AI.1: The student will use expressions and equations to model number relationships.

AI.1.1: Equations and Formulas

AI.1.1.a: Translate word phrases and sentences into expressions and equations and vice versa.

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

AI.1.1.b: Solve literal equations involving several variables for one variable in terms of the others.

Area of Triangles
Solving Formulas for any Variable

AI.1.1.c: Use the formulas from measurable attributes of geometric models (perimeter, circumference, area and volume), science, and statistics to solve problems within an algebraic context.

Area of Triangles

AI.1.1.d: Solve two-step and three-step problems using concepts such as rules of exponents, rate, distance, ratio and proportion, and percent.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percent of Change

AI.1.2: Expressions

AI.1.2.a: Simplify and evaluate linear, absolute value, rational and radical expressions.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Operations with Radical Expressions
Simplifying Radical Expressions
Solving Equations by Graphing Each Side
Standard Form of a Line

AI.1.2.b: Simplify polynomials by adding, subtracting or multiplying.

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions II

AI.1.2.c: Factor polynomial expressions.

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

AI.2: The student will use relations and functions to model number relationships.

AI.2.1: Relations and Functions

AI.2.1.a: Distinguish between linear and nonlinear data.

Absolute Value with Linear Functions
Linear Functions

AI.2.1.b: Distinguish between relations and functions.

Introduction to Functions
Linear Functions

AI.2.1.c: Identify dependent and independent variables, domain and range.

Introduction to Functions
Logarithmic Functions
Radical Functions

AI.2.1.d: Evaluate a function using tables, equations or graphs.

Exponential Functions
Introduction to Exponential Functions
Introduction to Functions
Linear Functions
Points, Lines, and Equations

AI.2.2: Linear Equations and Graphs

AI.2.2.a: Solve linear equations by graphing or using properties of equality.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Solving Algebraic Equations II
Solving Two-Step Equations
Standard Form of a Line

AI.2.2.b: Recognize the parent graph of the functions y = k, y = x, y = |x|, and predict the effects of transformations on the parent graph.

Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
Linear Functions
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line
Translating and Scaling Functions

AI.2.2.c: Slope

AI.2.2.c.I: Calculate the slope of a line using a graph, an equation, two points or a set of data points.

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

AI.2.2.c.II: Use the slope to differentiate between lines that are parallel, perpendicular, horizontal, or vertical.

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

AI.2.2.c.III: Interpret the slope and intercepts within the context of everyday life (e.g., telephone charges based on base rate [y-intercept] plus rate per minute [slope]).

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

AI.2.2.d: Develop the equation of a line and graph linear relationships given the following: slope and y-intercept, slope and one point on the line, two points on the line, x-intercept and y-intercept, a set of data points.

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

AI.2.2.e: Match appropriate equations to a graph, table, or situation and vice versa.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Solving Equations on the Number Line

AI.2.3: Linear Inequalities and Graphs

AI.2.3.a: Solve linear inequalities by graphing or using properties of inequalities.

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

AI.2.3.b: Match appropriate inequalities (with 1 or 2 variables) to a graph, table, or situation and vice versa.

Solving Linear Inequalities in One Variable

AI.2.4: Solve a system of linear equations by graphing, substitution or elimination.

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)

AI.2.5: Nonlinear Functions

AI.2.5.a: Match exponential and quadratic functions to a table, graph or situation and vice versa.

Addition and Subtraction of Functions
Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Translating and Scaling Functions
Zap It! Game

AI.2.5.b: Solve quadratic equations by graphing, factoring, or using the quadratic formula.

Modeling the Factorization of x²+bx+c
Parabolas
Quadratics in Polynomial Form
Quadratics in Vertex Form

AI.3: The student will use data analysis, probability and statistics to formulate and justify predictions from a set of data.

AI.3.1: Data Analysis

AI.3.1.a: Translate from one representation of data to another and understand that the data can be represented using a variety of tables, graphs, or symbols and that different modes of representation often convey different messages.

Stem-and-Leaf Plots

AI.3.1.b: Make valid inferences, predictions, and/or arguments based on data from graphs, tables, and charts.

Polling: City
Real-Time Histogram

AI.3.1.c: Solve two-step and three-step problems using concepts such as probability and measures of central tendency.

Estimating Population Size

AI.3.2: Collect data involving two variables and display on a scatter plot; interpret results using a linear model/equation and identify whether the model/equation is a line best fit for the data.

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