Organization: Pearson Education
Product Name: Indiana High School Math Algebra 2
Product Version: v1.0


Source:     IMS Online Validator
Profile:    1.2.0
Identifier: realize-9e7e347c-03cd-3797-9856-392ebd99d7ce
Timestamp:  Thursday, January 24, 2019 03:23 PM EST
Status:     VALID!
Conformant: true

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Resource Validation Results
The document is valid.

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Schema Location Results
Schema locations are valid.

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Schema Validation Results
The document is valid.

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Schematron Validation Results
The document is valid.

Curriculum Standards:

Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. - AII.EL.7
Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. - AII.SE.3
Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. - AII.EL.6
Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. - AII.EL.3
Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. - AII.EL.2
Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. - AII.EL.5
Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). - AII.SE.1
Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). - AII.EL.4
Solve systems of two or three linear equations in two or three variables algebraically and using technology. - AII.SE.2
Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. - AII.EL.1
Understand composition of functions and combine functions by composition. - AII.F.2
Determine whether a relation represented by a table, graph, or equation is a function. - AII.F.1
Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. - AII.F.4
Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. - AII.F.3
Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. - AII.CNE.1
Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. - AII.PR.1
Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). - AII.F.5
Translate expressions between radical and exponent form and simplify them using the laws of exponents. - AII.CNE.2
Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. - AII.PR.2
Reason abstractly and quantitatively. - PS.2
Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. - AII.CNE.3
Make sense of problems and persevere in solving them. - PS.1
Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). - AII.CNE.4
Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. - AII.CNE.5
Find partial sums of arithmetic and geometric series and represent them using sigma notation. - AII.CNE.6
Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. - AII.PR.3
Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. - AII.Q.1
Look for and express regularity in repeated reasoning. - PS.8
Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. - AII.Q.3
Look for and make use of structure. - PS.7
Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. - AII.Q.2
Model with mathematics. - PS.4
Construct viable arguments and critique the reasoning of others. - PS.3
Attend to precision. - PS.6
Use appropriate tools strategically. - PS.5
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. - AII.DSP.1
Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. - AII.DSP.2
Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. - AII.DSP.3
Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. - AII.DSP.4
Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. - AII.DSP.5
Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. - AII.DSP.6


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Title: Indiana High School Math Algebra 2 2017


         Tools

            Math Tools

            Glossary

            Virtual Nerd� Tutorials

            Dynamic Activities

            Student Resources Download Center

            Algebra 2 Accessible Student Edition

         Entry-Level Assessment

         Algebra 2 Next-Generation Practice Test

         Practice Performance Tasks

            3/4-Year Practice Performance Task 1

            3/4-Year Practice Performance Task 2

         Expressions, Equations, and Inequalities

            Homework Video Tutor: Adding rational numbers

            Homework Video Tutor: Subtracting rational numbers

            Homework Video Tutor: Multiplying rational numbers

            Homework Video Tutor: Dividing real numbers

            Homework Video Tutor: Using the order of operations to simplify an expression

            Chapter 1 Get Ready

            Chapter 1 My Math Video
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Attend to precision. Model with mathematics. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Patterns and Expressions

               Student eText Lesson 1-1
                 Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Identifying a Pattern
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Expressing a Pattern with Algebra
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using a Graph
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 3: Lesson Check and Step 4: Practice

                  1-1 Virtual Nerd� Tutorial: What Are Numerical and Algebraic Expressions?
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               1-1 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 5: Assess and Remediate

                  1-1 Lesson Quiz
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

            Properties of Real Numbers

               Student eText Lesson 1-2
                 Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Classifying a Variable
                    Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

                  Graphing Numbers on the Number Line
                    Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

                  Ordering Real Numbers
                    Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

                  Identifying Properties of Real Numbers
                    Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               Step 3: Lesson Check and Step 4: Practice

                  1-2 Virtual Nerd� Tutorial: How Do Different Categories of Numbers Compare To Each Other?
                    Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               1-2 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               Step 5: Assess and Remediate

                  1-2 Lesson Quiz
                    Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

            Algebraic Expressions

               Student eText Lesson 1-3
                 Curriculum Standards: Reason abstractly and quantitatively. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Modeling Words With an Algebraic Expression
                    Curriculum Standards: Reason abstractly and quantitatively. 

                  Modeling a Situation
                    Curriculum Standards: Reason abstractly and quantitatively. 

                  Evaluating Algebraic Expressions
                    Curriculum Standards: Reason abstractly and quantitatively. 

                  Writing and Evaluating an Expression
                    Curriculum Standards: Reason abstractly and quantitatively. 

                  Simplifying Algebraic Expressions
                    Curriculum Standards: Reason abstractly and quantitatively. 

                  Evaluating Algebraic Expressions
                    Curriculum Standards: Reason abstractly and quantitatively. 

               Step 3: Lesson Check and Step 4: Practice

                  1-3 Virtual Nerd� Tutorial: How Do You Plug Variables into an Algebraic Expression?
                    Curriculum Standards: Reason abstractly and quantitatively. 

               1-3 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Reason abstractly and quantitatively. 

               Step 5: Assess and Remediate

                  1-3 Lesson Quiz
                    Curriculum Standards: Reason abstractly and quantitatively. 

            Chapter 1 Math XL: Mid-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Attend to precision. Model with mathematics. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Chapter 1 Mid-Chapter Quiz
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Attend to precision. Model with mathematics. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Solving Equations

               Student eText Lesson 1-4
                 Curriculum Standards: Model with mathematics. Attend to precision. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Solving a One-Step Equation
                    Curriculum Standards: Model with mathematics. Attend to precision. 

                  Solving a Multi-Step Equation
                    Curriculum Standards: Model with mathematics. Attend to precision. 

                  Using an Equation to Solve a Problem
                    Curriculum Standards: Model with mathematics. Attend to precision. 

                  Equations with No Solution and Identities
                    Curriculum Standards: Model with mathematics. Attend to precision. 

                  Solving a Literal Equation
                    Curriculum Standards: Model with mathematics. Attend to precision. 

               Step 3: Lesson Check and Step 4: Practice

                  1-4 Virtual Nerd� Tutorial: What are Inverse Operations?
                    Curriculum Standards: Model with mathematics. Attend to precision. 

               1-4 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Model with mathematics. Attend to precision. 

               Step 5: Assess and Remediate

                  1-4 Lesson Quiz
                    Curriculum Standards: Model with mathematics. Attend to precision. 

            Solving Inequalities

               Student eText Lesson 1-5
                 Curriculum Standards: Look for and make use of structure. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Writing an Inequality From a Sentence
                    Curriculum Standards: Look for and make use of structure. 

                  Solving and Graphing an Inequality
                    Curriculum Standards: Look for and make use of structure. 

                  Using an Inequality
                    Curriculum Standards: Look for and make use of structure. 

                  No Solution or All Real Numbers as Solutions
                    Curriculum Standards: Look for and make use of structure. 

                  Solving a Compound Inequality Involving  the word 'And'
                  Solving a Compound Inequality Involving the word 'And'
                    Curriculum Standards: Look for and make use of structure. 

                  Solving a Compound Inequality Involving  the word 'Or'
                  Solving a Compound Inequality Involving the word 'Or'
                    Curriculum Standards: Look for and make use of structure. 

               Step 3: Lesson Check and Step 4: Practice

                  1-5 Virtual Nerd� Tutorial: How Do You Solve and Graph a Two-Step Inequality?
                    Curriculum Standards: Look for and make use of structure. 

               1-5 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Look for and make use of structure. 

               Step 5: Assess and Remediate

                  1-5 Lesson Quiz
                    Curriculum Standards: Look for and make use of structure. 

            Absolute Value Equations and Inequalities

               Student eText Lesson 1-6
                 Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Solving an Absolute Value Equation
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Solving a Multi-Step Absolute Value Equation
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Checking for Extraneous Solutions
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  An Absolute Value Inequality into an 'And' Compound Inequality
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  An Absolute Value Inequality into an 'Or' Compound Inequality
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Using an Absolute Value Inequality
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 3: Lesson Check and Step 4: Practice

                  1-6 Virtual Nerd� Tutorial: How Do You Solve a Less Than Absolute Value Inequality and Graph It On a Number Line?
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               1-6: Student eText Lesson Check and Practice Exercises
                 Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 5: Assess and Remediate

                  1-6 Lesson Quiz
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Chapter 1 Math XL: End-of-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Attend to precision. Model with mathematics. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Chapter 1 Test
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Attend to precision. Model with mathematics. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            The Draft Pick

         Functions, Equations, and Graphs

            Simplifying Algebraic Expressions
              Curriculum Standards: Reason abstractly and quantitatively. 

            Solving a One-Step Equation
              Curriculum Standards: Model with mathematics. Attend to precision. 

            Solving a Multi-Step Equation
              Curriculum Standards: Model with mathematics. Attend to precision. 

            Using an Equation to Solve a Problem
              Curriculum Standards: Model with mathematics. Attend to precision. 

            Equations with No Solution and Identities
              Curriculum Standards: Model with mathematics. Attend to precision. 

            Solving a Literal Equation
              Curriculum Standards: Model with mathematics. Attend to precision. 

            An Absolute Value Inequality into an 'And' Compound Inequality
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            An Absolute Value Inequality  into an 'Or' Compound Inequality
            An Absolute Value Inequality into an 'Or' Compound Inequality
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Using an Absolute Value Inequality
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Chapter 1 Math XL: Mid-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Attend to precision. Model with mathematics. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Chapter 1 Math XL: End-of-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Attend to precision. Model with mathematics. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Homework Video Tutor: Algebraic expressions and order of operations
              Curriculum Standards: Reason abstractly and quantitatively. 

            Homework Video Tutor: Solving multi-step equations
              Curriculum Standards: Model with mathematics. Attend to precision. 

            Homework Video Tutor: Solving multi-step equations by combining like terms
              Curriculum Standards: Model with mathematics. Attend to precision. 

            Homework Video Tutor: Solving equations with variables on both sides
              Curriculum Standards: Model with mathematics. Attend to precision. 

            Homework Video Tutor: Solving an absolute value inequality
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Chapter 2 Get Ready
              Curriculum Standards: Reason abstractly and quantitatively. Model with mathematics. Attend to precision. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Chapter 2 My Math Video
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Relations and Functions

               Student eText Lesson 2-1
                 Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

               Dynamic Activity: Domain of a Function
                 Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Representing a Relation
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

                  Finding Domain and Range
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

                  Identifying Functions
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

                  Using the Vertical-Line Test
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

                  Using Function Notation
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

                  Writing and Evaluating a Function
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

                  Finding Domain and Range
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

               Step 3: Lesson Check and Step 4: Practice

                  2-1 Virtual Nerd� Tutorial: What's a Function?
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

                  2-1 Virtual Nerd� Tutorial: How Can You Tell if a Relation is Not a Function?
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

               2-1 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

               Step 5: Assess and Remediate

                  2-1 Lesson Quiz
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

            Direct Variation

               Student eText Lesson 2-2
                 Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Identifying Direct Variation From Tables
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Identifying Direct Variation From Equations
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Using a Proportion to Solve a Direct Variation
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Using Direct Variation to Solve a Problem
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Graphing Direct Variation Equations
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 3: Lesson Check and Step 4: Practice

                  2-2 Virtual Nerd� Tutorial: What's the Direct Variation or Direct Proportionality Formula?
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               2-2 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 5: Assess and Remediate

                  2-2 Lesson Quiz
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            The Super Stairs

            Linear Functions and Slope-Intercept Form

               Student eText Lesson 2-3

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding Slope

                  Writing Linear Equations

                  Writing Equations in Slope-Intercept Form

                  Graphing a Linear Equation

                  Writing Equations in Slope-Intercept Form

               Step 3: Lesson Check and Step 4: Practice

                  2-3 Virtual Nerd� Tutorial: What's Slope-Intercept Form of a Linear Equation?

               2-3: Student eText Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  2-3 Lesson Quiz

            More about Linear Equations

               Student eText Lesson 2-4

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Writing an Equation Given a Point and the Slope

                  Writing an Equation Given Two Points

                  Writing an Equation in Standard Form

                  Graphing an Equation Using Intercepts

                  Drawing and Interpreting a Linear Graph

                  Equations of Parallel and Perpendicular Lines

                  Writing an Equation in Standard Form

               Step 3: Lesson Check and Step 4: Practice

                  2-4 Virtual Nerd� Tutorial: What's Point-Slope Form of a Linear Equation?

               2-4 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  2-4 Lesson Quiz

            Chapter 2 Math XL: Mid-Chapter Practice and Review
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Chapter 2 Mid-Chapter Test
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Using Linear Models

               Student eText Lesson 2-5
                 Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using a Scatter Plot
                    Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

                  Writing the Equation of a Trend Line
                    Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

                  Finding the Line of Best Fit
                    Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

               Step 3: Lesson Check and Step 4: Practice

                  2-5 Virtual Nerd� Tutorial: How Do You Write and Use a Prediction Equation?
                    Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

               2-5: Student eText Lesson Check and Practice Exercises
                 Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

               Step 5: Assess and Remediate

                  2-5 Lesson Quiz
                    Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

            Families of Functions

               Student eText Lesson 2-6
                 Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Vertical Translation
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Horizontal Translation
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Reflecting a Function Algebraically
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Stretching and Compressing a Function
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Combining Transformations
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Vertical Translation
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Reflecting a Function Algebraically
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

               Step 3: Lesson Check and Step 4: Practice

                  2-6 Virtual Nerd� Tutorial: How Do You Graph a Translation of a Function?
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

               2-6 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

               Step 5: Assess and Remediate

                  2-6 Lesson Quiz
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Absolute Value Functions and Graphs

               Student eText Lesson 2-7
                 Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Graphing an Absolute Value Function
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

                  Combining Translations
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

                  Vertical Stretch and Compression
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

                  Identifying Transformations
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

                  Writing an Absolute Value Function
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

                  Combining Translations
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

               Step 3: Lesson Check and Step 4: Practice

                  2-7 Virtual Nerd� Tutorial: The constant 'k' in an Absolute Value Equation
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

                  2-7 Virtual Nerd� Tutorial: How Do You Graph an Absolute Value Function?
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

               2-7 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

               Step 5: Assess and Remediate

                  2-7 Lesson Quiz
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Two Variable Inequalities

               Student eText Lesson 2-8

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Graphing Linear Inequalities

                  Using a Linear Inequality

                  Graphing an Absolute Value Inequality

                  Writing an Inequality Based on a Graph

                  Writing an Inequality Based on a Graph

               Step 3: Lesson Check and Step 4: Practice

                  2-8 Virtual Nerd� Tutorial: How Do You Graph a Greater Than Inequality on the Coordinate Plane?

               2-8: Student eText Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  2-8 Lesson Quiz

            Chapter 2 Math XL: End-of-Chapter Practice and Review
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Chapter 2 Test
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

         Identifying a Pattern
           Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

         Expressing a Pattern with Algebra
           Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

         Using a Graph
           Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

         1-1 Virtual Nerd� Tutorial: What Are Numerical and Algebraic Expressions?
           Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

         Classifying a Variable
           Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         Graphing Numbers on the Number Line
           Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         Ordering Real Numbers
           Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         Modeling Words With an Algebraic Expression
           Curriculum Standards: Reason abstractly and quantitatively. 

         Modeling a Situation
           Curriculum Standards: Reason abstractly and quantitatively. 

         Identifying Properties of Real Numbers
           Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         1-2 Virtual Nerd� Tutorial: How Do Different Categories of Numbers Compare To Each Other?
           Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         Evaluating Algebraic Expressions
           Curriculum Standards: Reason abstractly and quantitatively. 

         Simplifying Algebraic Expressions
           Curriculum Standards: Reason abstractly and quantitatively. 

         1-3 Virtual Nerd� Tutorial: How Do You Plug Variables into an Algebraic Expression?
           Curriculum Standards: Reason abstractly and quantitatively. 

         Solving a One-Step Equation
           Curriculum Standards: Model with mathematics. Attend to precision. 

         Solving a Multi-Step Equation
           Curriculum Standards: Model with mathematics. Attend to precision. 

         Writing and Evaluating an Expression
           Curriculum Standards: Reason abstractly and quantitatively. 

         Evaluating Algebraic Expressions
           Curriculum Standards: Reason abstractly and quantitatively. 

         Solving a Multi-Step Absolute Value Equation
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Checking for Extraneous Solutions
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         An Absolute Value Inequality into an 'And' Compound Inequality
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         An Absolute Value Inequality into an 'Or' Compound Inequality
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Using an Absolute Value Inequality
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         1-6 Virtual Nerd� Tutorial: How Do You Solve a Less Than Absolute Value Inequality and Graph It On a Number Line?
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Representing a Relation
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

         Finding Domain and Range
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

         Identifying Functions
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

         Using the Vertical-Line Test
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

         Using Function Notation
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

         Writing and Evaluating a Function
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

         Finding Domain and Range
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

         2-1 Virtual Nerd� Tutorial: What's a Function?
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

         2-1 Virtual Nerd� Tutorial: How Can You Tell if a Relation is Not a Function?
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

         Identifying Direct Variation From Tables
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Identifying Direct Variation From Equations
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Using a Proportion to Solve a Direct Variation
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Using Direct Variation to Solve a Problem
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Graphing Direct Variation Equations
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         2-2 Virtual Nerd� Tutorial: What's the Direct Variation or Direct Proportionality Formula?
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Finding Slope

         Writing Linear Equations

         Writing Equations in Slope-Intercept Form

         Graphing a Linear Equation

         Writing Equations in Slope-Intercept Form

         2-3 Virtual Nerd� Tutorial: What's Slope-Intercept Form of a Linear Equation?

         Writing an Equation Given a Point and the Slope

         Writing an Equation Given Two Points

         Writing an Equation in Standard Form

         Graphing an Equation Using Intercepts

         Drawing and Interpreting a Linear Graph

         Equations of Parallel and Perpendicular Lines

         Writing an Equation in Standard Form

         2-4 Virtual Nerd� Tutorial: What's Point-Slope Form of a Linear Equation?

         Using a Scatter Plot
           Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

         Writing the Equation of a Trend Line
           Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

         Finding the Line of Best Fit
           Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

         2-5 Virtual Nerd� Tutorial: How Do You Write and Use a Prediction Equation?
           Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

         Vertical Translation
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Horizontal Translation
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Reflecting a Function Algebraically
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Stretching and Compressing a Function
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Combining Transformations
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Vertical Translation
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Reflecting a Function Algebraically
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         2-6 Virtual Nerd� Tutorial: How Do You Graph a Translation of a Function?
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Graphing an Absolute Value Function
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

         Combining Translations
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

         Vertical Stretch and Compression
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

         Identifying Transformations
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

         Writing an Absolute Value Function
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

         Combining Translations
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

         2-7 Virtual Nerd� Tutorial: The constant 'k' in an Absolute Value Equation
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

         2-7 Virtual Nerd� Tutorial: How Do You Graph an Absolute Value Function?
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

         Graphing Linear Inequalities

         Using a Linear Inequality

         Graphing an Absolute Value Inequality

         Writing an Inequality Based on a Graph

         Writing an Inequality Based on a Graph

         2-8 Virtual Nerd� Tutorial: How Do You Graph a Greater Than Inequality on the Coordinate Plane?

         Using an Equation to Solve a Problem
           Curriculum Standards: Model with mathematics. Attend to precision. 

         Equations with No Solution and Identities
           Curriculum Standards: Model with mathematics. Attend to precision. 

         Solving a Literal Equation
           Curriculum Standards: Model with mathematics. Attend to precision. 

         1-4 Virtual Nerd� Tutorial: What are Inverse Operations?
           Curriculum Standards: Model with mathematics. Attend to precision. 

         Writing an Inequality From a Sentence
           Curriculum Standards: Look for and make use of structure. 

         Solving and Graphing an Inequality
           Curriculum Standards: Look for and make use of structure. 

         Using an Inequality
           Curriculum Standards: Look for and make use of structure. 

         No Solution or All Real Numbers as Solutions
           Curriculum Standards: Look for and make use of structure. 

         Solving a Compound Inequality Involving  ?the word 'And?'??
         Solving a Compound Inequality Involving ?the word 'And?'??
           Curriculum Standards: Look for and make use of structure. 

         Solving a Compound Inequality Involving  ?the word '?Or?'
         Solving a Compound Inequality Involving ?the word '?Or?'
           Curriculum Standards: Look for and make use of structure. 

         1-5 Virtual Nerd� Tutorial: How Do You Solve and Graph a Two-Step Inequality?
           Curriculum Standards: Look for and make use of structure. 

         Solving an Absolute Value Equation
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Benchmark Test 1
           Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Attend to precision. Model with mathematics. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Determine whether a relation represented by a table, graph, or equation is a function. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

         Linear Systems

            Evaluating Algebraic Expressions
              Curriculum Standards: Reason abstractly and quantitatively. 

            Writing and Evaluating an Expression
              Curriculum Standards: Reason abstractly and quantitatively. 

            Writing Equations in Slope-Intercept Form

            Graphing a Linear Equation

            Graphing Linear Inequalities

            Using a Linear Inequality

            Graphing an Absolute Value Inequality

            Chapter 1 Math XL: Mid-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Attend to precision. Model with mathematics. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Chapter 2 Math XL: Mid-Chapter Practice and Review
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Chapter 2 Math XL: End-of-Chapter Practice and Review
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Homework Video Tutor: Algebraic expressions and order of operations
              Curriculum Standards: Reason abstractly and quantitatively. 

            Homework Video Tutor: Graphing linear equations using intercepts

            Homework Video Tutor: Graphing linear equations using point-slope form

            Homework Video Tutor: Graphing linear inequalities

            2-8 Virtual Nerd� Tutorial: How do you put an equation in standard form into slope-intercept or point-slope form?

            Chapter 3 Get Ready
              Curriculum Standards: Reason abstractly and quantitatively. 

            Solving Systems Using Tables and Graphs

               Student eText Lesson 3-1
                 Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

               3-1 Dynamic Activity: Systems of Linear Equations and Inequalities
                 Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using a Graph or Table to Solve a System
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

                  Using a Table to Solve a Problem
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

                  Using Linear Regression
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

                  Classifying a System Without Graphing
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

                  Using a Graph or Table to Solve a System
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

                  Classifying a System Without Graphing
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

               Step 3: Lesson Check and Step 4: Practice

                  3-1 Virtual Nerd� Tutorial: How Do You Solve a System of Equations by Graphing?
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

               3-1 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

               Step 5: Assess and Remediate

                  3-1 Lesson Quiz
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

            Solving Systems Algebraically

               Student eText Lesson 3-2
                 Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Solving by Substitution
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

                  Using Substitution to Solve a Problem
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

                  Solving by Elimination
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

                  Solving an Equivalent System
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

                  Solving Systems Without Unique Solutions
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

               Step 3: Lesson Check and Step 4: Practice

                  3-2 Virtual Nerd� Tutorial: How Do You Solve a System of Equations Using the Substitution Method?
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

                  3-2 Virtual Nerd� Tutorial: How Do You Solve a System of Equations Using the Elimination by Multiplication Method?
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

               3-2 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

               Step 5: Assess and Remediate

                  3-2 Lesson Quiz
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

            Systems of Inequalities

               Student eText Lesson 3-3
                 Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Solving a System by Using a Table
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

                  Solving a System by Graphing
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

                  Using a System of Inequalities
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

                  Solving a Linear/Absolute-Value System
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

               Step 3: Lesson Check and Step 4: Practice

                  3-3 Virtual Nerd� Tutorial: How Do You Solve a System of Inequalities by Graphing?
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

                  3-3 Virtual Nerd� Tutorial: How Do You Solve a Word Problem Using a System of Inequalities?
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

               Lesson 3-3: Student eText Lesson Check and Practice Exercises
                 Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

               Step 5: Assess and Remediate

                  3-3 Lesson Quiz
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

            Chapter 3 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

            Chapter 3 Mid-Chapter Quiz
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

            Linear Programming

               Student eText Lesson 3-4

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Testing Vertices

                  Using Linear Programming to Maximize Profit

               Step 3: Lesson Check and Step 4: Practice

                  3-4 Virtual Nerd� Tutorial: What is Linear Programming?

                  3-4 Virtual Nerd� Tutorial: How Do You Solve an Optimization Word Problem?

               Lesson 3-4: Student eText Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  3-4 Lesson Quiz

            Systems With Three Variables

               Student eText Lesson 3-5
                 Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Solving a System Using Elimination
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. 

                  Solving an Equivalent System
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

                  Solving a System Using Substitution
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. 

                  Solving a Real-World Problem
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. 

               Step 3: Lesson Check and Step 4: Practice

                  3-5 Virtual Nerd� Tutorial: How Do You Solve a System of Equations in Three Variables Using Elimination?
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. 

               Lesson 3-5: Student eText Lesson Check and Practice Exercises
                 Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. 

               Step 5: Assess and Remediate

                  3-5 Lesson Quiz
                    Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. 

            Solving Systems Using Matrices

               Student eText Lesson 3-6
                 Curriculum Standards: Use appropriate tools strategically. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Identifying a Matrix Element
                    Curriculum Standards: Use appropriate tools strategically. 

                  Representing Systems With Matrices
                    Curriculum Standards: Use appropriate tools strategically. 

                  Writing a System from a Matrix
                    Curriculum Standards: Use appropriate tools strategically. 

                  Solving a System Using a Matrix
                    Curriculum Standards: Use appropriate tools strategically. 

                  Using a Calculator to Solve a Linear System
                    Curriculum Standards: Use appropriate tools strategically. 

               Step 3: Lesson Check and Step 4: Practice

                  3-6 Virtual Nerd� Tutorial: What is a Matrix?
                    Curriculum Standards: Use appropriate tools strategically. 

               Lesson 3-6: Student eText Lesson Check and Practice Exercises
                 Curriculum Standards: Use appropriate tools strategically. 

               Step 5: Assess and Remediate

                  3-6 Lesson Quiz
                    Curriculum Standards: Use appropriate tools strategically. 

            Chapter 3 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

            Chapter 3 Test

            The Grand Coin Count

         Quadratic Functions and Equations

            Solving a One-Step Equation
              Curriculum Standards: Model with mathematics. Attend to precision. 

            Solving a Multi-Step Equation
              Curriculum Standards: Model with mathematics. Attend to precision. 

            Using an Equation to Solve a Problem
              Curriculum Standards: Model with mathematics. Attend to precision. 

            Equations with No Solution and Identities
              Curriculum Standards: Model with mathematics. Attend to precision. 

            Solving a Literal Equation
              Curriculum Standards: Model with mathematics. Attend to precision. 

            An Absolute Value Inequality into an 'And' Compound Inequality
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            An Absolute Value Inequality into an Or' Compound Inequality
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Using an Absolute Value Inequality
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Writing Linear Equations

            Writing Equations in Slope-Intercept Form

            Graphing a Linear Equation

            Vertical Translation
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Horizontal Translation
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Reflecting a Function Algebraically
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Stretching and Compressing a Function
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Combining Transformations
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Solving by Substitution
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

            Using Substitution to Solve a Problem
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

            Solving by Elimination
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

            Solving an Equivalent System
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

            Solving Systems Without Unique Solutions
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

            Chapter 1 Math XL: End-of-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Attend to precision. Model with mathematics. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Chapter 2 Math XL: Mid-Chapter Practice and Review
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Chapter 2 Math XL: End-of-Chapter Practice and Review
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Chapter 3 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

            Homework Video Tutor: Solving equations with variables on both sides
              Curriculum Standards: Model with mathematics. Attend to precision. 

            Homework Video Tutor: Solving multi-step equations by combining like terms
              Curriculum Standards: Model with mathematics. Attend to precision. 

            Homework Video Tutor: Solving an absolute value inequality
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Homework Video Tutor: Writing an equation for the vertical translation of an absolute value equation
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Homework Video Tutor: Writing an equation for the horizontal translation of an absolute value equation
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Homework Video Tutor: Graphing a linear equation using slope-intercept form

            Homework Video Tutor: Solving linear systems using substitution
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

            Chapter 4 Get Ready
              Curriculum Standards: Model with mathematics. Attend to precision. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

            Quadratic Functions and Transformations

               Student eText Lesson 4-1
                 Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

               4-1 Dynamic Activity: Graphs of Quadratic Functions
                 Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Graphing a Quadratic Function?
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

                  Graphing Translations of Quadratic Functions?
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

                  Interpreting Vertex Form
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

                  Using Vertex Form
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

                  Writing a Quadratic Function in Vertex Form
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

               Step 3: Lesson Check and Step 4: Practice

                  4-1 Virtual Nerd� Tutorial: What is a Quadratic Function?
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

               Lesson 4-1: Student eText Lesson Check and Practice Exercises
                 Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

               Step 5: Assess and Remediate

                  4-1 Lesson Quiz
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Standard Form of a Quadratic Function

               Student eText Lesson 4-2
                 Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding the Features of a Quadratic Function
                    Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

                  Graphing a Quadratic Function in Standard Form?
                    Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

                  Converting Standard Form to Vertex Form
                    Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

                  Interpreting a Quadratic Graph
                    Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

                  Interpreting a Quadratic Graph
                    Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

               Step 3: Lesson Check and Step 4: Practice

                  4-2 Virtual Nerd� Tutorial: What is the Standard Form of a Quadratic?
                    Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

                  4-2 Virtual Nerd� Tutorial: How Do You Graph a Quadratic Function?
                    Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

               Lesson 4-2: Student eText Lesson Check and Practice Exercises
                 Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

               Step 5: Assess and Remediate

                  4-2 Lesson Quiz
                    Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Modeling With Quadratic Functions

               Student eText Lesson 4-3
                 Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Writing an Equation of a Parabola
                    Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

                  Comparing Quadratic Models
                    Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

                  Using Quadratic Regression
                    Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

               Step 3: Lesson Check and Step 4: Practice

                  4-3 Virtual Nerd� Tutorial: How Do You Write an Equation For a Quadratic if You Have Three Points?
                    Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

               Lesson 4-3: Student eText Lesson Check and Practice Exercises
                 Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

               Step 5: Assess and Remediate

                  4-3 Lesson Quiz
                    Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Piles of Tiles

            Factoring Quadratic Expressions

               Student eText Lesson 4-4

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Factoring when the Quadratic Coefficient 'a' is +1 or -1

                  Finding Common Factors

                  Factoring when the Quadratic Coefficient 'a' is Not Equal To 1

                  Factoring a Perfect Square Trinomial

                  Factoring a Difference of Two Squares

               Step 3: Lesson Check and Step 4: Practice

                  4-4 Virtual Nerd� Tutorial: How Do You Factor a Trinomial?

                  4-4 Virtual Nerd� Tutorial: How Do You Factor a Polynomial Using the A-C Method?

               Lesson 4-4: Student eText Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  4-4 Lesson Quiz

            Chapter 4 MathXL: Mid-Chapter Practice
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

            Chapter 4 Mid-Chapter Quiz
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

            Quadratic Equations

               Student eText Lesson 4-5

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Solving a Quadratic Equation by Factoring

                  Solving a Quadratic Equation With Tables

                  Solving a Quadratic Equation by Graphing

                  Using a Quadratic Equation

               Step 3: Lesson Check and Step 4: Practice

                  4-5 Virtual Nerd� Tutorial: How Do You Solve a Quadratic Equation with Two Solutions by Graphing?

                  4-5 Virtual Nerd� Tutorial: How Do You Solve a Quadratic Equation by Factoring?

               Lesson 4-5: Student eText Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  4-5 Lesson Quiz

            Completing the Square

               Student eText Lesson 4-6
                 Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Solving by Finding Square Roots
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

                  Determining Dimensions
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

                  Solving a Perfect Square Trinomial Equation
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

                  Completing the Square

                  Solving by Completing the Square
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

                  Writing in Vertex Form
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

               Step 3: Lesson Check and Step 4: Practice

                  4-6 Virtual Nerd� Tutorial: How Do You Solve a Quadratic Equation by Completing the Square?
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

                  4-6 Virtual Nerd� Tutorial: How Do You Convert a Quadratic from Standard Form to Vertex Form by Completing the Square?
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

               Lesson 4-6: Student eText Lesson Check and Practice Exercises
                 Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

               Step 5: Assess and Remediate

                  4-6 Lesson Quiz
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

            The Quadratic Formula

               Student eText Lesson 4-7
                 Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using the Quadratic Formula
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

                  Applying the Quadratic Formula
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

                  Using the Discriminant
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

                  Using the Discriminant to Solve a Problem
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

               Step 3: Lesson Check and Step 4: Practice

                  4-7 Virtual Nerd� Tutorial: How Do You Solve a Quadratic Equation by Using the Quadratic Formula?
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

                  4-7 Virtual Nerd� Tutorial: What is the Discriminant?
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

               Lesson 4-7: Student eText Lesson Check and Practice Exercises
                 Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

               Step 5: Assess and Remediate

                  4-7 Lesson Quiz
                    Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

            Complex Numbers

               Student eText Lesson 4-8
                 Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Simplifying a Number Using the Imaginary Unit?
                    Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

                  Graphing in the Complex Number Plane
                    Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

                  Adding and Subtracting Complex Numbers
                    Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

                  Multiplying Complex Numbers
                    Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

                  Dividing Complex Numbers
                    Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

                  Factoring using Complex Conjugates
                    Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

                  Finding Imaginary Solutions
                    Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

                  Adding and Subtracting Complex Numbers
                    Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

               Step 3: Lesson Check and Step 4: Practice

                  4-8 Virtual Nerd� Tutorial: What is the Imaginary Unit i?
                    Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

                  4-8 Virtual Nerd� Tutorial: How Do You Add Complex Numbers?
                    Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

               Lesson 4-8: Student eText Lesson Check and Practice Exercises
                 Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

               Step 5: Assess and Remediate

                  4-8 Lesson Quiz
                    Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

            Quadratic Systems

               Student eText Lesson 4-9
                 Curriculum Standards: Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Solving a Linear-Quadratic System by Graphing
                    Curriculum Standards: Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

                  Solving a Linear-Quadratic System Using Substitution
                    Curriculum Standards: Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

                  Solving a Quadratic System of Equations
                    Curriculum Standards: Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

                  Solving a Quadratic System of Inequalities
                    Curriculum Standards: Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

               Step 3: Lesson Check and Step 4: Practice

                  4-9 Virtual Nerd� Tutorial: How Do You Solve a System of Equations Using Substitution if One Equation is a Quadratic?
                    Curriculum Standards: Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

               Lesson 4-9: Student eText Lesson Check and Practice Exercises
                 Curriculum Standards: Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

               Step 5: Assess and Remediate

                  4-9 Lesson Quiz
                    Curriculum Standards: Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

            Chapter 4 MathXL: End-of-Chapter Practice
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

            Chapter 4 Test
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

         Using a Graph or Table to Solve a System
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

         Using a Table to Solve a Problem
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

         Using Linear Regression
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

         Classifying a System Without Graphing
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

         Using a Graph or Table to Solve a System
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

         Classifying a System Without Graphing
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

         3-1 Virtual Nerd� Tutorial: How Do You Solve a System of Equations by Graphing?
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

         Solving a System Using Substitution
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. 

         Solving a Real-World Problem
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. 

         3-5 Virtual Nerd� Tutorial: How Do You Solve a System of Equations in Three Variables Using Elimination?
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. 

         Identifying a Matrix Element
           Curriculum Standards: Use appropriate tools strategically. 

         Representing Systems With Matrices
           Curriculum Standards: Use appropriate tools strategically. 

         Writing a System from a Matrix
           Curriculum Standards: Use appropriate tools strategically. 

         Solving a System Using a Matrix
           Curriculum Standards: Use appropriate tools strategically. 

         Using a Calculator to Solve a Linear System
           Curriculum Standards: Use appropriate tools strategically. 

         3-6 Virtual Nerd� Tutorial: What is a Matrix?
           Curriculum Standards: Use appropriate tools strategically. 

         4-9 Virtual Nerd� Tutorial: How Do You Solve a System of Equations Using Substitution if One Equation is a Quadratic?
           Curriculum Standards: Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

         Graphing a Quadratic Function?
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         Graphing Translations of Quadratic Functions?
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         Interpreting Vertex Form
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         Using Vertex Form
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         Writing a Quadratic Function in Vertex Form
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         4-1 Virtual Nerd� Tutorial: What is a Quadratic Function?
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         Finding the Features of a Quadratic Function
           Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         Graphing a Quadratic Function in Standard Form?
           Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         Converting Standard Form to Vertex Form
           Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         Interpreting a Quadratic Graph
           Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         Interpreting a Quadratic Graph
           Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         4-2 Virtual Nerd� Tutorial: What is the Standard Form of a Quadratic?
           Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         4-2 Virtual Nerd� Tutorial: How Do You Graph a Quadratic Function?
           Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         Writing an Equation of a Parabola
           Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         Comparing Quadratic Models
           Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         Using Quadratic Regression
           Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         4-3 Virtual Nerd� Tutorial: How Do You Write an Equation For a Quadratic if You Have Three Points?
           Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         Factoring when the Quadratic Coefficient 'a' is +1 or -1

         Finding Common Factors

         Factoring when the Quadratic Coefficient 'a' is Not Equal To 1

         Factoring a Perfect Square Trinomial

         4-4 Virtual Nerd� Tutorial: How Do You Factor a Trinomial?

         4-4 Virtual Nerd� Tutorial: How Do You Factor a Polynomial Using the A-C Method?

         Factoring a Difference of Two Squares

         Solving a Quadratic Equation by Factoring

         Solving a Quadratic Equation With Tables

         Solving a Quadratic Equation by Graphing

         Using a Quadratic Equation

         4-5 Virtual Nerd� Tutorial: How Do You Solve a Quadratic Equation with Two Solutions by Graphing?

         4-5 Virtual Nerd� Tutorial: How Do You Solve a Quadratic Equation by Factoring?

         Solving by Finding Square Roots
           Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

         Determining Dimensions
           Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

         Solving a Perfect Square Trinomial Equation
           Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

         Completing the Square

         Solving by Completing the Square
           Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

         Writing in Vertex Form
           Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

         4-6 Virtual Nerd� Tutorial: How Do You Solve a Quadratic Equation by Completing the Square?
           Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

         4-6 Virtual Nerd� Tutorial: How Do You Convert a Quadratic from Standard Form to Vertex Form by Completing the Square?
           Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

         Using the Quadratic Formula
           Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

         Applying the Quadratic Formula
           Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

         Using the Discriminant
           Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

         Using the Discriminant to Solve a Problem
           Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

         4-7 Virtual Nerd� Tutorial: How Do You Solve a Quadratic Equation by Using the Quadratic Formula?
           Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

         3-2 Virtual Nerd� Tutorial: How Do You Solve a System of Equations Using the Elimination by Multiplication Method?
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

         4-7 Virtual Nerd� Tutorial: What is the Discriminant?
           Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

         Simplifying a Number Using the Imaginary Unit?
           Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

         Graphing in the Complex Number Plane
           Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

         Solving by Substitution
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

         Solving a System by Using a Table
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

         Solving a System by Graphing
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

         Using a System of Inequalities
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

         Solving a Linear/Absolute-Value System
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

         Adding and Subtracting Complex Numbers
           Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

         Multiplying Complex Numbers
           Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

         Dividing Complex Numbers
           Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

         Factoring using Complex Conjugates
           Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

         Finding Imaginary Solutions
           Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

         Using Substitution to Solve a Problem
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

         Solving by Elimination
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

         Solving an Equivalent System
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

         Solving Systems Without Unique Solutions
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

         3-2 Virtual Nerd� Tutorial: How Do You Solve a System of Equations Using the Substitution Method?
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

         3-3 Virtual Nerd� Tutorial: How Do You Solve a System of Inequalities by Graphing?
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

         3-3 Virtual Nerd� Tutorial: How Do You Solve a Word Problem Using a System of Inequalities?
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Look for and make use of structure. 

         Testing Vertices

         Using Linear Programming to Maximize Profit

         Adding and Subtracting Complex Numbers
           Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

         4-8 Virtual Nerd� Tutorial: What is the Imaginary Unit i?
           Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

         4-8 Virtual Nerd� Tutorial: How Do You Add Complex Numbers?
           Curriculum Standards: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

         Solving a Linear-Quadratic System by Graphing
           Curriculum Standards: Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

         3-4 Virtual Nerd� Tutorial: What is Linear Programming?

         3-4 Virtual Nerd� Tutorial: How Do You Solve an Optimization Word Problem?

         Solving a System Using Elimination
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. 

         Solving an Equivalent System
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. 

         Solving a Linear-Quadratic System Using Substitution
           Curriculum Standards: Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

         Solving a Quadratic System of Equations
           Curriculum Standards: Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

         Solving a Quadratic System of Inequalities
           Curriculum Standards: Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

         Benchmark Test 2
           Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

         Polynomials and Polynomial Functions

            Finding the Features of a Quadratic Function
              Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Graphing a Quadratic Function in Standard Form?
              Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Interpreting a Quadratic Graph
              Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Writing an Equation of a Parabola
              Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Using Quadratic Regression
              Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Solving a Quadratic Equation by Factoring

            Solving a Quadratic Equation by Graphing

            Using the Discriminant
              Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

            Using the Discriminant to Solve a Problem
              Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

            Chapter 4 MathXL: Mid-Chapter Practice
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

            Chapter 4 MathXL: End-of-Chapter Practice
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

            Homework Video Tutor: Graphing a quadratic function, y = ax^2 + bx + c
              Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Homework Video Tutor: Writing the equation of a parabola
              Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Homework Video Tutor: Solving quadratic equations by graphing

            Homework Video Tutor: Solving quadratic equations by factoring

            Homework Video Tutor: Using the discriminant to find the number of solutions and solve problems
              Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. 

            Chapter 5 Get Ready
              Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Polynomial Functions

               Student eText Lesson 5-1
                 Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

               5-1 Dynamic Activity: Graphs of Polynomial Functions
                 Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Classifying Polynomials
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

                  Describing End Behavior of Polynomial Functions
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

                  Graphing Cubic Functions
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

                  Using Differences to Determine Degree
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

                  Graphing Cubic Functions
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

               Step 3: Lesson Check and Step 4: Practice

                  5-1 Virtual Nerd?  Tutorial: How Do You Find the Degree of a Polynomial?
                  5-1 Virtual Nerd? Tutorial: How Do You Find the Degree of a Polynomial?
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

               5-1 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

               Step 5: Assess and Remediate

                  5-1 Lesson Quiz
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

            Polynomials, Linear Factors, and Zeros

               Student eText Lesson 5-2
                 Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Writing a Polynomial in Factored Form
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

                  Finding Zeros of a Polynomial Function
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

                  Writing a Polynomial Function From Its Zeros
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

                  Finding the Multiplicity of a Zero
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

                  Identifying a Relative Maximum and Minimum
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

                  Using a Polynomial Function to Maximize Volume
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

                  Using a Polynomial Function to Maximize Volume
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

               Step 3: Lesson Check and Step 4: Practice

                  5-2 Virtual Nerd?  Tutorial: What is the Factor Theorem?
                  5-2 Virtual Nerd? Tutorial: What is the Factor Theorem?
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

               5-2 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

               Step 5: Assess and Remediate

                  5-2 Lesson Quiz
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

            Solving Polynomial Equations

               Student eText Lesson 5-3
                 Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Solving Polynomial Equations Using Factors
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

                  Solving Polynomial Equations by Factoring
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

                  Finding Real Roots by Graphing
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

                  Modeling a Problem Situation
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               Step 3: Lesson Check and Step 4: Practice

                  5-3 Virtual Nerd?  Tutorial: How Do You Factor a Polynomial Using Sum of Cubes?
                  5-3 Virtual Nerd? Tutorial: How Do You Factor a Polynomial Using Sum of Cubes?
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               5-3 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               Step 5: Assess and Remediate

                  5-3 Lesson Quiz
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

            What Are the Rules?

            Dividing Polynomials

               Student eText Lesson 5-4
                 Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using Polynomial Long Division
                    Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

                  Checking Factors
                    Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

                  Using Synthetic Division
                    Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

                  Using Synthetic Division to Solve a Problem
                    Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

                  Evaluating a Polynomial
                    Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

                  Evaluating a Polynomial
                    Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

               Step 3: Lesson Check and Step 4: Practice

                  5-4 Virtual Nerd?  Tutorial: How Do You Do Long Division With Polynomials?
                  5-4 Virtual Nerd? Tutorial: How Do You Do Long Division With Polynomials?
                    Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

               5-4 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

               Step 5: Assess and Remediate

                  5-4 Lesson Quiz
                    Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

            Chapter 5 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Look for and make use of structure. Look for and express regularity in repeated reasoning. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Chapter 5 Mid-Chapter Quiz
              Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Look for and make use of structure. Look for and express regularity in repeated reasoning. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Theorems About Roots of Polynomial Equations

               Student eText Lesson 5-5
                 Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding a Rational Root
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

                  Using the Rational Root Theorem
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

                  Using the Conjugate Root Theorem to Identify Roots
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

                  Using Conjugates to Construct a Polynomial
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

                  Using Descartes' Rule of Signs
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

                  Using Conjugates to Construct a Polynomial
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

               5-5 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

               Step 3: Lesson Check and Step 4: Practice

                  5-5 Virtual Nerd� Tutorial: How Do You Find All the Rational Zeros of a Polynomial Function?
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

               Step 5: Assess and Remediate

                  5-5 Lesson Quiz
                    Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

            The Fundamental Theorem of Algebra

               Student eText Lesson 5-6

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using the Fundamental Theorem of Algebra

                  Finding All the Zeros of a Polynomial Function

               Step 3: Lesson Check and Step 4: Practice

                  5-6 Virtual Nerd?  Tutorial: What is the Fundamental Theorem of Algebra?
                  5-6 Virtual Nerd? Tutorial: What is the Fundamental Theorem of Algebra?

               5-6 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  5-6 Lesson Quiz

            The Binomial Theorem

               Student eText Lesson 5-7
                 Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using Pascal's Triangle
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

                  Expanding a Binomial
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 3: Lesson Check and Step 4: Practice

                  5-7 Virtual Nerd� Tutorial: How Do You Expand a Power of a Binomial Sum Using the Binomial Theorem?
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

               5-7 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 5: Assess and Remediate

                  5-7 Lesson Quiz
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

            Polynomial Models in the Real World

               Student eText Lesson 5-8
                 Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using A Polynomial Function to Model Data
                    Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

                  Modeling Data
                    Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

                  Comparing Models
                    Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

                  Using Interpolation and Extrapolation
                    Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

               Step 3: Lesson Check and Step 4: Practice

                  5-8 Virtual Nerd� Tutorial: How Do You Write an Equation For a Quadratic if You Have Three Points?
                    Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

               5-8 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

               Step 5: Assess and Remediate

                  5-8 Lesson Quiz
                    Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

            Transforming Polynomial Functions

               Student eText Lesson 5-9
                 Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Transforming y = x cubed
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Finding Zeros of a Transformed Cubic Function
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Constructing a Quartic Function with Two Real Zeros
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Modeling With a Power Function
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Transforming y = x cubed
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

               Step 3: Lesson Check and Step 4: Practice

                  5-9 Virtual Nerd� Tutorial: How Do You Translate a Polynomial Function Vertically?
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

               5-9 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

               Step 5: Assess and Remediate

                  5-9 Lesson Quiz
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Chapter 5 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Look for and make use of structure. Look for and express regularity in repeated reasoning. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Chapter 5 Test
              Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Look for and make use of structure. Look for and express regularity in repeated reasoning. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Radical Functions and Rational Exponents

            Finding Domain and Range
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

            Graphing a Quadratic Function?
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Graphing Translations of Quadratic Functions?
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Interpreting Vertex Form
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Using Vertex Form
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Factoring when the Quadratic Coefficient 'a' is Not Equal To 1

            Factoring a Perfect Square Trinomial

            Solving a Quadratic Equation by Factoring

            Solving Polynomial Equations Using Factors
              Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

            Solving Polynomial Equations by Factoring
              Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

            Chapter 2 Math XL: Mid-Chapter Practice and Review
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Chapter 4 MathXL: Mid-Chapter Practice
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

            Chapter 4 MathXL: End-of-Chapter Practice
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

            Chapter 5 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Look for and make use of structure. Look for and express regularity in repeated reasoning. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Homework Video Tutor: Determining a reasonable domain and range for a situation
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Homework Video Tutor: Graphing a quadratic function using a table
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Homework Video Tutor: Using vertex form of a parabola to graph the parabola
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Homework Video Tutor: Multiplying two binomials using FOIL

            Homework Video Tutor: Solving quadratic equations by factoring

            Chapter 6 Get Ready
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Roots and Radical Expressions

               Student eText Lesson 6-1
                 Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               6-1 Dynamic Activity: Graphs of Radical Functions
                 Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding All Real Roots
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Finding Roots
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Simplifying Radical Expressions
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Using a Radical Expression
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               Step 3: Lesson Check and Step 4: Practice

                  6-1 Virtual Nerd� Tutorial: How Do You Find the Cube Root of a Perfect Cube?
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               6-1 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               Step 5: Assess and Remediate

                  6-1 Lesson Quiz
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

            Multiplying and Dividing Radical Expressions

               Student eText Lesson 6-2
                 Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Multiplying Radical Expressions
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Simplifying a Radical Expression
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Simplifying a Product
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Dividing Radical Expressions
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Rationalizing the Denominator
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Multiplying Radical Expressions
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               Step 3: Lesson Check and Step 4: Practice

                  6-2 Virtual Nerd� Tutorial: How Do You Simplify a Radical Using the Product Property?
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               6-2 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               Step 5: Assess and Remediate

                  6-2 Lesson Quiz
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

            Binomial Radical Expressions

               Student eText Lesson 6-3
                 Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Adding and Subtracting Radical Expressions
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Using Radical Expressions
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Simplifying Before Adding or Subtracting
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Multiplying Binomial Radical Expressions
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Multiplying Conjugates
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Rationalizing the Denominator
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               Step 3: Lesson Check and Step 4: Practice

                  6-3 Virtual Nerd� Tutorial: How Do You Add Radicals with Like Radicands?
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               6-3 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               Step 5: Assess and Remediate

                  6-3 Lesson Quiz
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

            Rational Exponents

               Student eText Lesson 6-4
                 Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Simplifying Expressions with Rational Exponents
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Converting Exponential and Radical Forms
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Using Rational Exponents
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Combining Radical Expressions
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Simplifying Numbers With Rational Exponents
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

                  Writing Expressions in Simplest Form
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               Step 3: Lesson Check and Step 4: Practice

                  6-4 Virtual Nerd� Tutorial: What are Rational Exponents?
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               6-4 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

               Step 5: Assess and Remediate

                  6-4 Lesson Quiz
                    Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

            Chapter 6 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Understand composition of functions and combine functions by composition. Determine whether a relation represented by a table, graph, or equation is a function. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Chapter 6 Mid-Chapter Quiz
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Understand composition of functions and combine functions by composition. Determine whether a relation represented by a table, graph, or equation is a function. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Solving Square Root and Other Radical Equations

               Student eText Lesson 6-5
                 Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Solving a Square Root Equation
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Solving Other Radical Equations
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Using Radical Equations
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Checking for Extraneous Solutions
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Solving an Equation With Two Radicals
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Solving a Square Root Equation
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 3: Lesson Check and Step 4: Practice

                  6-5 Virtual Nerd� Tutorial: How Do You Solve a Radical Equation?
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               6-5 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 5: Assess and Remediate

                  6-5 Lesson Quiz
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            The Snack Shack

            Function Operations

               Student eText Lesson 6-6
                 Curriculum Standards: Understand composition of functions and combine functions by composition. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Adding and Subtracting Functions
                    Curriculum Standards: Understand composition of functions and combine functions by composition. 

                  Multiplying and Dividing Functions
                    Curriculum Standards: Understand composition of functions and combine functions by composition. 

                  Composing Functions
                    Curriculum Standards: Understand composition of functions and combine functions by composition. 

                  Using Composite Functions
                    Curriculum Standards: Understand composition of functions and combine functions by composition. 

               Step 3: Lesson Check and Step 4: Practice

                  6-6 Virtual Nerd� Tutorial: How Do You Find the Sum of Two Functions?
                    Curriculum Standards: Understand composition of functions and combine functions by composition. 

               6-6 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Understand composition of functions and combine functions by composition. 

               Step 5: Assess and Remediate

                  6-6 Lesson Quiz
                    Curriculum Standards: Understand composition of functions and combine functions by composition. 

            Inverse Relations and Functions

               Student eText Lesson 6-7
                 Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding the Inverse of a Relation
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Finding an Equation for the Inverse
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Graphing a Relation and Its Inverse
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Finding an Inverse Function
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Finding the Inverse of a Formula
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Composing Inverse Functions
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Finding an Equation for the Inverse
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Composing Inverse Functions
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 3: Lesson Check and Step 4: Practice

                  6-7 Virtual Nerd� Tutorial: What is a One-to-One Function?
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               6-7 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 5: Assess and Remediate

                  6-7 Lesson Quiz
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Graphing Radical Functions

               Student eText Lesson 6-8
                 Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Translating a Square Root Function Vertically
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Translating a Square Root Function Horizontally
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Graphing a Square Root Function
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Solving a Radical Equation by Graphing
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Graphing a Cube Root Function
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Rewriting a Radical Function
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 3: Lesson Check and Step 4: Practice

                  6-8 Virtual Nerd� Tutorial: What Does the Constant 'k' Do in the Function f(x) = square root of (x)+k?
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               6-8 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 5: Assess and Remediate

                  6-8 Lesson Quiz
                    Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Chapter 6 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Understand composition of functions and combine functions by composition. Determine whether a relation represented by a table, graph, or equation is a function. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Chapter 6 Test
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Understand composition of functions and combine functions by composition. Determine whether a relation represented by a table, graph, or equation is a function. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

         Classifying Polynomials
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

         Describing End Behavior of Polynomial Functions
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

         Graphing Cubic Functions
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

         Using Differences to Determine Degree
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

         Graphing Cubic Functions
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

         5-1 Virtual Nerd?  Tutorial: How Do You Find the Degree of a Polynomial?
         5-1 Virtual Nerd? Tutorial: How Do You Find the Degree of a Polynomial?
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

         Writing a Polynomial in Factored Form
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

         Finding Zeros of a Polynomial Function
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

         Writing a Polynomial Function From Its Zeros
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

         Finding the Multiplicity of a Zero
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

         Identifying a Relative Maximum and Minimum
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

         Using a Polynomial Function to Maximize Volume
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

         Using a Polynomial Function to Maximize Volume
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

         5-2 Virtual Nerd?  Tutorial: What is the Factor Theorem?
         5-2 Virtual Nerd? Tutorial: What is the Factor Theorem?
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. 

         Finding All the Zeros of a Polynomial Function

         5-6 Virtual Nerd?  Tutorial: What is the Fundamental Theorem of Algebra?
         5-6 Virtual Nerd? Tutorial: What is the Fundamental Theorem of Algebra?

         Using the Fundamental Theorem of Algebra

         Using Pascal's Triangle
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         Expanding a Binomial
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         5-7 Virtual Nerd� Tutorial: How Do You Expand a Power of a Binomial Sum Using the Binomial Theorem?
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         Using A Polynomial Function to Model Data
           Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

         Modeling Data
           Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

         Comparing Models
           Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

         Using Interpolation and Extrapolation
           Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

         5-8 Virtual Nerd� Tutorial: How Do You Write an Equation For a Quadratic if You Have Three Points?
           Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

         Transforming y = x cubed
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Finding Zeros of a Transformed Cubic Function
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Constructing a Quartic Function with Two Real Zeros
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Modeling With a Power Function
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Transforming y = x cubed
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         5-9 Virtual Nerd� Tutorial: How Do You Translate a Polynomial Function Vertically?
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Finding All Real Roots
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Finding Roots
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Simplifying Radical Expressions
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Using a Radical Expression
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         6-1 Virtual Nerd� Tutorial: How Do You Find the Cube Root of a Perfect Cube?
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Multiplying Radical Expressions
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Simplifying a Radical Expression
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Simplifying a Product
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Dividing Radical Expressions
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Rationalizing the Denominator
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Multiplying Radical Expressions
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         6-2 Virtual Nerd� Tutorial: How Do You Simplify a Radical Using the Product Property?
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Adding and Subtracting Radical Expressions
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Using Radical Expressions
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Simplifying Before Adding or Subtracting
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Multiplying Binomial Radical Expressions
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Multiplying Conjugates
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Rationalizing the Denominator
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         6-3 Virtual Nerd� Tutorial: How Do You Add Radicals with Like Radicands?
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Simplifying Expressions with Rational Exponents
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Converting Exponential and Radical Forms
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Using Rational Exponents
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Combining Radical Expressions
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Simplifying Numbers With Rational Exponents
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Writing Expressions in Simplest Form
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         6-4 Virtual Nerd� Tutorial: What are Rational Exponents?
           Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

         Solving a Square Root Equation
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Solving Other Radical Equations
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Using Radical Equations
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Checking for Extraneous Solutions
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Solving an Equation With Two Radicals
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Solving a Square Root Equation
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         6-5 Virtual Nerd� Tutorial: How Do You Solve a Radical Equation?
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Adding and Subtracting Functions
           Curriculum Standards: Understand composition of functions and combine functions by composition. 

         Multiplying and Dividing Functions
           Curriculum Standards: Understand composition of functions and combine functions by composition. 

         Composing Functions
           Curriculum Standards: Understand composition of functions and combine functions by composition. 

         Using Composite Functions
           Curriculum Standards: Understand composition of functions and combine functions by composition. 

         6-6 Virtual Nerd� Tutorial: How Do You Find the Sum of Two Functions?
           Curriculum Standards: Understand composition of functions and combine functions by composition. 

         Finding the Inverse of a Relation
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Finding an Equation for the Inverse
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Graphing a Relation and Its Inverse
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Finding an Inverse Function
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Finding the Inverse of a Formula
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Composing Inverse Functions
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Finding an Equation for the Inverse
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Composing Inverse Functions
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Solving Polynomial Equations Using Factors
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         Solving Polynomial Equations by Factoring
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         Finding Real Roots by Graphing
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         Modeling a Problem Situation
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         5-3 Virtual Nerd?  Tutorial: How Do You Factor a Polynomial Using Sum of Cubes?
         5-3 Virtual Nerd? Tutorial: How Do You Factor a Polynomial Using Sum of Cubes?
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         6-7 Virtual Nerd� Tutorial: What is a One-to-One Function?
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Translating a Square Root Function Vertically
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Translating a Square Root Function Horizontally
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Graphing a Square Root Function
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Solving a Radical Equation by Graphing
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Using Polynomial Long Division
           Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

         Checking Factors
           Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

         Using Synthetic Division
           Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

         Using Synthetic Division to Solve a Problem
           Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

         Evaluating a Polynomial
           Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

         Graphing a Cube Root Function
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Rewriting a Radical Function
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         6-8 Virtual Nerd� Tutorial: What Does the Constant 'k' Do in the Function f(x) = square root of (x)+k?
           Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Evaluating a Polynomial
           Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

         5-4 Virtual Nerd?  Tutorial: How Do You Do Long Division With Polynomials?
         5-4 Virtual Nerd? Tutorial: How Do You Do Long Division With Polynomials?
           Curriculum Standards: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Attend to precision. Look for and make use of structure. 

         Finding a Rational Root
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

         Using the Rational Root Theorem
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

         Using the Conjugate Root Theorem to Identify Roots
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

         Using Conjugates to Construct a Polynomial
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

         Using Descartes' Rule of Signs
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

         Using Conjugates to Construct a Polynomial
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

         5-5 Virtual Nerd� Tutorial: How Do You Find All the Rational Zeros of a Polynomial Function?
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. 

         Benchmark Test 3
           Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. Construct viable arguments and critique the reasoning of others. Attend to precision. Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Look for and make use of structure. Look for and express regularity in repeated reasoning. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Translate expressions between radical and exponent form and simplify them using the laws of exponents. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Understand composition of functions and combine functions by composition. Determine whether a relation represented by a table, graph, or equation is a function. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. 

         Exponential and Logarithmic Functions

            Evaluating Algebraic Expressions
              Curriculum Standards: Reason abstractly and quantitatively. 

            Writing and Evaluating an Expression
              Curriculum Standards: Reason abstractly and quantitatively. 

            Using a Scatter Plot
              Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

            Writing the Equation of a Trend Line
              Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

            Finding the Line of Best Fit
              Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

            Graphing Translations of Quadratic Functions?
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Transforming y = x cubed
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Simplifying Expressions with Rational Exponents
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

            Converting Exponential and Radical Forms
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

            Using Rational Exponents
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

            Combining Radical Expressions
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

            Simplifying Numbers With Rational Exponents
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

            Finding the Inverse of a Relation
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Finding an Equation for the Inverse
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Finding an Inverse Function
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Finding the Inverse of a Formula
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Composing Inverse Functions
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Chapter 1 Math XL: Mid-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Attend to precision. Model with mathematics. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Chapter 2 Math XL: End-of-Chapter Practice and Review
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Chapter 4 MathXL: Mid-Chapter Practice
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

            Chapter 5 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Look for and make use of structure. Look for and express regularity in repeated reasoning. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Chapter 6 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Understand composition of functions and combine functions by composition. Determine whether a relation represented by a table, graph, or equation is a function. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Chapter 6 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Understand composition of functions and combine functions by composition. Determine whether a relation represented by a table, graph, or equation is a function. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Homework Video Tutor: Evaluating algebraic expressions with exponents
              Curriculum Standards: Reason abstractly and quantitatively. 

            Homework Video Tutor: Making a scatter plot
              Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

            Homework Video Tutor: Writing an equation for a line of best fit
              Curriculum Standards: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. 

            Homework Video Tutor: Simplifying expressions with rational exponents
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

            Homework Video Tutor: Finding an inverse function
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Virtual Nerd?  Tutorial: How do you graph a translation of a function?
            Virtual Nerd? Tutorial: How do you graph a translation of a function?
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Chapter 7 Get Ready
              Curriculum Standards: Reason abstractly and quantitatively. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Translate expressions between radical and exponent form and simplify them using the laws of exponents. Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Exploring Exponential Models

               Student eText Lesson 7-1
                 Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

               7-1 Dynamic Activity: Comparing Linear and Exponential Functions
                 Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Graphing an Exponential Function
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

                  Identifying Exponential Growth and Decay
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

                  Modeling Exponential Growth
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

                  Using Exponential Growth
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

                  Writing an Exponential Function
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

               Step 3: Lesson Check and Step 4: Practice

                  7-1 Virtual Nerd� Tutorial: What's an Exponential Function?
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

                  7-1 Virtual Nerd� Tutorial: What is Exponential Growth?
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

               7-1 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

               Step 5: Assess and Remediate

                  7-1 Lesson Quiz
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

            Properties of Exponential Functions

               Student eText Lesson 7-2
                 Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Graphing y = ab to the power of x
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

                  Translating the Parent Function y = b to the power of x
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

                  Using an Exponential Model
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

                  Evaluating e to the power of x
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

                  Continuously Compounded Interest
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

                  Graphing y = ab to the power of x
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

               Step 3: Lesson Check and Step 4: Practice

                  7-2 Virtual Nerd� Tutorial: What is a Natural Base Exponential Function?
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

               7-2 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

               Step 5: Assess and Remediate

                  7-2 Lesson Quiz
                    Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

            The Crazy Conditioning

            Logarithmic Functions as Inverses

               Student eText Lesson 7-3
                 Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Exponential Equations in Logarithmic Form
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

                  Evaluating a Logarithm
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

                  Using a Logarithmic Scale
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

                  Graphing a Logarithmic Function
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

                  Translating y = logb (x)
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

                  Translating y = logb (x)
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

               Step 3: Lesson Check and Step 4: Practice

                  7-3 Virtual Nerd� Tutorial: What is a Logarithm?
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

                  7-3 Virtual Nerd� Tutorial: How Do You Convert From Exponential Form to Logarithmic Form?
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

               7-3 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

               Step 5: Assess and Remediate

                  7-3 Lesson Quiz
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

            Chapter 7 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

            Chapter 7 Mid-Chapter Quiz
              Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

            Properties of Logarithms

               Student eText Lesson 7-4
                 Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Simplifying Logarithms
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

                  Expanding Logarithms
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

                  Using the Change of Base Formula
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

                  Using a Logarithmic Scale
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

               Step 3: Lesson Check and Step 4: Practice

                  7-4 Virtual Nerd� Tutorial: What is the Product Property of Logarithms?
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

               7-4 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

               Step 5: Assess and Remediate

                  7-4 Lesson Quiz
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

            Exponential and Logarithmic Equations

               Student eText Lesson 7-5
                 Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Solving an Exponential Equation - Common Base
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

                  Solving an Exponential Equation - Different Bases
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

                  Solving an Equation With a Graph or Table
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

                  Modeling With an Exponential Equation
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

                  Solving a Logarithmic Equation
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

                  Using Logarithmic Properties to Solve an Equation
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

               Step 3: Lesson Check and Step 4: Practice

                  7-5 Virtual Nerd� Tutorial: How Do You Solve a Logarithmic Equation by Exponentiating?
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

               7-5 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

               Step 5: Assess and Remediate

                  7-5 Lesson Quiz
                    Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

            Natural Logarithms

               Student eText Lesson 7-6

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Simplifying a Natural Logarithmic Expression

                  Solving a Natural Logarithmic Equation

                  Solving an Exponential Equation

                  Using Natural Logarithms

               Step 3: Lesson Check and Step 4: Practice

                  7-6 Virtual Nerd� Tutorial: What is a Natural Logarithm?

                  7-6 Virtual Nerd� Tutorial: How Do You Convert From Exponential Form to Natural Logarithmic Form?

               7-6 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  7-6 Lesson Quiz

            Chapter 7 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

            Chapter 7 Test
              Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

         Rational Functions

            Identifying Direct Variation From Equations
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Using Direct Variation to Solve a Problem
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Factoring when the Quadratic Coefficient 'a' is +1 or -1

            Finding Common Factors

            Factoring when the Quadratic Coefficient 'a' is Not Equal To 1

            Factoring a Perfect Square Trinomial

            Factoring a Difference of Two Squares

            Solving a Quadratic Equation by Factoring

            Solving a Quadratic Equation With Tables

            Solving a Quadratic Equation by Graphing

            Using a Quadratic Equation

            Chapter 2 Math XL: Mid-Chapter Practice and Review
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Chapter 4 MathXL: Mid-Chapter Practice
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

            Chapter 4 MathXL: End-of-Chapter Practice
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

            Homework Video Tutor: Using a proportion as an equation of direct variation
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Homework Video Tutor: Solving quadratic equations by factoring

            Homework Video Tutor: Solving quadratic equations using completing the square

            Homework Video Tutor: Solving quadratic equations using completing the square when a does not equal 1

            Homework Video Tutor: Solving quadratic equations using the quadratic formula

            Chapter 8 Get Ready
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Inverse Variation

               Student eText Lesson 8-1
                 Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               8-1 Dynamic Activity: Exploring the Reciprocal Function
                 Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Identifying Direct and Inverse Variations
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Determining an Inverse Variation
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Modeling an Inverse Variation
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Using Combined Variation
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  Applying Combined Variation
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 3: Lesson Check and Step 4: Practice

                  8-1 Virtual Nerd� Tutorial: What's the Inverse Variation or Indirect Proportionality Formula?
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

                  8-1 Virtual Nerd� Tutorial: How Do You Use the Formula for Inverse Variation to Write an Equation?
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               8-1 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

               Step 5: Assess and Remediate

                  8-1 Lesson Quiz
                    Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            The Reciprocal Function Family

               Student eText Lesson 8-2
                 Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Graphing an Inverse Variation Function
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Identifying Reciprocal Function Transformations
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Graphing a Translation
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Writing the Equation of a Transformation
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Using a Reciprocal Function
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

                  Graphing a Translation
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

               Step 3: Lesson Check and Step 4: Practice

                  8-2 Virtual Nerd� Tutorial: How Do You Graph a Rational Function by Making a Table?
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

               8-2 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

               Step 5: Assess and Remediate

                  8-2 Lesson Quiz
                    Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Rational Functions and Their Graphs

               Student eText Lesson 8-3

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding Points of Discontinuity

                  Finding Vertical Asymptotes

                  Finding Horizontal Asymptotes

                  Graphing a Rational Function

                  Using a Rational Function

               Step 3: Lesson Check and Step 4: Practice

                  8-3 Virtual Nerd� Tutorial: What is a Continuous Function?

               8-3 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  8-3 Lesson Quiz

            Chapter 8 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

            Chapter 8 Mid-Chapter Quiz
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

            Rational Expressions

               Student eText Lesson 8-4
                 Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Simplifying a Rational Expression
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

                  Multiplying Rational Expressions
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

                  Dividing Rational Expressions
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

                  Using Rational Expressions to Solve a Problem
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

               Step 3: Lesson Check and Step 4: Practice

                  8-4 Virtual Nerd� Tutorial: How Do You Multiply Two Rational Expressions?
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

                  8-4 Virtual Nerd� Tutorial: How Do You Divide Two Polynomials by Factoring and Canceling?
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

               8-4 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

               Step 5: Assess and Remediate

                  8-4 Lesson Quiz
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

            Adding and Subtracting Rational Expressions

               Student eText Lesson 8-5
                 Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding the Least Common Multiple
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

                  Adding Rational Expressions
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

                  Subtracting Rational Expressions
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

                  Simplifying a Complex Fraction
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

                  Using Rational Expressions to Solve a Problem
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

                  Subtracting Rational Expressions
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

               Step 3: Lesson Check and Step 4: Practice

                  8-5 Virtual Nerd� Tutorial: How Do You Add Two Rational Expressions with Different Denominators?
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

                  8-5 Virtual Nerd� Tutorial: How Do You Find the Least Common Denominator of Two Rational Expressions?
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

               8-5 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

               Step 5: Assess and Remediate

                  8-5 Lesson Quiz
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

            Solving Rational Equations

               Student eText Lesson 8-6
                 Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Solving a Rational Equation
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

                  Using Rational Equations
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

                  Using a Graphing Calculator to Solve a Rational Equation
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

               Step 3: Lesson Check and Step 4: Practice

                  8-6 Virtual Nerd� Tutorial: How Do You Solve a Rational Equation by LCD Multiplication?
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

                  8-6 Virtual Nerd� Tutorial: How Do You Solve a Rational Equation By Adding Fractions?
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

               8-6 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

               Step 5: Assess and Remediate

                  8-6 Lesson Quiz
                    Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

            Chapter 8 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

            Chapter 8 Test
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

         Graphing an Exponential Function
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

         Identifying Exponential Growth and Decay
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

         Modeling Exponential Growth
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

         Using Exponential Growth
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

         Writing an Exponential Function
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

         7-1 Virtual Nerd� Tutorial: What's an Exponential Function?
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

         7-1 Virtual Nerd� Tutorial: What is Exponential Growth?
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

         7-2 Virtual Nerd� Tutorial: What is a Natural Base Exponential Function?
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

         Exponential Equations in Logarithmic Form
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

         Evaluating a Logarithm
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

         Using a Logarithmic Scale
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

         Graphing a Logarithmic Function
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

         Translating y = logb (x)
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

         Translating y = logb (x)
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

         7-3 Virtual Nerd� Tutorial: How Do You Convert From Exponential Form to Logarithmic Form?
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

         Graphing y = ab to the power of x
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

         7-3 Virtual Nerd� Tutorial: What is a Logarithm?
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

         Simplifying Logarithms
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

         Expanding Logarithms
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

         Using the Change of Base Formula
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

         Using a Logarithmic Scale
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

         7-4 Virtual Nerd� Tutorial: What is the Product Property of Logarithms?
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

         Solving an Exponential Equation - Common Base
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

         Solving an Exponential Equation - Different Bases
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

         Solving an Equation With a Graph or Table
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

         Modeling With an Exponential Equation
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

         Solving a Logarithmic Equation
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

         Using Logarithmic Properties to Solve an Equation
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

         7-5 Virtual Nerd� Tutorial: How Do You Solve a Logarithmic Equation by Exponentiating?
           Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

         Simplifying a Natural Logarithmic Expression

         Solving a Natural Logarithmic Equation

         Solving an Exponential Equation

         Using Natural Logarithms

         7-6 Virtual Nerd� Tutorial: What is a Natural Logarithm?

         7-6 Virtual Nerd� Tutorial: How Do You Convert From Exponential Form to Natural Logarithmic Form?

         Identifying Direct and Inverse Variations
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Determining an Inverse Variation
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Modeling an Inverse Variation
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Using Combined Variation
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Applying Combined Variation
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         8-1 Virtual Nerd� Tutorial: What's the Inverse Variation or Indirect Proportionality Formula?
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         8-1 Virtual Nerd� Tutorial: How Do You Use the Formula for Inverse Variation to Write an Equation?
           Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

         Graphing an Inverse Variation Function
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Identifying Reciprocal Function Transformations
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Graphing a Translation
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Writing the Equation of a Transformation
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Using a Reciprocal Function
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Graphing a Translation
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         8-2 Virtual Nerd� Tutorial: How Do You Graph a Rational Function by Making a Table?
           Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

         Finding Points of Discontinuity

         Finding Vertical Asymptotes

         Finding Horizontal Asymptotes

         Graphing a Rational Function

         Using a Rational Function

         8-3 Virtual Nerd� Tutorial: What is a Continuous Function?

         Simplifying a Rational Expression
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

         Multiplying Rational Expressions
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

         Dividing Rational Expressions
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

         Using Rational Expressions to Solve a Problem
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

         8-4 Virtual Nerd� Tutorial: How Do You Multiply Two Rational Expressions?
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

         8-4 Virtual Nerd� Tutorial: How Do You Divide Two Polynomials by Factoring and Canceling?
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

         Finding the Least Common Multiple
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

         Adding Rational Expressions
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

         Subtracting Rational Expressions
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

         Simplifying a Complex Fraction
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

         Using Rational Expressions to Solve a Problem
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

         Subtracting Rational Expressions
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

         8-5 Virtual Nerd� Tutorial: How Do You Add Two Rational Expressions with Different Denominators?
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

         8-5 Virtual Nerd� Tutorial: How Do You Find the Least Common Denominator of Two Rational Expressions?
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

         Solving a Rational Equation
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

         Using Rational Equations
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

         Using a Graphing Calculator to Solve a Rational Equation
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

         8-6 Virtual Nerd� Tutorial: How Do You Solve a Rational Equation by LCD Multiplication?
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

         8-6 Virtual Nerd� Tutorial: How Do You Solve a Rational Equation By Adding Fractions?
           Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

         Graphing y = ab to the power of x
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

         Translating the Parent Function y = b to the power of x
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

         Using an Exponential Model
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

         Evaluating e to the power of x
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

         Continuously Compounded Interest
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

         Benchmark Test 4
           Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

         Sequences and Series

            Expressing a Pattern with Algebra
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

            Using a Graph
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

            Using Function Notation
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

            Writing and Evaluating a Function
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. 

            Simplifying a Complex Fraction
              Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

            Using Rational Expressions to Solve a Problem
              Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

            Chapter 1 Math XL: Mid-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Attend to precision. Model with mathematics. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Chapter 2 Math XL: Mid-Chapter Practice and Review
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Chapter 8 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

            Homework Video Tutor: Algebraic expressions and order of operations
              Curriculum Standards: Reason abstractly and quantitatively. 

            Homework Video Tutor: Dividing a fraction by a fraction
              Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

            Virtual Nerd� Tutorial: How do you write a rule for a pattern?
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

            Chapter 9 Get Ready
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Determine whether a relation represented by a table, graph, or equation is a function. Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

            Mathematical Patterns

               Student eText Lesson 9-1
                 Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               9-1 Dynamic Activity: Sums of Geometric Series
                 Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Generating a Sequence Using an Explicit Formula
                    Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Writing a Recursive Definition for a Sequence
                    Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Writing an Explicit Formula for a Sequence
                    Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using Formulas to Find Terms of  a Sequence
                  Using Formulas to Find Terms of a Sequence
                    Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 3: Lesson Check and Step 4: Practice

                  9-1 Virtual Nerd� Tutorial: What's a Sequence?
                    Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               9-1 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 5: Assess and Remediate

                  9-1 Lesson Quiz
                    Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

            Arithmetic Sequences

               Student eText Lesson 9-2
                 Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Identifying Arithmetic Sequences
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

                  Analyzing Arithmetic Sequences
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

                  Using the Arithmetic Mean
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

                  Using an Explicit Formula for an Arithmetic Sequence
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

               Step 3: Lesson Check and Step 4: Practice

                  9-2 Virtual Nerd� Tutorial: What's an Arithmetic Sequence?
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

               9-2 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

               Step 5: Assess and Remediate

                  9-2 Lesson Quiz
                    Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

            Crack the Code!

            Chapter 9 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Model with mathematics. Use appropriate tools strategically. Attend to precision. Find partial sums of arithmetic and geometric series and represent them using sigma notation. 

            Chapter 9 Mid-Chapter Quiz
              Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Model with mathematics. Use appropriate tools strategically. Attend to precision. Find partial sums of arithmetic and geometric series and represent them using sigma notation. 

            Geometric Sequences

               Student eText Lesson 9-3
                 Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Attend to precision. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Identifying Geometric Sequences
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Attend to precision. 

                  Analyzing Geometric Sequences
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Attend to precision. 

                  Using a Geometric Sequence
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Attend to precision. 

                  Using the Geometric Mean
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Attend to precision. 

               Step 3: Lesson Check and Step 4: Practice

                  9-3 Virtual Nerd� Tutorial: What is the Explicit Formula for the nth Term in a Geometric Sequence?
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Attend to precision. 

               9-3 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Attend to precision. 

               Step 5: Assess and Remediate

                  9-3 Lesson Quiz
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Attend to precision. 

            Arithmetic Series

               Student eText Lesson 9-4
                 Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding the Sum of a Finite Arithmetic Series
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

                  Using the Sum of a Finite Arithmetic Series
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

                  Writing a Series in Summation Notation
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

                  Finding the Sum of a Series
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

                  Using a Graphing Calculator to Find the Sum of a Series
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

                  Finding the Sum of a Finite Arithmetic Series
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

               Step 3: Lesson Check and Step 4: Practice

                  9-4 Virtual Nerd� Tutorial: What is a Series?
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

               9-4 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

               Step 5: Assess and Remediate

                  9-4 Lesson Quiz
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

            Geometric Series

               Student eText Lesson 9-5
                 Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Instruction

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding the Sums of Finite Geometric Series
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

                  Using the Geometric Series Formula
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

                  Analyzing Infinite Geometric Series
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

                  Finding the Sums of Finite Geometric Series
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

                  Analyzing Infinite Geometric Series
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

               Step 3: Lesson Check and Step 4: Practice

                  9-5 Virtual Nerd?  Tutorial: What is an Infinite Geometric Series?
                  9-5 Virtual Nerd? Tutorial: What is an Infinite Geometric Series?
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

               9-5 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

               Step 5: Assess and Remediate

                  9-5 Lesson Quiz
                    Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

            Chapter 9 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Model with mathematics. Use appropriate tools strategically. Attend to precision. Find partial sums of arithmetic and geometric series and represent them using sigma notation. 

            Chapter 9 Test
              Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Model with mathematics. Use appropriate tools strategically. Attend to precision. Find partial sums of arithmetic and geometric series and represent them using sigma notation. 

         Quadratic Relations and Conic Sections

            Chapter 2 Math XL: End-of-Chapter Practice and Review
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Graphing an Absolute Value Function
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Combining Translations
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Vertical Stretch and Compression
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Graphing a Quadratic Function?
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Graphing Translations of Quadratic Functions?
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Using Vertex Form
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Using Quadratic Regression
              Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Chapter 4 MathXL: Mid-Chapter Practice
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

            Completing the Square

            Solving by Completing the Square
              Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

            Writing in Vertex Form
              Curriculum Standards: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

            Chapter 4 MathXL: End-of-Chapter Practice
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

            Homework Video Tutor: Graphing a quadratic function, y = ax^2 + bx + c
              Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Homework Video Tutor: Solving quadratic equations using completing the square

            Homework Video Tutor: Using vertex form of a parabola to graph the parabola
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Homework Video Tutor: Graphing absolute value functions
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Virtual Nerd� Tutorial: What is a quadratic function?
              Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

            Chapter 10 Get Ready
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. 

            Exploring Conic Sections

               Student eText Lesson 10-1

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Graphing a Circle

                  Graphing an Ellipse

                  Graphing a Hyperbola

                  Identifying Graphs of Conic Sections

                  Using Models

               Step 3: Lesson Check and Step 4: Practice

                  10-1 Virtual Nerd� Tutorial: What are Conic Sections?

               10-1 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  10-1 Lesson Quiz

            Parabolas

               Student eText Lesson 10-2

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Parabolas with Equation y = ax^2

                  Parabolas with Equation x = ay^2

                  Using Parabolas to Solve Problems

                  Analyzing a Parabola

                  Writing an Equation of a Parabola
                    Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

               Step 3: Lesson Check and Step 4: Practice

                  10-2 Virtual Nerd� Tutorial: What is a Parabola?

               10-2 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  10-2 Lesson Quiz

            Circles

               Student eText Lesson 10-3

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Writing an Equation of a Circle

                  Using Translations to Write an Equation

                  Using a Graph to Write an Equation

                  Finding the Center and Radius

                  Graphing a Circle Using Center and Radius

               Step 3: Lesson Check and Step 4: Practice

                  10-3 Virtual Nerd� Tutorial: What is a Circle?

               10-3 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  10-3 Lesson Quiz

            Watering the Lawn

            Chapter 10 MathXL: Mid-Chapter Practice and Review

            Chapter 10 Mid-Chapter Quiz

            Ellipses

               Student eText Lesson 10-4

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Writing an Equation of an Ellipse

                  Finding the Foci of an Ellipse

                  Using the Foci of an Ellipse

                  Using the Foci of an Ellipse

               Step 3: Lesson Check and Step 4: Practice

                  Virtual Nerd� Tutorial: What is an Ellipse?

               10-4 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  10-4 Lesson Quiz

            Hyperbolas

               Student eText Lesson 10-5

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  The Equation and Graph of a Hyperbola

                  Analyzing a Hyperbola from Its Equation

                  Modeling with a Hyperbola

               Step 3: Lesson Check and Step 4: Practice

                  10-5 Virtual Nerd� Tutorial: What is a Hyperbola?

               10-5 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  10-5 Lesson Quiz

            Translating Conic Sections

               Student eText Lesson 10-6

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Writing an Equation of a Translated Ellipse

                  Analyzing a Hyperbola from Its Equation

                  Identifying a Translated Conic Section

                  Modeling With a Conic Section

               Step 3: Lesson Check and Step 4: Practice

                  10-6 Virtual Nerd� Tutorial: What is the Standard Form of the Equation of a Horizontal Ellipse?

               10-6 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  10-6 Lesson Quiz

            Chapter 10 MathXL: End-of-Chapter Practice and Review

            Chapter 10 Test

         Generating a Sequence Using an Explicit Formula
           Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

         Writing a Recursive Definition for a Sequence
           Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

         Writing an Explicit Formula for a Sequence
           Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

         Using Formulas to Find Terms of  a Sequence
         Using Formulas to Find Terms of a Sequence
           Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

         9-1 Virtual Nerd� Tutorial: What's a Sequence?
           Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

         Identifying Arithmetic Sequences
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

         Analyzing Arithmetic Sequences
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

         Using the Sum of a Finite Arithmetic Series
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

         Writing a Series in Summation Notation
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

         Finding the Sum of a Series
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

         Using a Graphing Calculator to Find the Sum of a Series
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

         Finding the Sum of a Finite Arithmetic Series
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

         9-4 Virtual Nerd� Tutorial: What is a Series?
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

         Finding the Sums of Finite Geometric Series
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

         Using the Geometric Series Formula
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

         Finding the Sum of a Finite Arithmetic Series
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. 

         Analyzing Infinite Geometric Series
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

         Finding the Sums of Finite Geometric Series
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

         Analyzing Infinite Geometric Series
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

         9-5 Virtual Nerd?  Tutorial: What is an Infinite Geometric Series?
         9-5 Virtual Nerd? Tutorial: What is an Infinite Geometric Series?
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Use appropriate tools strategically. 

         Graphing a Circle

         Graphing an Ellipse

         Graphing a Hyperbola

         Identifying Graphs of Conic Sections

         Using Models

         10-1 Virtual Nerd� Tutorial: What are Conic Sections?

         Parabolas with Equation y = ax^2

         Parabolas with Equation x = ay^2

         Using Parabolas to Solve Problems

         Analyzing a Parabola

         Writing an Equation of a Parabola
           Curriculum Standards: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. 

         10-2 Virtual Nerd� Tutorial: What is a Parabola?

         Writing an Equation of a Circle

         Using Translations to Write an Equation

         Using a Graph to Write an Equation

         Finding the Center and Radius

         Graphing a Circle Using Center and Radius

         10-3 Virtual Nerd� Tutorial: What is a Circle?

         Writing an Equation of an Ellipse

         Finding the Foci of an Ellipse

         Using the Foci of an Ellipse

         Using the Foci of an Ellipse

         10-4 Virtual Nerd� Tutorial: What is an Ellipse?

         The Equation and Graph of a Hyperbola

         Analyzing a Hyperbola from Its Equation

         Modeling with a Hyperbola

         10-5 Virtual Nerd� Tutorial: What is a Hyperbola?

         Writing an Equation of a Translated Ellipse

         Analyzing a Hyperbola from Its Equation

         Identifying a Translated Conic Section

         Modeling With a Conic Section

         10-6 Virtual Nerd� Tutorial: What is the Standard Form of the Equation of a Horizontal Ellipse?

         Using the Arithmetic Mean
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

         Using an Explicit Formula for an Arithmetic Sequence
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

         9-2 Virtual Nerd� Tutorial: What's an Arithmetic Sequence?
           Curriculum Standards: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

         Identifying Geometric Sequences
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Attend to precision. 

         Analyzing Geometric Sequences
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Attend to precision. 

         Using a Geometric Sequence
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Attend to precision. 

         Using the Geometric Mean
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Attend to precision. 

         9-3 Virtual Nerd� Tutorial: What is the Explicit Formula for the nth Term in a Geometric Sequence?
           Curriculum Standards: Find partial sums of arithmetic and geometric series and represent them using sigma notation. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Attend to precision. 

         Benchmark Test 5
           Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Model with mathematics. Use appropriate tools strategically. Attend to precision. Find partial sums of arithmetic and geometric series and represent them using sigma notation. 

         Probability and Statistics

            Using Pascal's Triangle
              Curriculum Standards: Look for and express regularity in repeated reasoning. 

            Expanding a Binomial
              Curriculum Standards: Look for and express regularity in repeated reasoning. 

            Chapter 5 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Look for and make use of structure. Look for and express regularity in repeated reasoning. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). 

            Finding All Real Roots
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

            Finding Roots
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

            Simplifying Radical Expressions
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

            Chapter 6 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Understand composition of functions and combine functions by composition. Determine whether a relation represented by a table, graph, or equation is a function. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Homework Video Tutor: Writing fractions as percents

            Homework Video Tutor: Writing decimals as percents

            Homework Video Tutor: Using the order of operations to simplify an expression

            Homework Video Tutor: Using Pascal's Triangle
              Curriculum Standards: Look for and express regularity in repeated reasoning. 

            Homework Video Tutor: Simplifying square roots of rational numbers
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. 

            Chapter 11 Get Ready
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 

            Permutations and Combinations

               Student eText Lesson 11-1
                 Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               11-1 Dynamic Activity: Normal Distributions
                 Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using the Fundamental Counting Principle
                    Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

                  Finding the Number of Permutations of n Items
                    Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

                  Finding nPr
                    Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

                  Finding nCr
                    Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

                  Identifying Whether Order Is Important
                    Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               Step 3: Lesson Check and Step 4: Practice

                  11-1 Virtual Nerd� Tutorial: What is the Fundamental Counting Principle?
                    Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               11-1 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               Step 5: Assess and Remediate

                  11-1 Lesson Quiz
                    Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

            Probability

               Student eText Lesson 11-2
                 Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding Experimental Probability
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

                  Using a Simulation
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

                  Finding Theoretical Probability
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

                  Finding Probability Using Combinatorics
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

                  Finding Geometric Probability
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

               Step 3: Lesson Check and Step 4: Practice

                  11-2 Virtual Nerd� Tutorial: How Do You Find the Probability of a Simple Event?
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

               11-2 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

               Step 5: Assess and Remediate

                  11-2 Lesson Quiz
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

            Probability of Multiple Events

               Student eText Lesson 11-3
                 Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Classifying Events
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

                  Finding the Probability of Independent Events
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

                  Mutually Exclusive Events
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

                  Probability of Mutually Exclusive Events
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

                  Finding Probability
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

               Step 3: Lesson Check and Step 4: Practice

                  11-3 Virtual Nerd� Tutorial: How Do You Find the Probability of Independent Events?
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

               11-3 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

               Step 5: Assess and Remediate

                  11-3 Lesson Quiz
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

            Conditional Probability

               Student eText Lesson 11-4
                 Curriculum Standards: Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding Conditional Probability
                    Curriculum Standards: Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

                  Conditional Probability in Statistics
                    Curriculum Standards: Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

                  Using the Conditional Probability Formula
                    Curriculum Standards: Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

                  Using a Tree Diagram
                    Curriculum Standards: Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

               Step 3: Lesson Check and Step 4: Practice

                  11-4 Virtual Nerd� Tutorial: What is Conditional Probability?
                    Curriculum Standards: Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

               11-4 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

               Step 5: Assess and Remediate

                  11-4 Lesson Quiz
                    Curriculum Standards: Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

            Chapter 11 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Use appropriate tools strategically. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. Look for and express regularity in repeated reasoning. Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

            Chapter 11 Mid-Chapter Quiz
              Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Use appropriate tools strategically. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. Look for and express regularity in repeated reasoning. Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

            Probability Models

               Student eText Lesson 11-5
                 Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Model with mathematics. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Making a Fair Decision
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Model with mathematics. 

                  Using Random Numbers
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Model with mathematics. 

                  Modeling with a Simulation
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Model with mathematics. 

                  Using Probability to Analyze Decisions
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Model with mathematics. 

               Step 3: Lesson Check and Step 4: Practice

                  11-5 Virtual Nerd� Tutorial: How Do You Use a Simulation to Solve a Problem?
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Model with mathematics. 

               11-5 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Model with mathematics. 

               Step 5: Assess and Remediate

                  11-5 Lesson Quiz
                    Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Model with mathematics. 

            Analyzing Data

               Student eText Lesson 11-6
                 Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding Measures of Central Tendency
                    Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

                  Identifying an Outlier
                    Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

                  Comparing Data Sets
                    Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

                  Using a Box-and-Whisker Plot
                    Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

                  Finding Percentiles
                    Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

               Step 3: Lesson Check and Step 4: Practice

                  11-6 Virtual Nerd� Tutorial: How Do You Find the Mean of a Data Set?
                    Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

               11-6 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

               Step 5: Assess and Remediate

                  11-6 Lesson Quiz
                    Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

            The Express Lane

            Standard Deviation

               Student eText Lesson 11-7
                 Curriculum Standards: Use appropriate tools strategically. Look for and express regularity in repeated reasoning. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding Variance and Standard Deviation
                    Curriculum Standards: Use appropriate tools strategically. Look for and express regularity in repeated reasoning. 

                  Using a Calculator to Find Standard Deviation
                    Curriculum Standards: Use appropriate tools strategically. Look for and express regularity in repeated reasoning. 

                  Using Standard Deviation to Describe Data
                    Curriculum Standards: Use appropriate tools strategically. Look for and express regularity in repeated reasoning. 

               Step 3: Lesson Check and Step 4: Practice

                  11-7 Virtual Nerd� Tutorial: How Do You Find the Standard Deviation of a Data Set?
                    Curriculum Standards: Use appropriate tools strategically. Look for and express regularity in repeated reasoning. 

               11-7 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Use appropriate tools strategically. Look for and express regularity in repeated reasoning. 

               Step 5: Assess and Remediate

                  11-7 Lesson Quiz
                    Curriculum Standards: Use appropriate tools strategically. Look for and express regularity in repeated reasoning. 

            Samples and Surveys

               Student eText Lesson 11-8
                 Curriculum Standards: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Analyzing Sampling Methods
                    Curriculum Standards: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

                  Analyzing Study Methods
                    Curriculum Standards: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

                  Designing a Survey
                    Curriculum Standards: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

               Step 3: Lesson Check and Step 4: Practice

                  11-8 Virtual Nerd� Tutorial: What is an Unbiased Sample?
                    Curriculum Standards: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

               11-8 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

               Step 5: Assess and Remediate

                  11-8 Lesson Quiz
                    Curriculum Standards: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

            Binomial Distributions

               Student eText Lesson 11-9

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using a Formula to Find Probabilities

                  Expanding Binomials

                  Applying Binomial Probability

               Step 3: Lesson Check and Step 4: Practice

                  11-9 Virtual Nerd� Tutorial: How Do You Expand a Power of a Binomial Sum Using the Binomial Theorem?

               11-9 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  11-9 Lesson Quiz

            Normal Distributions

               Student eText Lesson 11-10
                 Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Analyzing Normally Distributed Data
                    Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

                  Sketching a Normal Curve
                    Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

                  Analyzing a Normal Distribution
                    Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

               Step 3: Lesson Check and Step 4: Practice

                  11-10 Virtual Nerd� Tutorial: What is a Normal Distribution?
                    Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

               11-10 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

               Step 5: Assess and Remediate

                  11-10 Lesson Quiz
                    Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

            Chapter 11 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Use appropriate tools strategically. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. Look for and express regularity in repeated reasoning. Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

            Chapter 11 Test
              Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Use appropriate tools strategically. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. Look for and express regularity in repeated reasoning. Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

         Matrices

            Chapter 1 Math XL: Mid-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Attend to precision. Model with mathematics. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Evaluating Algebraic Expressions
              Curriculum Standards: Reason abstractly and quantitatively. 

            Writing and Evaluating an Expression
              Curriculum Standards: Reason abstractly and quantitatively. 

            Solving by Substitution
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

            Using Substitution to Solve a Problem
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

            Solving by Elimination
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

            Solving an Equivalent System
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

            Solving Systems Without Unique Solutions
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

            Chapter 3 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

            Identifying a Matrix Element
              Curriculum Standards: Use appropriate tools strategically. 

            Solving a System Using a Matrix
              Curriculum Standards: Use appropriate tools strategically. 

            Using a Calculator to Solve a Linear System
              Curriculum Standards: Use appropriate tools strategically. 

            Chapter 3 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. 

            Homework Video Tutor: Algebraic expressions and order of operations
              Curriculum Standards: Reason abstractly and quantitatively. 

            Homework Video Tutor: Identifying a matrix element
              Curriculum Standards: Use appropriate tools strategically. 

            Homework Video Tutor: Solving linear systems using substitution
              Curriculum Standards: Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. 

            Chapter 12 Get Ready
              Curriculum Standards: Reason abstractly and quantitatively. Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

            Adding and Subtracting Matrices

               Student eText Lesson 12-1
                 Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Adding and Subtracting Matrices

                  Solving a Matrix Equation
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

                  Using Identity and Opposite Matrices
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

                  Finding Unknown Matrix Values
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 3: Lesson Check and Step 4: Practice

                  12-1 Virtual Nerd� Tutorial: How Do You Add Matrices?
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

               12-1 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 5: Assess and Remediate

                  12-1 Lesson Quiz
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

            Matrix Multiplication

               Student eText Lesson 12-2
                 Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using Scalar Products
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

                  Solving a Matrix Equation With Scalars
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

                  Multiplying Matrices
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

                  Applying Matrix Multiplication
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

                  Determining Whether Product Matrices Exist
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 3: Lesson Check and Step 4: Practice

                  12-2 Virtual Nerd� Tutorial: How Do You Multiply a Matrix by a Scalar?
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

               12-2 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 5: Assess and Remediate

                  12-2 Lesson Quiz
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

            Determinants and Inverses

               Student eText Lesson 12-3

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Determining Whether Matrices are Inverses

                  Evaluating the Determinants of Matrices

                  Finding the Area of a Polygon

                  Finding the Inverse of a Matrix

                  Encoding and Decoding With Matrices

               Step 3: Lesson Check and Step 4: Practice

                  12-3 Virtual Nerd� Tutorial: How Do You Find the Determinant of a 2x2 Matrix?

                  12-3 Virtual Nerd� Tutorial: How Do You Find the Inverse of a 2x2 Matrix?

               12-3 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  12-3 Lesson Quiz

            Chapter 12 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Look for and express regularity in repeated reasoning. 

            Chapter 12 Mid-Chapter Quiz
              Curriculum Standards: Look for and express regularity in repeated reasoning. 

            Inverse Matrices and Systems

               Student eText Lesson 12-4

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Solving Equations Using an Inverse Matrix

                  Writing Systems as a Matrix Equation

                  Solving a System of Two Equations

                  Solving a System of Three Equations

               Step 3: Lesson Check and Step 4: Practice

                  12-4 Virtual Nerd� Tutorial: What is a Coefficient Matrix?

               12-4 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  12-4 Lesson Quiz

            The Big Burger

            Geometric Transformations

               Student eText Lesson 12-5

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Translating a Figure

                  Dilating a Figure

                  Rotating a Figure

                  Reflecting a Figure

               Step 3: Lesson Check and Step 4: Practice

                  12-5 Virtual Nerd� Tutorial: How are Matrices Used to Translate a Figure?

               12-5 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  12-5 Lesson Quiz

            Vectors

               Student eText Lesson 12-6

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Representing a Vector

                  Rotating a Vector

                  Adding and Subtracting Vectors

                  Scalar Multiplication

                  Finding Dot Products

               Step 3: Lesson Check and Step 4: Practice

                  12-6 Virtual Nerd� Tutorial: What is a Vector?

               12-6 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  12-6 Lesson Quiz

            Chapter 12 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Look for and express regularity in repeated reasoning. 

            Chapter 12 Test
              Curriculum Standards: Look for and express regularity in repeated reasoning. 

         Using the Fundamental Counting Principle
           Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         Finding the Number of Permutations of n Items
           Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         Finding nPr
           Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         Finding nCr
           Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         Identifying Whether Order Is Important
           Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         11-1 Virtual Nerd� Tutorial: What is the Fundamental Counting Principle?
           Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. 

         Finding Experimental Probability
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

         Conditional Probability in Statistics
           Curriculum Standards: Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

         Adding and Subtracting Matrices

         Solving a Matrix Equation
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         Using Identity and Opposite Matrices
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         Finding Unknown Matrix Values
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         12-1 Virtual Nerd� Tutorial: How Do You Add Matrices?
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         12-1 Virtual Nerd� Tutorial: How Do You Find Values For x and y to Make Two Matrices Equal?
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         Using the Conditional Probability Formula
           Curriculum Standards: Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

         Using a Tree Diagram
           Curriculum Standards: Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

         12-6 Virtual Nerd� Tutorial: What is a Vector?

         11-4 Virtual Nerd� Tutorial: What is Conditional Probability?
           Curriculum Standards: Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

         Making a Fair Decision
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Model with mathematics. 

         Using Random Numbers
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Model with mathematics. 

         Modeling with a Simulation
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Model with mathematics. 

         Using Scalar Products
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         Solving a Matrix Equation With Scalars
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         Multiplying Matrices
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         Applying Matrix Multiplication
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         Determining Whether Product Matrices Exist
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         12-2 Virtual Nerd� Tutorial: How Do You Multiply a Matrix by a Scalar?
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         Using Probability to Analyze Decisions
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Model with mathematics. 

         11-5 Virtual Nerd� Tutorial: How Do You Use a Simulation to Solve a Problem?
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Model with mathematics. 

         Finding Measures of Central Tendency
           Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

         Identifying an Outlier
           Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

         Comparing Data Sets
           Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

         12-2 Virtual Nerd� Tutorial: How Do You Multiply Two 2x2 Matrices?
           Curriculum Standards: Look for and express regularity in repeated reasoning. 

         Determining Whether Matrices are Inverses

         Evaluating the Determinants of Matrices

         Finding the Area of a Polygon

         Finding the Inverse of a Matrix

         Using a Simulation
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

         Finding Theoretical Probability
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

         Finding Probability Using Combinatorics
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

         Using a Box-and-Whisker Plot
           Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

         Finding Percentiles
           Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

         11-6 Virtual Nerd� Tutorial: How Do You Find the Mean of a Data Set?
           Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

         Finding Variance and Standard Deviation
           Curriculum Standards: Use appropriate tools strategically. Look for and express regularity in repeated reasoning. 

         Using a Calculator to Find Standard Deviation
           Curriculum Standards: Use appropriate tools strategically. Look for and express regularity in repeated reasoning. 

         Encoding and Decoding With Matrices

         12-3 Virtual Nerd� Tutorial: How Do You Find the Determinant of a 2x2 Matrix?

         12-3 Virtual Nerd� Tutorial: How Do You Find the Inverse of a 2x2 Matrix?

         Solving Equations Using an Inverse Matrix

         Writing Systems as a Matrix Equation

         Finding Geometric Probability
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

         11-2 Virtual Nerd� Tutorial: How Do You Find the Probability of a Simple Event?
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Attend to precision. 

         Classifying Events
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

         Finding the Probability of Independent Events
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

         Mutually Exclusive Events
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

         Using Standard Deviation to Describe Data
           Curriculum Standards: Use appropriate tools strategically. Look for and express regularity in repeated reasoning. 

         11-7 Virtual Nerd� Tutorial: How Do You Find the Standard Deviation of a Data Set?
           Curriculum Standards: Use appropriate tools strategically. Look for and express regularity in repeated reasoning. 

         Analyzing Sampling Methods
           Curriculum Standards: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

         Analyzing Study Methods
           Curriculum Standards: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

         Designing a Survey
           Curriculum Standards: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

         Solving a System of Two Equations

         Solving a System of Three Equations

         12-4 Virtual Nerd� Tutorial: What is a Coefficient Matrix?

         Translating a Figure

         Dilating a Figure

         Probability of Mutually Exclusive Events
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

         Finding Probability
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

         11-8 Virtual Nerd� Tutorial: What is an Unbiased Sample?
           Curriculum Standards: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

         Using a Formula to Find Probabilities

         Expanding Binomials

         Applying Binomial Probability

         11-9 Virtual Nerd� Tutorial: How Do You Expand a Power of a Binomial Sum Using the Binomial Theorem?

         Rotating a Figure

         Reflecting a Figure

         12-5 Virtual Nerd� Tutorial: How are Matrices Used to Translate a Figure?

         Representing a Vector

         Rotating a Vector

         11-3 Virtual Nerd� Tutorial: How Do You Find the Probability of Independent Events?
           Curriculum Standards: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Attend to precision. 

         Finding Conditional Probability
           Curriculum Standards: Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

         Analyzing Normally Distributed Data
           Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

         Sketching a Normal Curve
           Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

         Analyzing a Normal Distribution
           Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

         11-10 Virtual Nerd� Tutorial: What is a Normal Distribution?
           Curriculum Standards: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. 

         Adding and Subtracting Vectors

         Scalar Multiplication

         Finding Dot Products

         Benchmark Test 6
           Curriculum Standards: Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Attend to precision. Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Use appropriate tools strategically. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Reason abstractly and quantitatively. Model with mathematics. Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. Look for and express regularity in repeated reasoning. Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

         Periodic Functions and Trigonometry

            Finding Points of Discontinuity

            Finding Vertical Asymptotes

            Finding Horizontal Asymptotes

            Graphing a Rational Function

            Chapter 8 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

            Simplifying a Complex Fraction
              Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

            Using Rational Expressions to Solve a Problem
              Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

            Chapter 8 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. 

            Generating a Sequence Using an Explicit Formula
              Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

            Writing a Recursive Definition for a Sequence
              Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

            Writing an Explicit Formula for a Sequence
              Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

            Chapter 9 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Reason abstractly and quantitatively. Model with mathematics. Use appropriate tools strategically. Attend to precision. Find partial sums of arithmetic and geometric series and represent them using sigma notation. 

            Writing an Equation of a Translated Ellipse

            Analyzing a Hyperbola from Its Equation

            Identifying a Translated Conic Section

            Modeling With a Conic Section

            Chapter 10 MathXL: End-of-Chapter Practice and Review

            Homework Video Tutor: Graphing a rational function using vertical and horizontal asymptotes

            Homework Video Tutor: Dividing a fraction by a fraction
              Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). 

            Homework Video Tutor: Using the recursive formula to generate patterns
              Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

            Homework Video Tutor: Using the explicit formula to generate patterns
              Curriculum Standards: Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

            Homework Video Tutor: Identifying a translated conic section

            Chapter 13 Get Ready
              Curriculum Standards: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

            Exploring Periodic Data

               Student eText Lesson 13-1
                 Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               13-1 Dynamic Activity: Modeling With Trigonometric Functions
                 Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Identifying Cycles and Periods
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. 

                  Identifying Periodic Functions
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. 

                  Amplitude and Midline of a Periodic Function
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. 

                  Using a Periodic Function to Solve a Problem
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               Step 3: Lesson Check and Step 4: Practice

                  13-1 Virtual Nerd� Tutorial: What is a Periodic Function?
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               13-1 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. 

               Step 5: Assess and Remediate

                  13-1 Lesson Quiz
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. 

            Angles and the Unit Circle

               Student eText Lesson 13-2
                 Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Measuring Angles in Standard Position
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

                  Sketching Angles in Standard Position
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

                  Identifying Coterminal Angles
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

                  Finding Cosines and Sines of Angles
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

                  Finding Exact Values of Cosine and Sine
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

               Step 3: Lesson Check and Step 4: Practice

                  13-2 Virtual Nerd� Tutorial: What is an Angle in Standard Position?
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

               13-2 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

               Step 5: Assess and Remediate

                  13-2 Lesson Quiz
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

            Radian Measure

               Student eText Lesson 13-3
                 Curriculum Standards: Attend to precision. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using Dimensional Analysis
                    Curriculum Standards: Attend to precision. 

                  Finding Cosine and Sine of a Radian Measure
                    Curriculum Standards: Attend to precision. 

                  Finding the Length of an Arc
                    Curriculum Standards: Attend to precision. 

                  Using Radian Measure to Solve a Problem
                    Curriculum Standards: Attend to precision. 

               Step 3: Lesson Check and Step 4: Practice

                  13-3 Virtual Nerd� Tutorial: What is a Sector and Central Angle?
                    Curriculum Standards: Attend to precision. 

               13-3 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Attend to precision. 

               Step 5: Assess and Remediate

                  13-3 Lesson Quiz
                    Curriculum Standards: Attend to precision. 

            The Sine Function

               Student eText Lesson 13-4
                 Curriculum Standards: Use appropriate tools strategically. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Estimating Sine Values Graphically
                    Curriculum Standards: Use appropriate tools strategically. 

                  Finding the Period of a Sine Curve
                    Curriculum Standards: Use appropriate tools strategically. 

                  Finding the Amplitude of a Sine Curve
                    Curriculum Standards: Use appropriate tools strategically. 

                  Sketching a Graph
                    Curriculum Standards: Use appropriate tools strategically. 

                  Graphing From a Function Rule
                    Curriculum Standards: Use appropriate tools strategically. 

                  Using the Sine Function to Model Light Waves
                    Curriculum Standards: Use appropriate tools strategically. 

               Step 3: Lesson Check and Step 4: Practice

                  13-4 Virtual Nerd� Tutorial: What Does the Graph of the Sine Function Look Like?
                    Curriculum Standards: Use appropriate tools strategically. 

               13-4 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Use appropriate tools strategically. 

               Step 5: Assess and Remediate

                  13-4 Lesson Quiz
                    Curriculum Standards: Use appropriate tools strategically. 

            What Note Was That?

            Chapter 13 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. Use appropriate tools strategically. Look for and make use of structure. 

            Chapter 13 Mid-Chapter Quiz
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. Use appropriate tools strategically. Look for and make use of structure. 

            The Cosine Function

               Student eText Lesson 13-5

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Interpreting a Graph

                  Sketching the Graph of a Cosine Function

                  Modeling With a Cosine Function

                  Solving a Cosine Equation

               Step 3: Lesson Check and Step 4: Practice

                  13-5 Virtual Nerd� Tutorial: What Does the Graph of the Cosine Function Look Like?

               13-5 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  13-5 Lesson Quiz

            The Tangent Function

               Student eText Lesson 13-6

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding Tangents Geometrically

                  Graphing a Tangent Function

                  Using the Tangent Function to Solve Problems

               Step 3: Lesson Check and Step 4: Practice

                  13-6 Virtual Nerd� Tutorial: What Does the Graph of the Tangent Function Look Like?

               13-6 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  13-6 Lesson Quiz

            Translating Sine and Cosine Functions

               Student eText Lesson 13-7
                 Curriculum Standards: Look for and make use of structure. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Identifying Phase Shifts
                    Curriculum Standards: Look for and make use of structure. 

                  Graphing Translations
                    Curriculum Standards: Look for and make use of structure. 

                  Graphing a Combined Translation
                    Curriculum Standards: Look for and make use of structure. 

                  Graphing a Translation of y = sin 2x
                    Curriculum Standards: Look for and make use of structure. 

                  Writing Translations
                    Curriculum Standards: Look for and make use of structure. 

                  Writing a Trigonometric Function
                    Curriculum Standards: Look for and make use of structure. 

               Step 3: Lesson Check and Step 4: Practice

                  13-7 Virtual Nerd� Tutorial: How Do You Horizontally Translate a Trigonometric Graph?
                    Curriculum Standards: Look for and make use of structure. 

               13-7 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Look for and make use of structure. 

               Step 5: Assess and Remediate

                  13-7 Lesson Quiz
                    Curriculum Standards: Look for and make use of structure. 

            Reciprocal Trigonometric Functions

               Student eText Lesson 13-8

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding Values Geometrically

                  Finding Values with a Calculator

                  Sketching a Graph
                    Curriculum Standards: Use appropriate tools strategically. 

                  Using Technology to Graph a Reciprocal Function

                  Using Reciprocal Functions to Solve a Problem

               Step 3: Lesson Check and Step 4: Practice

                  13-8 Virtual Nerd� Tutorial: What is the Secant Ratio?

               13-8 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  13-8 Lesson Quiz

            Chapter 13 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. Use appropriate tools strategically. Look for and make use of structure. 

            Chapter 13 Test
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. Use appropriate tools strategically. Look for and make use of structure. 

         Trigonometric Identities and Equations

            Solving a Quadratic Equation by Factoring

            Solving a Quadratic Equation With Tables

            Solving a Quadratic Equation by Graphing

            Using a Quadratic Equation

            Chapter 4 MathXL: End-of-Chapter Practice
              Curriculum Standards: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). 

            Finding an Equation for the Inverse
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Finding an Inverse Function
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Finding the Inverse of a Formula
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Composing Inverse Functions
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Chapter 6 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Translate expressions between radical and exponent form and simplify them using the laws of exponents. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Understand composition of functions and combine functions by composition. Determine whether a relation represented by a table, graph, or equation is a function. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. 

            Solving an Exponential Equation - Common Base
              Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

            Solving an Exponential Equation - Different Bases
              Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

            Solving an Equation With a Graph or Table
              Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

            Modeling With an Exponential Equation
              Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

            Solving a Logarithmic Equation
              Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

            Using Logarithmic Properties to Solve an Equation
              Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

            Chapter 7 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure. Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. 

            Estimating Sine Values Graphically
              Curriculum Standards: Use appropriate tools strategically. 

            Finding the Period of a Sine Curve
              Curriculum Standards: Use appropriate tools strategically. 

            Finding the Amplitude of a Sine Curve
              Curriculum Standards: Use appropriate tools strategically. 

            Sketching a Graph
              Curriculum Standards: Use appropriate tools strategically. 

            Graphing From a Function Rule
              Curriculum Standards: Use appropriate tools strategically. 

            Using the Sine Function to Model Light Waves
              Curriculum Standards: Use appropriate tools strategically. 

            Chapter 13 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. Use appropriate tools strategically. Look for and make use of structure. 

            Interpreting a Graph

            Sketching the Graph of a Cosine Function

            Modeling With a Cosine Function

            Solving a Cosine Equation

            Finding Tangents Geometrically

            Graphing a Tangent Function

            Using the Tangent Function to Solve Problems

            Chapter 13 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Attend to precision. Use appropriate tools strategically. Look for and make use of structure. 

            Homework Video Tutor: Solving quadratic equations by factoring

            Homework Video Tutor: Solving quadratic equations using completing the square

            Homework Video Tutor: Solving quadratic equations using completing the square when a does not equal 1

            Homework Video Tutor: Solving quadratic equations using the quadratic formula

            Homework Video Tutor: Finding an inverse function
              Curriculum Standards: Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. 

            Homework Video Tutor: Solving logarithmic equations
              Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

            Homework Video Tutor: Solving natural exponential equations
              Curriculum Standards: Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Look for and make use of structure. 

            Homework Video Tutor: Solving trigonometric functions
              Curriculum Standards: Use appropriate tools strategically. 

            Chapter 14 Get Ready
              Curriculum Standards: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Look for and express regularity in repeated reasoning. Determine whether a relation represented by a table, graph, or equation is a function. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. 

            Trigonometric Identities

               Student eText Lesson 14-1

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding the Domain of Validity

                  Verifying an Identity Using Basic Identities

                  Verifying a Pythagorean Identity

                  Verifying an Identity

                  Simplifying an Expression

               Step 3: Lesson Check and Step 4: Practice

                  14-1 Virtual Nerd� Tutorial: What are the Trigonometric Reciprocal Identities?

               14-1 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  14-1 Lesson Quiz

            Solving Trigonometric Equations Using Inverses

               Student eText Lesson 14-2

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using the Unit Circle

                  Using a Calculator to Find the Inverse of Sine

                  Using a Calculator to Find the Inverse of Tangent

                  Solving a Trigonometric Equation

                  Solving by Factoring

                  Using the Inverse of a Trigonometric Function

               Step 3: Lesson Check and Step 4: Practice

                  14-2 Virtual Nerd� Tutorial: How Do You Solve a Trigonometric Equation on a Given Interval?

               14-2 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  14-2 Lesson Quiz

            Right Triangles and Trigonometric Ratios

               Student eText Lesson 14-3

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Trigonometric Values Beyond the Unit Circle

                  Finding Distance

                  Finding Trigonometric Ratios

                  Using a Trigonometric Ratio to Solve a Problem

                  Finding an Angle Measure

                  Using an Inverse Trigonometric Ratio

               Step 3: Lesson Check and Step 4: Practice

                  14-3 Virtual Nerd� Tutorial: What is the Sine Ratio?

               14-3 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  14-3 Lesson Quiz

            Ramp Up Your Design

            Chatper 14 MathXL: Mid-Chapter Practice and Review
              Curriculum Standards: Look for and express regularity in repeated reasoning. 

            Chapter 14 Mid-Chapter Quiz
              Curriculum Standards: Look for and express regularity in repeated reasoning. 

            Area and the Law of Sines

               Student eText Lesson 14-4

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Finding the Area of a Triangle

                  Finding a Side of a Triangle

                  Finding an Angle of a Triangle

                  Using the Law of Sines to Solve a Problem

               Step 3: Lesson Check and Step 4: Practice

                  14-4 Virtual Nerd� Tutorial: What is the Law of Sines?

               14-4 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  14-4 Lesson Quiz

            The Law of Cosines

               Student eText Lesson 14-5

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Using the Law of Cosines to Solve a Problem

                  Finding an Angle Measure

                  Finding an Angle Measure

               Step 3: Lesson Check and Step 4: Practice

                  14-5 Virtual Nerd� Tutorial: What is the Law of Cosines?

               14-5 Student eText: Lesson Check and Practice Exercises

               Step 5: Assess and Remediate

                  14-5 Lesson Quiz

            Angle Identities

               Student eText Lesson 14-6
                 Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Verifying an Angle Identity
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

                  Deriving a Cofunction Identity
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

                  Solving a Trigonometric Equation

                  Using an Angle Difference Identity
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

                  Deriving a Sum Identity
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

                  Using an Angle Sum Identity
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 3: Lesson Check and Step 4: Practice

                  14-6 Virtual Nerd� Tutorial: What are the Trigonometric Cofunction Identities?
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

               14-6 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 5: Assess and Remediate

                  14-6 Lesson Quiz
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

            Double-Angle and Half-Angle Identities

               Student eText Lesson 14-7
                 Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 1: Interactive Learning

                  Solve It!
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

               Step 2: Guided Problem-Solving

                  Key Concept
                    Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. 

                  Deriving a Double-Angle Identity
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

                  Using a Double-Angle Identity
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

                  Verifying an Identity

                  Using Half-Angle Identities
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

                  Using a Half-Angle Identity
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 3: Lesson Check and Step 4: Practice

                  14-7 Virtual Nerd� Tutorial: What is the Trigonometric Double Angle Identity for Sine?
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

               14-7 Student eText: Lesson Check and Practice Exercises
                 Curriculum Standards: Look for and express regularity in repeated reasoning. 

               Step 5: Assess and Remediate

                  14-7 Lesson Quiz
                    Curriculum Standards: Look for and express regularity in repeated reasoning. 

            Chapter 14 MathXL: End-of-Chapter Practice and Review
              Curriculum Standards: Look for and express regularity in repeated reasoning. 

            Chapter 14 Test
              Curriculum Standards: Look for and express regularity in repeated reasoning. 

         End-of-Course Assessment
           Curriculum Standards: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Attend to precision. Model with mathematics. Solve real-world and other mathematical problems involving rational and radical functions, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise. Determine whether a relation represented by a table, graph, or equation is a function. Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient. Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, kf(x), f(kx), or f(x + k). Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. Solve systems of two or three linear equations in two or three variables algebraically and using technology. Represent real-world problems using a system of linear equations in three variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable. Use appropriate tools strategically. Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeroes, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula. Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a +/- bi for real numbers a and b. Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically with and without technology (e.g., find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3). Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division and synthetic division. Look for and express regularity in repeated reasoning. Translate expressions between radical and exponent form and simplify them using the laws of exponents. Understand composition of functions and combine functions by composition. Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse. Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeroes, domain and range, and asymptotic and end behavior. Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (.97)^t, y = (1.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression (1.15)^t can be rewritten as (1.15^1/12)^12t approx. = 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). Represent real-world problems using exponential equations in one or two variables and solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable. Know that the inverse of an exponential function is a logarithmic function. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide algebraic rational expressions. Rewrite algebraic rational expressions in equivalent forms (e.g., using laws of exponents and factoring techniques). Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. Find partial sums of arithmetic and geometric series and represent them using sigma notation. Understand the multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities. Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models. Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities. Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, interquartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data. Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 

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            Activities, Games and Puzzles
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            Reteaching
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            Teacher eText Lesson 3-3
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Teacher eText Lesson 3-4
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Teacher eText Lesson 3-5
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Teacher eText Lesson 3-6
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Additional Vocabulary Support
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            Enrichment
              Intended Role: Instructor

            Reteaching
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            Mathematical Modeling in 3 Acts: Teacher Support
              Intended Role: Instructor

            Mathematical Modeling in 3 Acts: Student Worksheets
              Intended Role: Instructor

            Activities, Games and Puzzles Answers
              Intended Role: Instructor

            All-In-One Teaching Resources Answers
              Intended Role: Instructor

            Chapter Project
              Intended Role: Instructor

            Chapter Project Teacher Notes
              Intended Role: Instructor

            Cumulative Review
              Intended Role: Instructor

            Extra Practice
              Intended Role: Instructor

            Extra Practice Answers
              Intended Role: Instructor

            Find the Errors!
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            Find the Errors! Answers
              Intended Role: Instructor

            Performance Task
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            Project Manager
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            Quiz 1 Form G
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            Chapter 4 Teacher eText
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            My Math Video
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            Teacher eText Lesson 4-1
              Intended Role: Instructor

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            Reteaching
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            Teacher eText Lesson 4-2
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Reteaching
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            Teacher eText Lesson 4-3
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Additional Vocabulary Support
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            Reteaching
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            Mathematical Modeling in 3 Acts: Student Worksheets
              Intended Role: Instructor

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              Intended Role: Instructor

            Activities, Games and Puzzles
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            Teacher eText Lesson 4-4
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Teacher eText Lesson 4-5
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Teacher eText Lesson 4-6
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Teacher eText Lesson 4-7
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Teacher eText Lesson 4-8
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Teacher eText Lesson 4-9
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Activities, Games and Puzzles Answers
              Intended Role: Instructor

            All-In-One Teaching Resources Answers
              Intended Role: Instructor

            Chapter Project
              Intended Role: Instructor

            Chapter Project Teacher Notes
              Intended Role: Instructor

            Cumulative Review
              Intended Role: Instructor

            Extra Practice
              Intended Role: Instructor

            Extra Practice Answers
              Intended Role: Instructor

            Find the Errors!
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            Find the Errors! Answers
              Intended Role: Instructor

            Performance Task
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            Quiz 1 Form G
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            Project Manager
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            Chapter 5 Teacher eText
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            Chapter 5 My Math Video
              Intended Role: Instructor

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            Teacher eText Lesson 5-1
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Teacher eText Lesson 5-2
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Think About a Plan
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            Teacher eText Lesson 5-3
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Enrichment
              Intended Role: Instructor

            Reteaching
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            Additional Vocabulary Support
              Intended Role: Instructor

            Mathematical Modeling in 3 Acts: Student Worksheets
              Intended Role: Instructor

            Mathematical Modeling in 3 Acts: Teacher Support
              Intended Role: Instructor

            Activities, Games and Puzzles
              Intended Role: Instructor

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            Reteaching
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            Teacher eText Lesson 5-4
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Reteaching
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            Reteaching
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            Teacher eText Lesson 5-5
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Reteaching
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            Reteaching
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            Teacher eText Lesson 5-6
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Additional Vocabulary Support
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            Enrichment
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            Reteaching
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            Activities, Games and Puzzles
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            Additional Vocabulary Support
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            Enrichment
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            Practice Form G
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            Reteaching
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            Teacher eText Lesson 5-7
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Enrichment
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            Reteaching
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Reteaching
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            Teacher eText Lesson 5-8
              Intended Role: Instructor

            Activities, Games and Puzzles
              Intended Role: Instructor

            Additional Vocabulary Support
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            Enrichment
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            Reteaching
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Enrichment
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            Practice Form G
              Intended Role: Instructor

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            Reteaching
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            Teacher eText Lesson 5-9
              Intended Role: Instructor

            Activities, Games and Puzzles
              Intended Role: Instructor

            Additional Vocabulary Support
              Intended Role: Instructor

            Enrichment
              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Activities, Games and Puzzles Answers
              Intended Role: Instructor

            All-In-One Teaching Resources Answers
              Intended Role: Instructor

            Chapter Project
              Intended Role: Instructor

            Chapter Project Teacher Notes
              Intended Role: Instructor

            Cumulative Review
              Intended Role: Instructor

            Extra Practice
              Intended Role: Instructor

            Extra Practice Answers
              Intended Role: Instructor

            Find the Errors!
              Intended Role: Instructor

            Find the Errors! Answers
              Intended Role: Instructor

            Performance Task
              Intended Role: Instructor

            Project Manager
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            Quiz 1 Form G
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              Intended Role: Instructor

            Quiz 2 Form G
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            Chapter 6 Teacher eText
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            Chapter 6 My Math Video
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Teacher eText Lesson 6-1
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Reteaching
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            Teacher eText Lesson 6-2
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Reteaching
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            Practice Form G
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            Teacher eText Lesson 6-3
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Reteaching
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            Activities, Games and Puzzles
              Intended Role: Instructor

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            Practice Form G
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            Reteaching
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            Teacher eText Lesson 6-4
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Reteaching
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              Intended Role: Instructor

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            Practice Form G
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            Teacher eText Lesson 6-5
              Intended Role: Instructor

            Activities, Games and Puzzles
              Intended Role: Instructor

            Additional Vocabulary Support
              Intended Role: Instructor

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              Intended Role: Instructor

            Reteaching
              Intended Role: Instructor

            Mathematical Modeling in 3 Acts: Student Worksheets
              Intended Role: Instructor

            Mathematical Modeling in 3 Acts: Teacher Support
              Intended Role: Instructor

            Activities, Games and Puzzles
              Intended Role: Instructor

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            Practice Form G
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            Reteaching
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            Teacher eText Lesson 6-6
              Intended Role: Instructor

            Activities, Games and Puzzles
              Intended Role: Instructor

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            Reteaching
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            Reteaching
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            Teacher eText Lesson 6-7
              Intended Role: Instructor

            Activities, Games and Puzzles
              Intended Role: Instructor

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            Teacher eText Lesson 6-8
              Intended Role: Instructor

            Activities, Games and Puzzles
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Reteaching
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            Activities, Games and Puzzles Answers
              Intended Role: Instructor

            All-In-One Teaching Resources Answers
              Intended Role: Instructor

            Chapter Project
              Intended Role: Instructor

            Chapter Project Teacher Notes
              Intended Role: Instructor

            Cumulative Review
              Intended Role: Instructor

            Extra Practice
              Intended Role: Instructor

            Extra Practice Answers
              Intended Role: Instructor

            Find the Errors!
              Intended Role: Instructor

            Find the Errors! Answers
              Intended Role: Instructor

            Performance Task
              Intended Role: Instructor

            Project Manager
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            Quiz 1 Form G
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            Chapter 7 Teacher eText
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            Chapter 7 My Math Video
              Intended Role: Instructor

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            Algebra 2 Student Edition eText

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