Northwest Territories

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Skills available for Northwest Territories grade 12 math curriculum

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Northwest Territories Curriculum: Mathematics 30-1 Northwest Territories Curriculum: Mathematics 30-1
Northwest Territories Curriculum: Mathematics 30-2 Northwest Territories Curriculum: Mathematics 30-2
Northwest Territories Curriculum: Mathematics 30-3 Northwest Territories Curriculum: Mathematics 30-3
WNCP Common Curriculum Frameworks: Foundations of Mathematics Grade 12 WNCP Common Curriculum Frameworks: Foundations of Mathematics Grade 12
WNCP Common Curriculum Frameworks: Pre-Calculus Grade 12 WNCP Common Curriculum Frameworks: Pre-Calculus Grade 12
WNCP Common Curriculum Frameworks: Apprenticeship and Workplace Mathematics Grade 12 WNCP Common Curriculum Frameworks: Apprenticeship and Workplace Mathematics Grade 12

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LR Logical Reasoning

LR.1 Develop logical reasoning.
- LR.1.1 Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies.
  - LR.1.1.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,
    - LR.1.1.1.a guess and check
    - LR.1.1.1.b look for a pattern
    - LR.1.1.1.c make a systematic list
    - LR.1.1.1.d draw or model
    - LR.1.1.1.e eliminate possibilities
    - LR.1.1.1.f simplify the original problem
    - LR.1.1.1.g work backward
    - LR.1.1.1.h develop alternative approaches.
  - LR.1.1.2 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game.
  - LR.1.1.3 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.
- LR.1.2 Solve problems that involve the application of set theory.
  - LR.1.2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context, and explain the reasoning.
  - LR.1.2.2 Organize information such as collected data and number properties, using graphic organizers, and explain the reasoning.
  - LR.1.2.3 Explain what a specified region in a Venn diagram represents, using connecting words (and, or, not) or set notation.
  - LR.1.2.4 Determine the elements in the complement, the intersection or the union of two sets.
  - LR.1.2.5 Explain how set theory is used in applications such as Internet searches, database queries, data analysis, games and puzzles.
  - LR.1.2.6 Identify and correct errors in a solution to a problem that involves sets.
  - LR.1.2.7 Solve a contextual problem that involves sets, and record the solution, using set notation.

P Probability

P.1 Develop critical thinking skills related to uncertainty.
- P.1.1 Interpret and assess the validity of odds and probability statements.
  - P.1.1.1 Provide examples of statements of probability and odds found in fields such as media, biology, sports, medicine, sociology and psychology.
  - P.1.1.2 Explain, using examples, the relationship between odds (part-part) and probability (part-whole).
  - P.1.1.3 Express odds as a probability and vice versa.
  - P.1.1.4 Determine the probability of, or the odds for and against, an outcome in a situation.
    - Calculate probabilities of events (12-Y.2)
  - P.1.1.5 Explain, using examples, how decisions may be based on probability or odds and on subjective judgments.
  - P.1.1.6 Solve a contextual problem that involves odds or probability.
- P.1.2 Solve problems that involve the probability of mutually exclusive and non–mutually exclusive events.
  - P.1.2.1 Classify events as mutually exclusive or non–mutually exclusive, and explain the reasoning.
  - P.1.2.2 Determine if two events are complementary, and explain the reasoning.
  - P.1.2.3 Represent, using set notation or graphic organizers, mutually exclusive (including complementary) and non–mutually exclusive events.
  - P.1.2.4 Solve a contextual problem that involves the probability of mutually exclusive or non–mutually exclusive events.
  - P.1.2.5 Solve a contextual problem that involves the probability of complementary events.
  - P.1.2.6 Create and solve a problem that involves mutually exclusive or non–mutually exclusive events.
- P.1.3 Solve problems that involve the probability of two events.
  - P.1.3.1 Compare, using examples, dependent and independent events.
    - Identify independent events (12-Y.6)
  - P.1.3.2 Determine the probability of an event, given the occurrence of a previous event.
    - Find conditional probabilities (12-Y.7)
    - Independence and conditional probability (12-Y.8)
  - P.1.3.3 Determine the probability of two dependent or two independent events.
  - P.1.3.4 Create and solve a contextual problem that involves determining the probability of dependent or independent events.
- P.1.4 Solve problems that involve the fundamental counting principle.
  - P.1.4.1 Represent and solve counting problems, using a graphic organizer.
  - P.1.4.2 Generalize, using inductive reasoning, the fundamental counting principle.
  - P.1.4.3 Identify and explain assumptions made in solving a counting problem.
  - P.1.4.4 Solve a contextual counting problem, using the fundamental counting principle, and explain the reasoning.
    - Counting principle (11-Y.4)
- P.1.5 Solve problems that involve permutations.
  - P.1.5.1 Represent the number of arrangements of n elements taken n at a time, using factorial notation.
  - P.1.5.2 Determine, with or without technology, the value of a factorial.
  - P.1.5.3 Simplify a numeric or an algebraic fraction that contains factorials in both the numerator and denominator.
  - P.1.5.4 Solve an equation that involves factorials.
  - P.1.5.5 Determine the number of permutations of n elements taken r at a time.
    - Permutations (11-Y.3)
  - P.1.5.6 Determine the number of permutations of n elements taken n at a time where some elements are not distinct.
  - P.1.5.7 Explain, using examples, the effect on the total number of permutations of n elements when two or more elements are identical.
  - P.1.5.8 Generalize strategies for determining the number of permutations of n elements taken r at a time.
  - P.1.5.9 Solve a contextual problem that involves probability and permutations.
    - Combinations and permutations (12-Y.3)
- P.1.6 Solve problems that involve combinations.
  - P.1.6.1 Explain, using examples, why order is or is not important when solving problems that involve permutations or combinations.
  - P.1.6.2 Determine the number of combinations of n elements taken r at a time.
    - Combinations and permutations (12-Y.3)
  - P.1.6.3 Generalize strategies for determining the number of combinations of n elements taken r at a time.
  - P.1.6.4 Solve a contextual problem that involves combinations and probability.
    - Find probabilities using combinations and permutations (12-Y.4)

RF Relations and Functions

RF.1 Develop algebraic and graphical reasoning through the study of relations.
- RF.1.1 Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials and binomials).
  - RF.1.1.1 Compare the strategies for writing equivalent forms of rational expressions to writing equivalent forms of rational numbers.
  - RF.1.1.2 Explain why a given value is non-permissible for a given rational expression.
  - RF.1.1.3 Determine the non-permissible values for a rational expression.
  - RF.1.1.4 Determine a rational expression that is equivalent to a given rational expression by multiplying the numerator and denominator by the same factor (limited to a monomial or a binomial), and state the non-permissible values of the equivalent rational expression.
  - RF.1.1.5 Simplify a rational expression.
    - Simplify rational expressions (11-M.4)
  - RF.1.1.6 Explain why the non-permissible values of a given rational expression and its simplified form are the same.
  - RF.1.1.7 Identify and correct errors in a given simplification of a rational expression, and explain the reasoning.
- RF.1.2 Perform operations on rational expressions (limited to numerators and denominators that are monomials and binomials).
  - RF.1.2.1 Compare the strategies for performing a given operation on rational expressions to the strategies for performing the same operation on rational numbers.
  - RF.1.2.2 Determine the non-permissible values when performing operations on rational expressions.
  - RF.1.2.3 Determine, in simplified form, the sum or difference of rational expressions that have the same denominator.
  - RF.1.2.4 Determine, in simplified form, the sum or difference of two rational expressions that have different denominators.
    - Add and subtract rational expressions (11-M.6)
  - RF.1.2.5 Determine, in simplified form, the product or quotient of two rational expressions.
    - Multiply and divide rational expressions (11-M.5)
- RF.1.3 Solve problems that involve rational equations (limited to numerators and denominators that are monomials and binomials).
  - RF.1.3.1 Determine the non-permissible values for the variable in a rational equation.
  - RF.1.3.2 Determine, algebraically, the solution to a rational equation, and explain the strategy used to solve the equation.
    - Solve rational equations (12-E.2)
  - RF.1.3.3 Explain why a value obtained in solving a rational equation may not be a solution of the equation.
  - RF.1.3.4 Solve a contextual problem that involves a rational equation.
- RF.1.4 Demonstrate an understanding of logarithms and the laws of logarithms.
  - RF.1.4.1 Express a logarithmic equation as an exponential equation and vice versa.
  - RF.1.4.2 Determine the value of a logarithmic expression, such as log? 8, without technology.
  - RF.1.4.3 Develop the laws of logarithms, using numeric examples and the exponent laws.
  - RF.1.4.4 Determine an equivalent expression for a logarithmic expression by applying the laws of logarithms.
  - RF.1.4.5 Determine the approximate value of a logarithmic expression, such as log? 9, with technology.
    - Evaluate logarithms (12-F.2)
    - Evaluate logarithms: mixed review (12-F.9)
- RF.1.5 Solve problems that involve exponential equations.
  - RF.1.5.1 Determine the solution of an exponential equation in which the bases are powers of one another; e.g., 2[superscript x – 1] = 4[superscript x – 2].
    - Solve exponential equations by rewriting the base (12-G.4)
  - RF.1.5.2 Determine the solution of an exponential equation in which the bases are not powers of one another; e.g., 2[superscript x – 1] = 3[superscript x + 1].
    - Solve exponential equations using common logarithms (12-G.5)
  - RF.1.5.3 Solve problems that involve the application of exponential equations to loans, mortgages and investments.
  - RF.1.5.4 Solve problems that involve logarithmic scales, such as the Richter scale and the pH scale.
- RF.1.6 Represent data, using exponential and logarithmic functions, to solve problems.
  - RF.1.6.1 Describe, orally and in written form, the characteristics of an exponential or logarithmic function by analyzing its graph.
  - RF.1.6.2 Describe, orally and in written form, the characteristics of an exponential or logarithmic function by analyzing its equation.
  - RF.1.6.3 Match equations in a given set to their corresponding graphs.
    - Match exponential functions and graphs (12-G.3)
  - RF.1.6.4 Graph data, and determine the exponential or logarithmic function that best approximates the data.
  - RF.1.6.5 Interpret the graph of an exponential or logarithmic function that models a situation, and explain the reasoning.
  - RF.1.6.6 Solve, using technology, a contextual problem that involves data that is best represented by graphs of exponential or logarithmic functions, and explain the reasoning.
- RF.1.7 Represent data, using polynomial functions (of degree ≤ 3), to solve problems.
  - RF.1.7.1 Describe, orally and in written form, the characteristics of a polynomial function by analyzing its graph.
  - RF.1.7.2 Describe, orally and in written form, the characteristics of a polynomial function by analyzing its equation.
  - RF.1.7.3 Match equations in a given set to their corresponding graphs.
    - Match polynomials and graphs (12-D.9)
  - RF.1.7.4 Graph data, and determine the polynomial function that best approximates the data.
  - RF.1.7.5 Interpret the graph of a polynomial function that models a situation, and explain the reasoning.
  - RF.1.7.6 Solve, using technology, a contextual problem that involves data that is best represented by graphs of polynomial functions, and explain the reasoning.
- RF.1.8 Represent data, using sinusoidal functions, to solve problems.
  - RF.1.8.1 Describe, orally and in written form, the characteristics of a sinusoidal function by analyzing its graph.
  - RF.1.8.2 Describe, orally and in written form, the characteristics of a sinusoidal function by analyzing its equation.
  - RF.1.8.3 Match equations in a given set to their corresponding graphs.
  - RF.1.8.4 Graph data, and determine the sinusoidal function that best approximates the data.
  - RF.1.8.5 Interpret the graph of a sinusoidal function that models a situation, and explain the reasoning.
  - RF.1.8.6 Solve, using technology, a contextual problem that involves data that is best represented by graphs of sinusoidal functions, and explain the reasoning.

MRP Mathematics Research Project

MRP.1 Develop an appreciation of the role of mathematics in society.
- MRP.1.1 Research and give a presentation on a current event or an area of interest that involves mathematics.
  - MRP.1.1.1 Collect primary or secondary data (statistical or informational) related to the topic.
  - MRP.1.1.2 Assess the accuracy, reliability and relevance of the primary or secondary data collected by:
    - MRP.1.1.2.a identifying examples of bias and points of view
    - MRP.1.1.2.b identifying and describing the data collection methods
    - MRP.1.1.2.c determining if the data is relevant
    - MRP.1.1.2.d determining if the data is consistent with information obtained from other sources on the same topic.
  - MRP.1.1.3 Interpret data, using statistical methods if applicable.
  - MRP.1.1.4 Identify controversial issues, if any, and present multiple sides of the issues with supporting data.
  - MRP.1.1.5 Organize and present the research project, with or without technology.

Northwest Territories

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LR Logical Reasoning

LR.1 Develop logical reasoning.

LR.1.1 Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies.

LR.1.1.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,

LR.1.1.1.a guess and check

LR.1.1.1.b look for a pattern

LR.1.1.1.c make a systematic list

LR.1.1.1.d draw or model

LR.1.1.1.e eliminate possibilities

LR.1.1.1.f simplify the original problem

LR.1.1.1.g work backward

LR.1.1.1.h develop alternative approaches.

LR.1.1.2 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game.

LR.1.1.3 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.

LR.1.2 Solve problems that involve the application of set theory.

LR.1.2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context, and explain the reasoning.

LR.1.2.2 Organize information such as collected data and number properties, using graphic organizers, and explain the reasoning.

LR.1.2.3 Explain what a specified region in a Venn diagram represents, using connecting words (and, or, not) or set notation.

LR.1.2.4 Determine the elements in the complement, the intersection or the union of two sets.

LR.1.2.5 Explain how set theory is used in applications such as Internet searches, database queries, data analysis, games and puzzles.

LR.1.2.6 Identify and correct errors in a solution to a problem that involves sets.

LR.1.2.7 Solve a contextual problem that involves sets, and record the solution, using set notation.

P Probability

P.1 Develop critical thinking skills related to uncertainty.

P.1.1 Interpret and assess the validity of odds and probability statements.

P.1.1.1 Provide examples of statements of probability and odds found in fields such as media, biology, sports, medicine, sociology and psychology.

P.1.1.2 Explain, using examples, the relationship between odds (part-part) and probability (part-whole).

P.1.1.3 Express odds as a probability and vice versa.

P.1.1.4 Determine the probability of, or the odds for and against, an outcome in a situation.

P.1.1.5 Explain, using examples, how decisions may be based on probability or odds and on subjective judgments.

P.1.1.6 Solve a contextual problem that involves odds or probability.

P.1.2 Solve problems that involve the probability of mutually exclusive and non–mutually exclusive events.

P.1.2.1 Classify events as mutually exclusive or non–mutually exclusive, and explain the reasoning.

P.1.2.2 Determine if two events are complementary, and explain the reasoning.

P.1.2.3 Represent, using set notation or graphic organizers, mutually exclusive (including complementary) and non–mutually exclusive events.

P.1.2.4 Solve a contextual problem that involves the probability of mutually exclusive or non–mutually exclusive events.

P.1.2.5 Solve a contextual problem that involves the probability of complementary events.

P.1.2.6 Create and solve a problem that involves mutually exclusive or non–mutually exclusive events.

P.1.3 Solve problems that involve the probability of two events.

P.1.3.1 Compare, using examples, dependent and independent events.

P.1.3.2 Determine the probability of an event, given the occurrence of a previous event.

P.1.3.3 Determine the probability of two dependent or two independent events.

P.1.3.4 Create and solve a contextual problem that involves determining the probability of dependent or independent events.

P.1.4 Solve problems that involve the fundamental counting principle.

P.1.4.1 Represent and solve counting problems, using a graphic organizer.

P.1.4.2 Generalize, using inductive reasoning, the fundamental counting principle.

P.1.4.3 Identify and explain assumptions made in solving a counting problem.

P.1.4.4 Solve a contextual counting problem, using the fundamental counting principle, and explain the reasoning.

P.1.5 Solve problems that involve permutations.

P.1.5.1 Represent the number of arrangements of n elements taken n at a time, using factorial notation.

P.1.5.2 Determine, with or without technology, the value of a factorial.

P.1.5.3 Simplify a numeric or an algebraic fraction that contains factorials in both the numerator and denominator.

P.1.5.4 Solve an equation that involves factorials.

P.1.5.5 Determine the number of permutations of n elements taken r at a time.

P.1.5.6 Determine the number of permutations of n elements taken n at a time where some elements are not distinct.

P.1.5.7 Explain, using examples, the effect on the total number of permutations of n elements when two or more elements are identical.

P.1.5.8 Generalize strategies for determining the number of permutations of n elements taken r at a time.

P.1.5.9 Solve a contextual problem that involves probability and permutations.

P.1.6 Solve problems that involve combinations.

P.1.6.1 Explain, using examples, why order is or is not important when solving problems that involve permutations or combinations.

P.1.6.2 Determine the number of combinations of n elements taken r at a time.

P.1.6.3 Generalize strategies for determining the number of combinations of n elements taken r at a time.

P.1.6.4 Solve a contextual problem that involves combinations and probability.

RF Relations and Functions

RF.1 Develop algebraic and graphical reasoning through the study of relations.

RF.1.1 Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials and binomials).

RF.1.1.1 Compare the strategies for writing equivalent forms of rational expressions to writing equivalent forms of rational numbers.

RF.1.1.2 Explain why a given value is non-permissible for a given rational expression.

RF.1.1.3 Determine the non-permissible values for a rational expression.

RF.1.1.4 Determine a rational expression that is equivalent to a given rational expression by multiplying the numerator and denominator by the same factor (limited to a monomial or a binomial), and state the non-permissible values of the equivalent rational expression.

RF.1.1.5 Simplify a rational expression.

RF.1.1.6 Explain why the non-permissible values of a given rational expression and its simplified form are the same.

RF.1.1.7 Identify and correct errors in a given simplification of a rational expression, and explain the reasoning.

RF.1.2 Perform operations on rational expressions (limited to numerators and denominators that are monomials and binomials).

RF.1.2.1 Compare the strategies for performing a given operation on rational expressions to the strategies for performing the same operation on rational numbers.

RF.1.2.2 Determine the non-permissible values when performing operations on rational expressions.

RF.1.2.3 Determine, in simplified form, the sum or difference of rational expressions that have the same denominator.