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Click on any standard to search for aligned resources. This data may be subject to copyright. You may download a CSV of the Saskatchewan Curriculum if your intention constitutes fair use.

Plan, assess, and analyze learning aligned to these standards using
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To define and illustrate, by means of examples, the term absolute value

To express square root radicals as mixed radicals in simplest form

Establish and apply criteria to evaluate own and others work.

Use feedback to evaluate own effectiveness and set goals in language learning and use.

Evaluate own and others contributions to group process and provide support where needed.

Contribute to the creation of rubrics and other assessment and evaluation tools used to assess visual, oral, written, multimedia, and other products submitted.

Celebrate special accomplishments by using language to congratulate and encourage, to publicly recognize, and to properly recount the achievement.

Set personal language learning goals and select strategies to enhance growth in language learning.

Establish and apply criteria to evaluate own and others work.

Use feedback to evaluate own effectiveness as a communicator.

Evaluate own and others contributions to group process and provide support where needed.

Set goals in language learning and use; identify strategies to achieve those goals.

Celebrate special accomplishments by using language to describe and discuss achievements.

To calculate discounts or penalties on taxes due, depending on when they are paid

To compare the advantages and disadvantages of various credit cards

To calculate the monthly interest charges and service charges on an unpaid credit card balance

To identify and compare an installment charge account and a thirty-day account

To calculate the monthly payments for a loan using formulas, tables, calculators, and computers

To determine the percent of the total amount repaid (or borrowed) which is devoted to interest

To factor polynomials of the following types: common factor, grouping, difference of squares, trinomial squares, trinomials where and combinations of all preceding types

To divide a polynomial by a binomial, by factoring, and long division

To simplify variable expressions with integral exponents using the following properties of exponents: product, quotient, power of a product, power of a quotient, negative exponent, and zero exponent

To determine the non-permissible values for the variable in rational expressions

To add and subtract rational expressions involving like and unlike monomial denominators

Compose and create a range of visual, multimedia, oral, and written texts that explore: identity (e.g., Foundational Stories); social responsibility (e.g., Destiny and Challenges of Life); social action (agency) (e.g., Human Existence).

Use representing, speaking, and writing to respond to experiences or texts (e.g., a staged dramatic scene, a television episode, a significant personal event).

Create spoken, written, and other representations that include:

A clear thesis and logical points to support messages and arguments.

Develop and present a project-based inquiry related to a theme or topic of the course:

Collaborate to determine group knowledge base and to define inquiry or research purpose and parameters.

Cite reference for all sources of information including summarized and paraphrased ideas from other authors.

Develop and use an inquiry or research plan to identify and access relevant ideas and information from a variety of sources.

Determine the credibility, accuracy, completeness, and usefulness of a variety of information sources for a particular inquiry or research plan.

Access information using a variety of tools (e.g., electronic networks, libraries, taped oral histories).

Organize information using appropriate forms (e.g., charts, diagrams, outlines, electronic databases).

Analyze and understand implications and consequences of plagiarism (i.e., ethical, legal, professional).

Draw logical conclusion from information and consider how to best present to identified audience.

Document sources accurately using standard format (such as Modern Language Association [MLA], and American Psychological Association [APA]).

Explain and present to a familiar audience the key ideas and events (actual or based on a text studied) through an appropriate combination of charts, diagrams, sound, models, drama, and print.

Prepare and deliver visual and multimedia presentations that:

Exhibit logical structures appropriate to audience, purpose, and context.

Use a variety of forms and technologies such as sound, photographs, and models.

Select, use, and evaluate purposefully a variety of before (page 28), during (page 29), and after (page 30) strategies to construct and communicate meaning when using other forms of representing.

Understand and apply the language cues and conventions to construct and communicate meaning when using various forms of representing.

Pragmatic cues and conventions: selecting and using language register appropriate for the subject, context, audience, and purpose; using conventional standard English when required.

Textual cues and conventions: selecting and using text form appropriate for subject, purpose, and audience.

Syntactic cues and conventions: selecting and using formal spoken and written sentences that are meaningful, clear, correctly punctuated, and devoid of ambiguous expressions; demonstrating control over such elements as subject-verb agreement, pronoun-antecedent agreement, verb forms, and parallelism.

Semantic/Lexical/Morphological cues and conventions: using words precisely, accurately, and for effect (e.g., to create imagery, to communicate figuratively, to communicate symbolically, as an allusion).

Graphophonic cues and conventions: using the sounds of letters and syllables and the placement of accents to determine the pronunciation and spelling of words.

Other cues and conventions: using communication elements such as handwriting, consistent font, neatness, underlining, indentations, spacing, and margins to enhance the clarity and the legibility of communication; using appropriate visual and multimedia aids to enhance presentation; choosing appropriate font size and style when word processing.

Prepare, rehearse, and confidently deliver a visual or multimedia presentation, explaining key ideas and events (actual or based on text studied) using appropriate combination of charts, diagrams, pictures, sounds, models, drama, and print with:

An effective introduction that sets the direction for presentation by getting attention of audience, introducing the topic, presenting the central idea or purpose, identifying the main point, and making audience eager to see and hear the rest of the presentation.

Present information using print and non-print aids to engage and inform a familiar audience.

Use props, visual aids, graphics, and electronic media to enhance the appeal and accuracy of presentations.

Use a variety of technological functions (including computer software) to publish original work.

Use and adapt production techniques and technologies to communicate information, ideas, narrative, or other messages, integrating verbal, visual, and dramatic features to achieve a range of effects.

Experiment with a variety of text forms (e.g., advertisement, tableau, drama) and techniques (e.g., graphics).

Use oral language to express a range of information and ideas in formal (including a prepared talk on a familiar topic, an oral presentation of a passage of prose or poetry, and a retelling of a narrative or a recounting of an experience or event) and informal (discussion and group work) situations.

Participate in small- and large-group discussions, observing the courtesies of group discussion, and demonstrate effective group interaction skills and strategies:

Develop harmony, listen, observe, and respond to and clarify one anothers ideas.

Work co-operatively and collaboratively with others in small groups on structured tasks.

Question others, exploring the potential of their contributions, and offer clarification and elaboration upon own ideas when necessary.

Assume some of the work necessary to maintain discussion and advance it (e.g., by summarizing, raising questions, extracting significant points, making connections, setting agenda).

Assume the responsibility for independent and individual summary and closure.

Select, use, and evaluate purposefully a variety of before (page 28), during (page 29), and after (page 30) strategies to construct and communicate meaning when speaking.

Understand and apply the language cues and conventions to construct and communicate meaning when speaking including:

Pragmatic cues and conventions: selecting and using language register appropriate for the subject, context, audience, and purpose; using conventional standard English when required.

Textual cues and conventions: selecting and using mode of discourse (e.g., descriptive, narrative, expository, or persuasive) and text form appropriate for subject, purpose, and audience.

Syntactic cues and conventions: selecting and using formal spoken sentences that are meaningful and devoid of ambiguous expressions; demonstrating control over such elements as subject-verb agreement, pronoun-antecedent agreement, verb forms, and parallelism (average spoken sentence length 10.9 words).

Semantic/Lexical/Morphological cues and conventions: using words precisely, accurately, and for effect (e.g., to create imagery, to communicate figuratively, to communicate symbolically).

Graphophonic cues and conventions: using the sounds of letters and syllables to correctly pronounce words.

Other cues and conventions: using appropriate volume and intonation; using appropriate non-verbal cues and body language; using appropriate gestures, facial expression, sound, visual, and multimedia aids to enhance presentation.

Prepare, rehearse, and deliver a talk on a familiar topic that includes:

An effective introduction that sets the direction for speech by getting attention of audience, introducing the topic, stating the central idea or purpose, identifying the main point, and making audience eager to hear what else you have to say.

An attention getter (e.g., an amazing fact or startling statement; an attention-grabbing illustration; a short demonstration or colourful visual aid; a series of questions or a short history of the topic; a strong statement of why the topic is important to you and audience).

A body logically and coherently organized so audience can follow.

A conclusion that helps audience understand what they listened to and why it was important.

Prepare, rehearse, and deliver an oral reading/interpretation of prose, poetry, or other texts including:

Using techniques of speech and delivery to interpret possible meanings.

Thinking about how the ideas and characters in the text could be communicated with voice.

Using voice (e.g., expression, pacing, tone, dialect) for characterization and effect.

Support the ongoing discourse of the classroom by contributing to the talk; listening attentively to the offerings of others; refraining from sarcasm or insult that silences others; and helping, when necessary, to draw others into the discussion.

Plan a class meeting on a real topic of concern with the aim of reaching a consensus about the action that might be taken.

Speak confidently, clearly, and persuasively to communicate and explore information, ideas, and opinions.

Recognize and adjust oral presentation elements effectively (i.e., articulation, pronunciation, volume, tempo, pitch, stress, gestures, eye contact, facial expression, and poise) in keeping with purpose, audience needs, and individual cultural and linguistic background.

Compose and create a variety of written literary (including a historical persona essay and a review) and informational (including an observation [eye-witness] report and researched or technical report) texts attending to various elements of discourse (e.g., purpose, speaker, audience, form).

Structure material in appropriate styles for different audiences.

Define the main idea by selecting relevant, logical details to achieve the purpose and o meet the readers perceived needs.

Select, use, and evaluate purposefully a variety of before (page 28), during (page 29), and after (page 30) strategies to construct and communicate meaning when writing.

Understand and apply the language cues and conventions to construct and communicate meaning when writing including:

Pragmatic cues and conventions: selecting and using language register appropriate for the subject, context, audience, and purpose; using conventional standard English when required.

Textual cues and conventions: selecting and using mode of discourse (e.g., descriptive, narrative, expository, or persuasive) and text form appropriate for subject, purpose, and audience.

Syntactic cues and conventions: selecting and using formal written sentences that are meaningful, clear, correctly punctuated, and devoid of ambiguous expressions; demonstrating control over such elements as subject-verb agreement, pronoun-antecedent agreement, verb forms, and parallelism (average written sentence length 11.7 words).

Semantic/Lexical/Morphological cues and conventions: using words precisely, accurately, and for effect (e.g., to create imagery, to communicate figuratively, to communicate symbolically, as an allusion).

Graphophonic cues and conventions: using the sounds of letters and syllables and the placement of accents to determine the pronunciation and spelling of words.

Other cues and conventions: using communication elements such as handwriting, consistent font, neatness, underlining, indentations, spacing, and margins to enhance the clarity and the legibility of communication; writing legibly with appropriate speed and control; choosing appropriate font size and style when word processing.

Retell a narrative or recount an experience or event (e.g., a memory, an essay of experience) that:

Identifies the storys main character and establishes the setting.

Uses dialogue to establish characters and create the drama.

Write an observation report/eyewitness account (e.g., an incident report, an event report) that:

Uses descriptive details (including sights, sounds, tastes, textures, and smells) that show the reader what happened, as if he or she were seeing it firsthand.

Includes thoughts and comments that bring experience to life.

Write an inquiry report (e.g., research report, an I-Search, a technical report) that:

Includes information related to focus or thesis, is current, and drawn from reliable, relevant sources that are cited.

Write a historical persona essay (e.g., biographical narrative, response to a historical photo) that:

Defines important moments in the historic persons life so essay is well-focused and organized.

Shows understanding of the person, the events, and gathered details about the place and time.

Includes reflections and observations about persons life and experiences.

Includes the people the person might have met and creates accurate depictions of those individuals.

Uses the I voice (imagined self to be the person and to be part of these events) in order to get a feel for the experience.

Includes thoughtful explanations and specific references to the text itself.

Explores strengths and weaknesses of work and includes passages from text as examples.

Addresses what makes the text interesting, exciting, engaging, believable, unforgettable, and significant.

Does not retell plot but recognizes theme (general observation about life or human nature) of the text and the relevance of literary techniques (e.g., setting, characters, point of view, basic conflicts, plot development, and use of literary elements such as figurative language and sound).

Experiment with and explore a variety of written text forms (such as poems, memorandums, legends) and techniques (such as foreshadowing, flashback, imagery, allegory, figurative language, symbolism, point of view, parallelism, hyperbole) and explain their appeal.

Compose and create a range of visual, multimedia, oral, and written texts to explore: identity (e.g., Diversity of Being); social responsibility (e.g., Degrees of Responsibility); and social action (agency) (e.g., Justice and Fairness).

Develop and articulate defensible points of view on individual, community, national, and world issues.

Create spoken, written, and other representations that include:

Develop a project-focused inquiry related to a theme or issue of the course:

Compile information from primary and secondary sources in systematic ways

Synthesize the content from several sources or works by various authors dealing with a single issue

Interpret and report on ideas and information from more than one source to develop and support positions on various topics.

Extend ideas presented in primary or secondary sources through original analysis, evaluation, and elaboration.

Compile ideas and information into reports, summaries, and other formats and draw conclusions.

Create and present a visual or multimedia presentation supporting a prepared talk on a researched issue, using either digital or other presentation tools.

Prepare and present visual and multimedia presentations and a research talk/report that:

Use logical structures appropriate to audience, purpose, and context.

Include smooth transitions and ensure smooth flow from visual to visual.

Exhibit a variety of forms and technologies such as sound, photographs, and models, and understand how ideas are communicated through elements of design such as colour, shape, line, and texture.

Use props, visual aids, graphics, music, sound effects, photos (clip-art), and electronic media to enhance the appeal and accuracy of presentations, and ensure words on visuals are easy to read.

Select, use, and evaluate purposefully a variety of before (page 28), during (page 29), and after (page 30) strategies to construct and communicate meaning when using other forms of representing.

Understand and apply language cues and conventions to construct and communicate meaning when using various forms of representing including:

Pragmatic cues and conventions: selecting and using language that includes people across cultures, races, genders, ages, and abilities and avoids common usage problems including imprecision and the use of jargon, slang, euphemism, clichs, gobbledygook, and abusages (such as Me and John, I cant get no,Like,).

Textual cues and conventions: creating visual and multimedia texts that are unified (i.e., all elements combined to form a single whole or oneness) and coherent (i.e., consistent, logically arranged, and connected).

Syntactic cues and conventions: using sentences that are varied in form (e.g., parallelism, inversion, subordination); are free of misplaced qualifiers and dangling qualifiers; show agreement of subject and verb, consistency in verb tense, pronoun agreement, and clear pronoun reference; and use correctly that/which, who/whom, and punctuation.

Semantic/lexical/morphological cues and conventions: using words correctly including prepositions (e.g., suited to, suited for), homonyms (e.g., to, too, two), plurals and possessives (e.g., the cats paws, students projects, peoples pets), and meaning (e.g., then/than; few, fewer/less, lesser).

Graphophonic cues and conventions: recognizing and using Canadian spelling conventions and clear pronunciation to aid spelling (e.g., accept, except).

Other cues and conventions: using appropriate visual elements (e.g., colour, layout, graphics, illustrations) and media technologies to clarify and enhance message.

Select, interpret, and synthesize information from visual texts and present it effectively, using a range of visual and layout features and appropriate technologies for variety of purposes.

Select a section of narrative text and use it as a basis for a dramatization using narrator where appropriate, dialogue, action, backgrounds, costumes, props, music, sound effects, and language that retain the intent and tone of the original text.

Prepare and present a real-life action or role play an event such as buying or selling something and present the role play to class.

Select a character from a novel and plan a seminar that gives an analysis of the character and includes the use of digital or other presentation tools to show the relationships between the character and other characters in the novel (e.g., a family tree), video or still photography to demonstrate ideas for a film setting, and a sound recording to record dialogue from the text or an interview with the character with appropriate musical accompaniment.

Develop imaginative or creative representations to share interpretations and ideas.

Use persuasive techniques (e.g., rhetorical question, repetition, parallelism, analogy, appeal to authority) in visual and multimedia texts.

Experiment with a variety of text forms (e.g., advertisements, posters, videos) and techniques (e.g., colour, typeface, graphics).

Use oral language to express a range of information and ideas in formal (including a prepared talk on a researched issue, an interview, an oral reading of prose or poetry, and an explanation and defence of a personal point of view) and informal (including discussion and group work) situations.

Participate in small- and large-group discussion, observing the courtesies of group discussion, and demonstrate effective group interaction skills and strategies including:

Assume some of the work necessary to maintain discussion and advance it (e.g., by summarizing, raising questions, seeking clarification, extracting significant points, making connections, setting agenda).

Co-operate by staying positive, waiting turn, and avoiding putdowns.

Encourage others by trying to understand their ideas and asking for opinions.

Select, use, and evaluate purposefully a variety of before (page 28), during (page 29), and after (page 30) strategies to construct and communicate meaning when speaking.

Understand and apply language cues and conventions to construct and communicate meaning when speaking including:

Pragmatic cues and conventions: selecting and using language that includes people across cultures, races, genders, ages, and abilities and avoids common usage problems including imprecision and the use of jargon, slang, euphemism, clichs, gobbledygook, and abusages (such as Me and John, I cant get no,Like,).

Textual cues and conventions: creating oral texts that are unified (i.e., all elements combined to form a single whole or oneness) and coherent (i.e., consistent, logically arranged, and connected).

Syntactic cues and conventions: using sentences that are varied in form (e.g., parallelism, inversion, subordination); are free of misplaced qualifiers and dangling qualifiers; show agreement of subject and verb, consistency in verb tense, pronoun agreement, and clear pronoun reference; and use correctly that/which, who/whom, and punctuation.

Semantic/lexical/morphological cues and conventions: using words correctly including prepositions (e.g., suited to, suited for), homonyms (e.g., to, too, two), plurals and possessives (e.g., the cats paws, students projects, peoples pets), and meaning (e.g., then/than; few, fewer/less, lesser).

Graphophonic cues and conventions: recognizing and using Canadian spelling conventions and clear pronunciation to aid spelling (e.g., accept, except).

Other cues and conventions: using appropriate oral elements (e.g., volume, intonation); using appropriate non-verbal cues and body language; using appropriate gestures, facial expressions, sound, and visual and multimedia aids to enhance message.

Use oral language to interact purposefully, confidently, and appropriately in a variety of situations including participating in one-to-one, small-group, and large-group discussions (demonstrating an awareness of the relationship of language to group and community membership, acknowledging and paraphrasing views that differ from own, reassessing own viewpoints, prompting and supporting others, solving problems, resolving conflicts, building consensus, articulating and explaining personal viewpoint, discussing preferences, speaking to extend current understanding, and celebrating special events and accomplishments).

Work in pairs to develop and script an interview on an issue of interest or on an incident in a literary text, for a particular audience and purpose.

In role, rehearse and record interview or present interview to the group.

Work in pairs to prepare and present closing argument for and against a selected fictional character on a charge which could have been levelled at a character.

Select three poems related to theme and present them to a group of peers using voice to clarify meaning by emphasizing rhythm, highlighting particular words or phrases, and signalling the role and effects of line endings, stanza breaks, and other elements of structure.

Recognize and use elements of classical speech forms (including introduction, body with transitions, conclusion) in formulating rational arguments and apply the art of persuasion.

Recognize and adjust oral presentation elements (i.e., articulation, pronunciation, volume, tempo, pitch, stress, gestures, eye contact, facial expression, and poise) in keeping with purpose, audience needs, and situation.

Create a variety of written informational (including a business letter, biographical profile, problem-solution essay) and literary (including fictionalized journal entries and a short script) communications.

Use various elements of discourse (e.g., purpose, speaker, audience, form) in narrative, expository, persuasive, informational, and/or descriptive texts.

Define the main idea by selecting relevant, logical details that meet the readers perceived needs.

Select, use, and evaluate purposefully a variety of before (page 28), during (page 29), and after (page 30) strategies to construct and communicate meaning when writing.

Understand and apply language cues and conventions to construct and communicate meaning when writing including:

Pragmatic cues and conventions: selecting and using language that includes people across cultures, races, genders, ages, and abilities, and avoids common usage problems including imprecision and the use of jargon, slang, euphemism, clichs, gobbledygook, and abusages (such as Me and John, I cant get no,Like,).

Syntactic cues and conventions: using sentences that are varied in form (e.g., parallelism, inversion, subordination); are free of misplaced qualifiers and dangling qualifiers; show agreement of subject and verb, consistency in verb tense, pronoun agreement, and clear pronoun reference; and use correctly that/which, who/whom, and punctuation.

Semantic/lexical/morphological cues and conventions: using words correctly including prepositions (e.g., suited to, suited for), homonyms (e.g., to, too, two), plurals and possessives (e.g., the cats paws, students projects, peoples pets), and meaning (e.g., then/than; few, fewer/less, lesser).

Graphophonic cues and conventions: recognizing and using Canadian spelling conventions and clear pronunciation to aid spelling (e.g., accept, except).

Other cues and conventions: using appropriate written elements (e.g., font size, type face, formatting); writing legibly with appropriate speed and control; using communication elements such as neatness, underlining, indentations, spacing, and margins to enhance clarity and legibility of communication.

Write an explanation and defence of personal point of view that:

Describes the subject and explains what he or she accomplished.

Write a problem-solution essay (e.g., an essay in which you analyze a problem and present one or more solutions) that:

Write a business letter (e.g., letter of complaint, e-mail request) that:

Presents information completely and in the correct order.

Includes all the parts of a business letter heading, inside address, salutation, body, complimentary closing, and signature.

Avoids expressions that are wordy, clichd, vague, or discriminatory.

Write fictionalized journal entries (e.g., of a literary character or a historical figure) that:

Focus on a made-up character or someone read about or observed.

Give insight into the personality and values of the character.

Write a short script (e.g., a short play or a script for an advertisement) that:

Includes stage directions that indicate the time and place of the action, entrances and exits, and what characters are doing on stage.

Gives details of setting that lead into the beginning of the script.

Employs dialogue (characters words) that moves the action along.

Includes (if multimedia) graphics, music, Blend In, Cut To, Fade In, Fade Out, Insert, and other elements.

Experiment with and explore a variety of written text forms (such as letter of complaint, obituary, brochure) and techniques (such as figurative language, literary devices, anecdotes).

Comprehend and respond to a variety of visual, oral, print, and multimedia texts that address: identity (e.g., Foundational Stories); social responsibility (e.g., Destiny and Challenges of Life); and social action (agency) (e.g., Human Existence).

View, listen to, read, and respond to First Nations and Mtis resources and other texts that reflect diverse personal identities, worldviews, and backgrounds (e.g., appearance, culture, socioeconomic status, ability, age, gender, language, social structures, and decision making).

Develop understanding and interpretations of a variety of texts by drawing upon personal experiences and prior knowledge of texts and language.

Comprehend key ideas and supporting details (both explicit and implicit), and determine their literal and implied meaning.

Identify and evaluate effectiveness of text organization and elements.

Respond thoughtfully and critically to text providing support from text to justify response.

Generate significant and thought-provoking questions about what is viewed, listened to, and read.

Respond personally and critically to individuals, events, and ideas presented in a variety of First Nations, Mtis, and other Canadian and international texts.

Generate relevant questions about texts on issues related to identity, social responsibility, and social action (agency).

Discuss ways in which texts convey, challenge, or support and affirm individual and community values and behaviours.

View, interpret, summarize, and draw conclusions about the ideas and information presented in a variety of illustrations, charts, graphs, and television, film, and video presentations including a documentary or current affairs program.

View, interpret, and summarize grade-appropriate literary and informational texts created by First Nations, Mtis, Saskatchewan, Canadian, and international authors from various cultural communities.

Select, use, and evaluate purposefully a variety of before (page 24), during (page 25), and after (page 26) strategies to construct meaning when viewing.

Understand and apply language cues and conventions to construct and confirm meaning when viewing including:

Textual cues: recognizing and understanding the distinctive formats of a range of visual and multimedia texts and their textual and organizational features.

Syntactic cues: recognizing and comprehending basic English sentence structures including common kernel structures and how they have been expanded with qualifiers and how they have been compounded and transformed (as questions, exclamations, inversions, negatives).

Semantic/Lexical/Morphological cues: recognizing and comprehending when and how words are used in a concrete or abstract and a denotative or connotative way.

Graphophonic cues: recognizing and comprehending the structure and patterns of high-frequency, topic-specific, and new words encountered in viewing.

Other cues: recognizing and comprehending textual features such as graphic aids (e.g., diagrams, graphs, timelines, table of contents and index) and illustrations (e.g., photographs, images, drawings, sketches); recognizing intonation, nonverbal cues and body language; recognizing gestures, facial expression, sound, visual, and multimedia aids that were used to enhance presentation.

Identify the intended audiences and points of view in the text.

Infer the assumptions, interests, beliefs, and values embedded in the text and the credibility and purpose of the author.

Recognize language and media techniques and conventions in television, film, and video presentations.

Analyze how the text uses argument, images, placement, editing, and music to create emotion and impact.

Analyze contrasting texts, evaluating the ways verbal and non-verbal (visual and multimedia) features are organized and combined for different meanings, effects, purposes, and audiences in different social contexts.

Investigate the source of media presentation or production including who made it, why, and for whom it was made.

Evaluate how genders and various cultures and socio-economic groups are portrayed in mass media.

Prepare and present a critical response to what was viewed.

View and discuss the meaning and characterization implicit in the action of a scene from a play, film, television production (e.g., dialogue, movement, physical position of characters), noting visual features (e.g., set, costumes, and character appearance).

Discuss the characterization, mood, and historical setting achieved by an actor and director in a live performance or film version of a play.

Listen to, interpret, summarize, and draw conclusions about the ideas and information presented in a variety of literary and informational texts including group discussions, oral readings, interviews, and prepared talks about a topic being studied.

Listen to and interpret grade-appropriate literary and informational texts created by First Nations, Mtis, Saskatchewan, Canadian, and international authors from various cultural communities.

Select, use, and evaluate purposefully a variety of before (page 24), during (page 25), and after (page 26) strategies to construct meaning when listening.

Understand and apply language cues and conventions to construct and confirm meaning when listening including:

Textual cues: recognizing and understanding the distinctive formats of a range of oral texts and their textual and organizational features.

Syntactic cues: recognizing and comprehending basic English sentence structures including common kernel structures and how they have been expanded with qualifiers and how they have been compounded and transformed (as questions, exclamations, inversions, negatives).

Semantic/Lexical/Morphological cues: recognizing and comprehending when and how words are used in a concrete or abstract and a denotative or connotative way; determining their meaning by context, structure (meanings of prefixes, roots, and suffixes), sound, or use of reference sources such as glossary, dictionary, thesauruses, and available technology to determine meanings and usage.

Graphophonic cues: recognizing and comprehending the structure and patterns of high-frequency, topic-specific, and new words encountered in listening; identifying and explaining word structure and patterns that help support understanding.

Other cues: recognizing non-verbal cues and body language, gestures, facial expression, sound, visual, and multimedia aids used to enhance presentation.

Analyzing explicit and implicit messages, viewpoints, and concepts

Using effective notemaking strategies and a variety of written or graphic forms to organize and share ideas acquired from what was listened to

Preparing and asking relevant questions and responding appropriately

Engage in reflective, critical, empathic, and appreciative listening.

Identify the language features and their effects in a range of oral and multimedia texts and describe and analyze their relationships to meaning, purpose, and audience.

ract appropriately with others (e.g., consider others ideas) to communicate and explore understanding, information, ideas, and opinions.

Identify attitudes and beliefs, relating them to personal experience and knowledge of other texts; and compare texts listened to in terms of attitudes and beliefs, viewpoints, and explicit and implied messages.

Listen respectfully to an invited guest with expertise on the subject, and make notes on the key points as well as the speakers purpose, attitude, and organization of ideas for effect.

Listen to a recorded speech and note the language features that were employed.

Comprehend and respond to a variety of visual, oral, print, and multimedia texts that address: identity (e.g., Diversity of Being); social responsibility (e.g., Degrees of Responsibility); and social action (agency) (e.g., Justice and Fairness).

View, listen to, read, comprehend, and respond to a variety of contemporary and traditional texts including First Nations and Mtis resources that present different viewpoints and perspectives on issues and reflect diverse personal identities, worldviews, and backgrounds (e.g., appearance, culture, socio-economic status, ability, age, gender, language).

Apply personal experiences and prior knowledge of texts and language to develop understanding and interpretations of variety of texts.

Respond personally and critically to individuals, events, and ideas presented in a variety of First Nations, Mtis, Canadian, and international texts.

Discuss ways in which texts convey and challenge individual and community values and behaviours.

Identify how human experiences and values are reflected in texts.

View, listen to, read, and respond to historically or culturally significant works (texts) that reflect and enhance studies in history and social science.

Analyze how a text is related to the themes and issues of a particular period in time.

View, interpret, and report on ideas and information from more than one source to develop and support positions on various topics related to the course including identity, social responsibility, and personal agency.

View, comprehend, interpret, and summarize grade-appropriate visual and multimedia texts created by First Nations, Mtis Saskatchewan, Canadian, and international developers and artists from various cultural communities that address identity, social responsibility, and personal agency.

Select, use, and evaluate purposefully a variety of before (page 24), during (page 25), and after (page 26) strategies to construct meaning when viewing.

Understand and apply language communication cues and conventions to construct and confirm meaning when viewing including:

Pragmatic cues: recognizing and comprehending language registers that are varied and used for effect.

Textual cues: recognizing and comprehending the organization of thoughts and ideas of a range of visual and multimedia texts and their organizational features.

Syntactic cues: recognizing and comprehending a variety of sentence patterns for communicating and clarifying meaning.

Semantic/Lexical/Morphological cues: using a dictionary or other source to determine a words meaning(s).

Graphophonic cues: recognizing the correct form and usage of a word. Other cues: recognizing and comprehending how features including graphic aids (e.g., diagrams, graphs, timelines) support and enhance the message.

View, interpret, and draw conclusions about the ideas and information presented in a variety of illustrations, maps, charts, graphs, and other visual texts.

Evaluate how genders and various cultures and socio-economic groups are portrayed in representations by the mass media.

Recognize persuasive techniques (including propaganda) being used in visual and multimedia texts, and analyze and assess the impact of specific media, techniques, and designs.

Identify and evaluate the verbal and visual features including images, colour, layout, graphics, and messages in consumer products (e.g., clothing, electronic products, food, entertainment services).

Respond to and discuss various meanings, ideas, and effects describing how verbal and static and moving visual features are combined for different purposes and audiences in CD covers, posters, and videos of popular songs and singers.

Attend a performance of a play and discuss the specific scenes, main character, and technical production aspects of the presentation.

Listen to, comprehend, interpret, and summarize information and ideas presented in a variety of literary and informational texts including group discussion, oral readings, interviews, prepared talks, and a talk-back show about a topic or issue being studied.

Listen to, interpret, and summarize grade-appropriate literary and informational texts created by First Nations, Mtis, Saskatchewan, Canadian, and international authors from various cultural communities that address identity, social responsibility, and personal agency.

Select, use, and evaluate purposefully a variety of before (page 24), during (page 25), and after (page 26) strategies to construct meaning when listening.

Understand and apply language cues and conventions to construct and confirm meaning when listening including:

Pragmatic cues: recognizing and comprehending language registers that are varied and used for effect (e.g., characterization, dialect) and that have been influenced by the context (e.g., community in which it was learned).

Textual cues: recognizing and comprehending the organization of thoughts and ideas of a range of oral texts and their organizational features.

Syntactic cues: recognizing and comprehending how word order and sentence patterns communicate meaning in English and also when they do not communicate clearly.

Semantic/Lexical/Morphological cues: using a dictionary or other source to determine a words meaning(s) and etymology.

Graphophonic cues: recognizing the correct form and usage of a word.

Other cues: recognizing and comprehending how features including voice production factors (e.g., articulation, tone, tempo, pronunciation, volume, emphasis, pitch, pause) and non-verbal cues (e.g., gestures, stance, eye contact) clarify intent of message.

Analyze explicit and implicit messages, viewpoints, and concepts.

Recognize overall plan or organization including transitional expressions.

Use effective notemaking strategies and a variety of written or graphic forms to organize, summarize, and share ideas acquired from listening.

Prepare and ask relevant questions and respond appropriately.

Understand the factors that interfere with good listening (e.g., environment, speaker, listener) and filter out distractions.

Prepare and present critical response to what was listened to and heard supporting conclusions with reference to what was presented.

Apply appropriate listening strategies when interviewing (including preparing and asking relevant questions, making notes, responding correctly and effectively, compiling and reporting responses).

Formulate and support judgements (using convincing evidence) about the ideas under discussion.

Listen to and evaluate several excerpts from a range of phone-in talk-back shows about a particular issue.

Read, interpret, and summarize a wide variety of classical and contemporary literary (including drama, biography, autobiography, poetry, short stories, novels) and informational (including letters, diaries, memoranda, electronic communications) texts.

Read, interpret, and summarize grade-appropriate literary and informational texts created by First Nations, Mtis, Saskatchewan, Canadian, and international authors from various cultural communities that address identity, social responsibility, and personal agency.

Select, use, and evaluate purposefully a variety of before (page 24), during (page 25), and after (page 26) strategies to construct meaning when reading.

Understand and apply language cues and conventions to construct and confirm meaning when reading including:

Pragmatic cues: recognizing and comprehending language registers that are varied and used for effect (e.g., characterization, dialect) and that have been influenced by the context (e.g., community in which it was learned).

Textual cues: recognizing and comprehending the organization of thoughts and ideas in a variety of written and other texts including distinctive features of genres (e.g., prose, poetry) and organizational patterns within each genre (e.g., chronological, spatial, enumerative, problem and solution, cause and effect, comparison and contrast).

Syntactic cues: recognizing and comprehending how word order and sentence patterns communicate meaning in English and also when they do not communicate clearly.

Semantic/Lexical/Morphological cues: using a dictionary or other source to determine a words meaning(s), usage, pronunciation, and etymology.

Graphophonic cues: recognizing and using the correct form and usage of a word to determine the pronunciation (e.g., project as a noun versus as a verb).

Other cues: recognizing and comprehending how features such as layout and accompanying graphics clarify intent of message.

Establish a purpose for reading such as to learn, interpret, and enjoy.

Recognize, comprehend, and discuss the significance of allusions and symbols in context.

Discuss and analyze meanings, ideas, language, and literary quality in a range of contemporary and historical texts, taking account of purpose, audience, and time.

Use notemaking, marginal notes, and outlining to better understand texts.

Identify and analyze explicit and implicit messages, viewpoints, concepts, persuasive techniques, and propaganda techniques (e.g., testimonial, band wagon, stereotyping).

Relate understanding of a range of texts to personal experience, purposes, audience, and other texts.

Read fluently and independently a wide range of contemporary and historical texts, adapting reading processes and strategies for different purposes (including for information and enjoyment).

Recognize stylistic devices and techniques such as characterization, flashback, foreshadowing, and hyperbole.

Describe, discuss, and analyze the distinctive conventions, structures, and language features of a range of texts and explain how they suit the topic and purpose.

Read about a particular event or issue, using texts from a range of sources, including magazines, newspapers, cartoons, and letters to the editor to identify different points of view or angles.

Compare the characteristics of different texts and consider the reason for these differences, in terms of topic, purpose, and point of view.

Read and interpret critically the main ideas, events, and themes of a variety of literary texts including stories, novels, scripts, poetry, and non-fiction works, and prepare and present critical responses to what was read.

Read and make generalizations, supported by specific details and examples, about key concepts, characters, themes, and techniques in literary texts.

To identify, graph, and determine the properties of quadratic functions

To determine the domain and range from the graph of a quadratic function

To analyze the graphs of quadratic functions that depict real-world situations

To solve problems involving the graphs of quadratic functions that depict real-world situations

To solve quadratic equations by: factoring, and by taking the square roots of both sides of an equation

To calculate the exact value of the length of a side of a right triangle using the Pythagorean Theorem

To calculate the experimental probability of simple events by performing repeated experiments

To calculate the theoretical probability of an event and the probability of its complement.

Demonstrate understanding of the mathematics involved in an historical event or an area of interest. [C, CN, ME, PS, R, T, V]

Collect primary or secondary data (quantitative or qualitative) related to the topic.

Assess the accuracy, reliability, and relevance of the primary or secondary data (quantitative/qualitative) collected by:

Determining whether or not the data are consistent with information obtained from other sources on the same topic.

Identify controversial issues, if any, and present multiple sides of the issues with supporting data.

Demonstrate understanding of inductive and deductive reasoning including: analyzing conjectures; analyzing spatial puzzles and games; providing conjectures; solving problems. [C, CN, PS, R, V]

Make conjectures by observing patterns and identifying properties, and justify the reasoning.

Provide examples of how inductive reasoning might lead to false conclusions.

Critique the following statement "Decisions can be made and actions taken based upon inductive reasoning".

Identify situations relevant to self, family, or community involving inductive and/or deductive reasoning.

Prove algebraic number relationships, such as divisibility rules, number properties, mental mathematics strategies, or algebraic number tricks using deductive reasoning.

Identify errors in proofs that lead to incorrect conclusions (e.g., a proof that ends with 2 = 1).

Solve situational questions that involve inductive or deductive reasoning.

Determine, explain, and verify strategies for solving puzzles or winning games, such as:

Expand and demonstrate understanding of proportional reasoning related to: rates, scale diagrams, scale factor, area, surface area, volume. [C, CN, PS, R, V]

Identify and describe situations relevant to one's self, family, or community that involve proportional reasoning.

Create non-symbolic representations for rates, including pictures and graphs.

Explain the meaning of rates given in context, such as the arts, commerce, the environment, medicine, or recreation.

Solve situational questions that require the use of proportional reasoning, including those that involve the isolation of a variable.

Analyze situations in which unit rates can be determined and suggest reasons why the rates would or would not be used to make decisions in each situation (i.e., are other factors in the situation outweighing the importance of the mathematical calculations?).

Explain, using examples, the relationship between the slope of a graph and a rate.

Identify and explain the effect of factors within given situations that could influence a particular rate.

Solve situational questions involving rates, including unit rates.

Identify and describe situations relevant to one's self, family, or community that involve scale diagrams of 2-D shapes and 3-D objects and determine the scale factor for the situations.

Develop, generalize, explain, and apply strategies for solving situational questions based upon scale diagrams of 2-D shapes and 3-D objects, including the determining of scale factors and unknown dimensions.

Draw, with or without the use of technology, a scale diagram of a 2-D shape relevant to self, family, or community to a specified scale factor (enlargement or reduction).

Solve situational problems involving scale diagrams of 2-D shapes and 3-D objects.

Determine relationships between scale factor and area of 2-D shapes or surface area of 3-D objects; and scale factor, surface area, and volume of 3-D objects.

Develop, generalize, explain, and apply strategies for determining scale factors, areas, surface areas, or volumes given the scale factor or the ratio of areas, surface areas, or volumes of 2-D shapes and 3-D objects.

Explain, with justification, the effect of a change in scale factor on the area of a 2-D shape or the surface area or volume of a 3-D object.

Solve situational questions that involve scale factors, areas, surface areas, and volumes, including ones that require the manipulation of formulas.

Demonstrate understanding of properties of angles and triangles including: deriving proofs based on theorems and postulates about congruent triangles; solving problems. [CN, PS, R, V]

Identify and describe situations relevant to self, family, or community that involve parallel lines cut by transversals.

Develop, generalize, explain, apply, and prove relationships between pairs of angles formed by transversals and parallel lines, with and without the use of technology.

Prove and apply the relationship relating the sum of the angles in a triangle.

Generalize, using inductive reasoning, a rule for the relationship between the sum of the interior angles and the number of sides (n) in a polygon, with or without technology.

Apply knowledge of angles formed by parallel lines and transversals to identify and correct errors in a given proof.

Explore and verify whether or not the angles formed by nonparallel lines and transversals create the same angle relationships as those created by parallel lines and transversals.

Demonstrate an understanding of normal distribution, including standard deviation and z-scores. [CN, PS, T, V]

Identify situations relevant to self, family, or community in which standard deviation and the normal distribution are used and explain the meaning and relevance of each.

Explain the meaning and purpose of the properties of a normal curve, including mean, median, mode, standard deviation, symmetry, and area under the curve.

Calculate, using technology, the population standard deviation of a data set.

Critique the statement "Every set of data will correspond to a normal distribution".

Analyze a data set to determine if it approximates a normal distribution.

Compare the properties of two or more normally distributed data sets and explain what the comparison tells you about the situations that the sets represent.

Explain, using examples that represent multiple perspectives, the application of standard deviation for making decisions in situations such as warranties, insurance, or opinion polls.

Solve situational questions that involve the interpretation of standard deviations to make decisions.

Determine, with or without technology, and explain the meaning of the z-score for a given value in a normally distributed data set.

Pose and solve situational questions relevant to self, family, or community that involve normal distributions and z-scores.

Demonstrate understanding of the interpretation of statistical data, including: confidence intervals, confidence levels, margin of error. [C, CN, R]

Identify and explain the significance of the confidence interval, margin of error, or confidence level stated with respect to statistical data relevant to self, family, or community.

Explain how confidence levels, margins of error, and confidence intervals can be impacted by the size of the random sample used.

Make inferences and decisions with justification about a population from sample data using confidence intervals.

Provide and critique examples from print or electronic media in which confidence intervals and confidence levels are used to support a particular position.

Support a position or decision relevant to self, family, or community by analyzing statistical data, as well as considering other factors.

Demonstrate understanding of systems of linear inequalities in two variables. [CN, PS, T, V]

Identify situations relevant to self, family, or community which could be described using a system of linear inequalities in two variables.

Develop, generalize, explain, and apply strategies for graphing and solving systems of linear inequalities, including justification of the choice of solid or broken lines.

Develop, generalize, explain, and apply strategies for verifying solutions to systems of linear inequalities, including the use of test points.

Explain, using examples, the meaning of the shaded region in the graphical solution of a system of linear inequalities.

Match optimization questions and the graphs of sets of linear inequalities.

Apply knowledge of graphing of systems of linear inequalities and linear programming to solve optimization questions.

Demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)^2 + q , including: vertex, intercepts, domain and range, axis of symmetry. [CN, PS, T, V]

Identify situations and objects relevant to self, family, or community which could be described using a quadratic function.

Develop, generalize, explain, and apply strategies for determining the intercepts of the graph of a quadratic function, including factoring, graphing (with or without the use of technology), and use of the quadratic formula.

Conjecture and verify a relationship among the roots of an equation, the zeros of the corresponding function, and the x-intercepts of the graph of the function.

Explain, using examples, why the graph of a quadratic function may have zero, one, or two x-intercepts.

Develop, generalize, explain, and apply strategies (with or without the use of technology) to determine the coordinates of the vertex of the graph of a quadratic function.

Develop, generalize, explain, and apply a strategy for determining the equation of the axis of symmetry of the graph of a quadratic function when given the x-intercepts of the graph.

Develop, generalize, explain, and apply strategies for determining the coordinates of the vertex of the graph of a quadratic function and for determining if the vertex is a maximum or a minimum.

Generalize about and explain the effects on the graph of a quadratic function when the values for a, p, and q are changed.

Develop, generalize, explain, and apply strategies for determining the domain and range of a quadratic function.

Explain what the domain and range of a quadratic function tell about the situation that the quadratic function models.

Develop, generalize, explain, and apply strategies for sketching the graph of a quadratic function.

Solve situational questions involving the characteristics and graphs of quadratic functions.

Critique the statement "Any function that can be written in the form y = a(x - p)^2 + q will have a parabolic graph."

Demonstrate understanding of financial decision making including analysis of: renting, leasing, and buying; credit; compound interest; investment portfolios. [C, CN, ME, PS, R, T]

Compare the advantages and disadvantages of simple interest and compound interest.

Identify and describe situations that involve compound interest.

Graph and compare the total interest paid or earned over different compounding periods for the same annual interest rate, principal, and time.

Develop, generalize, explain, and apply strategies for determining the total interest to be paid on a loan given the principal, interest rate, and number of compounding periods for the loan.

Determine, using technology, the total cost of a loan under a variety of conditions (e.g., different amortization periods, interest rates, compounding periods, and terms).

Analyze, using technology, different credit options that involve compound interest, including bank and store credit cards and special promotions, and provide justifications for the credit option.

Compare renting, leasing, and buying of large cost items and generate reasons for considering each choice.

Solve situational questions related to the costs of renting, leasing, and buying (including questions that require formula manipulation).

Solve, using technology, situational questions that involve cost-and-benefit analysis.

Demonstrate understanding of inductive and deductive reasoning including: analysis of conditional statements; analysis of puzzles and games involving numerical and logical reasoning; making and justifying decisions; solving problems. [C, CN, ME, PS, R]

Develop, generalize, verify, explain, and apply strategies to solve a puzzle or win a game such as:

Identify and correct errors in a solution to a puzzle or in a strategy to win a game.

Create a variation on a puzzle or game and describe a strategy for solving the puzzle or winning the game.

Analyze an "if-then" statement, make a conclusion, and explain the reasoning.

Make and justify decisions related to "what-if?" questions, in contexts such as probability, finance, sports, games, or puzzles, with or without technology.

Write the converse, inverse, and contrapositive of an "if-then" statement, determine if each new statement is true, and if it is false, provide a counterexample.

Critique statements such as "If an 'if-then' statement is known to be true, then its converse, inverse, and contrapositive also will be true".

Identify and describe situations relevant to one's self, family, and community in which a biconditional (if and only if) statement can be made.

Solve situational questions, using a graphic organizer such as a truth table or Venn diagram, that involve logical arguments based upon biconditional, converse, inverse, or contrapositive statements.

Demonstrate understanding of set theory and its applications. [CN, PS, R, V]

Provide and describe examples, relevant to one's self, family, and community, of empty set, disjoint sets, subsets, and universal sets.

Create graphic organizers such as Venn diagrams to display relationships within collected data or sets of numbers.

Name a specific region in a Venn diagram using the Boolean operators (or, and, not) or set notation, and explain in words what that region represents with respect to a specific situation.

Develop, generalize, and apply strategies for determining the elements in the complement, the intersection, or the union of sets.

Identify situations in which set theory is used and explain the role of set theory in each situation. (e.g., specific Internet searches, database queries, data analysis, games, and puzzles)

Solve situational questions that involve sets, including analysis of solutions for errors, using set notation where appropriate.

Provide and explain the meaning of statements of probability and odds relevant to one's self, family, and community (e.g., statements of probability found in media, science, medicine, sports, sociology, and psychology).

Explain, using examples, how decisions may be based on probability or odds and on subjective judgments.

Solve contextual problems that involve odds and probability.

Identify, describe, and justify examples of correct and incorrect use of the words "odds" or "probability" in daily language or in the media.

Extend understanding of the probability of two events, including events that are: mutually exclusive, non-mutually exclusive, dependent, independent. [CN, PS, R, V]

Provide examples of events relevant to one's self, family, and community that are mutually exclusive or non-mutually exclusive and explain the reasoning.

Represent, using set notation or graphic organizers, mutually exclusive (including complementary) and non-mutually exclusive events.

Create and solve contextual problems that involve the probability of mutually exclusive events.

Create and solve contextual problems that involve the probability of non-mutually exclusive events.

Provide examples of events relevant to one's self, family, and community that are dependent or independent and explain the reasoning.

Determine the probability of an event, given the occurrence of a previous event.

Determine the probability of two dependent or two independent events.

Solve situational questions that involve determining the probability of dependent and independent events.

Demonstrate understanding of combinatorics including: the fundamental counting principle, permutations (excluding circular permutations), combinations. [ME, PS, R, T, V]

Represent and solve counting problems using a graphic organizer.

Develop, generalize, explain, and apply the fundamental counting principle.

Identify and justify assumptions made in solving a counting problem.

Create and solve situational questions involving the fundamental counting principle.

Develop, generalize, explain, and apply strategies for determining the number of arrangements of n elements taken n at a time.

Explain, using examples, how factorials are related to the determination of permutations and combinations.

Determine, with or without technology, the value of a factorial.

Develop, generalize, explain, and apply strategies for determining the number of permutations of n elements taken r at a time.

Develop, generalize, explain, and apply strategies for determining the number of permutations of n elements taken n at a time where some of the elements are not distinguishable.

Solve situational questions involving probability and permutations.

Explain, using examples, why order is or is not important when counting arrangements.

Identify examples relevant to one's self, family, and community where the number of possible arrangements would be of interest to explain why the order within any particular arrangement does or does not matter.

Critique statements such as "If a question about determining the number of possible arrangements gives the names of the people involved, then it is a permutation question".

Demonstrate understanding of the representation and analysis of data using: polynomial functions of degree 3, logarithmic functions, exponential functions, sinusoidal functions. [C, CN, PS, T, V]

Analyze the graphs of polynomial functions and report on the characteristics of those graphs.

Develop, generalize, explain, and apply strategies for determining the characteristics of polynomial functions from their equations.

Analyze the graphs of exponential and logarithmic functions and report on the characteristics of those graphs.

Develop, generalize, explain, and apply strategies for determining the characteristics of exponential and logarithmic functions from their equations.

Analyze the graphs of sinusoidal functions and report on the characteristics of those graphs.

Develop, generalize, explain, and apply strategies for determining the characteristics of sinusoidal functions from their equations.

Match equations of polynomial, logarithmic, exponential, and sinusoidal functions to their corresponding graphs.

Interpret graphs of polynomial, logarithmic, exponential, and sinusoidal functions to describe the situations that each function models and explain the reasoning.

Research and give a presentation of a current event or an area of interest that requires data collection and analysis. [C, CN, ME, PS, R, T, V]

Develop a rubric or other scoring schema to assess the research and presentation.

Collect primary or secondary data (quantitative or qualitative) related to the topic.

Assess the accuracy, reliability, and relevance of the collected primary or secondary data (quantitative/qualitative) by:

Determining whether or not the data is consistent with information obtained from other sources on the same topic.

Identify controversial issues and present multiple sides of the issue with supporting data.

Demonstrate understanding of factors of whole numbers by determining the: prime factors, greatest common factor, least common multiple, principal square root, cube root. [CN, ME, R]

Develop, generalize, explain, and apply strategies for determining the greatest common factors or least common multiples.

Determine the prime factors of a whole number and explain the strategies used.

Analyze concretely, pictorially, or numerically and explain whether a whole number is a perfect square or a perfect cube.

Develop, generalize, explain, and apply strategies for determining the square root of a perfect square and the cube root of a perfect cube.

Investigate and report about the numbers 0 and 1 with respect to factors, multiples, square roots, and cube roots.

Solve problems that involve prime factors, greatest common factors, least common multiples, square roots, or cube roots.

Solve problems that involve systems of linear equations in two variables, graphically and algebraically. [CN, PS, R, T, V]

Match, with justification, situations and systems of linear equations.

Sketch, describe, provide and explain situational examples of the different ways that the graphs of two linear equations (two variables) can intersect and explain the meaning of the points of intersection.

Develop, generalize, explain, and apply strategies for solving systems of equations graphically, with and without the use of technology and verify the solutions.

Develop, generalize, explain, and apply strategies, including verification of solutions, for solving systems of equations algebraically.

Critique the statement ''two lines always intersect at exactly one point''.

Apply knowledge and skills with systems of linear equations to solve situational questions.

Demonstrate understanding of irrational numbers in both radical (including mixed radical) and exponent forms through: representing, identifying, simplifying, ordering, relating to rational numbers, applying exponent laws. [C, CN, ME, PS, R, V]

Sort, with justification, a set of numbers into rational and irrational numbers.

Approximate the value of a given irrational number and explain the strategy used.

Order a set of Real numbers, including rational and irrational numbers, on a number line and explain the strategies used.

Express a radical as a mixed radical in simplest form (limited to numerical radicands).

Express a mixed radical as an entire radical (limited to numerical radicands).

Explain, using examples, how changing the value of the index of a radical impacts the value of the radical.

Represent, such as through the use of a graphic organizer, the relationships among the subsets of the Real numbers: natural, whole, integer, rational, and irrational.

Analyze patterns to generalize why a^(-n) = 1/a^n, a is not equal to 0.

Analyze patterns to generalize why a^(1/n) = nth root (a), n is not equal to 0, n epsilon I and a > 0 when n is an even integer.

Extend and apply the exponent laws to powers with rational exponents (limited to expressions with rational and variable bases and integral and rational exponents).

Analyze simplifications of expressions involving radicals and/or powers for errors.

Express powers with rational exponents as radicals and vice versa.

Create a representation that conveys the relationship between powers, rational numbers, and irrational numbers.

Demonstrate understanding of SI and imperial units of measurement including: linear measurement; surface area of spheres, and right cones, cylinders, prisms, and pyramids; volume of spheres, and right cones, cylinders, prisms, and pyramids; relationships between and within measurement systems. [C, CN, ME, PS, R, V]

Justify the choice of units and or referents for determining or estimating linear, surface area, or volume measurements in different contexts.

Critique the statement ''the length of the wall is greater in yards than it is in metres''.

Compare the size of SI and imperial units of measurement (linear, surface area, and volume) using referents.

Develop, generalize, explain, and apply strategies and/or formulas for converting between units within the imperial or SI system of measurements, limited to linear, surface area, and volume units. (e.g., converting square feet to square yards or m^3 to cm^3).

Develop, generalize, explain and apply strategies and/or formulas for converting between:

SI and imperial units of linear, surface area, and volume measure .

Imperial and SI units of linear, surface area, and volume measure.

Verify, with explanation (such as unit analysis and/or mental mathematics and estimation), a conversion of units (within the SI or imperial systems of measurement or between them).

Analyze 3-D objects, their nets, and labelled diagrams to develop and generalize strategies and/or formulas for determining the surface area and volume of right cones, cylinders, prisms, and pyramids and composite objects.

Solve, using personal strategies and/or formulas, situational questions related to surface area, volume, and dimensions of right cones, cylinders, prisms, and pyramids, and composite 3-D objects.

Apply formulas to determine the surface area and/or volume of spheres.

Right cones and right cylinders with the same base and height.

Right pyramids and right prisms with the same base and height.

Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles. [C, CN, PS, R, T, V].

Develop, generalize, explain, and apply relationships between the ratios of side lengths and angle sizes in similar right triangles.

Demonstrate how to identify the hypotenuse of a right triangle and the adjacent and opposite sides to an acute angle in that right triangle.

Solve problems, with or without the use of technology, involving one or more right triangles by applying primary trigonometric ratios and/or the Pythagorean Theorem.

Create and solve problems that involve indirect and direct linear measurements by using the primary trigonometric ratios, the Pythagorean Theorem, and measurement instruments such as a clinometer or metre stick.

Demonstrate understanding of the multiplication and factoring of polynomial expressions (concretely, pictorially, and symbolically) including: multiplying of monomials, binomials, and trinomials; common factors; trinomial factoring; relating multiplication and factoring of polynomials. [C, CN, R, V]

Develop, generalize, explain, and apply a strategy of symbolic manipulation to determine the product of two binomials by analyzing concrete and pictorial models.

Explain the relationship between the multiplication of two binomial expressions and the area of a rectangular region.

Develop (concretely, pictorially, or symbolically), explain, and apply understanding of how multiplication of binomials is related to the multiplication of two-digit numbers (e.g., use algebra tiles and base ten blocks to compare and relate the products of (x+1)(3x+2) and (11)(32) ).

Develop, generalize, explain, and apply a strategy for multiplying polynomials.

Analyze the multiplication of two polynomials for errors and explain the strategy used.

Explain why evaluating at a value for the variable in a product of polynomials in factored form should give the same solution as evaluating the expanded and simplified form of the polynomial product at the same value (e.g., explain why x^2+5x+6 should have the same value as (x+3)(x+2) when evaluated at x = -4).

Explain, using concrete or visual models, how the processes of factoring and multiplication are related.

Develop (using concrete materials, pictures, or visualization), generalize, explain, and apply strategies for factoring and verifying the factors of binomials, including numerical binomial expressions (e.g., 32+20=4(8+5)).

Explain and apply strategies for determining whether given factors are those of a given polynomial.

Develop, generalize, explain, and apply strategies for factoring a trinomial.

Critique the statement ''any trinomial can be factored into two binomial factors''.

Explain how differences of squares can be factored using trinomial factoring strategies.

Explain why it is important to look for common factors first when factoring a trinomial.

Expand and apply understanding of relations and functions including: relating data, graphs, and situations; analyzing and interpreting; distinguishing between relations and functions. [C, CN, R, T, V]

Explain, by providing situational and graphical examples, the relationship between the categories of ''relations'' and ''functions''.

Critique the statement ''Relations and functions are the same thing''.

Graph, with or without technology, a set of data, and determine the restrictions on the domain and range.

Explain why data points should or should not be connected on the graph for a situation.

Provide and explain examples of situations that could be represented by a given graph.

Sketch a graph to represent a situation presented orally or in writing.

Determine, and express in a variety of ways, the domain and range of a graph, a set of ordered pairs, or a table of values.

Generalize, explain, and apply strategies for determining whether a set of ordered pairs or a graph represents a function.

Demonstrate, with and without the use of technology, understanding of slope (concretely, pictorially, and symbolically) with respect to: line segments and lines, rate of change, ratio of rise to run, parallel lines, perpendicular lines. [PS, R, V].

Provide examples, relevant to self, family, or community, to explain the importance of slope.

Illustrate and explain, using examples relevant to self, family, or community, how slope is rate of change.

Determine the slope of a line segment by using the measurement or calculation of the rise and run.

Classify lines in a given set as having positive or negative slopes, and explain how the sign of the slope affects the interpretation or meaning of the slope.

Explain why the slope of a straight line can be determined by using any two distinct points on that line.

Generalize, explain, and apply strategies for determining whether two lines are parallel or perpendicular.

Apply knowledge and skills related to slope to solve situational questions relevant to self, family, and community (e.g., determine the slopes of the poles in a tepee and the impact of changing the slopes on the dimensions and strength of the tepee).

Demonstrate understanding of linear relations including: representing in words, ordered pairs, tables of values, graphs, function notation, and equations; determining characteristics including intercepts, slope, domain, and range; relating different equation forms to each other and to graphs. [C, CN, PS, R, T, V]

Critique the statement ''any straight line is the graph of a linear function''.

Explain, using examples, the impact of the domain of a linear function on the graph of the function (e.g., if the domain is not all Real numbers, then the graph will not show a solid line).

Analyze situations, graphs, tables of values, equations, or sets of ordered pairs to determine if the relationship described is linear.

Match corresponding types of representations of linear relations (e.g., situations, graphs, tables of values, equations, and sets of ordered pairs).

Develop, generalize, explain, and apply strategies for determining the intercepts (as values and ordered pairs) of a linear relation from its graph.

Determine the slope, domain, and range of the graph of a linear relation.

Sketch examples of linear relations to demonstrate the number of x or y intercepts possible for any line.

Match, with explanation, slopes and y-intercepts to graphs of linear relations.

Solve a situational question that involves the intercepts, slope, domain, or range of a linear relation.

Express the equation of a linear relation in different forms (including the slope-intercept or general form) and compare the graphs of the linear relations.

Generalize, explain, and apply strategies for drawing or sketching the graph of a linear relation in slope-intercept, general, or slope-point form, or function notation.

Graph, with and without technology, a linear relation given in slope-intercept, general, or slope-point form, and explain the strategy used to create the graph.

Apply knowledge and skills related to function notation to solve situational questions.

Determine the related range value, given a domain value for a linear function (e.g., if f(x) = 3x - 2, determine f(-1)) and explain what the resulting value tells about the linear function.

Determine the related domain value, given a range value for a linear function (e.g., if g(t) = 7 + t, determine t so that g(t) = 15) and explain what the resulting value tells about the linear function.

Explain why a linear function would never have a term of x^2 when in simplified form.

Demonstrate understanding of the writing and application of equations of linear relations, given:, a graph of a relation, a point that satisfies a relation and the slope of the relation, two distinct points that satisfy a relation, a point that satisfies the relation and the equation of a line parallel or perpendicular to the relation. [CN, PS, R, V].

Develop, generalize, explain, and apply strategies for writing an equation for a linear relation using data obtained from a graph.

Develop, generalize, explain, and apply strategies for writing an equation for a linear relation when given:

A point that satisfies the relation and the slope of the relation.

Compare and critique the structure and purposes of different forms of linear relations, including y=mx+b, Ax+By=C, and y-y[1]=m(x-x[1]) (e.g., there is no way to write a vertical linear relation in the form y = mx+b).

Graph and write equations for linear data generated within an experiment or collected from a situation.

Apply knowledge and skills of linear relations and their equations to solve situational questions.

To informally and formally construct congruent angles and congruent triangles

To calculate the length of a missing side of two similar polygons

To show that two triangles are similar by the Angle Angle Similarity Theorem

To calculate the length of a missing side in two similar right triangles

To solve problems involving similar triangles, and other polygons

To determine surface area and volumes of similar polygons or solids

To determine whether triangles are congruent by SSS, SAS, ASA, AAS, or HL

To prove that two triangles are congruent by supplying the statements and reasons in a guided deductive proof

To prove triangles congruent by SSS, SAS, AAS, ASA, or HL in a two-column deductive proof or paragraph form

To prove corresponding parts of congruent triangles are congruent

To determine the measure of corresponding angles in two similar polygons

To define the measure of a minor arc, and to calculate the measure of a central angle

To determine the relationship that exists between the following: The radius of a circle and a tangent line drawn to it at the point of tangency

To determine the relationship that exists between the following: Chords and arcs in the same circle or in congruent circles

To determine the relationship that exists between the following: A diameter and a chord bisected by the diameter

To determine the relationship that exists between the following: Two chords that intersect in a circle

Demonstrate understanding of the absolute value of real numbers and equations and functions involving the absolute value of linear and quadratic functions. [C, PS, R, T, V]

Provide examples relevant to one's life, family, or community that illustrate different situations in which quantities referenced are positive, negative, or an absolute value and justify.

Determine the distance of two real numbers of the form a, a of the set R, from 0 on a number line, and relate this to the absolute value of a (|a|).

Explain, with the use of examples, how absolute value fits into the order of operations used on expressions involving real numbers.

Determine the value of numerical expressions involving absolute value(s).

Sketch the graph of y = |f(x)| given y = f(x) and explain the reasoning.

Develop and apply strategies for determining the intercepts, domain, and range of y = |f(x)| given the equation of the function or its graph.

Explain what the range of the function y = |f(x)| reveals about the graph of the function.

Develop, generalize, explain, and apply strategies for graphically determining (with and without the use of technology) the solution set of an equation involving absolute values of algebraic expressions.

Analyze and generalize conclusions about absolute value inequalities of the form |f(x)| < 0.

Demonstrate understanding of arithmetic and geometric (finite and infinite) sequences and series. [CN, PS, R, T]

Identify assumptions made in determining that a sequence or series is either arithmetic or geometric.

Provide an example of a sequence that follows an identifiable pattern, but that is neither arithmetic nor geometric.

Provide an example of an arithmetic or geometric sequence that is relevant to one's self, family, or community.

Generate arithmetic or geometric sequences from provided information.

Develop, generalize, explain, and apply a rule and other strategies for determining the values of t1, a, d, n, or tn in situational questions that involve arithmetic sequences.

Develop, generalize, explain, and apply a rule and other strategies for determining the values of t1, a, d, n, or Sn in situational questions that involve arithmetic series.

Solve situational questions that involve arithmetic sequences and series.

Develop, generalize, explain, and apply a rule and other strategies for determining the values of t1, a, r, n, or tn in situational questions that involve geometric sequences.

Develop, generalize, explain, and apply a rule and other strategies for determining the values of t1, a, r, n, or Sn in situational questions that involve geometric series.

Develop, generalize, and explain a rule and strategies for determining the sum of an infinite geometric series and apply this knowledge to the solving of situational questions.

Analyze a geometric series to determine if it is convergent or divergent and explain the reasoning.

Expand and demonstrate understanding of radicals with numerical and variable radicands including: computations, solving equations (limited to square roots and one or two radicals). [C, CN, ME, PS, R, T]

Develop, generalize, explain, and apply strategies for expressing an entire radical (with numerical or variable radicand) as a mixed radical.

Develop, generalize, explain, and apply strategies for expressing a mixed radical (with numerical or variable radicand) as an entire radical.

Develop, generalize, explain, and apply strategies for simplifying radical expressions (with numerical and/or variable radicands).

Develop, generalize, explain, and apply strategies for rationalizing the denominator of rational expressions with monomial or binomial denominators.

Describe the relationship between rationalizing a binomial denominator of a rational expression and the product of the factors of a difference of squares expression.

Verify and explain, using examples, that (-x)^2 = x^2, square root x^2 = |x| , and square root of x^2 is not equal to x.

Solve situational questions that involve radical expressions.

Develop, explain, and apply strategies for determining the values of a variable for which a given radical expression is defined.

Develop, explain, and apply strategies for determining non-permissible values (restrictions on values) for the variable in a radical equation.

Develop, explain, and apply algebraic strategies for determining and verifying the roots of a radical equation.

Explain why some roots determined in solving a radical equation are extraneous.

Model and solve situational questions that involve radical equations.

Expand and demonstrate understanding of rational expressions and equations (up to and including degree 2 numerators and denominators) including: equivalent forms of expressions; operations on expressions; solving equations that can be simplified to linear or quadratic equations. [C, CN, ME, R]

Develop, verify, explain, and apply strategies for determining equivalent rational expressions.

Compare the determining of equivalent rational expressions to determining equivalent rational numbers.

Verify, with explanation, whether or not a given value is permissible for a given rational expression.

Develop, explain, and apply strategies for determining the non-permissible values of a rational expression.

Develop, explain, and apply strategies for simplifying rational expressions.

Explain why the non-permissible values of a simplified rational expression must be stated as those of the original rational expression.

Apply understanding of rational expressions to locate and correct errors in the simplification of a rational expression.

Develop, verify, explain, and apply strategies for adding, subtracting, multiplying, and dividing rational expressions, including the determination of non-permissible values.

Compare the performing of operations on rational expressions to performing the same operations on rational numbers.

Develop, explain, and apply strategies for simplifying rational expressions that involve two or more operations on the rational expressions.

Develop, explain, and apply algebraic strategies for determining the solution, including non-permissible values, of equations involving rational expressions.

Explain why a value obtained in solving a rational equation may not be a solution of the equation.

Model and solve situational questions involving rational expressions.

Expand and demonstrate understanding of the primary trigonometric ratios including the use of reference angles (0 360) and the determination of exact values for trigonometric ratios. [C, ME, PS, R, T, V]

Develop, generalize, explain, and apply strategies for determining a point on the terminal arm of the angle in each quadrant that has the same reference angle as the angle with P(x, y) on its terminal arm.

Develop, explain, and apply strategies for determining the distance between the origin and a point P(x, y) on the terminal arm of an angle.

Develop, generalize, explain, and apply strategies for determining the value of sin, cos, and tan when given a point P(x, y) on the terminal arm of .

Develop, generalize, explain, and apply strategies for determining sin , cos , and tan for quadrantal angles.

Develop, generalize, explain, and apply strategies for determining the sign (without calculation or the use of technology) of sin , cos , or tan for a given value of .

Develop, explain, and apply strategies for solving, for all values of , equations of the form sin = a or cos =a, where -1 a 1, and equations of the form tan = a, where a is a real number.

Develop, generalize, explain, and apply strategies for determining the exact value of the sine, cosine, or tangent (without the use of technology) of an angle with a reference angle of 30, 45, or 60.

Describe and generalize the relationships and patterns in and among the values of the sine, cosine, and tangent ratios for angles from 0 to 360.

Create and solve a situational question relevant to one's self, family, or community which involves a trigonometric ratio.

Identify angles for which the tangent ratio does not exist and explain why.

Expand and demonstrate understanding of factoring polynomial expressions including those of the form: a^2x^2 - b^2y^2, a 0, b 0; a(f(x))^2 - b(f(x)) + c, a 0; a^2(f(x))^2 - b^2(g(y))^2, a 0, b 0 where a, b, and c are rational numbers. [CN, ME, R]

Develop, generalize, explain, and apply strategies for factoring polynomial expressions of the form:

da(f(x))^2 - db(f(x)) + dc, a 0, a, b, c, and d are real numbers

a^2(f(x))^2 - b^2(g(y))^2, a 0, b 0, a and b are real numbers

da^2(f(x))^2 - db^2(g(y))^2, a 0, b 0, a, b, and d are real numbers

Verify, with explanation, whether or not a given binomial is a factor for a given polynomial.

Demonstrate understanding of quadratic functions of the form y = ax^2 + bx + c and of their graphs, including: vertex, domain and range, direction of opening, axis of symmetry, x- and y-intercepts. [CN, PS, R, T, V]

Generalize a rule from sets of graphs, using inductive reasoning, and explain about how different values of a (including 1, 0, and -1) transform the graph of y = ax^2.

Generalize a rule from sets of graphs, using inductive reasoning, and explain about how different values of q (including 0) transform the graph of y = x^2 + q.

Generalize a rule from sets of graphs, using inductive reasoning, and explain how different values of p (including 0) transform the graph of y = (x - p)^2.

Develop, generalize, explain, and apply strategies for determining the coordinates of the vertex, the domain and range, the axis of symmetry, x- and y- intercepts, and direction of opening of the graph of the function f(x) = a(x-p)^2 + q without the use of technology.

Develop, explain, and apply strategies for graphing functions of the form f(x) = a(x - p)^2 + q by applying transformations related to the values of a, p, and q.

Develop, explain, and apply strategies (that do not require graphing or the use of technology) for determining whether a quadratic function will have zero, one, or two x-intercepts.

Develop, generalize, explain, verify, and apply a strategy (including completing the square) for writing a quadratic function in the form y = ax^2 + bx + c in the form y = a(x - p)^2 + q.

Using knowledge about completing the square, identify and correct errors in a given example of completing the square.

Develop, generalize, explain, and apply strategies for determining the coordinates of the vertex, the domain and range, the axis of symmetry, x- and y- intercepts, and direction of opening of the graph of a function in the form y = ax^2 + bx + c.

Sketch the graph of a quadratic function given in the form y = ax^2 + bx + c.

Write a quadratic function that models a given situation and explain any assumptions made.

Analyze quadratic functions (with or without the use of technology) to answer situational questions.

Demonstrate understanding of quadratic equations including the solution of: single variable equations, systems of linear-quadratic and quadratic-quadratic equations in two variables. [C, CN, PS, R, T, V]

Explain, using examples, the relationship among the roots of a quadratic equation, the zeros of the corresponding quadratic function and the x-intercepts of the graph of the quadratic function.

Apply strategies for solving quadratic equations of the form ax^2 + bx + c = 0 including:

Graphing its corresponding function, with and without the use of technology.

Explain different strategies for verifying the solution to a quadratic equation.

Explain, using examples, how the discriminant may be used to determine whether a quadratic equation has two, one, or no real roots; and relate this knowledge to the number of zeros that the corresponding quadratic function will have.

Apply knowledge of quadratic equations and functions to identify and correct any errors within a solution to a quadratic equation.

Solve situational questions involving the writing and solving of quadratic equations.

Match systems of linear-quadratic and quadratic-quadratic functions to situations.

Develop, generalize, explain, and apply strategies for solving systems of linear-quadratic and quadratic-quadratic functions, including:

Explain the meaning of the intersection point of a system of linear-quadratic or quadratic-quadratic equations in terms of the situation being modeled.

Illustrate and explain how a system of linear-quadratic or quadratic-quadratic equations may have zero, one, two, or an infinite number of solutions.

Solve situational questions by using systems of linear-quadratic or quadratic-quadratic equations.

Expand and demonstrate understanding of inequalities including: one-variable quadratic inequalities, two-variable linear and quadratic inequalities. [C, CN, PS, T, V]

Develop, generalize, explain, and apply strategies for determining the solution region for two-variable linear or two-variable quadratic inequalities.

Explain, using examples, how test points can be used to determine the solution region that satisfies a two-variable inequality.

Explain, using examples, when a solid or broken line should be used in the graphic solution of a two-variable inequality.

Explain what the solution region for a two-variable inequality means.

Solve a situational question that involves a two-variable inequality.

Develop, generalize, explain, and apply strategies, such as case analysis, graphing, roots and test points, or sign analysis, to solve one-variable quadratic inequalities.

Model and solve a situational question that involves a one-variable quadratic inequality.

Interpret the solution to a situational question that involves a one-variable quadratic inequality.

Extend understanding of angles to angles in standard position, expressed in degrees and radians. [CN, ME, R, V]

Sketch angles in standard position including positive and negative degrees.

Investigate and describe the relationship between different systems of angle measurements, with emphasis on radians and degrees.

Develop and apply strategies for converting between angle measures in degrees and radians (exact value or decimal approximation).

Develop, explain, and apply strategies for determining the general form for all angles that are coterminal to a given angle (in degrees and radians).

Explain the relationship between the radian measure of an angle in standard position and the length of the arc cut on a circle of radius r, and solve situational questions based on that relationship.

Demonstrate understanding of polynomials and polynomial functions of degree greater than 2 (limited to polynomials of degree 5 with integral coefficients). [C, CN, ME, T, V]

Develop, generalize, explain, and apply long division for dividing polynomials by binomials of the form x-a, a of the set I.

Compare long division of polynomial expressions by binomial expressions to synthetic division, and explain why synthetic division works.

Divide a polynomial expression by a binomial expression of the form x-a, a dI using synthetic division.

Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

Generalize, through inductive reasoning, the relationship between the remainder when a polynomial expression is divided by x-a, a of the set I and the value of the polynomial expression at x = a (The Remainder Theorem).

Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Categorize, with justification, a set of functions into polynomial functions and non-polynomial functions.

Analyze graphs of polynomial functions to determine the impact of changing the values of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

The x-intercepts of the graph of the polynomial function.

Sketch, with or without the use of technology, the graph of a polynomial function.

Solve situational questions by modelling the situations with polynomial functions and analyzing the graphs of the functions.

Demonstrate understanding of radical and rational functions with restrictions on the domain. [CN, R, T, V]

Sketch the graph of the function y = square root of x using a table of values, and state the domain and range of the function.

Develop, generalize, explain, and apply transformations to the function y = square root of x to sketch the graph of y - k = a(square root of b(x-h)).

Describe the relationship between the roots of a radical equation and the x-intercepts of the graph of the corresponding radical function.

Determine, graphically, the approximate solutions to radical equations.

Sketch rational functions, with and without the use of technology.

Explain the behaviour (shape and location) of the graphs of rational functions for values of the dependent variable close to the location of a vertical asymptote.

Analyze the equation of a rational function to determine where the graph of the rational function has an asymptote or a hole, and explain why.

Describe the relationship between the roots of a rational equation and the x-intercepts of the graph of the corresponding rational function.

Determine graphically an approximate solution to a rational equation.

Critique statements such as "Any value that makes the denominator of a rational function equal to zero will result in a vertical asymptote on the graph of the rational function".

Demonstrate understanding of permutations, including the fundamental counting principle. [C, PS, R, V]

Develop and apply strategies, such as lists or tree diagrams, to determine the total number of choices or arrangements possible in a situation.

Explain why the total number of possible choices is found by multiplying rather than adding the number of ways that individual choices can be made.

Provide examples of situations relevant to self, family, and community where the fundamental counting principle can be applied to determine the number of possible choices or arrangements.

Create and solve situational questions that involve the application of the fundamental counting principle.

Count, using graphic organizers, the number of ways to arrange the elements of a set in a row.

Develop, generalize, explain, and apply strategies, including the use of factorial notation, to determine the number of permutations possible if n different elements are taken n or r at a time.

Explain why n must be greater than or equal to r in the notation nPr.

Develop, generalize, explain, and apply strategies for determining the number of permutations possible when two or more elements in the set are identical (non-distinguishable).

Demonstrate understanding of combinations of elements, including the application to the binomial theorem. [C, CN, PS, R, V]

Explain, with examples, how to distinguish between situations that involve permutations and those that involve combinations.

Develop, generalize, explain, and apply strategies for expanding (x + y)^n, n 4.

Develop, generalize, explain, and apply strategies for determining specific terms within a particular expansion of (x + y)^n given n of the set N.

Demonstrate understanding of the unit circle and its relationship to the six trigonometric ratios for any angle in standard position. [CN, ME, PS, R, T, V]

Derive the equation of a circle with centre (0,0) and radius r.

Derive the equation of the unit circle from the application of the Pythagorean theorem or the distance formula.

Develop and generalize the six trigonometric ratios in terms of x, y, and r, using a point that is the intersection of the terminal arm of an angle with the unit circle.

Develop, generalize, and apply strategies for determining the six trigonometric ratios for any angle given a point on the terminal arm of the angle.

Determine, with technology, the approximate value of the trigonometric ratios for any angle (in radians or degrees).

Develop, generalize, explain, and apply strategies, including using the unit circle or a reference triangle, for determining the exact trigonometric ratios for angles whose measures are multiples of 0, 30, 45, 60, 90 (when expressed in degrees), 0, pi/6, pi/4, pi/3, or pi/2 (when expressed in radians).

Explain and apply strategies (with or without the use of technology) to determine the measures, in degrees or radians, of the angles in a specified domain that have a particular trigonometric ratio value.

Explain and apply strategies to determine the exact values of the other trigonometric ratios, given the value of one trigonometric ratio in a specified domain.

Sketch a diagram to represent the context of a problem that involves trigonometric ratios.

Demonstrate understanding of the graphs of the primary trigonometric functions. [CN, PS, T, V]

Sketch, with or without technology, the graph of y=sin x, y =cos x, and y=tan x.

Determine and summarize the characteristics (amplitude, asymptotes, domain, period, range, and zeros) of the graphs of y = sin x, y = cos x, or y = tan x.

Develop, generalize, and explain strategies for determining the transformational impact of changing the coefficients a, b, c, and d in y = a sin b(x - c) + d and y = a cos b(x - c) + d on the graph of y = sin x and y = cos x respectively, including amplitude, asymptotes, domain, period, phase shift, range, and zeros.

Develop and apply strategies to sketch, without technology, graphs of the form y = a sin b(x - c) + d or y = a cos b(x - c) + d.

Write equations for given graphs of sine or cosine functions.

Identify, with justification, a trigonometric function that models a situational question.

Explain how the characteristics of the graph of a trigonometric function relate to the conditions in a situational question.

Solve situational questions by analyzing the graph of trigonometric functions.

Demonstrate understanding of first- and second-degree trigonometric equations. [CN, PS, R, T, V]

Verify, with or without technology, whether or not a value is a solution to a particular trigonometric equation.

Develop and apply strategies for determining algebraically the exact form of the solution to a trigonometric equation.

Determine, using technology, the approximate solution in degrees and radians of a trigonometric equation in a restricted domain.

Explain the relationship between the general solution of trigonometric equations to the zeros of the related trigonometric functions limited to sine and cosine functions.

Determine, using technology, the general solutions for trigonometric equations.

Analyze solutions for given trigonometric equations to identify errors, and correct if necessary.

Demonstrate understanding of trigonometric identities including: reciprocal identities; quotient identities; Pythagorean identities; sum or difference identities (restricted to sine, cosine, and tangent); double-angle identities (restricted to sine, cosine, and tangent) [R, T, V]

Explain the difference between a trigonometric identity and a trigonometric equation.

Verify numerically (using degrees or radians) whether or not a trigonometric statement is a trigonometric identity.

Critique statements such as "If three different values verify a trigonometric identity, then the identity is valid".

Determine, with the use of graphing technology, the potential validity of a trigonometric identity.

Determine the non-permissible values of a trigonometric identity.

Develop, explain, and apply strategies for proving trigonometric identities algebraically.

Explain and apply strategies for determining the exact value of a trigonometric ratio by using sum, difference, and double-angle identities.

Demonstrate an understanding of operations on, and compositions of, functions. [CN, R, T, V]

Sketch the graph of a function that is the sum, difference, product, or quotient of two functions whose graphs are given.

Write the equation of a function that results from the sum, difference, product, or quotient of two or more functions.

Develop, generalize, explain, and apply strategies for determining the domain and range of a function that is the sum, difference, product, or quotient of two other functions.

Write a function as the sum, difference, product, or quotient (or some combination thereof) of two or more functions.

Develop, generalize, explain, and apply strategies for determining the composition of two functions:

Develop, generalize, explain, and apply strategies for evaluating a composition of functions at a particular point.

Develop, generalize, explain, and apply strategies for sketching the graph of composite functions in the form:

g(f(x)), where the equations or graphs of (x) and g(x) are given.

Write a function by combining two or more functions through operations on, and compositions of, functions.

Extend understanding of transformations to include functions (given in equation or graph form) in general, including horizontal and vertical translations, and horizontal and vertical stretches. [C, CN, R, V]

Compare and analyze various graphs of transformations of the function y = f(x), and generalize about the effect of the placement of different coefficients on the original graph of y = f(x).

Develop, generalize, explain, and apply strategies for sketching transformations of the graph of y = f(x) to give the graph of y - k = af(b(x - h)).

Write the equation of a function that has undergone specified vertical translations, horizontal translations, vertical stretches, and/or horizontal translations of the function y = f(x) for which the equation is given.

Demonstrate understanding of functions, relations, inverses and their related equations resulting from reflections through the: x-axis, y-axis, line y = x. [C, CN, R, V]

Generalize and apply the relationship between the coordinates of an ordered pair and the coordinates of the corresponding ordered pair that results from a reflection through the x-axis, the y-axis, or the line y = x.

Develop and apply strategies for sketching the reflection of a function y = f(x) through the x-axis, the y-axis, or the line y = x when the graph of f(x) is given but the equation is not.

Develop and apply strategies for sketching the graphs of y = -f(x), y = f(-x), and x = -f(y) when the graph of f(x) is given and the equation is not.

Develop and apply strategies for writing the equation of a function that is the reflection of the function f(x) through the x-axis, y-axis, or line y = x.

Develop and apply strategies for sketching the inverse of a relation, including reflection across the line y = x and the transformation (x, y) => (y, x).

Sketch the graph of the inverse relation, given the graph of the relation.

Develop, generalize, explain, and apply strategies for determining if one or both of a relation and its inverse are functions.

Determine what restrictions must be placed on the domain of a function for its inverse to be a function.

Critique statements such as "If a relation is not a function, then its inverse also will not be a function".

Determine the equation and sketch the graph of the inverse relation, given the equation of a linear or quadratic relation.

Explain the relationship between the domains and ranges of a relation and its inverse.

Develop and apply numeric, algebraic, and graphic strategies to determine if two relations are inverses of each other.

Demonstrate an understanding of logarithms including: evaluating logarithms, relating logarithms to, exponents, deriving laws of logarithms, solving equations, graphing. [C, CN, ME, PS, R, T, V]

Explain the relationship between powers, exponentials, logarithms, and radicals.

Express a logarithmic expression as an exponential expression and vice versa.

Determine, without technology, the exact value of a logarithm such as (log2)8.

Explain how to estimate the value of a logarithm using benchmarks (e.g., since (log2)8 = 3 and (log2)16 = 4, (log2)9 is approximately equal to 3.1).

Apply the laws of logarithms to determine equivalent expressions for given logarithmic statements.

Determine, using technology, the approximate value of a logarithmic expression (e.g., (log2)9).

Solve exponential equations in which the bases are powers of one another.

Solve exponential equations in which the bases are not powers of one another.

Solve situational questions that involve exponential growth or decay, such as loans, mortgages, and investments.

Solve situational questions involving logarithmic scales, such as the Richter scale and pH scale.

Analyze graphs of exponential functions of the form y = a^x, a > 0 and report about the relationships between the value of a and the domain, range, horizontal asymptote, and intercepts.

Sketch, with or without the use of technology, the graphs of exponential functions of the form y = a^x, a > 0.

Explain the role of the horizontal asymptote for exponential functions.

Analyze graphs of logarithmic functions of the form y = (log b)x, b > 1 and report about the relationships between the value of b and the domain, range, vertical asymptote, and intercepts.

Sketch, with or without technology, the graphs of logarithmic functions of the form y = (log b)x, b > 1.

Explain the role of the vertical asymptote for logarithm functions.

Demonstrate graphically that y = (log b)x, b > 1 and y = b^x, b > 0 = x are inverses of each other.

Demonstrate understanding of the preservation of equality including solving problems that involve the manipulation and application of formulas related to: perimeter, area, the Pythagorean Theorem, primary trigonometric ratios, income. [C, CN, ME, PS, R, T].

Verify, using examples, and explain why different forms of the same formula are equivalent.

Describe, using examples, how a given formula is used in a trade or an occupation.

Create, solve, and verify the reasonableness of solutions to situational questions relevant to self, family, or community that involve the use of a formula.

Analyze solutions to questions that involve formulae to verify the preservation of equality and correct, with explanation, if necessary.

Solve situational questions that involve the application of a formula that:

Apply proportional reasoning to solve problems involving unit pricing and currency exchange. [CN, ME, PS, R, T]

Create and solve problems relevant to self, family, and community that involve best buy, and explain the solution in terms of the cost as well as other factors, such as quality and quantity.

Describe and analyze, using relevant examples taken from print and other media, different sales promotion techniques (e.g., deli meat at $2 per 100g seems less expensive than $20 per kilogram).

Determine the percent increase or decrease from an original price to a new price and explain the reasoning for the method.

Develop (using proportional reasoning), explain, and apply strategies for:

Determining percent increase or decrease for a given situation.

Analyze solutions to situational questions that involve unit pricing or conversions of currency to determine if they are reasonable and explain the reasoning.

Demonstrate understanding of income including: wages, salary, contracts, commissions, piecework, self-employment, gross pay, net pay. [C, CN, R, T]

Describe, using examples, various methods of earning income.

Research and record jobs that commonly use different methods of earning income, including hourly wage, wage and tips, salary, commission, contract, bonus, and shift premiums.

Describe the advantages and disadvantages for a variety of methods of earning income, such as hourly wage, tips, piecework, salary, commission, contract work, and self-employment.

Base hourly wage, with and without tips, from given or calculated hours worked.

Base hourly wage, plus overtime (time and a half, double time) from given or calculated hours worked.

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