Grade 11, Math HSCE
A3.4.3
Analyze the graphs of power functions, noting reflectional or rotational symmetry.
 
Scatterplots
HSCE
MI Grade 11, Math HSCE
S2.1.1
Construct a scatterplot for a bivariate data set with appropriate labels and scales.
 
MI Grade 11, Math HSCE
S2.1.2
Given a scatterplot, identify patterns, clusters, and outliers. Recognize no correlation, weak correlation, and strong correlation.
 
MI Grade 11, Math HSCE
S2.1.3
Estimate and interpret Pearson’s correlation coefficient for a scatterplot of a bivariate data set. Recognize that correlation measures the strength of linear association.
 
MI Grade 11, Math HSCE
S2.1.4
Differentiate between correlation and causation. Know that a strong correlation does not imply a cause-and-effect relationship. Recognize the role of lurking variables in correlation.
 
MI Grade 11, Math HSCE
S2.2.1
For bivariate data that appear to form a linear pattern, find the least squares regression line by estimating visually and by calculating the equation of the regression line. Interpret the slope of the equation for a regression line.
 
MI Grade 11, Math HSCE
S2.2.2
Use the equation of the least squares regression line to make appropriate predictions.
 
Vectors
HSCE
MI Grade 11, Math HSCE
L1.2.3
Use vectors to represent quantities that have magnitude and direction, interpret direction and magnitude of a vector numerically, and calculate the sum and difference of two vectors.
 
Convert Units
HSCE
MI Grade 11, Math HSCE
L2.3.1
Convert units of measurement within and between systems; explain how arithmetic operations on measurements affect units, and carry units through calculations correctly.
 
Mathematical Reasoning and Logic
HSCE
MI Grade 11, Math HSCE
L3.1.1
Distinguish between inductive and deductive reasoning, identifying and providing examples of each.
 
MI Grade 11, Math HSCE
L3.1.2
Differentiate between statistical arguments (statements verified empirically using examples or data) and logical arguments based on the rules of logic.
 
MI Grade 11, Math HSCE
L3.1.3
Define and explain the roles of axioms (postulates), definitions, theorems, counterexamples, and proofs in the logical structure of mathematics. Identify and give examples of each.
 
MI Grade 11, Math HSCE
L3.2.1
Know and use the terms of basic logic.
 
MI Grade 11, Math HSCE
L3.2.2
Use the connectives “not,” “and,” “or,” and “if…, then,” in mathematical and everyday settings. Know the truth table of each connective and how to logically negate statements involving these connectives.
 
MI Grade 11, Math HSCE
L3.2.3
Use the quantifiers “there exists” and “all” in mathematical and everyday settings and know how to logically negate statements involving them.
 
MI Grade 11, Math HSCE
L3.2.4
Write the converse, inverse, and contrapositive of an “if…, then…” statement. Use the fact, in mathematical and everyday settings, that the contrapositive is logically equivalent to the original, while the inverse and converse are not.
 
MI Grade 11, Math HSCE
L3.3.1
Know the basic structure for the proof of an “if…, then…” statement (assuming the hypothesis and ending with the conclusion) and that proving the contrapositive is equivalent.
 
MI Grade 11, Math HSCE
L3.3.2
Construct proofs by contradiction. Use counterexamples, when appropriate, to disprove a statement.
 
MI Grade 11, Math HSCE
L3.3.3
Explain the difference between a necessary and a sufficient condition within the statement of a theorem. Determine the correct conclusions based on interpreting a theorem in which necessary or sufficient conditions in the theorem or hypothesis are satisfied.
 
Angles
HSCE
MI Grade 11, Math HSCE
G1.1.1
Solve multistep problems and construct proofs involving vertical angles, linear pairs of angles supplementary angles, complementary angles, and right angles.
 
MI Grade 11, Math HSCE
G1.1.2
Solve multistep problems and construct proofs involving corresponding angles, alternate interior angles, alternate exterior angles, and same-side (consecutive) interior angles.
 
Distance and Midpoint
HSCE
MI Grade 11, Math HSCE
G1.1.5
Given a line segment in terms of its endpoints in the coordinate plane, determine its length and midpoint.
 
Triangles
HSCE
MI Grade 11, Math HSCE
G1.2.1
Prove that the angle sum of a triangle is 180° and that an exterior angle of a triangle is the sum of the two remote interior angles.
 
MI Grade 11, Math HSCE
G1.2.2
Construct and justify arguments and solve multistep problems involving angle measure, side length, perimeter, and area of all types of triangles.
 
MI Grade 11, Math HSCE
G1.2.3
Know a proof of the Pythagorean Theorem, and use the Pythagorean Theorem and its converse to solve multistep problems.
 
MI Grade 11, Math HSCE
G1.2.4
Prove and use the relationships among the side lengths and the angles of 30º- 60º- 90º triangles and 45º- 45º- 90º triangles.
 
MI Grade 11, Math HSCE
G1.2.5
Solve multistep problems and construct proofs about the properties of medians, altitudes, perpendicular bisectors to the sides of a triangle, and the angle bisectors of a triangle. Using a straightedge and compass, construct these lines.
 
Trigonometry
HSCE
MI Grade 11, Math HSCE
G1.3.1
Define the sine, cosine, and tangent of acute angles in a right triangle as ratios of sides. Solve problems about angles, side lengths, or areas using trigonometric ratios in right triangles.
 
MI Grade 11, Math HSCE
G1.3.2
Know and use the Law of Sines and the Law of Cosines and use them to solve problems. Find the area of a triangle with sides a and b and included angle
using the formula Area = (1/2) absin
.
 
MI Grade 11, Math HSCE
G1.3.3
Determine the exact values of sine, cosine, and tangent for 0°, 30°, 45°, 60°, and their integer multiples and apply in various contexts.
 
Polygons
HSCE
MI Grade 11, Math HSCE
G1.4.1
Solve multistep problems and construct proofs involving angle measure, side length, diagonal length, perimeter, and area of squares, rectangles, parallelograms, kites, and trapezoids.
 
MI Grade 11, Math HSCE
G1.4.2
Solve multistep problems and construct proofs involving quadrilaterals using Euclidean methods or coordinate geometry.
 
MI Grade 11, Math HSCE
G1.4.3
Describe and justify hierarchical relationships among quadrilaterals.
 
MI Grade 11, Math HSCE
G1.4.4
Prove theorems about the interior and exterior angle sums of a quadrilateral.
 
MI Grade 11, Math HSCE
G2.1.1
Know and demonstrate the relationships between the area formula of a triangle, the area formula of a parallelogram, and the area formula of a trapezoid.
 
MI Grade 11, Math HSCE
G2.1.2
Know and demonstrate the relationships between the area formulas of various quadrilaterals.
 
MI Grade 11, Math HSCE
G1.5.1
Know and use subdivision or circumscription methods to find areas of polygons.
 
MI Grade 11, Math HSCE
G1.5.2
Know, justify, and use formulas for the perimeter and area of a regular n-gon and formulas to find interior and exterior angles of a regular n-gon and their sums.
 
Circles
HSCE
MI Grade 11, Math HSCE
G1.6.1
Solve multistep problems involving circumference and area of circles.
 
MI Grade 11, Math HSCE
G1.6.2
Solve problems and justify arguments about chords and lines tangent to circles.
 
MI Grade 11, Math HSCE
G1.6.3
Solve problems and justify arguments about central angles, inscribed angles, and triangles in circles.
 
MI Grade 11, Math HSCE
G1.6.4
Know and use properties of arcs and sectors and find lengths of arcs and areas of sectors.
 
Surface Area and Volume
HSCE
MI Grade 11, Math HSCE
G1.8.1
Solve multistep problems involving surface area and volume of pyramids, prisms, cones, cylinders, hemispheres, and spheres.
 
MI Grade 11, Math HSCE
G2.1.3
Know and use the relationship between the volumes of pyramids and prisms (of equal base and height) and cones and cylinders (of equal base and height).
 
Drawing Objects
HSCE
MI Grade 11, Math HSCE
G2.2.1
Identify or sketch a possible three-dimensional figure, given two-dimensional views. Create a two-dimensional representation of a three-dimensional figure.
 
MI Grade 11, Math HSCE
G2.2.2
Identify or sketch cross sections of three-dimensional figures. Identify or sketch solids formed by revolving two-dimensional figures around lines.
 
Similar and Congruent Triangles
HSCE
MI Grade 11, Math HSCE
G2.3.1
Prove that triangles are congruent using the SSS, SAS, ASA, and AAS criteria, and that right triangles, are congruent using the hypotenuse-leg criterion.
 
MI Grade 11, Math HSCE
G2.3.2
Use theorems about congruent triangles to prove additional theorems and solve problems, with and without use of coordinates.
 
MI Grade 11, Math HSCE
G2.3.3
Prove that triangles are similar by using SSS, SAS, and AA conditions for similarity.
 
MI Grade 11, Math HSCE
G2.3.4
Use theorems about similar triangles to solve problems with and without use of coordinates.
 
Change in Dimension
HSCE
MI Grade 11, Math HSCE
G2.3.5
Know and apply the theorem stating that the effect of a scale factor of k relating one two-dimensional figure to another or one three-dimensional figure to another, on the length, area, and volume of the figures is to multiply each by k, k2, and k3, respectively.
 
Object Transformations
HSCE
MI Grade 11, Math HSCE
G3.1.1
Define reflection, rotation, translation, and glide reflection and find the image of a figure under a given isometry.
 
MI Grade 11, Math HSCE
G3.1.2
Given two figures that are images of each other under an isometry, find the isometry and describe it completely.
 
MI Grade 11, Math HSCE
G3.1.3
Find the image of a figure under the composition of two or more isometries and determine whether the resulting figure is a reflection, rotation, translation, or glide reflection image of the original figure.
 
MI Grade 11, Math HSCE
G3.2.1
Know the definition of dilation and find the image of a figure under a given dilation.
 
MI Grade 11, Math HSCE
G3.2.2
Given two figures that are images of each other under some dilation, identify the center and magniture of the dilation.
 
Counting Techniques
HSCE
MI Grade 11, Math HSCE
L1.3.1
Describe, explain, and apply various counting techniques; relate combinations to Pascal’s triangle; know when to use each technique.
 
Complex Numbers
HSCE
MI Grade 11, Math HSCE
L2.1.4
Know that the complex number i is one of two solutions to x2 = -1.
 
MI Grade 11, Math HSCE
L2.1.5
Add, subtract, and multiply complex numbers; use conjugates to simplify quotients of complex numbers.
 
Sequences and Series
HSCE
MI Grade 11, Math HSCE
L2.2.1
Find the nth term in arithmetic, geometric, or other simple sequences.
 
MI Grade 11, Math HSCE
L2.2.2
Compute sums of finite arithmetic and geometric sequences.
 
MI Grade 11, Math HSCE
L2.2.3
Use iterative processes in such examples as computing compound interest or applying approximation procedures.
 
Accuracy, Estimation, and Error
HSCE
MI Grade 11, Math HSCE
L2.4.1
Determine what degree of accuracy is reasonable for measurements in a given situation; express accuracy through use of significant digits, error tolerance, or percent of error; describe how errors in measurements are magnified by computation; recognize accumulated error in applied situations.
 
MI Grade 11, Math HSCE
L2.4.2
Describe and explain round-off error, rounding, and truncating.
 
MI Grade 11, Math HSCE
L2.4.3
Know the meaning of and interpret statistical significance, margin of error, and confidence level.
 
Polynomials and Rational Expressions
HSCE
MI Grade 11, Math HSCE
A1.1.3
Factor algebraic expressions using, for example, greatest common factor, grouping, and the special product identities.
 
MI Grade 11, Math HSCE
A1.1.4
Add, subtract, multiply, and simplify polynomials and rational expressions.
 
MI Grade 11, Math HSCE
A1.1.5
Divide a polynomial by a monomial.
 
Polynomial and Rational Functions
HSCE
MI Grade 11, Math HSCE
A1.2.5
Solve polynomial equations and equations involving rational expressions, and justify steps in the solution.
 
MI Grade 11, Math HSCE
A3.5.1
Write the symbolic form and sketch the graph of simple polynomial functions.
 
MI Grade 11, Math HSCE
A3.5.2
Understand the effects of degree, leading coefficient, and number of real zeros on the graphs of polynomial functions of degree greater than 2.
 
MI Grade 11, Math HSCE
A3.5.3
Determine the maximum possible number of zeros of a polynomial function, and understand the relationship between the x-intercepts of the graph and the factored form of the function.
 
MI Grade 11, Math HSCE
A3.6.1
Write the symbolic form and sketch the graph of simple rational functions.
 
MI Grade 11, Math HSCE
A3.6.2
Analyze graphs of simple rational functions and understand the relationship between the zeros of the numerator and denominator and the function’s intercepts, asymptotes, and domain.
 
Exponential and Logarithmic Functions
HSCE
MI Grade 11, Math HSCE
L2.1.3
Explain the exponential relationship between a number and its base 10 logarithm and use it to relate rules of logarithms to those of exponents in expressions involving numbers.
 
MI Grade 11, Math HSCE
L2.3.2
Describe and interpret logarithmic relationships in such contexts as the Richter scale, the pH scale, or decibel measurements; solve applied problems.
 
MI Grade 11, Math HSCE
A1.1.6
Transform exponential and logarithmic expressions into equivalent forms using the properties of exponents and logarithms, including the inverse relationship between exponents and logarithms.
 
MI Grade 11, Math HSCE
A1.2.7
Solve exponential and logarithmic equations, and justify steps in the solution.
 
MI Grade 11, Math HSCE
A3.2.1
Write the symbolic form and sketch the graph of an exponential function given appropriate information.
 
MI Grade 11, Math HSCE
A3.2.2
Interpret the symbolic forms and recognize the graphs of exponential and logarithmic functions; recognize the logarithmic function as the inverse of the exponential function.
 
MI Grade 11, Math HSCE
A3.2.3
Apply properties of exponential and logarithmic functions.
 
MI Grade 11, Math HSCE
A3.2.4
Understand and use the fact that the base of an exponential function determines whether the function increases or decreases and understand how the base affects the rate of growth or decay.
 
MI Grade 11, Math HSCE
A3.2.5
Relate exponential and logarithmic functions to real phenomena, including half-life and doubling time.
 
Trigonometric Functions and Equations
GLCE
MI Grade HS, Math GLCE
L1.1.6
Explain the importance of the irrational numbers  2 and  3 in basic right triangle trigonometry, and the importance of    because of its role in circle relationships.
 
MI Grade HS, Math GLCE
A1.2.10
Use special values of the inverse trigonometric functions to solve trigonometric equations over specific intervals.
 
MI Grade HS, Math GLCE
A3.7.1
Use the unit circle to define sine and cosine; approximate values of sine and cosine; use sine and cosine to define the remaining trigonometric functions; explain why the trigonometric functions are periodic.
 
MI Grade HS, Math GLCE
A3.7.2
Use the relationship between degree and radian measures to solve problems.
 
MI Grade HS, Math GLCE
A3.7.3
Use the unit circle to determine the exact values of sine and cosine, for integer multiples of   /6 and   /4.
 
Graphs of Trigonometric Functions
HSCE
MI Grade 11, Math HSCE
A3.7.4
Graph the sine and cosine functions; analyze graphs by noting domain, range, period, amplitude, and location of maxima and minima.
 
MI Grade 11, Math HSCE
A3.7.5
Graph transformations of basic trigonometric functions (involving changes in period, amplitude, and midline) and understand the relationship between constants in the formula and the transformed graph.
 
Conic Sections
HSCE
MI Grade 11, Math HSCE
G1.7.1
Find an equation of a circle given its center and radius; given the equation of a circle, find its center and radius.
 
MI Grade 11, Math HSCE
G1.7.2
Identify and distinguish among geometric representations of parabolas, circles, ellipses, and hyperbolas; describe their symmetries, and explain how they are related to cones.
 
MI Grade 11, Math HSCE
G1.7.3
Graph ellipses and hyperbolas with axes parallel to the x- and y-axes, given equations.
 
Interpret Graphs
HSCE
MI Grade 11, Math HSCE
L1.2.4
Organize and summarize a data set in a table, plot, chart, or spreadsheet; find patterns in a display of data; understand and critique data displays in the media.
 
MI Grade 11, Math HSCE
S1.1.1
Construct and interpret dot plots, histograms, relative frequency histograms, bar graphs, basic control charts, and box plots with appropriate labels and scales; determine which kinds of plots are appropriate for different types of data; compare data sets and interpret differences based on graphs and summary statistics.
 
Box Plots
HSCE
MI Grade 11, Math HSCE
L1.2.4
Organize and summarize a data set in a table, plot, chart, or spreadsheet; find patterns in a display of data; understand and critique data displays in the media.
 
MI Grade 11, Math HSCE
S1.1.1
Construct and interpret dot plots, histograms, relative frequency histograms, bar graphs, basic control charts, and box plots with appropriate labels and scales; determine which kinds of plots are appropriate for different types of data; compare data sets and interpret differences based on graphs and summary statistics.
 
Central Tendency and Distributions
HSCE
MI Grade 11, Math HSCE
L2.1.1
Explain the meaning and uses of weighted averages.
 
MI Grade 11, Math HSCE
S1.1.2
Given a distribution of a variable in a data set, describe its shape, including symmetry or skewness, and state how the shape is related to measures of center (mean and median) and measures of variation (range and standard deviation) with particular attention to the effects of outliers on these measures.
 
MI Grade 11, Math HSCE
S1.2.1
Calculate and interpret measures of center including: mean, median, and mode; explain uses, advantages and disadvantages of each measure given a particular set of data and its context.
 
MI Grade 11, Math HSCE
S1.2.2
Estimate the position of the mean, median, and mode in both symmetrical and skewed distributions, and from a frequency distribution or histogram.
 
MI Grade 11, Math HSCE
S1.2.3
Compute and interpret measures of variation, including percentiles, quartiles, interquartile range, variance, and standard deviation.
 
MI Grade 11, Math HSCE
S1.3.1
Explain the concept of distribution and the relationship between summary statistics for a data set and parameters of a distribution.
 
MI Grade 11, Math HSCE
S1.3.2
Describe characteristics of the normal distribution, including its shape and the relationships among its mean, median, and mode.
 
MI Grade 11, Math HSCE
S1.3.3
Know and use the fact that about 68%, 95%, and 99.7% of the data lie within one, two, and three standard deviations of the mean, respectively in a normal distribution.
 
MI Grade 11, Math HSCE
S1.3.4
Calculate z-scores, use z-scores to recognize outliers, and use z-scores to make informed decisions.
 
Sampling Analysis
HSCE
MI Grade 11, Math HSCE
S3.1.1
Know the meanings of a sample from a population and a census of a population, and distinguish between sample statistics and population parameters.
 
MI Grade 11, Math HSCE
S3.1.2
Identify possible sources of bias in data collection and sampling methods and simple experiments; describe how such bias can be reduced and controlled by random sampling; explain the impact of such bias on conclusions made from analysis of the data; and know the effect of replication on the precision of estimates.
 
MI Grade 11, Math HSCE
S3.1.3
Distinguish between an observational study and an experimental study, and identify, in context, the conclusions that can be drawn from each.
 
Probablility Theory
HSCE
MI Grade 11, Math HSCE
L1.3.2
Define and interpret commonly used expressions of probability.
 
MI Grade 11, Math HSCE
L1.3.3
Recognize and explain common probability misconceptions such as “hot streaks” and “being due.”
 
MI Grade 11, Math HSCE
S4.1.1
Understand and construct sample spaces in simple situations.
 
MI Grade 11, Math HSCE
S4.1.2
Define mutually exclusive events, independent events, dependent events, compound events, complementary events and conditional probabilities; and use the definitions to compute probabilities.
 
MI Grade 11, Math HSCE
S4.2.1
Compute probabilities of events using tree diagrams, formulas for combinations and permutations, Venn diagrams, or other counting techniques.
 
SCIENCE:
Biology
     Inquiry, Reflection, and Social Implication - Scientific Investigations
GLCE
MI Grade High School, Biology GLCE
B1.1A
Generate new questions that can be investigated in the laboratory or field.
 
MI Grade High School, Biology GLCE
B1.1B
Evaluate the uncertainties or validity of scientific conclusions using an understanding of sources of measurement error, the challenges of controlling variables, accuracy of data analysis, logic of argument, logic of experimental design, and/or the dependence on underlying assumptions.
 
MI Grade High School, Biology GLCE
B1.1C
Conduct scientific investigations using appropriate tools and techniques (e.g., selecting an instrument that measures the desired quantity—length, volume, weight, time interval, temperature—with the appropriate level of precision).
 
MI Grade High School, Biology GLCE
B1.1D
Identify patterns in data and relate them to theoretical models.
 
MI Grade High School, Biology GLCE
B1.1E
Describe a reason for a given conclusion using evidence from an investigation.
 
MI Grade High School, Biology GLCE
B1.2A
Critique whether or not specific questions can be answered through scientific investigations.
 
MI Grade High School, Biology GLCE
B1.2B
Identify and critique arguments about personal or societal issues based on scientific evidence.
 
Chemistry
GLCE
MI Grade High School, Chemistry GLCE
C1.1A
Generate new questions that can be investigated in the laboratory or field.
 
MI Grade High School, Chemistry GLCE
C1.1B
Evaluate the uncertainties or validity of scientific conclusions using an understanding of sources of measurement error, the challenges of controlling variables, accuracy of data analysis, logic of argument, logic of experimental design, and/or the dependence on underlying assumptions. 
 
MI Grade High School, Chemistry GLCE
C1.1C
Conduct scientific investigations using appropriate tools and techniques (e.g., selecting an instrument that measures the desired quantity—length, volume, weight, time interval, temperature—with the appropriate level of precision).
 
MI Grade High School, Chemistry GLCE
C1.1D
Identify patterns in data and relate them to theoretical models.
 
MI Grade High School, Chemistry GLCE
C1.1E
Describe a reason for a given conclusion using evidence from an investigation.
 
MI Grade High School, Chemistry GLCE
C1.2A
Critique whether or not specific questions can be answered through scientific investigations.
 
MI Grade High School, Chemistry GLCE
C1.2B
Identify and critique arguments about personal or societal issues based on scientific evidence.
 
Earth Science
GLCE
MI Grade High School, Earth Science GLCE
E1.1A
Generate new questions that can be investigated in the laboratory or field.
 
MI Grade High School, Earth Science GLCE
E1.1B
Evaluate the uncertainties or validity of scientific conclusions using an understanding of sources of measurement error, the challenges of controlling variables, accuracy of data analysis, logic of argument, logic of experimental design, and/or the dependence on underlying assumptions.
 
MI Grade High School, Earth Science GLCE
E1.1C
Conduct scientific investigations using appropriate tools and techniques (e.g., selecting an instrument that measures the desired quantity—length, volume, weight, time interval, temperature—with the appropriate level of precision).
 
MI Grade High School, Earth Science GLCE
E1.1D
Identify patterns in data and relate them to theoretical models.
 
MI Grade High School, Earth Science GLCE
E1.1E
Describe a reason for a given conclusion using evidence from an investigation.
 
MI Grade High School, Earth Science GLCE
E1.2A
Critique whether or not specific questions can be answered through scientific investigations.
 
MI Grade High School, Earth Science GLCE
E1.2B
Identify and critique arguments about personal or societal issues based on scientific evidence.
 
Physics
GLCE
MI Grade High School, Physics GLCE
P1.1A
Generate new questions that can be investigated in the laboratory or field.
 
MI Grade High School, Physics GLCE
P1.1B
Evaluate the uncertainties or validity of scientific conclusions using an understanding of sources of measurement error, the challenges of controlling variables, accuracy of data analysis, logic of argument, logic of experimental design, and/or the dependence on underlying assumptions.
 
MI Grade High School, Physics GLCE
P1.1C
Conduct scientific investigations using appropriate tools and techniques (e.g., selecting an instrument that measures the desired quantity–length, volume, weight, time interval, temperature–with the appropriate level of precision).
 
MI Grade High School, Physics GLCE
P1.1D
Identify patterns in data and relate them to theoretical models.
 
MI Grade High School, Physics GLCE
P1.1E
Describe a reason for a given conclusion using evidence from an investigation.
 
MI Grade High School, Physics GLCE
P1.2A
Critique whether or not specific questions can be answered through scientific investigations.
 
MI Grade High School, Physics GLCE
P1.2B
Identify and critique arguments about personal or societal issues based on scientific evidence.