AI.3.0: Students solve equations and inequalities involving absolute values.

Inequalities Involving Absolute Values

AI.4.0: Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x - 5) + 4(x - 2) = 12.

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

AI.5.0: Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations

AI.6.0: Students graph a linear equation and compute the x-and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).

Defining a Line with Two Points
Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form) - Activity A

AI.7.0: Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A

AI.8.0: Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.

Slope - Activity B

AI.9.0: Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.

Linear Programming - Activity A
Modeling Linear Systems - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

AI.10.0: Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.

Addition of Polynomials - Activity A
Dividing Exponential Expressions
Multiplying Exponential Expressions

AI.11.0: Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.

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

AI.12.0: Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.

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

AI.14.0: Students solve a quadratic equation by factoring or completing the square.

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

AI.16.0: Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions

AI.17.0: Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.

Introduction to Functions

AI.18.0: Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.

Introduction to Functions
Linear Functions

AI.19.0: Students know the quadratic formula and are familiar with its proof by completing the square.

Roots of a Quadratic

AI.20.0: Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.

Roots of a Quadratic

AI.21.0: Students graph quadratic functions and know that their roots are the x-intercepts.

Function Machines 2 (Functions, Tables, and Graphs)
Parabolas - Activity A
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

AI.22.0: Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.

Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Roots of a Quadratic

AI.25.2: Students judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied correctly at each step.

Order of Operations

AI.25.3: Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, students determine whether the statement is true sometimes, always, or never.

Inequalities Involving Absolute Values
Modeling and Solving Two-Step Equations
Quadratic Inequalities - Activity A
Road Trip (Problem Solving)
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations