A: Students demonstrate an understanding of and proficiency with calculations, including making decisions concerning which arithmetic operation or operations to use to solve a problem and then solve the problem.

A.1: classify numbers as natural, whole, integer, rational, or irrational and describe contexts where they are used

Rational Numbers, Opposites, and Absolute Values

A.5: explain and apply the exponent laws for powers of numbers, including

A.5.1: x to the m power ? x to the n power = x to the m+n power

Multiplying Exponential Expressions

A.5.2: x to the m power ÷ x to the n power = x to the m-n power

Dividing Exponential Expressions

A.5.3: (x to the m power) to the n power = x to the mn power

Dividing Exponential Expressions
Multiplying Exponential Expressions

A.5.4: (xy) to the m power = x to the m power y to the m power

Multiplying Exponential Expressions

A.5.5: (x/y) to the m power = x to the m power / y to the m power, y does not equal 0

Dividing Exponential Expressions

A.5.6: x to the 0 power = 1, x does not equal 0

Dividing Exponential Expressions
Multiplying Exponential Expressions

A.5.7: xto the -m power = 1 / x to the m power, x does not equal 0

Dividing Exponential Expressions
Multiplying Exponential Expressions

B: Students use algebraic and graphical models to generalize patterns, make predictions, and solve problems.

B.1: use expressions to represent general terms for arithmetic growth, and apply these expressions to solve problems

Arithmetic Sequences

B.4: factor polynomial expressions of the form

B.4.1: ax² + bx + c

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

B.4.2: a²x² - b²y²

Factoring Special Products

B.5: find the product of polynomials (i.e., monomials, binomials, trinomials)

Modeling the Factorization of x²+bx+c

B.6: divide a polynomial (P or P(x)) by a binomial (D or D(x)) and express the result in the forms

B.6.1: P / D = Q + R / D

Dividing Polynomials Using Synthetic Division

B.6.2: P(x) = D(x)Q(x) + R, where Q and Q(x) denote the quotient and R denotes the remainder

Dividing Polynomials Using Synthetic Division

B.11: describe a linear function in terms of

B.11.1: ordered pairs

Linear Functions
Points, Lines, and Equations

B.11.2: a rule, in word or equation form

Compound Interest
Linear Functions
Slope-Intercept Form of a Line

B.11.3: a graph

Compound Interest
Exponential Functions
Linear Functions
Slope-Intercept Form of a Line

B.13: determine the following characteristics of the graph of a linear function, given its equation

B.13.1: x- and y-intercepts

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems) - Metric
Exponential Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

B.13.2: slope

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems) - Metric
Compound Interest
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

B.13.3: domain

Exponential Functions

B.13.4: range

Exponential Functions

B.14: sketch the graph of a linear function given its equation in the form

B.14.1: ax + by + c = 0 (general form)

Standard Form of a Line

B.14.2: y = mx + b (slope-intercept form)

Absolute Value with Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

B.15: represent linear data, using linear function models

Compound Interest
Linear Functions
Slope-Intercept Form of a Line

B.16: solve problems involving partial variation and arithmetic sequences as applications of linear functions

Arithmetic Sequences
Arithmetic and Geometric Sequences
Direct and Inverse Variation

C: Students describe and compare everyday phenomena, using either direct or indirect measurement and describe the characteristics of 3-D objects and 2-D shapes, and analyse the relationships among them.

C.1: solve 2-D and 3-D problems involving two right triangles

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

C.6: solve problems involving rise, run, and slope of line segments

Slope
Slope-Intercept Form of a Line

C.7: determine the equation of a line, given information that uniquely determines the line

Point-Slope Form of a Line
Points, Lines, and Equations
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

C.8: solve problems using slopes of

C.8.1: parallel lines

Cat and Mouse (Modeling with Linear Systems) - Metric