I: Students will expand number sense to understand, perform operations, and solve problems with real numbers.

I.1: Represent real numbers as points on the number line and distinguish rational numbers from irrational numbers.

I.1.c: Classify pi and square roots of non-perfect square numbers as irrational.

Circumference and Area of Circles
Simplifying Radical Expressions

I.1.d: Place rational and irrational numbers on a number line between two integers.

Adding and Subtracting Integers
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

I.2: Compute fluently and make reasonable estimates with rational and irrational numbers.

I.2.b: Evaluate and simplify numerical expressions containing rational numbers and square roots using the order of operations.

Order of Operations
Solving Equations on the Number Line

I.2.d: Calculate the measures of the sides of a right triangle using the Pythagorean Theorem.

Cosine Function
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Tangent Function

II: Students will extend concepts of proportion to represent and analyze linear relations.

II.1: Represent and analyze the slope of a line.

II.1.a: Identify the slope of a line when given points, a graph, or an equation.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Elevator Operator (Line Graphs)
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

II.1.b: Identify horizontal and vertical lines given the equations or slopes.

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

II.1.c: Determine the effect of changes in slope or y-intercept in y = mx + b.

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

II.1.d: Determine and explain the meaning of slopes and intercepts using real-world examples.

Cat and Mouse (Modeling with Linear Systems)
Slope-Intercept Form of a Line

II.2: Model and interpret problems having a constant rate of change using linear functions.

II.2.b: Represent linear equations in slope-intercept form, y = mx + b, and standard form, Ax+ By =C.

Linear Inequalities in Two Variables
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

II.2.c: Distinguish between linear and non-linear functions by examining a table, equation, or graph.

Absolute Value with Linear Functions
Linear Functions

II.2.d: Interpret the slope of a linear function as a rate of change in real-world situations.

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Slope-Intercept Form of a Line

II.3: Represent and analyze linear relationships using algebraic equations, expressions, and graphs.

II.3.a: Write the equation of a line when given two points or the slope and a point on the line.

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

II.3.c: Identify the x- and y-intercepts from an equation or graph of a line or a table of values.

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

II.3.d: Graph linear relations and inequalities by plotting points, by finding x- and y-intercepts, or by using the slope and any point on the line.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form)

III: Students will develop fluency with the language and operations of algebra to analyze and represent relationships.

III.1: Simplify polynomials and the quotient of monomials.

III.1.a: Simplify and evaluate monomial expressions and formulas.

Dividing Exponential Expressions
Multiplying Exponential Expressions
Simplifying Algebraic Expressions II

III.1.b: Add and subtract polynomials.

Addition and Subtraction of Functions
Addition of Polynomials

III.1.d: Multiply binomials.

Modeling the Factorization of x²+bx+c

III.1.e: Simplify the quotient of monomials using positive exponents.

Dividing Exponential Expressions

III.2: Solve and interpret linear equations and inequalities in various situations including real-world problems.

III.2.a: Solve single-variable linear equations and inequalities algebraically and graphically.

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Equations by Graphing Each Side
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Systems of Linear Inequalities (Slope-intercept form)

III.2.b: Solve real-world problems involving constant rates of change.

Compound Interest
Determining a Spring Constant
Dilations
Direct and Inverse Variation
Estimating Population Size

III.2.c: Solve equations for a specified variable.

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Formulas for any Variable

III.2.d: Solve proportions that include algebraic first-degree expressions.

Compound Interest

III.3: Solve and interpret pairs of linear equations and inequalities.

III.3.a: Solve systems of two linear equations graphically and algebraically with and without technology.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

III.3.b: Determine the number of possible solutions for a system of two linear equations.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

III.3.c: Graph a system of linear inequalities and identify the solution.

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

III.4: Factor polynomials with common monomial factors and factor simple quadratic expressions.

III.4.a: Find the greatest common monomial factor of a polynomial.

Factoring Special Products

III.4.b: Factor trinomials with integer coefficients of the form x2 + bx + c.

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

III.4.c: Factor the difference of two squares and perfect square trinomials.

Factoring Special Products

III.5: Solve quadratic equations using factoring or by taking square roots.

III.5.a: Solve quadratic equations that can be simplified to the form x2 = a where a ¡Ý 0 by taking square roots.

Roots of a Quadratic

III.5.b: Solve quadratic equations using factoring.

Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Roots of a Quadratic

IV: Students will understand concepts from statistics and apply statistical methods to solve problems.

IV.1: Summarize, display, and analyze bivariate data.

IV.1.a: Collect, record, organize, and display a set of data with at least two variables.

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Graphing Skills
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

IV.2: Estimate, interpret, and use lines fit to bivariate data.

IV.2.b: Interpret the slope and y-intercept of a line through data.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

IV.2.c: Predict y-values for given x-values when appropriate using a line fitted to bivariate numerical data.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots