A1.1: Students simplify and compare expressions. They use rational exponents and simplify square roots.

A1.1.2: Simplify square roots using factors.

Operations with Radical Expressions

A1.1.3: Understand and use the distributive, associative, and commutative properties.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

A1.1.5: Use dimensional (unit) analysis to organize conversions and computations.

Unit Conversions

A1.2: Students solve linear equations and inequalities in one variable. They solve word problems that involve linear equations, inequalities, or formulas.

A1.2.1: Solve linear equations.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Two-Step Equations

A1.2.3: Find solution sets of linear inequalities when possible numbers are given for the variable.

Systems of Linear Inequalities (Slope-intercept form)

A1.2.4: Solve linear inequalities using properties of order.

Compound Inequalities
Linear Inequalities in Two Variables
Solving Linear Inequalities in One Variable

A1.2.5: Solve combined linear inequalities.

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

A1.2.6: Solve word problems that involve linear equations, formulas, and inequalities.

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

A1.3: Students sketch and interpret graphs representing given situations. They understand the concept of a function and analyze the graphs of functions.

A1.3.1: Sketch a reasonable graph for a given relationship.

Absolute Value with Linear Functions
Distance-Time Graphs
Quadratics in Polynomial Form

A1.3.3: Understand the concept of a function, decide if a given relation is a function, and link equations to functions.

Absolute Value Equations and Inequalities
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
Points, Lines, and Equations

A1.3.4: Find the domain and range of a relation.

Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Logarithmic Functions
Radical Functions

A1.4: Students graph linear equations and inequalities in two variables. They write equations of lines and find and use the slope and y-intercept of lines. They use linear equations to model real data.

A1.4.1: Graph a linear equation.

Absolute Value with Linear Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Solving Equations by Graphing Each Side
Standard Form of a Line

A1.4.2: Find the slope, x-intercept and y-intercept of a line given its graph, its equation, or two points on the line.

Cat and Mouse (Modeling with Linear Systems)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Point-Slope Form of a Line
Points, Lines, and Equations
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

A1.4.3: Write the equation of a line in slope-intercept form. Understand how the slope and y-intercept of the graph are related to the equation.

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

A1.4.4: Write the equation of a line given appropriate information.

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Solving Equations on the Number Line
Standard Form of a Line

A1.4.6: Graph a linear inequality in two variables.

Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

A1.5: Students solve pairs of linear equations using graphs and using algebra. They solve pairs of linear inequalities using graphs. They solve word problems involving pairs of linear equations.

A1.5.2: Use a graph to find the solution set of a pair of linear inequalities in two variables.

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

A1.5.3: Understand and use the substitution method to solve a pair of linear equations in two variables.

Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

A1.5.4: Understand and use the addition or subtraction method to solve a pair of linear equations in two variables.

Solving Linear Systems (Standard Form)

A1.5.5: Understand and use multiplication with the addition or subtraction method to solve a pair of linear equations in two variables.

Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

A1.5.6: Use pairs of linear equations to solve word problems.

Cat and Mouse (Modeling with Linear Systems)
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

A1.6: Students add, subtract, multiply, and divide polynomials. They factor quadratics.

A1.6.1: Add and subtract polynomials.

Addition and Subtraction of Functions
Addition of Polynomials

A1.6.2: Multiply and divide monomials.

Dividing Exponential Expressions
Multiplying Exponential Expressions

A1.6.4: Multiply polynomials.

Modeling the Factorization of x²+bx+c

A1.6.5: Divide polynomials by monomials.

Dividing Polynomials Using Synthetic Division

A1.6.6: Find a common monomial factor in a polynomial.

Factoring Special Products

A1.6.7: Factor the difference of two squares and other quadratics.

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

A1.8: Students graph and solve quadratic and radical equations. They graph cubic equations.

A1.8.1: Graph quadratic, cubic, and radical equations.

Parabolas
Quadratics in Polynomial Form
Radical Functions
Roots of a Quadratic

A1.8.2: Solve quadratic equations by factoring.

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form

A1.8.4: Complete the square to solve quadratic equations.

Roots of a Quadratic

A1.8.5: Derive the quadratic formula by completing the square.

Roots of a Quadratic

A1.8.6: Solve quadratic equations by using the quadratic formula.

Roots of a Quadratic

A1.8.8: Solve equations that contain radical expressions.

Operations with Radical Expressions

A1.9: Mathematical Reasoning and Problem Solving

A1.9.1: Use a variety of problem solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards.

Estimating Population Size
Linear Inequalities in Two Variables
Modeling One-Step Equations
Solving Equations on the Number Line
Using Algebraic Equations

A1.9.3: Use the properties of the real number system and the order of operations to justify the steps of simplifying functions and solving equations.

Solving Algebraic Equations II
Solving Equations on the Number Line

A1.9.4: Understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation, and that the steps taken when solving equations create new equations that have, in most cases, the same solution set as the original. Understand that similar logic applies to solving systems of equations simultaneously.

Solving Linear Systems (Standard Form)

A1.9.7: Identify the hypothesis and conclusion in a logical deduction.

Conditional Statements