# British Columbia Prescribed Learning Outcomes — Grade 9

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#### 12.AWM.1.1.

Demonstrate an understanding of the limitations of measuring instruments, including: precision; accuracy; uncertainty; tolerance and solve problems. [C, PS, R, T, V]

#### 12.AWM.1.1.1.

Explain why, in a given context, a certain degree of precision is required.

#### 12.AWM.1.1.2.

Explain why, in a given context, a certain degree of accuracy is required.

#### 12.AWM.1.1.3.

Explain, using examples, the difference between precision and accuracy.

#### 12.AWM.1.1.4.

Compare the degree of accuracy of two given instruments used to measure the same attribute.

#### 12.AWM.1.1.5.

Relate the degree of accuracy to the uncertainty of a given measure.

#### 12.AWM.1.1.6.

Analyze precision and accuracy in a contextual problem.

#### 12.AWM.1.1.8.

Describe, using examples, the limitations of measuring instruments used in a specific trade or industry; e.g., tape measure versus Vernier caliper.

#### 12.AWM.1.1.9.

Solve a problem that involves precision, accuracy or tolerance.

#### 12.AWM.2.2.

Solve problems that involve: triangles; quadrilaterals; regular polygons. [C, CN, PS, V]

#### 12.AWM.2.2.1.

Describe and illustrate properties of triangles, including isosceles and equilateral.

#### 12.AWM.2.2.2.

Describe and illustrate properties of quadrilaterals in terms of angle measures, side lengths, diagonal lengths and angles of intersection.

#### 12.AWM.2.2.3.

Describe and illustrate properties of regular polygons.

#### 12.AWM.2.2.4.

Explain, using examples, why a given property does or does not apply to certain polygons.

#### 12.AWM.2.2.5.

Identify and explain an application of the properties of polygons in construction, industrial, commercial, domestic and artistic contexts.

#### 12.AWM.2.2.6.

Solve a contextual problem that involves the application of the properties of polygons.

#### 12.AWM.2.3.

Demonstrate an understanding of transformations on a 2-D shape or a 3-D object, including: translations; rotations; reflections; dilations. [C, CN, R, T, V]

#### 12.AWM.2.3.2.

Draw the image of a 2-D shape that results from a given single transformation.

#### 12.AWM.2.3.4.

Create, analyze and describe designs, using translations, rotations and reflections in all four quadrants of a coordinate grid.

#### 12.AWM.2.3.5.

Identify and describe applications of transformations in construction, industrial, commercial, domestic and artistic contexts.

#### 12.AWM.2.3.7.

Determine and explain whether a given image is a dilation of another given shape, using the concept of similarity.

#### 12.AWM.2.3.8.

Draw, with or without technology, a dilation image for a given 2-D shape or 3-D object, and explain how the original 2-D shape or 3-D object and its image are proportional.

#### 12.AWM.2.3.9.

Solve a contextual problem that involves transformations.

#### 12.AWM.3.1.

Analyze puzzles and games that involve logical reasoning, using problem-solving strategies. [C, CN, PS, R]

#### 12.AWM.3.1.1.

Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,

#### 12.AWM.3.1.1.e.

Eliminate possibilities.

#### 12.AWM.3.1.1.f.

Simplify the original problem.

#### 12.AWM.3.1.1.h.

Develop alternative approaches.

#### 12.AWM.3.2.

Solve problems that involve the acquisition of a vehicle by: buying; leasing; leasing to buy. [C, CN, PS, R, T]

#### 12.AWM.3.2.1.

Describe and explain various options for buying, leasing and leasing to buy a vehicle.

#### 12.AWM.3.2.2.

Solve, with or without technology, problems that involve the purchase, lease or lease to purchase of a vehicle.

#### 12.AWM.3.2.3.

Justify a decision related to buying, leasing or leasing to buy a vehicle, based on factors such as personal finances, intended use, maintenance, warranties, mileage and insurance.

#### 12.AWM.3.3.

Critique the viability of small business options by considering: expenses; sales; profit or loss. [C, CN, R]

#### 12.AWM.3.3.1.

Identify expenses in operating a small business, such as a hot dog stand.

#### 12.AWM.3.3.2.

Identify feasible small business options for a given community.

#### 12.AWM.3.3.3.

Generate options that might improve the profitability of a small business.

#### 12.AWM.3.3.4.

Determine the break-even point for a small business.

#### 12.AWM.3.3.5.

Explain factors, such as seasonal variations and hours of operation, that might impact the profitability of a small business.

#### 12.AWM.4.1.

Demonstrate an understanding of linear relations by: recognizing patterns and trends; graphing; creating tables of values; writing equations; interpolating and extrapolating; solving problems. [CN, PS, R, T, V]

#### 12.AWM.4.1.1.

Identify and describe the characteristics of a linear relation represented in a graph, table of values, number pattern or equation.

#### 12.AWM.4.1.11.

Relate slope and rate of change to linear relations.

#### 12.AWM.4.1.12.

Match given contexts with their corresponding graphs, and explain the reasoning.

#### 12.AWM.4.1.13.

Solve a contextual problem that involves the application of a formula for a linear relation.

#### 12.AWM.4.1.2.

Sort a set of graphs, tables of values, number patterns and/or equations into linear and nonlinear relations.

#### 12.AWM.4.1.3.

Write an equation for a given context, including direct or partial variation.

#### 12.AWM.4.1.4.

Create a table of values for a given equation of a linear relation.

#### 12.AWM.4.1.5.

Sketch the graph for a given table of values.

#### 12.AWM.4.1.7.

Create, with or without technology, a graph to represent a data set, including scatterplots.

#### 12.AWM.4.1.8.

Describe the trends in the graph of a data set, including scatterplots.

#### 12.AWM.4.1.9.

Sort a set of scatterplots according to the trends represented (linear, nonlinear or no trend).

#### 12.AWM.5.1.

Solve problems that involve measures of central tendency, including: mean; median; mode; weighted mean; trimmed mean. [C, CN, PS, R]

#### 12.AWM.5.1.1.

Explain, using examples, the advantages and disadvantages of each measure of central tendency.

#### 12.AWM.5.1.10.

Solve a contextual problem that involves measures of central tendency.

#### 12.AWM.5.1.2.

Determine the mean, median and mode for a set of data.

#### 12.AWM.5.1.3.

Identify and correct errors in a calculation of a measure of central tendency.

#### 12.AWM.5.1.4.

Identify the outlier(s) in a set of data.

#### 12.AWM.5.1.5.

Explain the effect of outliers on mean, median and mode.

#### 12.AWM.5.1.6.

Calculate the trimmed mean for a set of data, and justify the removal of the outliers.

#### 12.AWM.5.1.7.

Explain, using examples such as course marks, why some data in a set would be given a greater weighting in determining the mean.

#### 12.AWM.5.1.9.

Explain, using examples from print and other media, how measures of central tendency and outliers are used to provide different interpretations of data.

#### 12.AWM.5.2.

Analyze and describe percentiles. [C, CN, PS, R]

#### 12.AWM.5.2.1.

Explain, using examples, percentile ranks in a context.

#### 12.AWM.5.2.2.

Explain decisions based on a given percentile rank.

#### 12.AWM.5.2.3.

Explain, using examples, the difference between percent and percentile rank.

#### 12.AWM.5.2.4.

Explain the relationship between median and percentile.

#### 12.AWM.5.2.5.

Solve a contextual problem that involves percentiles.

#### 12.AWM.6.1.

Analyze and interpret problems that involve probability. [C, CN, PS, R]

#### 12.AWM.6.1.1.

Describe and explain the applications of probability; e.g., medication, warranties, insurance, lotteries, weather prediction, 100-year flood, failure of a design, failure of a product, vehicle recalls, approximation of area.

#### 12.AWM.6.1.2.

Calculate the probability of an event based on a data set; e.g., determine the probability of a randomly chosen light bulb being defective.

#### 12.AWM.6.1.3.

Express a given probability as a fraction, decimal and percent and in a statement.

#### 12.AWM.6.1.5.

Determine the probability of an event, given the odds for or against.

#### 12.AWM.6.1.6.

Explain, using examples, how decisions may be based on a combination of theoretical probability calculations, experimental results and subjective judgements.

#### 12.AWM.6.1.7.

Solve a contextual problem that involves a given probability.

#### 12.FMP.1.1.

Solve problems that involve compound interest in financial decision making. [C, CN, PS, T, V]

#### 12.FMP.1.1.2.

Identify situations that involve compound interest.

#### 12.FMP.1.1.3.

Graph and compare, in a given situation, the total interest paid or earned for different compounding periods.

#### 12.FMP.1.1.4.

Determine, given the principal, interest rate and number of compounding periods, the total interest of a loan.

#### 12.FMP.1.1.5.

Graph and describe the effects of changing the value of one of the variables in a situation that involves compound interest.

#### 12.FMP.1.1.6.

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.

#### 12.FMP.1.1.7.

Compare and explain, using technology, different credit options that involve compound interest, including bank and store credit cards and special promotions.

#### 12.FMP.1.1.8.

Solve a contextual problem that involves compound interest.

#### 12.FMP.1.2.

Analyze costs and benefits of renting, leasing and buying. [CN, PS, R, T]

#### 12.FMP.1.2.2.

Compare, using examples, renting, leasing and buying.

#### 12.FMP.1.2.3.

Justify, for a specific set of circumstances, if renting, buying or leasing would be advantageous.

#### 12.FMP.1.2.4.

Solve a problem involving renting, leasing or buying that requires the manipulation of a formula.

#### 12.FMP.1.2.5.

Solve, using technology, a contextual problem that involves cost-and-benefit analysis.

#### 12.FMP.1.3.

Analyze an investment portfolio in terms of: interest rate; rate of return; total return. [ME, PS, R, T]

#### 12.FMP.1.3.1.

Determine and compare the strengths and weaknesses of two or more portfolios.

#### 12.FMP.1.3.2.

Determine, using technology, the total value of an investment when there are regular contributions to the principal.

#### 12.FMP.1.3.3.

Graph and compare the total value of an investment with and without regular contributions.

#### 12.FMP.1.3.4.

Apply the Rule of 72 to solve investment problems, and explain the limitations of the rule.

#### 12.FMP.1.3.5.

Determine, using technology, possible investment strategies to achieve a financial goal.

#### 12.FMP.1.3.7.

Explain, using examples, why smaller investments over a longer term may be better than larger investments over a shorter term.

#### 12.FMP.1.3.8.

Solve an investment problem.

#### 12.FMP.2.1.

Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies. [CN, ME, PS, R]

#### 12.FMP.2.1.1.

Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,

#### 12.FMP.2.1.1.e.

Eliminate possibilities.

#### 12.FMP.2.1.1.f.

Simplify the original problem.

#### 12.FMP.2.1.1.h.

Develop alternative approaches.

#### 12.FMP.2.2.

Solve problems that involve the application of set theory. [CN, PS, R, V]

#### 12.FMP.2.2.1.

Provide examples of the empty set, disjoint sets, subsets and universal sets in context, and explain the reasoning.

#### 12.FMP.2.2.2.

Organize information such as collected data and number properties, using graphic organizers, and explain the reasoning.

#### 12.FMP.2.2.3.

Explain what a specified region in a Venn diagram represents, using connecting words (and, or, not) or set notation.

#### 12.FMP.2.2.4.

Determine the elements in the complement, the intersection or the union of two sets.

#### 12.FMP.2.2.5.

Explain how set theory is used in applications such as Internet searches, database queries, data analysis, games and puzzles.

#### 12.FMP.2.2.6.

Identify and correct errors in a given solution to a problem that involves sets.

#### 12.FMP.2.2.7.

Solve a contextual problem that involves sets, and record the solution, using set notation.

#### 12.FMP.2.3.

Solve problems that involve conditional statements. [C, CN, PS, R]

#### 12.FMP.2.3.1.

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

#### 12.FMP.2.3.2.

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

#### 12.FMP.2.3.3.

Determine the converse, inverse and contrapositive of an if-then statement; determine its veracity; and, if it is false, provide a counterexample.

#### 12.FMP.2.3.4.

Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its converse or inverse.

#### 12.FMP.2.3.5.

Demonstrate, using examples, that the veracity of any statement does imply the veracity of its contrapositive.

#### 12.FMP.2.3.6.

Identify and describe contexts in which a biconditional statement can be justified.

#### 12.FMP.2.3.7.

Analyze and summarize, using a graphic organizer such as a truth table or Venn diagram, the possible results of given logical arguments that involve biconditional, converse, inverse or contrapositive statements.

#### 12.FMP.3.1.

Interpret and assess the validity of odds and probability statements. [C, CN, ME]

#### 12.FMP.3.1.1.

Provide examples of statements of probability and odds found in fields such as media, biology, sports, medicine, sociology and psychology.

#### 12.FMP.3.1.5.

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

#### 12.FMP.3.2.

Solve problems that involve the probability of mutually exclusive and nonmutually exclusive events. [CN, PS, R, V]

#### 12.FMP.3.2.1.

Classify events as mutually exclusive or non mutually exclusive, and explain the reasoning.

#### 12.FMP.3.2.2.

Determine if two events are complementary, and explain the reasoning.

#### 12.FMP.3.2.3.

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

#### 12.FMP.3.2.4.

Solve a contextual problem that involves the probability of mutually exclusive or nonmutually exclusive events.

#### 12.FMP.3.2.5.

Solve a contextual problem that involves the probability of complementary events.

#### 12.FMP.3.2.6.

Create and solve a problem that involves mutually exclusive or nonmutually exclusive events.

#### 12.FMP.3.3.

Solve problems that involve the probability of two events. [CN, PS, R]

#### 12.FMP.3.3.1.

Compare, using examples, dependent and independent events.

#### 12.FMP.3.3.2.

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

#### 12.FMP.3.3.3.

Determine the probability of two dependent or two independent events.

#### 12.FMP.3.3.4.

Create and solve a contextual problem that involves determining the probability of dependent or independent events.

#### 12.FMP.3.4.

Solve problems that involve the fundamental counting principle. [PS, R, V]

#### 12.FMP.3.4.1.

Represent and solve counting problems, using a graphic organizer.

#### 12.FMP.3.4.2.

Generalize the fundamental counting principle, using inductive reasoning.

#### 12.FMP.3.4.3.

Identify and explain assumptions made in solving a counting problem.

#### 12.FMP.3.4.4.

Solve a contextual counting problem, using the fundamental counting principle, and explain the reasoning.

#### 12.FMP.3.5.

Solve problems that involve permutations. [ME, PS, R, T, V]

#### 12.FMP.3.5.1.

Represent the number of arrangements of n elements taken n at a time, using factorial notation.

#### 12.FMP.3.5.2.

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

#### 12.FMP.3.5.3.

Simplify a numeric or algebraic fraction containing factorials in both the numerator and denominator.

#### 12.FMP.3.5.4.

Solve an equation that involves factorials.

#### 12.FMP.3.5.5.

Determine the number of permutations of n elements taken r at a time.

#### 12.FMP.3.5.6.

Determine the number of permutations of n elements taken n at a time where some elements are not distinct.

#### 12.FMP.3.5.7.

Explain, using examples, the effect on the total number of permutations of n elements when two or more elements are identical.

#### 12.FMP.3.5.8.

Generalize strategies for determining the number of permutations of n elements taken r at a time.

#### 12.FMP.3.5.9.

Solve a contextual problem that involves probability and permutations.

#### 12.FMP.3.6.

Solve problems that involve combinations. [ME, PS, R, T, V]

#### 12.FMP.3.6.1.

Explain, using examples, why order is or is not important when solving problems that involve permutations or combinations.

#### 12.FMP.4.1.

Represent data, using polynomial functions (of degree < 3), to solve problems. [C, CN, PS, T, V]

#### 12.FMP.4.1.1.

Describe, orally and in written form, the characteristics of polynomial functions by analyzing their graphs.

#### 12.FMP.4.1.2.

Describe, orally and in written form, the characteristics of polynomial functions by analyzing their equations.

#### 12.FMP.4.1.3.

Match equations in a given set to their corresponding graphs.

#### 12.FMP.4.1.5.

Interpret the graph of a polynomial function that models a situation, and explain the reasoning.

#### 12.FMP.4.1.6.

Solve, using technology, a contextual problem that involves data that is best represented by graphs of polynomial functions, and explain the reasoning.

#### 12.FMP.4.2.

Represent data, using exponential and logarithmic functions, to solve problems. [C, CN, PS, T, V]

#### 12.FMP.4.2.1.

Describe, orally and in written form, the characteristics of exponential or logarithmic functions by analyzing their graphs.

#### 12.FMP.4.2.3.

Match equations in a given set to their corresponding graphs.

#### 12.FMP.4.2.4.

Graph data and determine the exponential or logarithmic function that best approximates the data.

#### 12.FMP.4.2.5.

Interpret the graph of an exponential or logarithmic function that models a situation, and explain the reasoning.

#### 12.FMP.4.2.6.

Solve, using technology, a contextual problem that involves data that is best represented by graphs of exponential or logarithmic functions, and explain the reasoning.

#### 12.FMP.4.3.

Represent data, using sinusoidal functions, to solve problems. [C, CN, PS, T, V]

#### 12.FMP.4.3.1.

Describe, orally and in written form, the characteristics of sinusoidal functions by analyzing their graphs.

#### 12.FMP.4.3.2.

Describe, orally and in written form, the characteristics of sinusoidal functions by analyzing their equations.

#### 12.FMP.4.3.3.

Match equations in a given set to their corresponding graphs.

#### 12.FMP.4.3.4.

Graph data and determine the sinusoidal function that best approximates the data.

#### 12.FMP.4.3.5.

Interpret the graph of a sinusoidal function that models a situation, and explain the reasoning.

#### 12.FMP.4.3.6.

Solve, using technology, a contextual problem that involves data that is best represented by graphs of sinusoidal functions, and explain the reasoning.

#### 12.FMP.5.1.

Research and give a presentation on a current event or an area of interest that involves mathematics. [C, CN, ME, PS, R, T, V]

#### 12.FMP.5.1.1.

Collect primary or secondary data (statistical or informational) related to the topic.

#### 12.FMP.5.1.2.

Assess the accuracy, reliability and relevance of the primary or secondary data collected by:

#### 12.FMP.5.1.2.a.

Identifying examples of bias and points of view.

#### 12.FMP.5.1.2.b.

Identifying and describing the data collection methods.

#### 12.FMP.5.1.2.c.

Determining if the data is relevant.

#### 12.FMP.5.1.2.d.

Determining if the data is consistent with information obtained from other sources on the same topic.

#### 12.FMP.5.1.3.

Interpret data, using statistical methods if applicable.

#### 12.FMP.5.1.4.

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

#### 12.PC.1.1.

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

#### 12.PC.1.1.2.

Describe the relationship among different systems of angle measurement, with emphasis on radians and degrees.

#### 12.PC.1.1.5.

Express the measure of an angle in radians (exact value or decimal approximation), given its measure in degrees.

#### 12.PC.1.1.6.

Express the measure of an angle in degrees, given its measure in radians (exact value or decimal approximation).

#### 12.PC.1.1.9.

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 problems based upon that relationship.

#### 12.PC.1.2.

Develop and apply the equation of the unit circle. [CN, R, V]

#### 12.PC.1.2.1.

Derive the equation of the unit circle from the Pythagorean theorem.

#### 12.PC.1.2.2.

Describe the six trigonometric ratios, using a point P (x, y) that is the intersection of the terminal arm of an angle and the unit circle.

#### 12.PC.1.2.3.

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

#### 12.PC.1.3.

Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees. [ME, PS, R, T, V]

#### 12.PC.1.3.1.

Determine, with technology, the approximate value of a trigonometric ratio for any angle with a measure expressed in either degrees or radians.

#### 12.PC.1.3.2.

Determine, using a unit circle or reference triangle, the exact value of a trigonometric ratio for angles expressed in degrees that are multiples of 0, 30, 45, 60 or 90, or for angles expressed in radians that are multiples of 0, 6/, 4/, 3/ or 2/, and explain the strategy.

#### 12.PC.1.3.3.

Determine, with or without technology, the measures, in degrees or radians, of the angles in a specified domain, given the value of a trigonometric ratio.

#### 12.PC.1.3.4.

Explain how to determine the exact values of the six trigonometric ratios, given the coordinates of a point on the terminal arm of an angle in standard position.

#### 12.PC.1.3.5.

Determine the measures of the angles in a specified domain in degrees or radians, given a point on the terminal arm of an angle in standard position.

#### 12.PC.1.3.6.

Determine the exact values of the other trigonometric ratios, given the value of one trigonometric ratio in a specified domain.

#### 12.PC.1.3.7.

Sketch a diagram to represent a problem that involves trigonometric ratios.

#### 12.PC.1.3.8.

Solve a problem, using trigonometric ratios.

#### 12.PC.1.4.

Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems. [CN, PS, T, V]

#### 12.PC.1.4.1.

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

#### 12.PC.1.4.10.

Determine a trigonometric function that models a situation to solve a problem.

#### 12.PC.1.4.11.

Explain how the characteristics of the graph of a trigonometric function relate to the conditions in a problem situation.

#### 12.PC.1.4.12.

Solve a problem by analyzing the graph of a trigonometric function.

#### 12.PC.1.4.2.

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

#### 12.PC.1.4.3.

Determine how varying the value of a affects the graphs of y = a sin x and y = a cos x.

#### 12.PC.1.4.4.

Determine how varying the value of d affects the graphs of y = sin x + d and y = cos x + d.

#### 12.PC.1.4.5.

Determine how varying the value of c affects the graphs of y = sin (x + c) and y = cos (x + c).

#### 12.PC.1.4.6.

Determine how varying the value of b affects the graphs of y = sin bx and y = cos bx.

#### 12.PC.1.4.7.

Sketch, without technology, graphs of the form y = a sin b(x - c) + d or y = a cos b(x - c) + d, using transformations, and explain the strategies.

#### 12.PC.1.4.8.

Determine the characteristics (amplitude, asymptotes, domain, period, phase shift, range and zeros) of the graph of a trigonometric function of the form y = a sin b(x - c) + d or y = a cos b(x - c) + d.

#### 12.PC.1.4.9.

Determine the values of a, b, c and d for functions of the form y = a sin b(x - c) + d or y = a cos b(x - c) + d that correspond to a given graph, and write the equation of the function.

#### 12.PC.1.5.

Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians. [CN, PS, R, T, V]

#### 12.PC.1.5.1.

Verify, with or without technology, that a given value is a solution to a trigonometric equation.

#### 12.PC.1.5.2.

Determine, algebraically, the solution of a trigonometric equation, stating the solution in exact form when possible.

#### 12.PC.1.5.3.

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

#### 12.PC.1.5.4.

Relate the general solution of a trigonometric equation to the zeros of the corresponding trigonometric function (restricted to sine and cosine functions).

#### 12.PC.1.5.5.

Determine, using technology, the general solution of a given trigonometric equation.

#### 12.PC.1.5.6.

Identify and correct errors in a solution for a trigonometric equation.

#### 12.PC.1.6.

Prove trigonometric identities, using: 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]

#### 12.PC.1.6.1.

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

#### 12.PC.1.6.2.

Verify a trigonometric identity numerically for a given value in either degrees or radians.

#### 12.PC.1.6.3.

Explain why verifying that the two sides of a trigonometric identity are equal for given values is insufficient to conclude that the identity is valid.

#### 12.PC.1.6.4.

Determine, graphically, the potential validity of a trigonometric identity, using technology.

#### 12.PC.1.6.5.

Determine the non-permissible values of a trigonometric identity.

#### 12.PC.1.6.6.

Prove, algebraically, that a trigonometric identity is valid.

#### 12.PC.1.6.7.

Determine, using the sum, difference and double-angle identities, the exact value of a trigonometric ratio.

#### 12.PC.2.1.

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

#### 12.PC.2.1.2.

Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

#### 12.PC.2.1.3.

Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

#### 12.PC.2.1.4.

Write a function h(x) as the sum, difference, product or quotient of two or more functions.

#### 12.PC.2.1.5.

Determine the value of the composition of functions when evaluated at a point, including: f(f(a)), f(g(a)), g(f(a))

#### 12.PC.2.1.6.

Determine, given the equations of two functions f(x) and g(x), the equation of the composite function:

#### 12.PC.2.1.6.a.

f(f(x)) and explain any restrictions.

#### 12.PC.2.1.6.b.

f(g(x)) and explain any restrictions.

#### 12.PC.2.1.6.c.

g(f(x)) and explain any restrictions.

#### 12.PC.2.1.7.

Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function:

#### 12.PC.2.1.8.

Write a function h(x) as the composition of two or more functions.

#### 12.PC.2.1.9.

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

#### 12.PC.2.10.

Solve problems that involve exponential and logarithmic equations. [C, CN, PS, R]

#### 12.PC.2.10.1.

Determine the solution of an exponential equation in which the bases are powers of one another.

#### 12.PC.2.10.2.

Determine the solution of an exponential equation in which the bases are not powers of one another, using a variety of strategies.

#### 12.PC.2.10.5.

Solve a problem that involves exponential growth or decay.

#### 12.PC.2.10.6.

Solve a problem that involves the application of exponential equations to loans, mortgages and investments.

#### 12.PC.2.10.8.

Solve a problem by modelling a situation with an exponential or a logarithmic equation.

#### 12.PC.2.11.

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree < 5 with integral coefficients). [C, CN, ME]

#### 12.PC.2.11.1.

Explain how long division of a polynomial expression by a binomial expression of the form x-a, aI, is related to synthetic division.

#### 12.PC.2.11.2.

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

#### 12.PC.2.11.3.

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

#### 12.PC.2.11.4.

Explain the relationship between the remainder when a polynomial expression is divided by x-a, aI, and the value of the polynomial expression at x=a (remainder theorem).

#### 12.PC.2.11.5.

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

#### 12.PC.2.12.

Graph and analyze polynomial functions (limited to polynomial functions of degree < 5 ). [C, CN, T, V]

#### 12.PC.2.12.1.

Identify the polynomial functions in a set of functions, and explain the reasoning.

#### 12.PC.2.12.2.

Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

#### 12.PC.2.12.3.

Generalize rules for graphing polynomial functions of odd or even degree.

#### 12.PC.2.12.4.

Explain the relationship between:

#### 12.PC.2.12.4.a.

The zeros of a polynomial function.

#### 12.PC.2.12.4.b.

The roots of the corresponding polynomial equation.

#### 12.PC.2.12.4.c.

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

#### 12.PC.2.12.6.

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

#### 12.PC.2.12.7.

Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

#### 12.PC.2.13.

Graph and analyze radical functions (limited to functions involving one radical). [CN, R, T, V]

#### 12.PC.2.13.1.

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

#### 12.PC.2.13.2.

Sketch the graph of the function y-k = a_(b(x - h)) by applying transformations to the graph of the function y = _x, and state the domain and range.

#### 12.PC.2.13.3.

Sketch the graph of the function y = _(f(x)), given the graph of the function y = f(x), and explain the strategies used.

#### 12.PC.2.13.6.

Determine, graphically, an approximate solution of a radical equation.

#### 12.PC.2.14.

Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials). [CN, R, T, V]

#### 12.PC.2.14.1.

Graph, with or without technology, a rational function.

#### 12.PC.2.14.3.

Explain the behaviour of the graph of a rational function for values of the variable near a non-permissible value.

#### 12.PC.2.14.4.

Determine if the graph of a rational function will have an asymptote or a hole for a non-permissible value.

#### 12.PC.2.14.5.

Match a set of rational functions to their graphs, and explain the reasoning.

#### 12.PC.2.14.6.

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

#### 12.PC.2.14.7.

Determine, graphically, an approximate solution of a rational equation.

#### 12.PC.2.2.

Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations. [C, CN, R, V]

#### 12.PC.2.2.1.

Compare the graphs of a set of functions of the form y k = f (x) to the graph of y = f (x), and generalize, using inductive reasoning, a rule about the effect of k.

#### 12.PC.2.2.2.

Compare the graphs of a set of functions of the form y = f (x - h) to the graph of y = f (x), and generalize, using inductive reasoning, a rule about the effect of h.

#### 12.PC.2.2.3.

Compare the graphs of a set of functions of the form y - k = f (x - h) to the graph of y = f (x), and generalize, using inductive reasoning, a rule about the effects of h and k.

#### 12.PC.2.2.4.

Sketch the graph of y - k = f (x), y = f (x - h) or y - k = f (x - h) for given values of h and k, given a sketch of the function y = f (x), where the equation of y = f (x) is not given.

#### 12.PC.2.2.5.

Write the equation of a function whose graph is a vertical and/or horizontal translation of the graph of the function y = f (x).

#### 12.PC.2.3.

Demonstrate an understanding of the effects of horizontal and vertical stretches on the graphs of functions and their related equations. [C, CN, R, V]

#### 12.PC.2.3.1.

Compare the graphs of a set of functions of the form y = af(x) to the graph of y = f(x), and generalize, using inductive reasoning, a rule about the effect of a.

#### 12.PC.2.3.2.

Compare the graphs of a set of functions of the form y = f(bx) to the graph of y = f(x), and generalize, using inductive reasoning, a rule about the effect of b.

#### 12.PC.2.3.3.

Compare the graphs of a set of functions of the form y =af(bx) to the graph of y = f(x), and generalize, using inductive reasoning, a rule about the effects of a and b.

#### 12.PC.2.3.4.

Sketch the graph of y = af(x), y = f(bx) or y =af(bx) for given values of a and b, given a sketch of the function y = f(x), where the equation of y = f(x) is not given.

#### 12.PC.2.3.5.

Write the equation of a function, given its graph which is a vertical and/or horizontal stretch of the graph of the function y = f(x).

#### 12.PC.2.4.

Apply translations and stretches to the graphs and equations of functions. [C, CN, R, V]

#### 12.PC.2.4.1.

Sketch the graph of the function y-k = af(b(x-h)) for given values of a, b, h and k, given the graph of the function y = f(x), where the equation of y = f(x) is not given.

#### 12.PC.2.4.2.

Write the equation of a function, given its graph which is a translation and/or stretch of the graph of the function y = f(x).

#### 12.PC.2.5.

Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections through the: x-axis; y-axis; line y = x. [C, CN, R, V]

#### 12.PC.2.5.2.

Sketch the reflection of the graph of a function y = f(x) through the x-axis, the y-axis or the line y = x, given the graph of the function y = f(x) , where the equation of y = f(x) is not given.

#### 12.PC.2.5.3.

Generalize, using inductive reasoning, and explain rules for the reflection of the graph of the function y = f(x) through the x-axis, the y-axis or the line y = x.

#### 12.PC.2.5.4.

Sketch the graphs of the functions y = -f(x), y = f(-x) and x = -f(y), given the graph of the function y = f (x), where the equation of y = f(x) is not given.

#### 12.PC.2.5.5.

Write the equation of a function, given its graph which is a reflection of the graph of the function y = f(x) through the x-axis, the y-axis or the line y = x.

#### 12.PC.2.6.

Demonstrate an understanding of inverses of relations. [C, CN, R, V]

#### 12.PC.2.6.1.

Explain how the graph of the line y = x can be used to sketch the inverse of a relation.

#### 12.PC.2.6.2.

Explain how the transformation (x, y) =&gt; (y, x) can be used to sketch the inverse of a relation.

#### 12.PC.2.6.3.

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

#### 12.PC.2.6.4.

Determine if a relation and its inverse are functions.

#### 12.PC.2.6.5.

Determine restrictions on the domain of a function in order for its inverse to be a function.

#### 12.PC.2.6.6.

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

#### 12.PC.2.6.8.

Determine, algebraically or graphically, if two functions are inverses of each other.

#### 12.PC.2.7.

Demonstrate an understanding of logarithms. [CN, ME, R]

#### 12.PC.2.7.1.

Explain the relationship between logarithms and exponents.

#### 12.PC.2.7.2.

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

#### 12.PC.2.7.3.

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

#### 12.PC.2.7.4.

Estimate the value of a logarithm, using benchmarks, and explain the reasoning; e.g., since log2(8) = 3 and log2(16) = 4, log2(9) is approximately equal to 3.1.

#### 12.PC.2.8.

Demonstrate an understanding of the product, quotient and power laws of logarithms. [C, CN, R, T]

#### 12.PC.2.8.1.

Develop and generalize the laws for logarithms, using numeric examples and exponent laws.

#### 12.PC.2.8.2.

Derive each law of logarithms.

#### 12.PC.2.8.3.

Determine, using the laws of logarithms, an equivalent expression for a logarithmic expression.

#### 12.PC.2.8.4.

Determine, with technology, the approximate value of a logarithmic expression, such as log2(9).

#### 12.PC.2.9.

Graph and analyze exponential and logarithmic functions. [C, CN, T, V]

#### 12.PC.2.9.1.

Sketch, with or without technology, a graph of an exponential function of the form y = a^x, a &gt; 0.

#### 12.PC.2.9.2.

Identify the characteristics of the graph of an exponential function of the form y = a^x, a &gt; 0, including the domain, range, horizontal asymptote and intercepts, and explain the significance of the horizontal asymptote.

#### 12.PC.2.9.3.

Sketch the graph of an exponential function by applying a set of transformations to the graph of y = a^x, a &gt; 0, and state the characteristics of the graph.

#### 12.PC.2.9.4.

Sketch, with or without technology, the graph of a logarithmic function of the form y = logb(x), b &gt; 1.

#### 12.PC.2.9.5.

Identify the characteristics of the graph of a logarithmic function of the form y = logb(x), b &gt; 1, including the domain, range, vertical asymptote and intercepts, and explain the significance of the vertical asymptote.

#### 12.PC.2.9.6.

Sketch the graph of a logarithmic function by applying a set of transformations to the graph of y = logb(x), b &gt; 1, and state the characteristics of the graph.

#### 12.PC.2.9.7.

Demonstrate, graphically, that a logarithmic function and an exponential function with the same base are inverses of each other.

#### 12.PC.3.1.

Apply the fundamental counting principle to solve problems. [C, PS, R, V]

#### 12.PC.3.1.1.

Count the total number of possible choices that can be made, using graphic organizers such as lists and tree diagrams.

#### 12.PC.3.1.2.

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

#### 12.PC.3.1.3.

Solve a simple counting problem by applying the fundamental counting principle.

#### 12.PC.3.2.

Determine the number of permutations of n elements taken r at a time to solve problems. [C, PS, R, V]

#### 12.PC.3.2.1.

Count, using graphic organizers such as lists and tree diagrams, the number of ways of arranging the elements of a set in a row.

#### 12.PC.3.2.2.

Determine, in factorial notation, the number of permutations of n different elements taken n at a time to solve a problem.

#### 12.PC.3.2.3.

Determine, using a variety of strategies, the number of permutations of n different elements taken r at a time to solve a problem.

#### 12.PC.3.2.5.

Solve an equation that involves P(n,r) notation, such as P(n,2)=30.

#### 12.PC.3.2.6.

Explain, using examples, the effect on the total number of permutations when two or more elements are identical.

#### 12.PC.3.3.

Determine the number of combinations of n different elements taken r at a time to solve problems. [C, PS, R, V]

#### 12.PC.3.3.1.

Explain, using examples, the difference between a permutation and a combination.

#### 12.PC.3.4.

Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers). [CN, R, V]

#### 12.PC.3.4.1.

Explain the patterns found in the expanded form of (x+y)^n, n<4 and nN, by multiplying n factors of (x+y).

#### 12.PC.3.4.4.

Explain, using examples, how the coefficients of the terms in the expansion of (x+y)^n are determined by combinations.

#### 12.PC.3.4.5.

Expand, using the binomial theorem, (x+y)^n.

#### 12.PC.3.4.6.

Determine a specific term in the expansion of (x+y)^n.

#### 9.BI.1.

The principles and processes underlying operations with numbers apply equally to algebraic situations and can be described and analyzed.

#### 9.BI.2.

Computational fluency and flexibility with numbers extend to operations with rational numbers.

#### 9.BI.3.

Continuous linear relationships can be identified and represented in many connected ways to identify regularities and make generalizations.

#### 9.BI.4.

Similar shapes have proportional relationships that can be described, measured, and compared.

#### 9.BI.5.

Analyzing the validity, reliability, and representation of data enables us to compare and interpret.

#### 9.C.1.

Operations with rational numbers (addition, subtraction, multiplication, division, and order of operations)

#### 9.C.1.5.

Elements of visual/graphic texts

#### 9.C.2.

Exponents and exponent laws with whole-number exponents

#### 9.C.2.2.

Human sexual reproduction

#### 9.C.2.3.

Metacognitive strategies

#### 9.C.3.

Operations with polynomials, of degree less than or equal to 2

#### 9.C.3.1.

Features of oral language

#### 9.C.3.10.

Connotation and denotation

#### 9.C.3.6.

Syntax and sentence fluency

#### 9.C.3.8.

Presentation techniques

#### 9.C.4.

Two-variable linear relations, using graphing, interpolation, and extrapolation

#### 9.C.5.

Multi-step one-variable linear equations

#### 9.C.6.

Spatial proportional reasoning

#### 9.C.7.

Statistics in society

#### 9.C.8.

Financial literacy simple budgets and transaction

#### 9.CC.1.

Reasoning and analyzing

#### 9.CC.1.1.

Use logic and patterns to solve puzzles and play games

#### 9.CC.1.10.

Explain how literary elements, techniques, and devices enhance and shape meaning

#### 9.CC.1.11.

Recognize an increasing range of text structures and how they contribute to meaning

#### 9.CC.1.12.

Recognize and appreciate the role of story, narrative, and oral tradition in expressing First Peoples perspectives, values, beliefs, and points of view

#### 9.CC.1.13.

Develop an awareness of the diversity within and across First Peoples societies represented in texts

#### 9.CC.1.14.

Recognize the influence of place in First Peoples and other Canadian texts

#### 9.CC.1.2.

Use reasoning and logic to explore, analyze, and apply mathematical ideas

#### 9.CC.1.3.

Formulate multiple hypotheses and predict multiple outcomes

#### 9.CC.1.4.

Demonstrate and apply mental math strategies

#### 9.CC.1.5.

Use tools or technology to explore and create patterns and relationships, and test conjectures

#### 9.CC.1.6.

Model mathematics in contextualized experiences

#### 9.CC.1.7.

Recognize how language constructs personal, social, and cultural identity

#### 9.CC.1.8.

Construct meaningful personal connections between self, text, and world

#### 9.CC.1.9.

Respond to text in personal, creative, and critical ways

#### 9.CC.2.

Understanding and solving

#### 9.CC.2.1.

Apply multiple strategies to solve problems in both abstract and contextualized situations

#### 9.CC.2.2.

Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving

#### 9.CC.2.3.

Visualize to explore mathematical concepts

#### 9.CC.2.4.

Engage in problem-solving experiences that are connected to place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures

#### 9.CC.2.5.

Use and experiment with oral storytelling processes

#### 9.CC.2.6.

Select and use appropriate features, forms, and genres according to audience, purpose, and message

#### 9.CC.2.7.

Transform ideas and information to create original texts

#### 9.CC.2.8.

Express an opinion and support it with credible evidence

#### 9.CC.3.

Communicating and representing

#### 9.CC.3.1.

Use mathematical vocabulary and language to contribute to mathematical discussions

#### 9.CC.3.2.

Explain and justify mathematical ideas and decisions

#### 9.CC.3.3.

Communicate mathematical thinking in many ways

#### 9.CC.3.4.

Construct, analyze and interpret graphs (including interpolation and extrapolation), models and/or diagrams

#### 9.CC.3.5.

Use knowledge of scientific concepts to draw conclusions that are consistent with evidence

#### 9.CC.3.6.

Analyze cause-and-effect relationships

#### 9.CC.4.

Connecting and reflecting

#### 9.CC.4.1.

Reflect on mathematical thinking

#### 9.CC.4.2.

Connect mathematical concepts to each other and to other areas and personal interests

#### 9.CC.4.3.

Use mathematical arguments to support personal choices

#### 9.CC.4.4.

Demonstrate an awareness of assumptions, question information given, and identify bias in their own work and secondary sources

#### 9.CC.4.5.

Consider the changes in knowledge over time as tools and technologies have developed

#### 9.CC.4.6.

Connect scientific explorations to careers in science

#### 9.CC.4.7.

Exercise a healthy, informed skepticism, and use scientific knowledge and findings to form their own investigations and to evaluate claims in secondary sources

#### 9.CC.4.8.

Consider social, ethical, and environmental implications of the findings from their own and others' investigations

#### 9.CC.4.9.

Critically analyze the validity of information in secondary sources and evaluate the approaches used to solve problems

#### 9.CC.5.

Assess how prevailing conditions and the actions of individuals or groups affect events, decisions, or developments (cause and consequence)

#### 9.CC.5.1.

Contribute to care for self, others, community, and world through individual or collaborative approaches

#### 9.CC.5.2.

Transfer and apply learning to new situations

#### 9.CC.5.3.

Generate and introduce new or refined ideas when problem solving

#### 9.CC.5.4.

Contribute to finding solutions to problems at a local and/or global level through inquiry

#### 9.CC.5.5.

Consider the role of scientists in innovation

#### 9.CC.6.

Explain and infer different perspectives on past or present people, places, issues, or events by considering prevailing norms, values, worldviews, and beliefs (perspective)

#### 9.CC.6.1.

Formulate physical or mental theoretical models to describe a phenomenon

#### 9.CC.6.2.

Communicate scientific ideas, claims, information, and perhaps a suggested course of action, for a specific purpose and audience, constructing evidence-based arguments and using appropriate scientific language, conventions, and representations

#### 9.CC.7.

Recognize implicit and explicit ethical judgments in a variety of sources (ethical judgment)

#### 9.CC.8.

Make reasoned ethical judgments about actions in the past and present, and determine appropriate ways to remember and respond (ethical judgment)

#### A1.1.

Support and extend the learning of self and others

#### A1.2.

Explore experiences, ideas, and information

#### A1.3.

Gain insight into others&apos; perspectives

#### A1.4.

Respond to and analyse a variety of texts

#### A1.5.

Create a variety of texts

#### A10.1.

Personalizing ideas and information

#### A10.2.

Explaining relationships among ideas and information

#### A10.3.

Applying new ideas and information

#### A10.4.

Transforming existing ideas and information

#### A10.5.

Contextualizing ideas and information

#### A11.1.

Referring to criteria

#### A11.2.

Setting goals for improvement

#### A11.3.

Creating a plan for achieving goals

#### A11.4.

Evaluating progress and setting new goals

#### A12.6.

Rhetorical devices

#### A12.8.

Nonverbal techniques

#### A12.9.

Idiomatic expressions

#### A2.1.

Explore and respond

#### A2.2.

Recall and describe

#### A2.3.

Narrate and explain

#### A2.5.

Engage and entertain

#### A3.5.

Effects and impact

#### A3.7.

Context, including historical and cultural influences

#### A4.1.

Initiating and sharing responsibilities

#### A4.2.

Listening actively

#### A4.3.

Contributing ideas and supporting the ideas of others

#### A4.4.

Acknowledging and discussing diverse points of view

#### A4.5.

Reaching consensus or agreeing to differ

#### A5.1.

Interpreting a task and setting a purpose

#### A5.2.

Generating ideas:

#### A5.3.

Considering multiple perspectives

#### A5.5.

Planning and rehearsing presentations

#### A6.3.

Nonverbal techniques

#### A6.5.

Organizational and memory aids

#### A6.6.

Monitoring methods

#### A7.1.

Extending understanding by accessing prior knowledge

#### A7.2.

Making plausible predictions

#### A7.3.

Summarizing main points

#### A7.4.

Generating thoughtful questions

#### A7.5.

Clarifying and confirming meaning

#### A8.1.

Making connections with prior knowledge and experiences

#### A8.2.

Relating reactions and emotions to understanding of the text

#### A8.3.

Generating thoughtful questions

#### A8.4.

Making inferences

#### A8.5.

Explaining opinions using reasons and evidence

#### A9.1.

Making and supporting reasoned judgments

#### A9.2.

Examining and comparing ideas and elements among texts

#### A9.3.

Describing and comparing perspectives

#### A9.4.

Describing bias, contradictions, and non-represented perspectives

#### A9.5.

Identifying the importance and impact of historical and cultural contexts

#### B1.1.

Literature reflecting a variety of times, places, and perspectives

#### B1.2.

Literature reflecting a variety of prose forms

#### B1.3.

Poetry in a variety of narrative and lyric forms

#### B1.4.

Significant works of Canadian literature (e.g., the study of plays, short stories, poetry, or novels)

#### B1.5.

Traditional forms from Aboriginal and other cultures

#### B1.6.

Student-generated material

#### B10.1.

Personalizing ideas and information

#### B10.2.

Explaining relationships among ideas and information

#### B10.5.

Contextualizing ideas and information

#### B11.1.

Referring to criteria

#### B11.2.

Setting goals for improvement

#### B11.3.

Creating a plan for achieving goals

#### B11.4.

Evaluating progress and setting new goals

#### B12.6.

Non-fiction elements

#### B13.1.

Analysing the origins and roots of words

#### B13.2.

Determining meanings and uses of words based on context

#### B13.3.

Identifying, selecting, and using appropriate academic and technical language

#### B13.4.

Using vocabulary appropriate to audience and purpose

#### B13.5.

Discerning nuances in meaning of words considering historical, cultural, and literary contexts

#### B2.1.

Articles and reports

#### B2.2.

Biographies and autobiographies

#### B2.3.

Textbooks, magazines, and newspapers

#### B2.4.

Print and electronic reference material

#### B2.6.

Opinion-based material

#### B2.7.

Student-generated material

#### B3.8.

Student-generated material

#### B5.2.

Setting a purpose or multiple purposes

#### B5.3.

Accessing prior knowledge, including knowledge of genre, form, and context

#### B5.5.

Generating guiding or speculative questions

#### B6.1.

Comparing and refining predictions, questions, images, and connections

#### B6.2.

Making inferences and drawing conclusions

#### B6.3.

Summarizing and paraphrasing

#### B6.4.

Using text features

#### B6.5.

Determining the meaning of unknown words and phrases

#### B6.6.

Clarifying meaning

#### B7.2.

Reviewing text and purpose for reading

#### B7.3.

Making inferences and drawing conclusions

#### B7.4.

Summarizing, synthesizing, and applying ideas:

#### B7.5.

Identifying stylistic techniques

#### B8.1.

Making comparisons to other ideas and concepts

#### B8.2.

Relating reactions and emotions to understanding of the text

#### B8.3.

Explaining opinions using reasons and evidence

#### B8.4.

Suggesting contextual influences

#### B9.1.

Making and supporting reasoned judgments

#### B9.2.

Comparing ideas and elements among texts

#### B9.3.

Identifying and describing diverse voices

#### B9.4.

Describing bias, contradictions, and non-represented perspectives

#### B9.5.

Identifying the importance and impact of historical and cultural contexts

#### C1.4.

Reflect and respond

#### C10.1.

Personalizing ideas and information

#### C10.2.

Explaining relationships among ideas and information

#### C12.1.

Syntax and sentence fluency

#### C13.1.

Organization of ideas and information

#### C14.4.

Presentation/layout

#### C2.2.

Record and describe

#### C2.3.

Analyse and explain

#### C2.4.

Speculate and consider

#### C3.1.

Strengthen connections and insights

#### C3.2.

Explore and adapt literary forms and techniques

#### C3.3.

Experiment with increasingly sophisticated language and style

#### C3.4.

Engage and entertain

#### C4.1.

Explore and respond

#### C4.2.

Record and describe

#### C5.1.

Making connections

#### C5.2.

Setting a purpose and considering audience

#### C5.3.

Gathering and summarizing ideas from personal interest, knowledge, and inquiry

#### C5.4.

Analysing writing samples or models

#### C6.1.

Using a variety of sources to collect ideas and information

#### C6.4.

Analysing writing samples or models

#### C7.2.

Enhancing supporting details and examples

#### C7.3.

Refining specific aspects and features of text

#### C8.2.

Relating reactions and emotions to understanding of the text

#### C8.3.

Developing opinions using reasons and evidence

#### C8.4.

Suggesting contextual influences

#### C9.1.

Making and supporting reasoned judgments

#### C9.2.

Describing and comparing perspectives

#### C9.3.

Describing bias, contradictions, and non-represented perspectives

#### C9.4.

Identifying the importance and impact of historical and cultural contexts