AI.RNE: Real Numbers and Expressions

AI.RNE.4: Simplify square roots of non-perfect square integers and algebraic monomials.

Operations with Radical Expressions
Simplifying Radical Expressions

AI.RNE.6: Factor common terms from polynomials and factor polynomials completely. Factor the difference of two squares, perfect square trinomials, and other quadratic expressions.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form

AI.RNE.7: Understand polynomials are closed under the operations of addition, subtraction, and multiplication with integers; add, subtract, and multiply polynomials and divide polynomials by monomials.

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

AI.F: Functions

AI.F.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. Understand that if f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. Understand the graph of f is the graph of the equation y = f(x).

Absolute Value with Linear Functions
Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Exponential Functions
Introduction to Functions
Linear Functions
Logarithmic Functions
Parabolas
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Standard Form of a Line

AI.F.2: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, has a maximum or minimum value). Sketch a graph that exhibits the qualitative features of a function that has been verbally described. Identify independent and dependent variables and make predictions about the relationship.

Absolute Value with Linear Functions
Arithmetic Sequences
Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Slope
Slope-Intercept Form of a Line

AI.F.3: Identify the domain and range of relations represented in tables, graphs, verbal descriptions, and equations.

Introduction to Functions
Logarithmic Functions
Radical Functions

AI.F.4: Understand and interpret statements that use function notation in terms of a context; relate the domain of the function to its graph and to the quantitative relationship it describes.

Absolute Value with Linear Functions
General Form of a Rational Function
Introduction to Functions
Logarithmic Functions
Radical Functions
Rational Functions
Translating and Scaling Functions

AI.L: Linear Equations, Inequalities, and Functions

AI.L.1: Understand that the steps taken when solving linear equations create new equations that have the same solution as the original. Solve fluently linear equations and inequalities in one variable with integers, fractions, and decimals as coefficients. Explain and justify each step in solving an equation, starting from the assumption that the original equation has a solution. Justify the choice of a solution method.

Solving Algebraic Equations II
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

AI.L.2: Represent real-world problems using linear equations and inequalities in one variable and solve such problems. Interpret the solution and determine whether it is reasonable.

Linear Inequalities in Two Variables
Solving Two-Step Equations

AI.L.3: Represent real-world and other mathematical problems using an algebraic proportion that leads to a linear equation and solve such problems.

Direct and Inverse Variation

AI.L.4: Represent linear functions as graphs from equations (with and without technology), equations from graphs, and equations from tables and other given information (e.g., from a given point on a line and the slope of the line).

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

AI.L.5: Represent real-world problems that can be modeled with a linear function using equations, graphs, and tables; translate fluently among these representations, and interpret the slope and intercepts.

Arithmetic Sequences
Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Geometric Sequences
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line

AI.L.6: Translate among equivalent forms of equations for linear functions, including slope-intercept, point-slope, and standard. Recognize that different forms reveal more or less information about a given situation.

Points, Lines, and Equations

AI.L.7: Represent real-world problems using linear inequalities in two variables and solve such problems; interpret the solution set and determine whether it is reasonable. Solve other linear inequalities in two variables by graphing.

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

AI.L.8: Solve compound linear inequalities in one variable, and represent and interpret the solution on a number line. Write a compound linear inequality given its number line representation.

Compound Inequalities
Solving Linear Inequalities in One Variable

AI.L.10: Graph absolute value linear equations in two variables.

Absolute Value with Linear Functions

AI.L.11: Solve equations and formulas for a specified variable, including equations with coefficients represented by variables.

Area of Triangles
Circles
Solving Formulas for any Variable

AI.SEI: Systems of Equations and Inequalities

AI.SEI.1: Understand the relationship between a solution of a pair of linear equations in two variables and the graphs of the corresponding lines. Solve pairs of linear equations in two variables by graphing; approximate solutions when the coordinates of the solution are non-integer numbers.

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)

AI.SEI.2: Understand that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve pairs of linear equations in two variables using substitution and elimination.

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

AI.SEI.3: Write a system of two linear equations in two variables that represents a real-world problem and solve the problem with and without technology. Interpret the solution and determine whether the solution is reasonable.

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

AI.SEI.4: Represent real-world problems using a system of two linear inequalities in two variables and solve such problems; interpret the solution set and determine whether it is reasonable. Solve other pairs of linear inequalities by graphing with and without technology.

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

AI.QE: Quadratic and Exponential Equations and Functions

AI.QE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions. Understand that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Compare linear functions and exponential functions that model real-world situations using tables, graphs, and equations.

Compound Interest
Direct and Inverse Variation
Exponential Functions
Exponential Growth and Decay
Introduction to Exponential Functions
Linear Functions
Slope-Intercept Form of a Line

AI.QE.2: Represent real-world and other mathematical problems that can be modeled with exponential functions using tables, graphs, and equations of the form y = ab^x (for integer values of x > 1, rational values of b > 0 and b ≠ 1); translate fluently among these representations and interpret the values of a and b.

Compound Interest
Exponential Functions
Introduction to Exponential Functions

A1.QE.3: Graph exponential and quadratic equations in two variables with and without technology.

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.QE.4: Solve quadratic equations in one variable by inspection (e.g., for x^2 = 49), finding square roots, using the quadratic formula, and factoring, as appropriate to the initial form of the equation.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Points in the Complex Plane
Roots of a Quadratic

AI.QE.5: Represent real-world problems using quadratic equations in one or two variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable.

Translating and Scaling Functions

AI.QE.6: Use the process of factoring to determine zeros, lines of symmetry, and extreme values in real-world and other mathematical problems involving quadratic functions; interpret the results in the real-world contexts.

Addition and Subtraction of Functions
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

AI.DS: Data Analysis and Statistics

AI.DS.1: Distinguish between random and non-random sampling methods, identify possible sources of bias in sampling, describe how such bias can be controlled and reduced, evaluate the characteristics of a good survey and well-designed experiment, design simple experiments or investigations to collect data to answer questions of interest, and make inferences from sample results.

Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Populations and Samples
Real-Time Histogram

AI.DS.2: Graph bivariate data on a scatter plot and describe the relationship between the variables.

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

AI.DS.3: Use technology to find a linear function that models a relationship for a bivariate data set to make predictions; interpret the slope and y-intercept, and compute (using technology) and interpret the correlation coefficient.

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

AI.DS.4: Distinguish between correlation and causation.

Correlation

AI.DS.5: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns (including joint, marginal, and conditional relative frequencies) to describe possible associations and trends in the data.

Histograms

AI.DS.6: Understand that statistics and data are non-neutral and designed to serve a particular interest. Analyze the possibilities for whose interest might be served and how the representations might be misleading.

Polling: City
Polling: Neighborhood
Populations and Samples