CDEFG
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LAST UPDATE: February 2022
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NOTE: This breakdown does not suggest an order in which topics can be addressed with a class. It does suggest a progression within concepts/topics.
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CYCLE 1 (~20 periods)CYCLE 2 (~20 periods)CYCLE 3 (~20 periods)
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AA: SOCIAL EMOTIONAL LEARNING IN MATHEMATICS
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AA1: develop and explore a variety of social-emotional learning skills in a context that supports and reflects this learning in connection with the expectations across all other strandsExplicit teaching on social-emotional learning skills (eg. the Learning Pit) and individual reflection and goal-settingSEL check-in, opportunity for reflection and next steps.SEL check-in, opportunity for reflection and next steps.
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A: MATHEMATICAL THINKING AND MAKING CONNECTIONS
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A1: apply the mathematical processes to develop a conceptual understanding of, and procedural fluency with, the mathematics they are learningEmbed throughout.
Provide lots of opportunities for self-assessment and feedback.
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A2: make connections between mathematics and various knowledge systems, their lived experiences, and various real-life applications of mathematics, including careers
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B: NUMBER
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B1.1 research a number concept to tell a story about its development and use in a specific culture, and describe its relevance in a current contextEmbed throughout.
OPTION: provide opportunities for students to research and present concept of their choosing.
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B1.2 describe how various subsets of a number system are defined, and describe similarities and differences between these subsetsUnderstand different subsets of a number system (option: respond to students' presentations/stories about number systems)
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Describe similarities and differences between subsets (option: respond to students' presentations/stories about number systems)ERROR CORRECTED SEPTEMBER 9, 2021
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B1.3 use patterns and number relationships to explain density, infinity, and limit as they relate to number setsUse patterns and number relationships to explain density
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Use patterns and number relationships to explain infinity
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Use patterns and number relationships to explain limit
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B2.1 analyse, through the use of patterning, the relationship between the sign and size of an exponent and the value of a power, and use this relationship to express numbers in scientific notation and evaluate powersEvaluate powers with positive whole number basesUse patterning to understand and evaluate powers with zero exponentERROR CORRECTED SEPTEMBER 9, 2021
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Evaluate powers with integer basesUse patterning to understand and evaluate powers with negative exponents
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Evaluate powers with rational bases
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Express numbers in scientific notation
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B2.2 analyse, through the use of patterning, the relationships between the exponents of powers and the operations with powers, and use these relationships to simplify numeric and algebraic expressionsMultiply powers with the same numeric baseSimplify numeric expressions using the power of a power exponent lawMultiply powers with the algebraic bases
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Divide powers with the same numeric baseDivide powers with the algebraic bases
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Simplify algebraic expressions using the power of a power exponent law
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B3.1 apply an understanding of integers to describe location, direction, amount, and changes in any of these, in various contextsUnderstand that integers describe location on a number line and in the four quadrantsUnderstand that integers describe quantities (e.g., in a budget)
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B3.2 apply an understanding of unit fractions and their relationship to other fractional amounts, in various contexts, including the use of measuring toolsCompare non unit fractions in terms of size (different strategies to compare: common denominator, visual representations, converting to percents / decimals)
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B3.3 apply an understanding of integers to explain the effects that positive and negative signs have on the values of ratios, rates, fractions, and decimals, in various contextsCompare positive and negative fractions and decimals in terms of location on a number lineUnderstand the equivalence of different forms of negative rational numbers (e.g., -a/b, a/-b or -(a/b))Explain effects of positive and negative signs on ratios and rates
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B3.4 solve problems involving operations with positive and negative fractions and mixed numbers, including problems involving formulas, measurements, and linear relations, using technology when appropriateAdd and subtract positive and negative fractions and mixed numbers
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Multiply and divide positive and negative fractions and mixed numbers
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B3.5 pose and solve problems involving rates, percentages, and proportions in various contexts, including contexts connected to real-life applications of data, measurement, geometry, linear relations, and financial literacyCalculate and compare ratesConvert fractions, decimals to percentages as needed to solve problems
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Solve problems involving proportions
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C: ALGEBRA
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C1.1 research an algebraic concept to tell a story about its development and use in a specific culture, and describe its relevance in a current contextEmbed throughout.
OPTION: provide opportunities for students to research and present concept of their choosing.
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C1.2 create algebraic expressions to generalize relationships expressed in words, numbers, and visual representations, in various contextsCreate an algebraic expression from a visual representation, words and numbersFlexibly create algebraic expressions given various contexts
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C1.3 compare algebraic expressions using concrete, numerical, graphical, and algebraic methods to identify those that are equivalent, and justify their choicesCompare algebraic expressions using concrete methods (e.g., algebra tiles, visuals), numerical methods (e.g., substituting values, tables of values), graphical methods, and algebraic methods to identify those that are equivalent and justify choices (see C1.4)Continue to compare algebraic expressions using graphical and algebraic methods to identify those that are equivalent and justify choices
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C1.4 simplify algebraic expressions by applying properties of operations of numbers, using various representations and tools, in different contextsIdentify and use terminology: monomial, binomial, polynomials, like and unlike terms, etc.
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Simplify algebraic expressions by adding/subtracting like termsExpand algebraic expressions with a numerical multiplier and a monomial multiplier (distributive property)Simplify and expand algebraic expressions
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C1.5 create and solve equations for various contexts, and verify their solutionsCreate and solve one-step equations (increase complexity to include fractional coefficients) and verify solutions using a way that makes sense (e.g., substituting values, graphing each side)Create and solve two-step equations (increase complexity to include fractional coefficients) and verify solutions using a way that makes sense (e.g., substituting values, graphing each side)Create and solve multi-step equations (increase complexity to include fractional coefficients and distributive property) and verify solutions using a way that makes sense (e.g., substituting values, graphing each side)
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Create and solve equations involving taking the square root and verify solutions using a way that makes sense (e.g., substituting values, graphing each side)
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C2.1 use coding to demonstrate an understanding of algebraic concepts including variables, parameters, equations, and inequalitiesEmbed throughout.
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C2.2 create code by decomposing situations into computational steps in order to represent mathematical concepts and relationships, and to solve problems
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C2.3 read code to predict its outcome, and alter code to adjust constraints, parameters, and outcomes to represent a similar or new mathematical situation
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C3.1 compare the shapes of graphs of linear and non-linear relations to describe their rates of change, to make connections to growing and shrinking patterns, and to make predictionsDetermine whether a relation is linear or non-linear from the graphDescribe and determine rate of change between two points (rise/run) and compare rates of change (steepness, growing/shrinking)
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Determine whether a pattern is growing or shrinking from the graphMake predictions about situations growing or shrinking, by using graphical information.
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C3.2 represent linear relations using concrete materials, tables of values, graphs, and equations, and make connections between the various representations to demonstrate an understanding of rates of change and initial valuesRepresent linear relations using concrete materials, tables of values, graphs or informal sketchesDetermine other representations of a linear relation arising from a realistic situation, given one representation
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Make connections between representations of a linear relation to show an understanding of rate of change and initial value
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C3.3 compare two linear relations of the form y = ax + b graphically and algebraically, and interpret the meaning of their point of intersection in terms of a given contextCompare two linear relations (y = ax + b) graphically (using technology) and interpret the meaning of the point of intersection given a contextCompare two linear relations (y = ax + b) algebraically and interpret the meaning of the point of intersection given a context
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C4.1 compare characteristics of graphs, tables of values, and equations of linear and non-linear relationsCompare constant and inconsistent rates of change of tables of values of linear and nonlinear relationsCompare characteristics of linear and nonlinear equations
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Compare constant and inconsistent rates of change of graphs of linear and nonlinear relations and explain that a linear graph is a line and a non-linear graph is a curve or not a line
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C4.2 graph relations represented as algebraic equations of the forms x = k, y = k, x + y = k, x – y = k, ax + by = k, and xy = k, and their associated inequalities, where a, b, and k are constants, to identify various characteristics and the points and/or regions defined by these equations and inequalitiesUnderstand horizontal and vertical lines x = k and y = k and their associated inequalities
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Graph x + y = k and x - y = k and their inequalities and identify characteristics, points and regions defined
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Graph ax + by = k and associated inequalities and identify characteristics, points and regions defined
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Graph xy = k and associated inequalities and identify characteristics, points and regions defined
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C4.3 translate, reflect, and rotate lines defined by y = ax, where a is a constant, and describe how each transformation affects the graphs and equations of the defined linesInvestigate reflections of the line y=ax (positive vs. negative slope) and describe how the transformations affect the graph and equation
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Investigate rotations of the line y=ax and describe how the transformations affect the graph and equation (steepness)
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[NEED CLARIFICATION FROM MINISTRY] Investigate translations the line y = ax [up or down] and describe how the transformations affect the graph and equation (vertical shifts only)
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C4.4 determine the equations of lines from graphs, tables of values, and concrete representations of linear relations by making connections between rates of change and slopes, and between initial values and y-intercepts, and use these equations to solve problemsDetermine the slope of a line between two points (rise/run, change in y / change in x) - DO NOT USE FORMAL SLOPE FORMULA
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Determine the y-intercept of a line from a graph and table of values (zero term)
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Determine equations of lines from graphs, tables and concrete representations by identifying the slope and y-intercept
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D: DATA
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D1.1 identify a current context involving a large amount of data, and describe potential implications and consequences of its collection, storage, representation, and useEmbed throughout.
OPTION: provide opportunities for students to research and present concept of their choosing.
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D1.2 represent and statistically analyse data from a real-life situation involving a single variable in various ways, including the use of quartile values and box plotsCalculate one variable measures for dataset : mean, median, mode, maximum, minimum, rangeCalculate one variable measures for dataset: quartiles, IQR (interquartile range) - consider outliers
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Define key measures : we know what they are, what do they mean in context of the data set
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Represent data with a box plot - by hand/technology
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Interpret a given box plot (max/min, median (Q2), quartiles, range, IQR, IQR%)
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Use box plots to compare data sets (spread - where medians are same, distributions - where data is consistent or spread out)
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D1.3 create a scatter plot to represent the relationship between two variables, determine the correlation between these variables by testing different regression models using technology, and use a model to make predictions when appropriateCreate a scatter plot with technology (Google Sheets, Desmos, etc)
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Describe what makes a good "line of best fit" (generally)
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Determine the correlation between two variables by testing different regression models for data sets using technology (Google Sheets)
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Use models (i.e., lines of best fit) to make predictions using the graph when appropriateUse equation of line of best fit (determined by tech) to make predictions (linear)
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D2.1 describe the value of mathematical modelling and how it is used in real life to inform decisionsEmbed throughout.
Provide opportunities for students to examine a personal question of interest and related processes to explore the question through mathematical modelling.
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D2.2 identify a question of interest requiring the collection and analysis of data, and identify the information needed to answer the question
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D2.3 create a plan to collect the necessary data on the question of interest from an appropriate source, identify assumptions, identify what may vary and what may remain the same in the situation, and then carry out the plan
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D2.4 determine ways to display and analyse the data in order to create a mathematical model to answer the original question of interest, taking into account the nature of the data, the context, and the assumptions made
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D2.5 report how the model can be used to answer the question of interest, how well the model fits the context, potential limitations of the model, and what predictions can be made based on the model
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E: GEOMETRY AND MEASUREMENT
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E1.1 research a geometric concept or a measurement system to tell a story about its development and use in a specific culture or community, and describe its relevance in connection to careers and to other disciplinesEmbed throughout.
OPTION: provide opportunities for students to research and present concept of their choosing.
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E1.2 create and analyse designs involving geometric relationships and circle and triangle properties, using various toolsUnderstand properties of angles in triangles (sum of angles, exterior angles)
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Understand inscribed angle theorems, angle in a semicircle theorem.
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Understand tangent angle to circle property
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Create and analyze geometric designs
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E1.3 solve problems involving different units within a measurement system and between measurement systems, including those from various cultures or communities, using various representations and technology, when appropriateCompare different units within measurement systems (various cultures)
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Make conversions between measurement system by solving proportions
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E1.4 show how changing one or more dimensions of a two-dimensional shape and a three-dimensional object affects perimeter/circumference, area, surface area, and volume, using technology when appropriateShow how changing one or more dimensions in a 2D shape affects perimeterShow how changing one or more dimensions in a 3D shape affects volume
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Show how changing one or more dimensions in a 2D shape affects areaShow how changing one or more dimensions in a 3D shape affects surface area
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E1.5 solve problems involving the side-length relationship for right triangles in real-life situations, including problems that involve composite shapesFind the length of an unknown hypotenuseUse (side-length) right triangle relationship to solve problems with 2D composite shapes
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Find the length of an unknown legUse (side-length) right triangle relationship to solve problems with 3D shapes (e.g., height or slant height of pyramid, cone)
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E1.6 solve problems using the relationships between the volume of prisms and pyramids and between the volume of cylinders and cones, involving various units of measureInvestigate and apply the relationship between the volume of a prism and pyramid with the same base and height
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Investigate and apply the relationship between the volume of a cylinder and cone with the same base and height
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F: FINANCIAL LITERACY
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F1.1 identify a past or current financial situation and explain how it can inform financial decisions, by applying an understanding of the context of the situation and related mathematical knowledgeEmbed throughout.
OPTION: provide opportunities for students to research and present situation of their choosing.
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F1.2 identify financial situations that involve appreciation and depreciation, and use associated graphs to answer related questionsIdentify situations of personal items that appreciate such as a house, property, business, and coins in various graphing scenarios
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Identify situations of things that depreciate such as vehicles, computers, and appliances from graphs
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Interpret a graph to determine the future value of items
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Identify and explain a financial situation (involving appreciation/depreciation) depicted on a graph
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F1.3 compare the effects that different interest rates, lengths of borrowing time, ways in which interest is calculated, and amounts of down payments have on the overall costs associated with purchasing goods or services, using appropriate toolsUse online mortgage calculators to discover how changing interest rates, down payments, etc., changes the overall monthly payments and interest paid.
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Describe/explain how changing interest rates, down payments, etc., changes the overall monthly payments and interest paid
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Interpret and explain various scenarios given on tables, graphs, etc. with changing variables such as interest rates, down payments, etc.
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F1.4 modify budgets displayed in various ways to reflect specific changes in circumstances, and provide a rationale for the modificationsUse technology such as spreadsheets to modify given budgets to reflect a change in circumstance
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Provide a rationale for modifications within a given budget after a change in circumstance