Skill Descriptor: Solve problems involving polynomial functions (of degree ≤ 3).

Global Competencies: CM, CTPS

Achievement Indicators:

• Describe characteristics of polynomial functions given their graphs
• Describe characteristics of polynomial functions given their equations
• Match equations in a given set to their corresponding graphs
• Graph data and determine the type of polynomial function that best approximates the data
• Interpret and explain given graphs of polynomial functions that model situations
• Solve contextual problems, and justify solutions, involving data that is best represented by given graphs or equations of polynomial functions

Skill Descriptor: Solve problems by representing data using exponential and logarithmic functions.

Global Competencies: CM, CTPS

Achievement Indicators:

• Describe characteristics of exponential or logarithmic functions given their graphs
• Describe characteristics of exponential or logarithmic functions given their equations
• Match equations in a given set to their corresponding graphs
• Graph data and determine whether exponential or logarithmic functions best approximate the data
• Interpret graphs of exponential or logarithmic functions that model situations (e.g., population growth)
• Solve contextual problems involving data that is best represented given graphs or equations of exponential or logarithmic functions

Skill Descriptor: Solve problems by representing data using sinusoidal functions.

Global Competencies: CM, CTPS

Achievement Indicators:

• Describe characteristics of sinusoidal functions given their graphs
• Describe characteristics of sinusoidal functions given their equations
• Match equations in given sets to the corresponding graphs
• Graph data and determine if sinusoidal functions best approximate the data
• Interpret graphs of sinusoidal functions that model situations (e.g., ocean tides)
• Solve contextual problems involving data that is best represented by given graphs, or equations, of sinusoidal functions

Skill Descriptor: Analyze puzzles and games that involve numerical and logical reasoning.

Global Competencies: CTPS, SASM

Achievement Indicators:

• Reflect on ways to develop strategies to solve puzzles and games involving numerical and logical reasoning
• Reflect on ways to verify strategies to solve puzzles and games involving numerical and logical reasoning
• Create variations on puzzles and games involving numerical and logical reasoning including rules and the way(s) to win or solution(s)

Skill Descriptor: Solve problems involving set theory.

Global Competencies: CM, CTPS

Achievement Indicators:

• Explain empty sets, disjoint sets, subsets, and universal sets using contextual examples
• Outline the process of defining sets by their properties
• Organize information using Venn diagrams and set notation
• Describe specified regions in Venn Diagrams using words such as and, or, not
• Determine elements in the complement, intersection, or union of two sets
• Identify applications of set theory (e.g., internet searches, data analysis, library catalogues)
• Identify commonly made errors in problems involving sets
• Record solutions to problems involving sets using set notation

Skill Descriptor: Solve logical reasoning problems that involve conditional statements.

Global Competencies: CM, CTPS

Achievement Indicators:

• Analyze if-then, only-if, if-and-only-if statements
• Determine the converse, inverse and contrapositive of if-then statements
• Describe logical reasoning problems using words such as converse, inverse, contrapositive
• Outline probabilities and justify sequences of what if and if-then decisions in logical reasoning contexts and conditional statements
• Prove the truth of conditional statements do not imply the truth of the converse or inverse using examples and truth tables
• Prove the truth of conditional statements does imply the truth of the contrapositive using examples and truth tables
• Justify if-and-only-if statements and describe their contexts
• Summarize the results of logical arguments in graphic organizers and truth tables using words such as bi-conditional, converse, inverse, contrapositive

Skill Descriptor: Solve contextual problems involving a normal distribution, standard deviation, and z-scores.

Global Competencies: CM, CTPS

Achievement Indicators:

• Explain the meaning of standard deviation using examples
• Calculate standard deviation of a data set using a standard deviation formula and technology
• Explain the properties of a normal distribution using examples
• Justify if data sets approximate a normal distribution
• Compare the properties of normally distributed data sets of similar contexts (e.g., animal populations)
• Discuss examples of where standard deviation is used in decision-making
• Discuss the z-score for normally distributed data sets and their contexts
• Calculate z-scores for specific points in data sets (e.g., z-score table)

Skill Descriptor: Interpret data using confidence intervals, confidence levels, margin of error.

Global Competencies: CM, CTPS

Achievement Indicators:

• Explain the meaning of confidence intervals, margins of error, and confidence levels using examples
• Justify inferences about population data using confidence intervals
• Discuss examples where confidence intervals and confidence levels are used to support positions
• Support or critique positions or arguments using statistical data in media

Skill Descriptor: Solve problems involving odds and probability statements.

Global Competencies: CM, CTPS

Achievement Indicators:

• Explain the relationship between odds and probability using examples
• Express odds as probabilities and vice versa
• Determine the odds for and odds against outcomes in probability problems
• Explain how decisions may be based on probability or odds, and subjective judgments, using examples
• Solve contextual problems involving odds or probability

Skill Descriptor: Solve problems involving the probability of mutually exclusive and non-mutually exclusive events.

Global Competencies: CM, CTPS

Achievement Indicators:

• Classify and explain mutually exclusive or non–mutually exclusive events
• Explain when two events are complementary
• Represent mutually exclusive (including complementary events) and non–mutually exclusive events using set notation, graphic organizers, or Venn Diagrams
• Solve contextual problems involving the probability of mutually exclusive, non-mutually exclusive, and complementary events
• Create problems that involve mutually exclusive or non–mutually exclusive events

Skill Descriptor: Solve problems that involve the probability of two events.

Global Competencies: CTPS

Achievement Indicators:

• Compare dependent and independent events using examples
• Determine the probability of events given the occurrence of previous events
• Determine the probability of two dependent or two independent events
• Create contextual problems that require determining the probability of dependent or independent events

Skill Descriptor: Solve problems that involve the fundamental counting principle.

Global Competencies: CM, CTPS

Achievement Indicators:

• Count the total number of possible choices that can be made using graphic organizers, lists, or tree diagrams
• Represent and solve counting problems using graphic organizers
• Explain why the total number of possible choices is found by multiplying rather than adding the number of ways the individual choices can be made, using examples, and the word and
• Solve contextual problems by applying the fundamental counting principle

Skill Descriptor: Apply permutations to solve problems

Global Competencies: CM, CTPS

Achievement Indicators:

• Count the number of ways of ordering the elements of a finite set
• Determine the number of permutations for all elements of a finite set using factorial notation
• Determine the value of factorials
• Simplify numeric or algebraic fractions containing factorials in both the numerator and denominators
• Simplify or evaluate ratios of factorials
• Evaluate expressions involving factorials
• Determine the number of permutations of 𝑛 different elements taken 𝑟 at a time
• Analyze the effect on the total number of permutations when two or more elements of the set are identical
• Solve contextual problems involving probability and permutations

Skill Descriptor: Solve problems involving combinations.

Global Competencies: CM, CTPS

Achievement Indicators:

• Explain the difference between a permutation and a combination
• Determine the number of combinations of n different elements taken r at a time
• Solve contextual problems involving combinations and probability

Skill Descriptor: Expand powers of a binomial

Global Competencies: CM, CTPS

Achievement Indicators:

• Explain the patterns found in the expanded form of (𝑥 + 𝑦)ⁿ, 𝑛 ≤ 4, by multiplying 𝑛 factors of (𝑥 + 𝑦)
• Explain how to determine the subsequent row in Pascal’s triangle given any row
• Relate the coefficients of the terms in the expansion of (𝑥 + 𝑦)ⁿ to the (𝑛 + 1)^th row in Pascal’s triangle
• Explain how the coefficients of the terms in the expansion of (𝑥 + 𝑦)ⁿ are determined using combinations
• Expand (𝑥 +𝑦)ⁿ using the binomial theorem
• Determine a specific term in the expansion of (𝑥 + 𝑦)ⁿ