1: Arithmetic with Polynomials and Rational Expressions

1.1: Add, subtract, and multiply polynomials and understand that polynomials are closed under these operations. (Limit to linear; quadratic.)

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x²+bx+c

2: Creating Equations

2.1: Create and solve equations and inequalities in one variable that model real-world problems involving linear, quadratic, simple rational, and exponential relationships. Interpret the solutions and determine whether they are reasonable. (Limit to linear; quadratic; exponential with integer exponents.)

Compound Inequalities
Linear Inequalities in Two Variables
Solving Equations on the Number Line
Solving Two-Step Equations

2.2: Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. (Limit to linear; quadratic; exponential with integer exponents; direct and indirect variation.)

Direct and Inverse Variation
Point-Slope Form of a Line
Points, Lines, and Equations
Solving Equations by Graphing Each Side
Standard Form of a Line

2.3: Solve literal equations and formulas for a specified variable including equations and formulas that arise in a variety of disciplines.

Area of Triangles
Solving Formulas for any Variable

3: Reasoning with Equations and Inequalities

3.1: Understand and justify that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

3.2: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Area of Triangles
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Formulas for any Variable
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

3.3: Solve mathematical and real-world problems involving quadratic equations in one variable.

3.3.1: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x -h)² = k that has the same solutions. Derive the quadratic formula from this form.

Roots of a Quadratic

3.3.2: Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b. (Limit to non-complex roots.)

Modeling the Factorization of x²+bx+c
Points in the Complex Plane
Roots of a Quadratic

3.4: Justify that the solution to a system of linear equations is not changed when one of the equations is replaced by a linear combination of the other equation.

Solving Linear Systems (Standard Form)

3.5: Solve systems of linear equations algebraically and graphically focusing on pairs of linear equations in two variables.

3.5.1: Solve systems of linear equations using the substitution method.

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

3.5.2: Solve systems of linear equations using linear combination.

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

3.6: Explain that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

Absolute Value Equations and Inequalities
Circles
Parabolas
Point-Slope Form of a Line
Points, Lines, and Equations
Standard Form of a Line

3.7: Solve an equation of the form f(x) = g(x) graphically by identifying the x - coordinate(s) of the point(s) of intersection of the graphs of y = f (x) and y = g(x). (Limit to linear; quadratic; exponential.)

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

3.8: Graph the solutions to a linear inequality in two variables.

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

4: Structure and Expressions

4.1: Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions. (Limit to linear; quadratic; exponential.)

Addition and Subtraction of Functions
Compound Interest

4.2: Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions.

Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

4.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

4.3.1: Find the zeros of a quadratic function by rewriting it in equivalent factored form and explain the connection between the zeros of the function, its linear factors, the x-intercepts of its graph, and the solutions to the corresponding quadratic equation.

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

5: Building Functions

5.1: Describe the effect of the transformations kf (x), f(x) + k, f(x + k), and combinations of such transformations on the graph of y = f(x) for any real number k. Find the value of k given the graphs and write the equation of a transformed parent function given its graph. (Limit to linear; quadratic; exponential with integer exponents; vertical shift and vertical stretch.)

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

6: Interpreting Functions

6.1: Extend previous knowledge of a function to apply to general behavior and features of a function.

6.1.1: 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.

Introduction to Functions
Logarithmic Functions
Radical Functions

6.1.2: Represent a function using function notation and explain that f(x) denotes the output of function f that corresponds to the input x.

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

6.1.3: Understand that the graph of a function labeled as f is the set of all ordered pairs (x,y) that satisfy 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
Radical Functions
Standard Form of a Line

6.3: Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. (Limit to linear; quadratic; exponential.)

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Compound Interest
Exponential Functions
Function Machines 1 (Functions and Tables)
Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Introduction to Exponential Functions
Introduction to Functions
Linear Functions
Logarithmic Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game

6.4: Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes. (Limit to linear; quadratic; exponential.)

Exponential Functions
Function Machines 3 (Functions and Problem Solving)
Logarithmic Functions

6.5: Given a function in graphical, symbolic, or tabular form, determine the average rate of change of the function over a specified interval. Interpret the meaning of the average rate of change in a given context. (Limit to linear; quadratic; exponential.)

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Slope-Intercept Form of a Line
Translating and Scaling Functions

6.6: Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases. (Limit to linear; quadratic; exponential only in the form y = aˣ + k.)

Compound Interest
Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Slope-Intercept Form of a Line
Translating and Scaling Functions

6.7: Translate between different but equivalent forms of a function equation to reveal and explain different properties of the function. (Limit to linear; quadratic; exponential.)

6.7.1: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

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

6.8: Compare properties of two functions given in different representations such as algebraic, graphical, tabular, or verbal. (Limit to linear; quadratic; exponential.)

Exponential Functions
Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Slope-Intercept Form of a Line
Translating and Scaling Functions

7: Linear, Quadratic, and Exponential

7.1: Distinguish between situations that can be modeled with linear functions or exponential functions by recognizing situations in which one quantity changes at a constant rate per unit interval as opposed to those in which a quantity changes by a constant percent rate per unit interval.

7.1.1: Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.

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

7.2: Create symbolic representations of linear and exponential functions, including arithmetic and geometric sequences, given graphs, verbal descriptions, and tables. (Limit to linear; exponential.)

Absolute Value with Linear Functions
Arithmetic Sequences
Arithmetic and Geometric Sequences
Compound Interest
Exponential Functions
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Geometric Sequences
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

7.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or more generally as a polynomial function.

Compound Interest
Introduction to Exponential Functions

7.4: Interpret the parameters in a linear or exponential function in terms of the context. (Limit to linear.)

Arithmetic Sequences
Compound Interest
Introduction to Exponential Functions

10: Interpreting Data

10.1: Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

10.2: Create a linear function to graphically model data from a real-world problem and interpret the meaning of the slope and intercept(s) in the context of the given problem.

Correlation
Solving Using Trend Lines

10.3: Using technology, compute and interpret the correlation coefficient of a linear fit.

Correlation