A.1: The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables.

Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

A.2: The student will perform operations on polynomials, including

A.2.a: applying the laws of exponents to perform operations on expressions;

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

A.2.b: adding, subtracting, multiplying, and dividing polynomials; and

Addition and Subtraction of Functions
Addition of Polynomials
Dividing Polynomials Using Synthetic Division
Modeling the Factorization of x²+bx+c

A.2.c: factoring completely first- and second-degree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorizations.

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

A.3: The student will express the square roots and cube roots of whole numbers and the square root of a monomial algebraic expression in simplest radical form.

Operations with Radical Expressions
Simplifying Radical Expressions

A.4: Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions. The student will solve multistep linear and quadratic equations in two variables, including

A.4.a: solving literal equations (formulas) for a given variable;

Area of Triangles
Solving Formulas for any Variable

A.4.b: justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets;

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

A.4.c: solving quadratic equations algebraically and graphically;

Parabolas
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

A.4.d: solving multistep linear equations algebraically and graphically;

Point-Slope Form of a Line
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Two-Step Equations
Standard Form of a Line

A.4.e: solving systems of two linear equations in two variables algebraically and graphically; and

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

A.4.f: solving real-world problems involving equations and systems of equations.

Solving Linear Systems (Standard Form)

A.5: The student will solve multistep linear inequalities in two variables, including

A.5.a: solving multistep linear inequalities algebraically and graphically;

Compound Inequalities
Linear Inequalities in Two Variables
Systems of Linear Inequalities (Slope-intercept form)

A.5.c: solving real-world problems involving inequalities; and

Compound Inequalities
Linear Inequalities in Two Variables

A.5.d: solving systems of inequalities.

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

A.6: The student will graph linear equations and linear inequalities in two variables, including

A.6.a: determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined; and

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

A.6.b: writing the equation of a line when given the graph of the line, two points on the line, 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

A.7: The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including

A.7.a: determining whether a relation is a function;

Introduction to Functions
Linear Functions
Points, Lines, and Equations

A.7.b: domain and range;

Function Machines 3 (Functions and Problem Solving)

A.7.c: zeros of a function;

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game

A.7.d: x- and y-intercepts;

Cat and Mouse (Modeling with Linear Systems)
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Slope-Intercept Form of a Line
Zap It! Game

A.7.f: making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic.

Arithmetic Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Geometric Sequences
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form

A.8: The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.

Direct and Inverse Variation

A.9: The student, given a set of data, will interpret variation in real-world contexts and calculate and interpret mean absolute deviation, standard deviation, and z-scores.

Box-and-Whisker Plots
Polling: City
Real-Time Histogram
Sight vs. Sound Reactions

A.10: The student will compare and contrast multiple univariate data sets, using box-and-whisker plots.

Box-and-Whisker Plots

A.11: The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve real-world problems, using mathematical models. Mathematical models will include linear and quadratic functions.

Absolute Value with Linear Functions
Describing Data Using Statistics
Estimating Population Size
Least-Squares Best Fit Lines
Polling: City
Real-Time Histogram
Solving Using Trend Lines
Trends in Scatter Plots