toc.md

Table of Contents

• Getting Started
  • About this Course
  • Teachers Start Here
    • Quick Start
    • Using Desmos
    • Additional Resources
  • Students Start Here
    • Quick Start
    • Using Desmos
    • Additional Resources
• Supporting All Learners
  • English Language Learners (ELL)
    • Standards Overview
    • Aligning to the ELPS
    • Navigating Resources (ELL)
    • Theory of Action
    • Mathematical Language Routines
    • Resources and References for ELL
  • Students with Disabilities (SWD)
    • Universal Design for Learning
    • Inclusion in Texas Learning Abilities
    • Navigating Resources (SWD)
    • Curriculum Features Supporting Access
    • Instructional Strategies Supporting Access
    • Strategies to Support Mathematical Processes
    • Modifications & Accommodations for Specific Learning Disabilities
    • Resources and References for Differentiated Math
  • Gifted Students
    • Gifted and Talented Standards Overview
    • Extending the Learning
    • Resources and References
  • Preparing for Success
    • Study Tips
    • Creating Your Best Self
    • Building Relationships
• Unit 1: Linear Equations
  • Unit 1 Teacher Guide
    • Unit 1 Overview and Readiness
    • Unit 1 Narrative
    • Unit 1 Family Support Materials
    • Building Character: Social Intelligence
    • Supporting English Language Proficiency Standards (ELPS)
  • Unit 1 Overview and Readiness
    • Unit 1 Overview: Why Should I Care?
    • Unit 1 Overview: Am I Ready to Learn This?
    • Question #1: Solve Linear Equations
    • Solve Linear Equations: Mini-Lesson Review
    • Question #2: Classify Equations
    • Classify Equations: Mini-Lesson Review
    • Question #3: Find Coordinates
    • Find Coordinates: Mini-Lesson Review
    • Unit 1 Overview: Wrap Up
  • Unit 1 Section A Overview: Writing and Modeling with Equations
  • Lesson 1.1: Teacher Guide: Exploring Expressions and Equations
    • 1.1.0: Lesson Overview
    • 1.1.1: Understanding Value
    • 1.1.2: Creating Expressions to Estimate Cost, Part 1
    • 1.1.3: Understanding Constraints
    • 1.1.4: Creating Expressions to Estimate Costs, Part 2
    • 1.1.5: Practice
    • 1.1.6: Lesson Synthesis
  • Lesson 1.1: Exploring Expressions and Equations
    • 1.1.0: Lesson Overview
    • 1.1.1: Understanding Value
    • 1.1.2: Creating Expressions to Estimate Cost, Part 1
    • 1.1.2: Self Check
    • 1.1.2: Additional Resources
    • 1.1.3: Understanding Constraints
    • 1.1.3: Self Check
    • 1.1.3: Additional Resources
    • 1.1.4: Creating Expressions to Estimate Cost, Part 2
    • 1.1.5: Practice
    • 1.1.6: Lesson Summary
  • Lesson 1.2 Teacher Guide: Writing Equations to Model Relationships, Part 1
    • 1.2.0: Lesson Overview
    • 1.2.1: Finding the Percent of 200
    • 1.2.2: Modeling with Equations to Find Edges in Platonic Solids
    • 1.2.3: Writing Equations to Represent Relationships
    • 1.2.4 Writing Equations to Represent Relationships with Percents
    • 1.2.5: Writing Equations to Represent T-Shirts
    • 1.2.6: Practice
    • 1.2.7: Lesson Synthesis
  • Lesson 1.2: Writing Equations to Model Relationships, Part 1
    • 1.2.0: Lesson Overview
    • 1.2.1: Finding the Percent of 200
    • 1.2.2: Modeling with Equations to Find Edges in Platonic Solids
    • 1.2.2: Self Check
    • 1.2.2: Additional Resources
    • 1.2.3: Writing Equations to Represent Relationships
    • 1.2.3: Self Check
    • 1.2.3: Additional Resources
    • 1.2.4: Writing Equations to Represent Relationships with Percentages
    • 1.2.4: Self Check
    • 1.2.4: Additional Resources
    • 1.2.5: Writing Equations to Represent T-Shirts
    • 1.2.6: Practice
    • 1.2.7: Lesson Summary
  • Lesson 1.3 Teacher Guide: Writing Equations to Model Relationships, Part 2
    • 1.3.0: Lesson Overview
    • 1.3.1: Finding a Relationship between x and y
    • 1.3.2: Describing Relationships Using Words and Equations
    • 1.3.3: Identifying and Representing Relationships
    • 1.3.4: Writing an Equation to Represent a Relationship
    • 1.3.5: Practice
    • 1.3.6: Lesson Synthesis
  • Lesson 1.3: Writing Equations to Model Relationships, Part 2
    • 1.3.0: Lesson Overview
    • 1.3.1: Finding a Relationship between 𝒙 and 𝒚
    • 1.3.2: Describing Relationships Using Words and Equations
    • 1.3.2: Self Check
    • 1.3.2: Additional Resources
    • 1.3.3: Identifying and Representing Relationships
    • 1.3.3: Self Check
    • 1.3.3: Additional Resources
    • 1.3.4: Writing an Equation to Represent a Relationship
    • 1.3.5: Practice
    • 1.3.6: Lesson Summary
  • Lesson 1.4 Teacher Guide: Equations and Their Solutions
    • 1.4.0: Lesson Overview
    • 1.4.1: Finding the Solution to an Equation in One Variable, Part 1
    • 1.4.2: Writing Equations to Represent Constraints
    • 1.4.3 Finding the Solution to an Equation in Two Variables
    • 1.4.4 Finding the Solution to an Equation in One Variable, Part 2
    • 1.4.5: Practice
    • 1.4.6: Lesson Synthesis
  • Lesson 1.4: Equations and Their Solutions
    • 1.4.0: Lesson Overview
    • 1.4.1: Finding the Solution to an Equation in One Variable, Part 1
    • 1.4.2: Writing Equations to Represent Constraints
    • 1.4.2: Self Check
    • 1.4.2: Additional Resources
    • 1.4.3: Finding the Solution to an Equation in Two Variables
    • 1.4.3: Self Check
    • 1.4.3: Additional Resources
    • 1.4.4: Finding the Solution to an Equation in One Variable, Part 2
    • 1.4.5: Practice
    • 1.4.6: Lesson Summary
  • Lesson 1.5 Teacher Guide: Equations and Their Graphs
    • 1.5.0: Lesson Overview
    • 1.5.1: Analyzing Graphs of Linear Equations
    • 1.5.2 Graphing Linear Functions in Two Variables
    • 1.5.3: Examining an Equation in Two Variables and Its Graph, Part 1
    • 1.5.4: Writing, Graphing, and Solving a Linear Equation
    • 1.5.5: Examining an Equation in Two Variables and Its Graph, Part 2
    • 1.5.6: Practice
    • 1.5.7: Lesson Synthesis
  • Lesson 1.5: Equations and Their Graphs
    • 1.5.0: Lesson Overview
    • 1.5.1: Analyzing Graphs of Linear Equations
    • 1.5.2 Graphing Linear Functions in Two Variables
    • 1.5.2 Self Check
    • 1.5.2 Additional Resources
    • 1.5.3: Examining an Equation in Two Variables and Its Graph, Part 1
    • 1.5.3: Self Check
    • 1.5.3: Additional Resources
    • 1.5.4: Writing, Graphing, and Solving a Linear Equation
    • 1.5.4: Self Check
    • 1.5.4: Additional Resources
    • 1.5.5: Examining an Equation in Two Variables and Its Graph, Part 2
    • 1.5.6: Practice
    • 1.5.7: Lesson Summary
  • Unit 1 Section B Overview: Manipulating Equations and Understanding Their Structure
  • Lesson 1.6 Teacher Guide: Equivalent Equations
    • 1.6.0: Lesson Overview
    • 1.6.1: Exploring Equivalent Expressions
    • 1.6.2: Expressing Relationships as Equations
    • 1.6.3: Exploring Related Equations
    • 1.6.4: Recognizing Related Equations
    • 1.6.5: Practice
    • 1.6.6: Lesson Synthesis
  • Lesson 1.6: Equivalent Equations
    • 1.6.0: Lesson Overview
    • 1.6.1: Exploring Equivalent Expressions
    • 1.6.2: Expressing Relationships as Equations
    • 1.6.2: Self Check
    • 1.6.2: Additional Resources
    • 1.6.3: Exploring Related Equations
    • 1.6.3: Self Check
    • 1.6.3: Additional Resources
    • 1.6.4: Recognizing Related Equations
    • 1.6.5: Practice
    • 1.6.6: Lesson Summary
  • Lesson 1.7 Teacher Guide: Explaining Steps for Rewriting Equations
    • 1.7.0: Lesson Overview
    • 1.7.1: Determining if Zero Is a Solution
    • 1.7.2: Explaining Acceptable Moves to Solve an Equation
    • 1.7.3: Understanding Equations with No Solution or Infinitely Many
    • 1.7.4: Solving Equations by Dividing Values
    • 1.7.5: Practice
    • 1.7.6: Lesson Synthesis
  • Lesson 1.7: Explaining Steps for Rewriting Equations
    • 1.7.0: Lesson Overview
    • 1.7.1: Determining if Zero Is a Solution
    • 1.7.2: Explaining Acceptable Moves to Solve an Equation
    • 1.7.2: Self Check
    • 1.7.2: Additional Resources
    • 1.7.3: Understanding Equations with No Solution or Infinitely Many
    • 1.7.3: Self Check
    • 1.7.3: Additional Resources
    • 1.7.4: Solving Equations by Dividing Values
    • 1.7.5: Practice
    • 1.7.6: Lesson Summary
  • Lesson 1.8 Teacher Guide: Choosing the Correct Variable to Solve For, Part 1
    • 1.8.0: Lesson Overview
    • 1.8.1: Expressing Relationships between Two Quantities
    • 1.8.2: Identifying the Most Useful Form of an Equation
    • 1.8.3: Writing Equations and Isolating Variables
    • 1.8.4: Writing Equations Given Dimensions of Shapes
    • 1.8.5: Practice
    • 1.8.6: Lesson Synthesis
  • Lesson 1.8: Choosing the Correct Variable to Solve For, Part 1
    • 1.8.0: Lesson Overview
    • 1.8.1: Expressing Relationships between Two Quantities
    • 1.8.2: Identifying the Most Useful Form of an Equation
    • 1.8.2: Self Check
    • 1.8.2: Additional Resources
    • 1.8.3: Writing Equations and Isolating Variables
    • 1.8.3: Self Check
    • 1.8.3: Additional Resources
    • 1.8.4: Writing Equations Given Dimensions of Shapes
    • 1.8.5: Practice
    • 1.8.6: Lesson Summary
  • Lesson 1.9 Teacher Guide: Choosing the Correct Variable to Solve For, Part 2
    • 1.9.0: Lesson Overview
    • 1.9.1: Rearranging an Equation in Three Variables
    • 1.9.2: Writing an Equation to Represent a Constraint
    • 1.9.3: Writing and Rearranging Equations in Two Variables
    • 1.9.4: Solving for a Specified Variable
    • 1.9.5: Practice
    • 1.9.6: Lesson Synthesis
  • Lesson 1.9: Choosing the Correct Variable to Solve For, Part 2
    • 1.9.0: Lesson Overview
    • 1.9.1: Rearranging an Equation in Three Variables
    • 1.9.2: Writing an Equation to Represent a Constraint
    • 1.9.2: Self Check
    • 1.9.2: Additional Resources
    • 1.9.3: Writing and Rearranging Equations in Two Variables
    • 1.9.3: Self Check
    • 1.9.3: Additional Resources
    • 1.9.4: Solving for a Specified Variable
    • 1.9.5: Practice
    • 1.9.6: Lesson Summary
  • Lesson 1.10 Teacher Guide: Connecting Equations to Graphs, Part 1
    • 1.10.0: Lesson Overview
    • 1.10.1: Interpreting Equations in Context
    • 1.10.2: Graphing Equations in Context
    • 1.10.3: Writing and Graphing Equations in Standard Form
    • 1.10.4: Matching Equations and Graphs
    • 1.10.5: Practice
    • 1.10.6: Lesson Synthesis
  • Lesson 1.10: Connecting Equations to Graphs, Part 1
    • 1.10.0: Lesson Overview
    • 1.10.1: Interpreting Equations in Context
    • 1.10.2: Graphing Equations in Context
    • 1.10.2: Self Check
    • 1.10.2: Additional Resources
    • 1.10.3: Writing and Graphing Equations in Standard Form
    • 1.10.3: Self Check
    • 1.10.3: Additional Resources
    • 1.10.4: Matching Equations and Graphs
    • 1.10.5: Practice
    • 1.10.6: Lesson Summary
  • Lesson 1.11 Teacher Guide: Connecting Equations to Graphs, Part 2
    • 1.11.0: Lesson Overview
    • 1.11.1: Applying the Distributive Property to Rewrite Expressions
    • 1.11.2: Relating Two-Variable Equations, Their Graphs, and Situations
    • 1.11.3: Reasoning Symbolically and Abstractly about Linear Equations
    • 1.11.4: Identifying the Features of a Graph
    • 1.11.5: Practice
    • 1.11.6: Lesson Synthesis
  • Lesson 1.11: Connecting Equations to Graphs, Part 2
    • 1.11.0: Lesson Overview
    • 1.11.1: Applying the Distributive Property to Rewrite Expressions
    • 1.11.2: Relating Two-Variable Equations, Their Graphs, and Situations
    • 1.11.2: Self Check
    • 1.11.2: Additional Resources
    • 1.11.3: Reasoning Symbolically and Abstractly about Linear Equations
    • 1.11.3: Self Check
    • 1.11.3: Additional Resources
    • 1.11.4: Identifying the Features of a Graph
    • 1.11.5: Practice
    • 1.11.6: Lesson Summary
  • Unit 1 Section C Overview: Writing Linear Equations
  • Lesson 1.12 Teacher Guide: Writing the Equation of a Line
    • 1.12.0: Lesson Overview
    • 1.12.1: Using the Slope Formula
    • 1.12.2: Writing an Equation Given the Slope and y-Intercept
    • 1.12.3: Writing an Equation Given the Slope and a Point
    • 1.12.4: Writing Equations in Different Forms
    • 1.12.5: Writing an Equation Given Two Points
    • 1.12.6: Choosing a Method to Write an Equation
    • 1.12.7: Practice
    • 1.12.8: Lesson Synthesis
  • Lesson 1.12: Writing the Equation of a Line
    • 1.12.0: Lesson Overview
    • 1.12.1: Using the Slope Formula
    • 1.12.2: Writing an Equation Given the Slope and y-Intercept
    • 1.12.2: Self Check
    • 1.12.2: Additional Resources
    • 1.12.3: Writing an Equation Given the Slope and a Point
    • 1.12.3: Self Check
    • 1.12.3: Additional Resources
    • 1.12.4: Writing Equations in Different Forms
    • 1.12.4 Self Check
    • 1.12.4 Additional Resources
    • 1.12.5: Writing an Equation Given Two Points
    • 1.12.5: Self Check
    • 1.12.5: Additional Resources
    • 1.12.6: Choosing a Method to Write an Equation
    • 1.12.7: Practice
    • 1.12.8: Lesson Summary
  • Lesson 1.13 Teacher Guide: Lines from Tables and Graphs
    • 1.13.0: Lesson Overview
    • 1.13.1: Writing Linear Equations
    • 1.13.2: Creating Tables From Verbal Descriptions
    • 1.13.3: Matching Tables, Equations, and Graphs
    • 1.13.4: Creating a Table from an Equation
    • 1.13.5: Practice
    • 1.13.6: Lesson Synthesis
  • Lesson 1.13: Lines from Tables and Graphs
    • 1.13.0: Lesson Overview
    • 1.13.1: Writing Linear Equations
    • 1.13.2: Creating Tables from Verbal Descriptions
    • 1.13.2: Self Check
    • 1.13.2: Additional Resources
    • 1.13.3: Matching Tables, Equations, and Graphs
    • 1.13.3: Self Check
    • 1.13.3: Additional Resources
    • 1.13.4: Creating a Table from an Equation
    • 1.13.5: Practice
    • 1.13.6: Lesson Summary
  • Lesson 1.14 Teacher Guide: Writing Equations of Parallel and Perpendicular Lines
    • 1.14.0: Lesson Overview
    • 1.14.1: Using Point-Slope Form to Write the Equation of a Line
    • 1.14.2 Writing Equations for Point-Slope and Slope-Intercept
    • 1.14.3: Writing an Equation of a Line Parallel to a Given Line
    • 1.14.4: Writing an Equation of a Line Perpendicular to a Given Line
    • 1.14.5: Writing an Equation of a Line Parallel or Perpendicular to an Axis
    • 1.14.6: Drawing Parallel and Perpendicular Lines
    • 1.14.7: Practice
    • 1.14.8: Lesson Synthesis
  • Lesson 1.14: Writing Equations of Parallel and Perpendicular Lines
    • 1.14.0: Lesson Overview
    • 1.14.1: Using Point-Slope Form to Write the Equation of a Line
    • 1.14.2 Writing Equations for Point-Slope and Slope-Intercept
    • 1.14.2 Self Check
    • 1.14.2 Additional Resources
    • 1.14.3: Writing an Equation of a Line Parallel to a Given Line
    • 1.14.3: Self Check
    • 1.14.3: Additional Resources
    • 1.14.4: Writing an Equation of a Line Perpendicular to a Given Line
    • 1.14.4: Self Check
    • 1.14.4: Additional Resources
    • 1.14.5: Writing an Equation of a Line Parallel or Perpendicular to an Axis
    • 1.14.5: Self Check
    • 1.14.5: Additional Resources
    • 1.14.6: Drawing Parallel and Perpendicular Lines
    • 1.14.7: Practice
    • 1.14.8: Lesson Summary
  • Lesson 1.15 Teacher Guide: Direct Variation
    • 1.15.0: Lesson Overview
    • 1.15.1: Solving Proportions
    • 1.15.2: Modeling Equations Using Direct Variation
    • 1.15.3: Using Direct Variation to Solve Application Problems, Part 1
    • 1.15.4: Using Direct Variation to Solve Application Problems, Part 2
    • 1.15.5: Practice
    • 1.15.6: Lesson Synthesis
  • Lesson 1.15: Direct Variation
    • 1.15.0: Lesson Overview
    • 1.15.1: Solving Proportions
    • 1.15.2: Modeling Equations Using Direct Variation
    • 1.15.2: Self Check
    • 1.15.2: Additional Resources
    • 1.15.3: Using Direct Variation to Solve Application Problems, Part 1
    • 1.15.3: Self Check
    • 1.15.3: Additional Resources
    • 1.15.4: Using Direct Variation to Solve Application Problems, Part 2
    • 1.15.5: Practice
    • 1.15.6: Lesson Summary
  • Project 1 Teacher Guide: Slopes and Intercepts
    • Project 1 Overview
    • Notice and Wonder Graph Features
    • Matching Graphs and Equations
  • Project 1: Slopes and Intercepts
    • Project 1 Overview
    • Notice and Wonder Graph Features
    • Matching Graph and Equations
  • Unit 1 Wrap Up
• Unit 2: Linear Inequalities and Systems
  • Unit 2 Teacher Guide
    • Unit 2 Overview and Readiness
    • Unit 2 Narrative
    • Unit 2 Family Support Materials
    • Building Character: Growth Mindset
    • Supporting English Language Proficiency Standards (ELPS)
  • Unit 2 Overview and Readiness
    • Unit 2 Overview: Why should I care?
    • Unit 2 Overview: Am I ready to learn this?
    • Question #1: Determine the Ordered Pair
    • Determine the Ordered Pair: Mini-Lesson Review
    • Question #2: Find the Slope and y-Intercept
    • Find the Slope and y-Intercept: Mini-Lesson Review
    • Question #3: Find x- and y-Intercepts
    • Find the x- and y-Intercepts: Mini-Lesson Review
    • Unit 2 Overview: Wrap Up
  • Section A Overview: Linear Systems
  • Lesson 2.1 Teacher Guide: Writing and Graphing Systems of Equations
    • 2.1.0: Lesson Overview
    • 2.1.1: Understanding Constraints and Values
    • 2.1.2: Writing and Graphing Equations
    • 2.1.3: Meeting Constraints
    • 2.1.4: Exploring a System of Equations
    • 2.1.5: Practice
    • 2.1.6: Lesson Synthesis
  • Lesson 2.1: Writing and Graphing Systems of Equations
    • 2.1.0: Lesson Overview
    • 2.1.1: Understanding Constraints and Values
    • 2.1.2: Writing and Graphing Equations
    • 2.1.2: Self Check
    • 2.1.2 Additional Resources
    • 2.1.3: Meeting Constraints
    • 2.1.3 Self Check
    • 2.1.3 Additional Resources
    • 2.1.4: Exploring a System of Equations
    • 2.1.5 Practice
    • 2.1.6 Lesson Summary
  • Lesson 2.2 Teacher Guide: Writing Systems of Equations
    • 2.2.0: Lesson Overview
    • 2.2.1: Interpreting Graphs of Systems of Equations
    • 2.2.2: Writing Systems of Equations from Tables
    • 2.2.3: Graphs of Systems of Equations
    • 2.2.4: Systems of Equations in the Real-World
    • 2.2.5: Practice
    • 2.2.6: Lesson Synthesis
  • Lesson 2.2: Writing Systems of Equations
    • 2.2.0: Lesson Overview
    • 2.2.1: Interpreting Graphs of Systems of Equations
    • 2.2.2: Writing Systems of Equations from Tables
    • 2.2.2: Self Check
    • 2.2.2: Additional Resources
    • 2.2.3: Graphs of Systems of Equations
    • 2.2.3: Self Check
    • 2.2.3: Additional Resources
    • 2.2.4: Systems of Equations in the Real-World
    • 2.2.5: Practice
    • 2.2.6: Lesson Summary
  • Lesson 2.3 Teacher Guide: Solving Systems by Substitution
    • 2.3.0: Lesson Overview
    • 2.3.1: Finding Connections between Graphs and Equations
    • 2.3.2: Checking Solutions in Systems
    • 2.3.3: Solving Equations Using Substitution
    • 2.3.4: Solving More Equations
    • 2.3.5: Practice
    • 2.3.6: Lesson Synthesis
  • Lesson 2.3: Solving Systems by Substitution
    • 2.3.0: Lesson Overview
    • 2.3.1: Finding Connections between Graphs and Equations
    • 2.3.2: Checking Solutions in Systems
    • 2.3.2: Self Check
    • 2.3.2: Additional Resources
    • 2.3.3: Solving Equations Using Substitution
    • 2.3.3: Self Check
    • 2.3.3: Additional Resources
    • 2.3.4: Solving More Equations
    • 2.3.5: Practice
    • 2.3.6: Lesson Summary
  • Lesson 2.4 Teacher Guide: Solving Systems by Elimination, Part 1
    • 2.4.0: Lesson Overview
    • 2.4.1: Combining Two True Equations
    • 2.4.2: Adding Equations
    • 2.4.3: Adding and Subtracting Systems of Equations and Using Their Graphs
    • 2.4.4: Determining the Best Method for Solving a System of Equations
    • 2.4.5: Practice
    • 2.4.6: Lesson Synthesis
  • Lesson 2.4: Solving Systems by Elimination, Part 1
    • 2.4.0: Lesson Overview
    • 2.4.1: Combining Two True Equations
    • 2.4.2: Adding Equations
    • 2.4.2: Self Check
    • 2.4.2: Additional Resources
    • 2.4.3: Adding and Subtracting Systems of Equations and Using Their Graphs
    • 2.4.3: Self Check
    • 2.4.3: Additional Resources
    • 2.4.4: Determining the Best Method for Solving a System of Equations
    • 2.4.5: Practice
    • 2.4.6: Lesson Summary
  • Lesson 2.5 Teacher Guide: Solving Systems by Elimination, Part 2
    • 2.5.0: Lesson Overview
    • 2.5.1: Writing and Evaluating New Equations
    • 2.5.2: Adding Two Equations in a System
    • 2.5.3: Solving Systems of Linear Equations in Two Variables
    • 2.5.4: Solving Systems of Equations Using Real-World Examples
    • 2.5.5: Practice
    • 2.5.6: Lesson Synthesis
  • Lesson 2.5: Solving Systems by Elimination, Part 2
    • 2.5.0: Lesson Overview
    • 2.5.1: Writing and Evaluating New Equations
    • 2.5.2: Adding Two Equations in a System
    • 2.5.2: Self Check
    • 2.5.2: Additional Resources
    • 2.5.3: Solving Systems of Linear Equations in Two Variables
    • 2.5.3: Self Check
    • 2.5.3: Additional Resources
    • 2.5.4: Solving Systems of Equations Using Real-World Examples
    • 2.5.5: Practice
    • 2.5.6: Lesson Summary
  • Lesson 2.6 Teacher Guide: Solving Systems by Elimination, Part 3
    • 2.6.0: Lesson Overview
    • 2.6.1: Multiplying Equations by a Number
    • 2.6.2: Writing a New System to Solve a Given System
    • 2.6.3: Finding Solutions to Unordered Sets of Equivalent Systems
    • 2.6.4: Building Equivalent Systems
    • 2.6.5: Practice
    • 2.6.6: Lesson Synthesis
  • Lesson 2.6: Solving Systems by Elimination, Part 3
    • 2.6.0: Lesson Overview
    • 2.6.1: Multiplying Equations by a Number
    • 2.6.2: Writing a New System to Solve a Given System
    • 2.6.2: Self Check
    • 2.6.2: Additional Resources
    • 2.6.3: Finding Solutions to Unordered Sets of Equivalent Systems
    • 2.6.3: Self Check
    • 2.6.3: Additional Resources
    • 2.6.4: Building Equivalent Systems
    • 2.6.5: Practice
    • 2.6.6: Lesson Summary
  • Lesson 2.7 Teacher Guide: Systems of Linear Equations and Their Solutions
    • 2.7.0: Lesson Overview
    • 2.7.1: Systems of Linear Equations with Infinitely Many Solutions
    • 2.7.2: Systems of Linear Equations with No Solution
    • 2.7.3: Sorting Systems of Equations Based on Number of Solutions
    • 2.7.4: Writing Consistent and Inconsistent Systems of Equations
    • 2.7.5: Practice
    • 2.7.6: Lesson Synthesis
  • Lesson 2.7: Systems of Linear Equations and Their Solutions
    • 2.7.0: Lesson Overview
    • 2.7.1: Systems of Linear Equations with Infinitely Many Solutions
    • 2.7.2: Systems of Linear Equations with No Solution
    • 2.7.2 Self Check
    • 2.7.2: Additional Resources
    • 2.7.3: Sorting Systems of Equations Based on Number of Solutions
    • 2.7.3: Self Check
    • 2.7.3: Additional Resources
    • 2.7.4: Writing Consistent and Inconsistent Systems of Equations
    • 2.7.5: Practice
    • 2.7.6: Lesson Summary
  • Section B Overview: Linear Inequalities in One Variable
  • Lesson 2.8 Teacher Guide: Representing Situations with Inequalities
    • 2.8.0: Lesson Overview
    • 2.8.1: Understanding Inequality Symbols
    • 2.8.2: Identifying Constraints in Inequalities
    • 2.8.3: Writing Inequalities to Represent Constraints
    • 2.8.4: Writing More Inequalities
    • 2.8.5: Practice
    • 2.8.6: Lesson Synthesis
  • Lesson 2.8: Representing Situations with Inequalities
    • 2.8.0: Lesson Overview
    • 2.8.1: Understanding Inequality Symbols
    • 2.8.2: Identifying Constraints in Inequalities
    • 2.8.2 Self Check
    • 2.8.2 Additional Resources
    • 2.8.3: Writing Inequalities to Represent Constraints
    • 2.8.3 Self Check
    • 2.8.3 Additional Resources
    • 2.8.4: Writing More Inequalities
    • 2.8.5: Practice
    • 2.8.6: Lesson Summary
  • Lesson 2.9 Teacher Guide: Solutions to Inequalities
    • 2.9.0: Lesson Overview
    • 2.9.1: Writing Solutions to Inequalities
    • 2.9.2: Graphing Inequalities
    • 2.9.3: Understanding the Meaning of an Inequality
    • 2.9.4: Making Sense of Inequalities and Their Solutions
    • 2.9.5: Comparing Equality and Inequality
    • 2.9.6: Using Technology to Visualize Inequality Solutions
    • 2.9.7: Identifying Inequality Solutions on a Graph
    • 2.9.8: Practice
    • 2.9.9: Lesson Synthesis
  • Lesson 2.9: Solutions to Inequalities
    • 2.9.0: Lesson Overview
    • 2.9.1: Writing Solutions to Inequalities
    • 2.9.2: Graphing Inequalities
    • 2.9.2: Self Check
    • 2.9.2: Additional Resources
    • 2.9.3: Understanding the Meaning of an Inequality
    • 2.9.3: Self Check
    • 2.9.3: Additional Resources
    • 2.9.4: Making Sense of Inequalities and Their Solutions
    • 2.9.5: Comparing Equality and Inequality
    • 2.9.5: Self Check
    • 2.9.5: Additional Resources
    • 2.9.6: Using Technology to Visualize Inequality Solutions
    • 2.9.7: Identifying Inequality Solutions on a Graph
    • 2.9.8: Practice
    • 2.9.9: Lesson Summary
  • Lesson 2.10 Teacher Guide: Writing and Solving Inequalities in One Variable
    • 2.10.0: Lesson Overview
    • 2.10.1: Writing an Inequality to Represent a Constraint
    • 2.10.2: Using Inequalities to Solve a Problem
    • 2.10.3: Different Ways of Solving an Inequality
    • 2.10.4: Matching Inequalities and Solutions
    • 2.10.5: Solving Inequalities
    • 2.10.6: Writing Inequalities to Represent a Situation
    • 2.10.7: Practice
    • 2.10.8: Lesson Synthesis
  • Lesson 2.10: Writing and Solving Inequalities in One Variable
    • 2.10.0: Lesson Overview
    • 2.10.1: Writing an Inequality to Represent a Constraint
    • 2.10.2: Using Inequalities to Solve a Problem
    • 2.10.2: Self Check
    • 2.10.2: Additional Resources
    • 2.10.3: Different Ways of Solving an Inequality
    • 2.10.3: Self Check
    • 2.10.3: Additional Resources
    • 2.10.4: Matching Inequalities and Solutions
    • 2.10.5: Solving Inequalities
    • 2.10.5: Self Check
    • 2.10.5: Additional Resources
    • 2.10.6: Writing Inequalities to Represent a Situation
    • 2.10.7: Practice
    • 2.10.8: Lesson Summary
  • Section C Overview: Linear Inequalities in Two Variables
  • Lesson 2.11 Teacher Guide: Graphing Linear Inequalities in Two Variables
    • 2.11.0: Lesson Overview
    • 2.11.1: Using Computation and Reasoning
    • 2.11.2: Finding Solutions to Inequalities on the Coordinate Plane
    • 2.11.3: Sketching Solutions to Inequalities
    • 2.11.4: Shading Boundary Line Regions
    • 2.11.5: Practice
    • 2.11.6: Lesson Synthesis
  • Lesson 2.11: Graphing Linear Inequalities in Two Variables
    • 2.11.0: Lesson Overview
    • 2.11.1: Using Computation and Reasoning
    • 2.11.2: Finding Solutions to Inequalities on the Coordinate Plane
    • 2.11.2: Self Check
    • 2.11.2: Additional Resources
    • 2.11.3: Sketching Solutions to Inequalities
    • 2.11.3: Self Check
    • 2.11.3: Additional Resources
    • 2.11.4: Shading Boundary Line Regions
    • 2.11.5: Practice
    • 2.11.6: Lesson Summary
  • Lesson 2.12 Teacher Guide: Using Linear Inequalities as Constraints
    • 2.12.0: Lesson Overview
    • 2.12.1: Sketching a Graph to Represent an Equation
    • 2.12.2: Write an Inequality to Represent a Constraint
    • 2.12.3: Graphing Solutions and Interpreting Points
    • 2.12.4: Reasoning Points Along Boundary Line
    • 2.12.5: Recognizing Points for an Inequality
    • 2.12.6: Practice
    • 2.12.7: Lesson Synthesis
  • Lesson 2.12: Using Linear Inequalities as Constraints
    • 2.12.0: Lesson Overview
    • 2.12.1: Sketching a Graph to Represent an Equation
    • 2.12.2: Writing an Inequality to Represent a Constraint
    • 2.12.2: Self Check
    • 2.12.2: Additional Resources
    • 2.12.3: Graphing Solutions and Interpreting Points
    • 2.12.3: Self Check
    • 2.12.3: Additional Resources
    • 2.12.4: Recognizing Points Along Boundary Line
    • 2.12.5: Recognizing Points for an Inequality
    • 2.12.6: Practice
    • 2.12.7: Lesson Summary
  • Lesson 2.13 Teacher Guide: Solving Problems with Inequalities in Two Variables
    • 2.13.0: Lesson Overview
    • 2.13.1: Graphing Inequalities with Technology
    • 2.13.2: Solving Problems with Inequalities in Two Variables
    • 2.13.3: Matching Representations of Inequalities
    • 2.13.4 Solving Inequality Problems Using Tables
    • 2.13.5: Graphing Solutions to an Inequality
    • 2.13.6: Practice
    • 2.13.7: Lesson Synthesis
  • Lesson 2.13: Solving Problems with Inequalities in Two Variables
    • 2.13.0: Lesson Overview
    • 2.13.1: Graphing Inequalities with Technology
    • 2.13.2: Solving Problems with Inequalities in Two Variables
    • 2.13.2: Self Check
    • 2.13.2: Additional Resources
    • 2.13.3: Matching Representations of Inequalities
    • 2.13.3: Self Check
    • 2.13.3: Additional Resources
    • 2.13.4: Solving Inequality Problems Using Tables
    • 2.13.4 Self Check
    • 2.13.4 Additional Resources
    • 2.13.5: Graphing Solutions to an Inequality
    • 2.13.6: Practice
    • 2.13.7: Lesson Summary
  • Section D Overview: Systems of Linear Inequalities in Two Variables
  • Lesson 2.14 Teacher Guide: Solutions to Systems of Linear Inequalities in Two Variables
    • 2.14.0: Lesson Overview
    • 2.14.1: Modeling Equations to Solve a Riddle
    • 2.14.2: Finding a Pair of Values that Satisfies Multiple Inequalities
    • 2.14.3: Writing Systems of Inequalities that Represent Situations
    • 2.14.4: Graphing Solutions of Systems of Inequalities
    • 2.14.5: Writing Inequalities for Situations and Representing on a Graph
    • 2.14.6: Practice
    • 2.14.7: Lesson Synthesis
  • Lesson 2.14: Solutions to Systems of Linear Inequalities in Two Variables
    • 2.14.0: Lesson Overview
    • 2.14.1: Modeling Equations to Solve a Riddle
    • 2.14.2: Finding a Pair of Values that Satisfies Multiple Inequalities
    • 2.14.2: Self Check
    • 2.14.2: Additional Resources
    • 2.14.3: Writing Systems of Inequalities that Represent Situations
    • 2.14.3: Self Check
    • 2.14.3: Additional Resources
    • 2.14.4: Graphing Solutions of Systems of Inequalities
    • 2.14.4: Self Check
    • 2.14.4: Additional Resources
    • 2.14.5: Writing Inequalities for Situations and Representing on a Graph
    • 2.14.6: Practice
    • 2.14.7: Lesson Summary
  • Lesson 2.15 Teacher Guide: Solving Problems with Systems of Linear Inequalities in Two Variables
    • 2.15.0: Lesson Overview
    • 2.15.1: Analyzing Graphs that Represent Linear Equations and Inequalities
    • 2.15.2: Determining if Points on Boundary Lines Are Solutions to a System
    • 2.15.3: Solving Problems to Satisfy Multiple Constraints Simultaneously
    • 2.15.4: Identifying Graph Regions Included in a System's Solution
    • 2.15.5: Practice
    • 2.15.6: Lesson Synthesis
  • Lesson 2.15: Solving Problems with Systems of Linear Inequalities in Two Variables
    • 2.15.0: Lesson Overview
    • 2.15.1: Analyzing Graphs that Represent Linear Equations and Inequalities
    • 2.15.2: Determining if Points on Boundary Lines Are Solutions to a System
    • 2.15.2: Self Check
    • 2.15.2: Additional Resources
    • 2.15.3: Solving Problems to Satisfy Multiple Constraints Simultaneously
    • 2.15.3: Self Check
    • 2.15.3: Additional Resources
    • 2.15.4: Identifying Graph Regions Included in a System’s Solution
    • 2.15.5: Practice
    • 2.15.6: Lesson Summary
  • Project 2 Teacher Guide: Modeling with Systems of Inequalities in Two Variables
    • Project 2 Overview
    • Determine a Solution to Inequalities
    • Interpret a Set of Mathematical Models
    • Perform Mathematical Modeling
  • Project 2: Modeling with Systems of Inequalities in Two Variables
    • Project 2 Overview
    • Determine a Solution to Inequalities
    • Interpret a Set of Mathematical Models
    • Perform Mathematical Modeling
  • Unit 2 Wrap Up
• Unit 3: Two-Variable Statistics
  • Unit 3 Teacher Guide
    • Unit 3 Overview and Readiness
    • Unit 3 Narrative
    • Unit 3 Family Support Materials
    • Building Character: Purpose
    • Supporting English Language Proficiency Standards (ELPS)
  • Unit 3 Overview and Readiness
    • Unit 3 Overview: Why Should I Care?
    • Unit 3 Overview: Am I Ready to Learn This?
    • Question #1: Distinguish Patterns
    • Distinguish Patterns: Mini-Lesson Review
    • Question #2: Identify Positive and Negative Trends
    • Identify Positive and Negative Trends: Mini-Lesson Review
    • Question #3: Interpret Slope and y-Intercept
    • Interpret Slope and y-Intercept: Mini-Lesson Review
    • Unit 3 Overview: Wrap Up
  • Unit 3 Section A Overview: Scatter Plots
  • Lesson 3.1 Teacher Guide: Linear Models
    • 3.1.0: Lesson Overview
    • 3.1.1: Exploring Scatter Plots
    • 3.1.2: Creating a Scatter Plot Using Data
    • 3.1.3: Interpreting the Slope and Vertical Intercept of a Linear Model
    • 3.1.4: Interpreting the Slope and Vertical Intercept of a Scatter Plot
    • 3.1.5: Using an Equation for a Fit Line
    • 3.1.6: Practice
    • 3.1.7: Lesson Synthesis
  • Lesson 3.1: Linear Models
    • 3.1.0: Lesson Overview
    • 3.1.1: Exploring Scatter Plots
    • 3.1.2: Creating a Scatter Plot Using Data
    • 3.1.2: Self Check
    • 3.1.2: Additional Resources
    • 3.1.3: Interpreting the Slope and Vertical Intercept of a Linear Model
    • 3.1.3: Self Check
    • 3.1.3: Additional Resources
    • 3.1.4: Interpreting the Slope and Vertical Intercept of a Scatter Plot
    • 3.1.4: Self Check
    • 3.1.4: Additional Resources
    • 3.1.5: Using an Equation for a Fit Line
    • 3.1.6: Practice
    • 3.1.7: Lesson Summary
  • Lesson 3.2 Teacher Guide: Fitting Lines
    • 3.2.0: Lesson Overview
    • 3.2.1: Selecting the Best Line
    • 3.2.2: Determining the Best Line That Fits the Data
    • 3.2.3: Writing Linear Models without Technology
    • 3.2.4: Assessing the Fit of a Linear Model
    • 3.2.5: Working with Fitted Lines
    • 3.2.6: Practice
    • 3.2.7: Lesson Synthesis
  • Lesson 3.2: Fitting Lines
    • 3.2.0: Lesson Overview
    • 3.2.1: Selecting the Best Line
    • 3.2.2: Determining the Best Line That Fits the Data
    • 3.2.2: Self Check
    • 3.2.2: Additional Resources
    • 3.2.3: Writing Linear Models without Technology
    • 3.2.3 Self Check
    • 3.2.3 Additional Resources
    • 3.2.4: Assessing the Fit of a Linear Model
    • 3.2.4: Self Check
    • 3.2.4: Additional Resources
    • 3.2.5: Working with Fitted Lines
    • 3.2.6: Practice
    • 3.2.7: Lesson Summary
  • Lesson 3.3 Teacher Guide: Residuals
    • 3.3.0: Lesson Overview
    • 3.3.1: Subtracting an Estimated Value from an Actual Value
    • 3.3.2: Plotting and Analyzing Residuals
    • 3.3.3: Matching Residuals Graphs to Scatter Plots
    • 3.3.4: Identifying Best Fit Line for Residuals on a Graph
    • 3.3.5: Practice
    • 3.3.6: Lesson Synthesis
  • Lesson 3.3: Residuals
    • 3.3.0: Lesson Overview
    • 3.3.1: Subtracting an Estimated Value from an Actual Value
    • 3.3.2: Plotting and Analyzing Residuals
    • 3.3.2: Self Check
    • 3.3.2: Additional Resources
    • 3.3.3: Matching Residuals Graphs to Scatter Plots
    • 3.3.3: Self Check
    • 3.3.3: Additional Resources
    • 3.3.4: Identifying Best Fit Line for Residuals on a Graph
    • 3.3.5: Practice
    • 3.3.6: Lesson Summary
  • Unit 3 Section B Overview: Correlation Coefficient
  • Lesson 3.4 Teacher Guide: The Correlation Coefficient
    • 3.4.0: Lesson Overview
    • 3.4.1: Comparing Scatter Plots with Linear and Nonlinear Trends
    • 3.4.2: Scatter Plot Differences and Connections to Correlation Coefficient
    • 3.4.3: Finding the Correlation Coefficient with Technology
    • 3.4.4: Matching Correlation Coefficients
    • 3.4.5: Using Correlation Coefficient to Determine Best Fit
    • 3.4.6: Practice
    • 3.4.7: Lesson Synthesis
  • Lesson 3.4: The Correlation Coefficient
    • 3.4.0: Lesson Overview
    • 3.4.1: Comparing Scatter Plots with Linear and Nonlinear Trends
    • 3.4.2: Recognizing Differences in Scatter Plots
    • 3.4.2: Self Check
    • 3.4.2: Additional Resources
    • 3.4.3: Finding the Correlation Coefficient with Technology
    • 3.4.3 Self Check
    • 3.4.3 Additional Resources
    • 3.4.4: Matching Correlation Coefficients
    • 3.4.4: Self Check
    • 3.4.4: Additional Resources
    • 3.4.5: Using Correlation Coefficient to Determine Best Fit
    • 3.4.6: Practice
    • 3.4.7: Lesson Summary
  • Lesson 3.5 Teacher Guide: Using the Correlation Coefficient
    • 3.5.0: Lesson Overview
    • 3.5.1: Using Bivariate Data in Context
    • 3.5.2: Finding and Using Correlation Coefficient to Interpret the Strength of Linear Relationships
    • 3.5.3: Using Correlation Coefficient to Describe Relationships between Two Variables
    • 3.5.4: Interpreting the Correlation Coefficient
    • 3.5.5: Practice
    • 3.5.6: Lesson Synthesis
  • Lesson 3.5: Using the Correlation Coefficient
    • 3.5.0: Lesson Overview
    • 3.5.1: Using Bivariate Data in Context
    • 3.5.2: Finding and Using Correlation Coefficient to Interpret the Strength of Linear Relationships
    • 3.5.2: Self Check
    • 3.5.2: Additional Resources
    • 3.5.3: Using Correlation Coefficient to Describe Relationships between Two Variables
    • 3.5.3: Self Check
    • 3.5.3: Additional Resources
    • 3.5.4: Interpreting the Correlation Coefficient
    • 3.5.5: Practice
    • 3.5.6: Lesson Summary
  • Lesson 3.6 Teacher Guide: Causal Relationships
    • 3.6.0: Lesson Overview
    • 3.6.1: Describe the Relationship between Variables
    • 3.6.2: Describing How Two Variables Are Related
    • 3.6.3: Using the Term Causal Relationship
    • 3.6.4: Determining the Type of Relationship
    • 3.6.5: Practice
    • 3.6.6: Lesson Synthesis
  • Lesson 3.6: Causal Relationships
    • 3.6.0: Lesson Overview
    • 3.6.1: Describe the Relationship between Variables
    • 3.6.2: Describing How Two Variables Are Related
    • 3.6.2: Self Check
    • 3.6.2: Additional Resources
    • 3.6.3: Using the Term Causal Relationship
    • 3.6.3: Self Check
    • 3.6.3: Additional Resources
    • 3.6.4: Determining the Type of Relationship
    • 3.6.5: Practice
    • 3.6.6: Lesson Summary
  • Project 3 Teacher Guide: Two-Variable Statistics
    • Project 3 Overview
    • Estimate Lengths
    • Analyze Data
  • Project 3: Two-Variable Statistics
    • Project 3 Overview
    • Estimate Lengths
    • Analyze Data
  • Unit 3 Wrap Up
• Unit 4: Functions
  • Unit 4 Teacher Guide
    • Unit 4 Overview and Readiness
    • Unit 4 Narrative
    • Unit 4 Family Support Materials
    • Building Character: Creativity
    • Supporting English Language Proficiency Standards (ELPS)
  • Inquiry Project Teacher Guide: Defining Functions
    • Inquiry Project Overview
    • Simulating Relationships
    • What is a function?
    • Different Kinds of Functions
  • Inquiry Project: Defining Functions
    • Inquiry Project Overview
    • Simulating Relationships
    • What is a function?
    • Different Kinds of Functions
  • Unit 4 Overview and Readiness
    • Unit 4 Overview: Why Should I Care?
    • Unit 4 Overview: Am I Ready to Learn This?
    • Question #1: Find Slope
    • Find Slope: Mini-Lesson Review
    • Question #2: Describe Graphs
    • Describe Graphs: Mini-Lesson Review
    • Question #3: Extend a Pattern
    • Extend a Pattern: Mini-Lesson Review
    • Unit 4 Overview: Wrap Up
  • Unit 4 Section A Overview: Functions and Their Representations
  • Lesson 4.1 Teacher Guide: Describing and Graphing Situations
    • 4.1.0: Lesson Overview
    • 4.1.1: Contrasting Two Relationships by Reasoning
    • 4.1.2: Reasoning Graphically about the Relationship between the Two Quantities
    • 4.1.3: Examining Relations and Functions
    • 4.1.4: Describing Functional Relationships
    • 4.1.5: Modeling Relationships between Two Variables
    • 4.1.6: Practice
    • 4.1.7: Lesson Synthesis
  • Lesson 4.1: Describing and Graphing Situations
    • 4.1.0: Lesson Overview
    • 4.1.1: Contrasting Two Relationships by Reasoning
    • 4.1.2: Reasoning Graphically about the Relationship between the Two Quantities
    • 4.1.2: Self Check
    • 4.1.2: Additional Resources
    • 4.1.3: Examining Relations and Functions
    • 4.1.3: Self Check
    • 4.1.3: Additional Resources
    • 4.1.4: Describing Functional Relationships
    • 4.1.4: Self Check
    • 4.1.4: Additional Resources
    • 4.1.5: Modeling Relationships between Two Variables
    • 4.1.6: Practice
    • 4.1.7: Lesson Summary
  • Lesson 4.2 Teacher Guide: Function Notation
    • 4.2.0: Lesson Overview
    • 4.2.1: Interpreting Graphs to Answer Questions
    • 4.2.2: Interpreting Statements Written in Function Notation
    • 4.2.3: Finding a Unique Output for Each Input
    • 4.2.4: Understanding Function Notation Using Application Problems
    • 4.2.5: Practice
    • 4.2.6: Lesson Synthesis
  • Lesson 4.2: Function Notation
    • 4.2.0: Lesson Overview
    • 4.2.1: Interpreting Graphs to Answer Questions
    • 4.2.2: Interpreting Statements Written in Function Notation
    • 4.2.2: Self Check
    • 4.2.2: Additional Resources
    • 4.2.3: Finding a Unique Output for Each Input
    • 4.2.3: Self Check
    • 4.2.3: Additional Resources
    • 4.2.4: Understanding Function Notation Using Application Problems
    • 4.2.5: Practice
    • 4.2.6: Lesson Summary
  • Lesson 4.3 Teacher Guide: Interpreting & Using Function Notation
    • 4.3.0: Lesson Overview
    • 4.3.1: Comparing Function Values
    • 4.3.2: Writing Statements from Function Notation
    • 4.3.3: Comparing Statements in Function Notation
    • 4.3.4: Using Function Notation with a Real-World Example
    • 4.3.5: Practice
    • 4.3.6: Lesson Synthesis
  • Lesson 4.3: Interpreting & Using Function Notation
    • 4.3.0: Lesson Overview
    • 4.3.1: Comparing Function Values
    • 4.3.2: Writing Statements from Function Notation
    • 4.3.2: Self Check
    • 4.3.2: Additional Resources
    • 4.3.3: Comparing Statements in Function Notation
    • 4.3.3: Self Check
    • 4.3.3: Additional Resources
    • 4.3.4: Using Function Notation with a Real-World Example
    • 4.3.5: Practice
    • 4.3.6: Lesson Summary
  • Lesson 4.4 Teacher Guide: Using Function Notation to Describe Rules, Part 1
    • 4.4.0: Lesson Overview
    • 4.4.1: Using Function Notation in Tables of Values
    • 4.4.2: Defining Functions by a Rule
    • 4.4.3: Using Tables to Find Function Rules
    • 4.4.4: Writing a Rule Using Function Notation
    • 4.4.5: Practice
    • 4.4.6: Lesson Synthesis
  • Lesson 4.4: Using Function Notation to Describe Rules, Part 1
    • 4.4.0: Lesson Overview
    • 4.4.1: Using Function Notation in Tables of Values
    • 4.4.2: Defining Functions by a Rule
    • 4.4.2: Self Check
    • 4.4.2: Additional Resources
    • 4.4.3: Using Tables to Find Function Rules
    • 4.4.3: Self Check
    • 4.4.3: Additional Resources
    • 4.4.4: Writing a Rule Using Function Notation
    • 4.4.5: Practice
    • 4.4.6: Lesson Summary
  • Lesson 4.5 Teacher Guide: Using Function Notation to Describe Rules, Part 2
    • 4.5.0: Lesson Overview
    • 4.5.1: Finding Solutions of Equations
    • 4.5.2: Using the Vertical Line Test
    • 4.5.3: Comparing Functions
    • 4.5.4: Using Function Notation and Graphing Technology
    • 4.5.5: Using Graphical and Algebraic Approaches for Finding Unknowns of Linear Functions.
    • 4.5.6: Practice
    • 4.5.7: Lesson Synthesis
  • Lesson 4.5: Using Function Notation to Describe Rules, Part 2
    • 4.5.0: Lesson Overview
    • 4.5.1: Finding Solutions of Equations
    • 4.5.2: Using the Vertical Line Test
    • 4.5.2: Self Check
    • 4.5.2: Additional Resources
    • 4.5.3: Comparing Functions
    • 4.5.3: Self Check
    • 4.5.3: Additional Resources
    • 4.5.4: Using Function Notation and Graphing Technology
    • 4.5.4: Self Check
    • 4.5.4: Additional Resources
    • 4.5.5: Using Graphical and Algebraic Approaches for Finding Unknowns of Linear Functions
    • 4.5.6: Practice
    • 4.5.7: Lesson Summary
  • Unit 4 Section B Overview: Analyzing and Creating Graphs of Functions
  • Lesson 4.6 Teacher Guide: Features of Graphs
    • 4.6.0: Lesson Overview
    • 4.6.1: Interpreting Statements in Function Notation
    • 4.6.2: Analyzing Graphs of Functions
    • 4.6.3: Connecting Graphical and Verbal Representations of a Function
    • 4.6.4: Key Features of Linear Functions
    • 4.6.5: Interpreting Graphs
    • 4.6.6: Practice
    • 4.6.7: Lesson Synthesis
  • Lesson 4.6: Features of Graphs
    • 4.6.0: Lesson Overview
    • 4.6.1: Interpreting Statements in Function Notation
    • 4.6.2: Analyzing Graphs of Functions
    • 4.6.2: Self Check
    • 4.6.2: Additional Resources
    • 4.6.3: Connecting Graphical and Verbal Representations of a Function
    • 4.6.3: Self Check
    • 4.6.3: Additional Resources
    • 4.6.4: Key Features of Linear Functions
    • 4.6.4: Self Check
    • 4.6.4 Additional Resources
    • 4.6.5: Interpreting Graphs
    • 4.6.6: Practice
    • 4.6.7: Lesson Summary
  • Lesson 4.7 Teacher Guide: Finding Slope
    • 4.7.0: Lesson Overview
    • 4.7.1: Evaluating Fractions
    • 4.7.2: Finding Slope From Tables, Graphs, and Points
    • 4.7.3: Writing Linear Equations
    • 4.7.4: Writing Equations From Two Points
    • 4.7.5: Practice
    • 4.7.6: Lesson Synthesis
  • Lesson 4.7: Finding Slope
    • 4.7.0: Lesson Overview
    • 4.7.1: Evaluating Fractions
    • 4.7.2: Finding Slope From Tables, Graphs, and Points
    • 4.7.2: Self Check
    • 4.7.2: Additional Resources
    • 4.7.3: Writing Linear Equations
    • 4.7.3: Self Check
    • 4.7.3: Additional Resources
    • 4.7.4: Writing Equations From Two Points
    • 4.7.5: Practice
    • 4.7.6: Lesson Summary
  • Lesson 4.8 Teacher Guide: Using Graphs to Find Average Rate of Change
    • 4.8.0: Lesson Overview
    • 4.8.1: Comparing Changes in Output Based on Input
    • 4.8.2: Average Rate of Change and Slope
    • 4.8.3: Finding and Interpreting Average Rates of Change
    • 4.8.4: Rate of Change of Linear Functions
    • 4.8.5: Interpreting Average Rates of Change with Real-World Examples
    • 4.8.6: Practice
    • 4.8.7: Lesson Synthesis
  • Lesson 4.8: Using Graphs to Find Average Rate of Change
    • 4.8.0: Lesson Overview
    • 4.8.1: Comparing Changes in Output Based on Input
    • 4.8.2: Average Rate of Change and Slope
    • 4.8.2: Self Check
    • 4.8.2: Additional Resources
    • 4.8.3: Finding and Interpreting Average Rates of Change
    • 4.8.3: Self Check
    • 4.8.3: Additional Resources
    • 4.8.4: Rate of Change of Linear Functions
    • 4.8.4: Self Check
    • 4.8.4: Additional Resources
    • 4.8.5: Interpreting Average Rates of Change with Real-World Examples
    • 4.8.6: Practice
    • 4.8.7: Lesson Summary
  • Lesson 4.9 Teacher Guide: Interpreting and Creating Graphs
    • 4.9.0: Lesson Overview
    • 4.9.1: Analyzing and Comparing the Properties of Graphs
    • 4.9.2: Interpreting Graphs Without Units
    • 4.9.3: Sketching Graphs of Functions
    • 4.9.4: Representing Quantities in a Situation
    • 4.9.5: Using Verbal Descriptions to Create Graphs of Functions
    • 4.9.6: Practice
    • 4.9.7: Lesson Synthesis
  • Lesson 4.9: Interpreting and Creating Graphs
    • 4.9.0: Lesson Overview
    • 4.9.1: Analyzing and Comparing the Properties of Graphs
    • 4.9.2: Interpreting Graphs Without Units
    • 4.9.2: Self Check
    • 4.9.2: Additional Resources
    • 4.9.3: Sketching Graphs of Functions
    • 4.9.3: Self Check
    • 4.9.3: Additional Resources
    • 4.9.4: Representing Quantities in a Situation
    • 4.9.5: Using Verbal Descriptions to Create Graphs of Functions
    • 4.9.6: Practice
    • 4.9.7: Lesson Summary
  • Lesson 4.10 Teacher Guide: Comparing Graphs
    • 4.10.0: Lesson Overview
    • 4.10.1: Analyzing Graphs and Statements in Function Notation
    • 4.10.2: Interpreting Graphs and Statements in Terms of a Situation
    • 4.10.3: Comparing Functions Represented in Separate Graphs
    • 4.10.4: Compare Graphs and Statements that Represent Functions without a Context
    • 4.10.5: Analyzing Functions Using Real-World Context
    • 4.10.6: Practice
    • 4.10.7: Lesson Synthesis
  • Lesson 4.10: Comparing Graphs
    • 4.10.0: Lesson Overview
    • 4.10.1: Analyzing Graphs and Statements in Function Notation
    • 4.10.2: Interpreting Graphs and Statements in Terms of a Situation
    • 4.10.2: Self Check
    • 4.10.2: Additional Resources
    • 4.10.3: Comparing Functions Represented in Separate Graphs
    • 4.10.3: Self Check
    • 4.10.3: Additional Resources
    • 4.10.4: Comparing Graphs and Statements that Represent Functions without a Context
    • 4.10.4: Self Check
    • 4.10.4: Additional Resources
    • 4.10.5: Analyzing Functions Using Real-World Context
    • 4.10.6 Practice
    • 4.10.7: Lesson Summary
  • Lesson 4.11 Teacher Guide: Graphing a Function Using Transformations
    • 4.11.0: Lesson Overview
    • 4.11.1: Graphing Linear Functions
    • 4.11.2: Vertical Shifts
    • 4.11.3: Horizontal Shifts
    • 4.11.4: Vertical Stretches and Compressions
    • 4.11.5: Horizontal Stretches and Compressions
    • 4.11.6: Graphing Using Transformations
    • 4.11.7: Practice
    • 4.11.8: Lesson Synthesis
  • Lesson 4.11: Graphing a Function Using Transformations
    • 4.11.0: Lesson Overview
    • 4.11.1: Graphing Linear Functions
    • 4.11.2: Vertical Shifts
    • 4.11.2: Self Check
    • 4.11.2: Additional Resources
    • 4.11.3: Horizontal Shifts
    • 4.11.3: Self Check
    • 4.11.3: Additional Resources
    • 4.11.4: Vertical Stretches and Compressions
    • 4.11.4: Self Check
    • 4.11.4: Additional Resources
    • 4.11.5: Horizontal Stretches and Compressions
    • 4.11.5: Self Check
    • 4.11.5: Additional Resources
    • 4.11.6: Graphing Using Transformations
    • 4.11.7: Practice
    • 4.11.8: Lesson Summary
  • Unit 4 Section C Overview: A Closer Look at Inputs and Outputs
  • Lesson 4.12 Teacher Guide: Domain and Range, Part 1
    • 4.12.0: Lesson Overview
    • 4.12.1: Determining Reasonable Inputs and Outputs
    • 4.12.2: Domain: The Input of a Function
    • 4.12.3: Range: The Output of a Function
    • 4.12.4: Using Graphs to Determine the Domain of a Function
    • 4.12.5: Using Functions to Answer Real-World Questions
    • 4.12.6: Practice
    • 4.12.7: Lesson Synthesis
  • Lesson 4.12: Domain and Range, Part 1
    • 4.12.0: Lesson Overview
    • 4.12.1: Determining Reasonable Inputs and Outputs
    • 4.12.2: Domain: The Input of a Function
    • 4.12.2: Self Check
    • 4.12.2: Additional Resources
    • 4.12.3: Range: The Output of a Function
    • 4.12.3: Self Check
    • 4.12.3: Additional Resources
    • 4.12.4: Using Graphs to Determine the Domain of a Function
    • 4.12.5: Using Functions to Answer Real-World Questions
    • 4.12.6: Practice
    • 4.12.7: Lesson Summary
  • Lesson 4.13 Teacher Guide: Domain and Range, Part 2
    • 4.13.0: Lesson Overview
    • 4.13.1: Different Features of a Graph
    • 4.13.2: Graphs of Functions
    • 4.13.3: Finding Domain and Range Using a Graph
    • 4.13.4: Real-World Domain and Range
    • 4.13.5: Graph of a Function and the Domain and Range Connection
    • 4.13.6: Practice
    • 4.13.7: Lesson Synthesis
  • Lesson 4.13: Domain and Range, Part 2
    • 4.13.0: Lesson Overview
    • 4.13.1: Different Features of a Graph
    • 4.13.2: Graphs of Functions
    • 4.13.2: Self Check
    • 4.13.2: Additional Resources
    • 4.13.3: Finding Domain and Range Using a Graph
    • 4.13.3: Self Check
    • 4.13.3: Additional Resources
    • 4.13.4: Real-World Domain and Range
    • 4.13.4: Self Check
    • 4.13.4: Additional Resources
    • 4.13.5: Graph of a Function and the Domain and Range Connection
    • 4.13.6: Practice
    • 4.13.7: Lesson Summary
  • Unit 4 Section D Overview: Sequences
  • Lesson 4.14 Teacher Guide: Sequences
    • 4.14.0: Lesson Overview
    • 4.14.1: Describe the Pattern
    • 4.14.2: What Is a Sequence?
    • 4.14.3: The Connection between Sequences and Terms
    • 4.14.4: Rules for a Sequence
    • 4.14.5: Practice
    • 4.14.6: Lesson Synthesis
  • Lesson 4.14: Sequences
    • 4.14.0: Lesson Overview
    • 4.14.1: Describe the Pattern
    • 4.14.2: What Is a Sequence?
    • 4.14.2: Self Check
    • 4.14.2: Additional Resources
    • 4.14.3: The Connection between Sequences and Terms
    • 4.14.3: Self Check
    • 4.14.3: Additional Resources
    • 4.14.4: Rules for a Sequence
    • 4.14.5: Practice
    • 4.14.6: Lesson Summary
  • Lesson 4.15 Teacher Guide: Introducing Geometric Sequences
    • 4.15.0: Lesson Overview
    • 4.15.1: What Are the Patterns?
    • 4.15.2: Using Tables and Graphs to Represent Geometric Sequences
    • 4.15.3: Complete the Sequence
    • 4.15.4: Connecting the Common Ratio and the Term in a Sequence
    • 4.15.5: Practice
    • 4.15.6: Lesson Synthesis
  • Lesson 4.15: Introducing Geometric Sequences
    • 4.15.0: Lesson Overview
    • 4.15.1: What Are the Patterns?
    • 4.15.2: Using Tables and Graphs to Represent Geometric Sequences
    • 4.15.2: Self Check
    • 4.15.2: Additional Resources
    • 4.15.3: Complete the Sequence
    • 4.15.3: Self Check
    • 4.15.3: Additional Resources
    • 4.15.4: Connecting the Common Ratio and the Term in a Sequence
    • 4.15.5: Practice
    • 4.15.6: Lesson Summary
  • Lesson 4.16 Teacher Guide: Introducing Arithmetic Sequences
    • 4.16.0: Lesson Overview
    • 4.16.1: Interpreting Function Notation
    • 4.16.2: What Is an Arithmetic Sequence?
    • 4.16.3: A Sequence is a Type of Function
    • 4.16.4: Identify and Generate Sequences
    • 4.16.5: Practice
    • 4.16.6: Lesson Synthesis
  • Lesson 4.16: Introducing Arithmetic Sequences
    • 4.16.0: Lesson Overview
    • 4.16.1: Interpreting Function Notation
    • 4.16.2: What Is an Arithmetic Sequence?
    • 4.16.2: Self Check
    • 4.16.2: Additional Resources
    • 4.16.3: A Sequence Is a Type of Function
    • 4.16.3: Self Check
    • 4.16.3: Additional Resources
    • 4.16.4: Identify and Generate Sequences
    • 4.16.5: Practice
    • 4.16.6: Lesson Summary
  • Lesson 4.17 Teacher Guide: Representing Sequences
    • 4.17.0: Lesson Overview
    • 4.17.1: Define a Sequence
    • 4.17.2: What Is a Recursive Definition?
    • 4.17.3: Ways to Represent a Sequence
    • 4.17.4: Geometric Recursive Definitions
    • 4.17.5: Practice
    • 4.17.6: Lesson Synthesis
  • Lesson 4.17: Representing Sequences
    • 4.17.0: Lesson Overview
    • 4.17.1: Define a Sequence
    • 4.17.2: What Is a Recursive Definition?
    • 4.17.2: Self Check
    • 4.17.2: Additional Resources
    • 4.17.3: Ways to Represent a Sequence
    • 4.17.3: Self Check
    • 4.17.3: Additional Resources
    • 4.17.4: Geometric Recursive Definitions
    • 4.17.5: Practice
    • 4.17.6: Lesson Summary
  • Lesson 4.18 Teacher Guide: The nth Term of a Sequence
    • 4.18.0: Lesson Overview
    • 4.18.1: Repeated Operations
    • 4.18.2 Identifying a Domain for a Function
    • 4.18.3: Define an Arithmetic Sequence by the nth Term
    • 4.18.4: Define a Geometric Sequence by the nth Term
    • 4.18.5: Interchanging between Formulas
    • 4.18.6: Different Types of Equations
    • 4.18.7: Practice
    • 4.18.8: Lesson Synthesis
  • Lesson 4.18: The nth Term of a Sequence
    • 4.18.0: Lesson Overview
    • 4.18.1: Repeated Operations
    • 4.18.2: Identifying Domain for a Function
    • 4.18.3: Define an Arithmetic Sequence by the nth Term
    • 4.18.3: Self Check
    • 4.18.3: Additional Resources
    • 4.18.4: Define a Geometric Sequence by the nth Term
    • 4.18.4: Self Check
    • 4.18.4: Additional Resources
    • 4.18.5: Interchanging between Formulas
    • 4.18.5: Self Check
    • 4.18.5: Additional Resources
    • 4.18.6: Different Types of Equations
    • 4.18.7: Practice
    • 4.18.8: Lesson Summary
  • Project 4 Teacher Guide: Using Functions to Model Battery Power
    • Project 4 Overview
    • Estimate Time to Charge a Battery
    • Analyze Percent Change Over Time
    • Write an Equation to Model Data
  • Project 4: Using Functions to Model Battery Power
    • Project 4 Overview
    • Estimate Time to Charge a Battery
    • Analyze Percent Change Over Time
    • Write an Equation to Model Data
  • Unit 4 Wrap Up
• Unit 5: Introduction to Exponential Functions
  • Unit 5 Teacher Guide
    • Unit 5 Overview and Readiness
    • Unit 5 Narrative
    • Unit 5 Family Support Materials
    • Building Character: Grit
    • Supporting English Language Procifiency Standards (ELPS)
  • Unit 5 Overview and Readiness
    • Unit 5 Overview: Why Should I Care?
    • Unit 5 Overview: Am I Ready to Learn This?
    • Question #1: Write Linear Functions from a Graph
    • Write Linear Functions from a Graph: Mini-Lesson Review
    • Question #2: Interpret Linear Functions
    • Interpret Linear Functions: Mini-Lesson Review
    • Question #3: Evaluate Exponential Expressions
    • Evaluate Exponential Expressions: Mini-Lesson Review
    • Unit 5 Overview: Wrap Up
  • Unit 5 Section A Overview: Looking at Growth and Decay
  • Lesson 5.1 Teacher Guide: Properties of Exponents
    • 5.1.0: Lesson Overview
    • 5.1.1: Understanding Exponents
    • 5.1.2: Using Product and Quotient Properties for Exponents
    • 5.1.3: Using Zero Exponent Property and Negative Exponents
    • 5.1.4: Using Power Properties for Exponents
    • 5.1.5: Simplifying Exponents
    • 5.1.6: Practice
    • 5.1.7: Lesson Synthesis
  • Lesson 5.1: Properties of Exponents
    • 5.1.0: Lesson Overview
    • 5.1.1: Understanding Exponents
    • 5.1.2: Using Product and Quotient Properties for Exponents
    • 5.1.2: Self Check
    • 5.1.2: Additional Resources
    • 5.1.3: Using Zero Exponent Property and Negative Exponents
    • 5.1.3: Self Check
    • 5.1.3: Additional Resources
    • 5.1.4: Using Power Properties for Exponents
    • 5.1.4: Self Check
    • 5.1.4: Additional Resources
    • 5.1.5: Simplifying Exponents
    • 5.1.6: Practice
    • 5.1.7: Lesson Summary
  • Lesson 5.2 Teacher Guide: Rational Exponents
    • 5.2.0: Lesson Overview
    • 5.2.1: Perfect Squares Revisited
    • 5.2.2: The nth Root
    • 5.2.3: Radicals and Rational Exponents
    • 5.2.4: Properties of Exponents with Rationals
    • 5.2.5: Practice
    • 5.2.6: Lesson Synthesis
  • Lesson 5.2: Rational Exponents
    • 5.2.0: Lesson Overview
    • 5.2.1: Perfect Squares Revisited
    • 5.2.2: The nth Root
    • 5.2.2: Self Check
    • 5.2.2: Additional Resources
    • 5.2.3: Radicals and Rational Exponents
    • 5.2.3: Self Check
    • 5.2.3: Additional Resources
    • 5.2.4: Properties of Exponents with Rationals
    • 5.2.5: Practice
    • 5.2.6: Lesson Summary
  • Lesson 5.3 Teacher Guide: Patterns of Growth
    • 5.3.0: Lesson Overview
    • 5.3.1: Creating a Pictorial Representation of Exponential Growth
    • 5.3.2: Exploring Different Growth Patterns
    • 5.3.3: Compare and Contrast Two Patterns
    • 5.3.4: Match Expressions and Tables with Situations
    • 5.3.5: Describe Mathematically Changes in Growth
    • 5.3.6: Practice
    • 5.3.7: Lesson Synthesis
  • Lesson 5.3: Patterns of Growth
    • 5.3.0: Lesson Overview
    • 5.3.1: Creating a Pictorial Representation of Exponential Growth
    • 5.3.2: Exploring Different Growth Patterns
    • 5.3.2: Self Check
    • 5.3.2: Additional Resources
    • 5.3.3: Compare and Contrast Two Patterns
    • 5.3.3: Self Check
    • 5.3.3: Additional Resources
    • 5.3.4: Match Expressions and Tables with Situations
    • 5.3.4: Self Check
    • 5.3.4: Additional Resources
    • 5.3.5: Describe Mathematically Changes in Growth
    • 5.3.6: Practice
    • 5.3.7: Lesson Summary
  • Lesson 5.4 Teacher Guide: Representing Exponential Growth
    • 5.4.0: Lesson Overview
    • 5.4.1: Exponent Rules
    • 5.4.2: Zero Exponent Rule
    • 5.4.3: Exponential Change: The Growth Factor
    • 5.4.4: Graphing Exponential Expressions
    • 5.4.5: Interpret the Growth Factor of the Equation
    • 5.4.6: Practice
    • 5.4.7: Lesson Synthesis
  • Lesson 5.4: Representing Exponential Growth
    • 5.4.0: Lesson Overview
    • 5.4.1: Exponent Rules
    • 5.4.2: Zero Exponent Rule
    • 5.4.2: Self Check
    • 5.4.2: Additional Resources
    • 5.4.3: Exponential Change: The Growth Factor
    • 5.4.3: Self Check
    • 5.4.3: Additional Resources
    • 5.4.4: Graphing Exponential Expressions
    • 5.4.4: Self Check
    • 5.4.4: Additional Resources
    • 5.4.5: Interpret the Growth Factor of the Equation
    • 5.4.6: Practice
    • 5.4.7: Lesson Summary
  • Lesson 5.5 Teacher Guide: Representing Exponential Decay
    • 5.5.0: Lesson Overview
    • 5.5.1: Identifying Linear and Exponential Quantities
    • 5.5.2: Exponential Decay
    • 5.5.3: Using Graphs to Represent Exponential Decay
    • 5.5.4: Justifying Exponential Models
    • 5.5.5: Writing Equations to Represent Exponential Decay
    • 5.5.6: Practice
    • 5.5.7: Lesson Synthesis
  • Lesson 5.5: Representing Exponential Decay
    • 5.5.0: Lesson Overview
    • 5.5.1: Identifying Linear and Exponential Quantities
    • 5.5.2: Exponential Decay
    • 5.5.2: Self Check
    • 5.5.2: Additional Resources
    • 5.5.3: Using Graphs to Represent Exponential Decay
    • 5.5.3: Self Check
    • 5.5.3: Additional Resources
    • 5.5.4: Justifying Exponential Models
    • 5.5.4: Self Check
    • 5.5.4: Additional Resources
    • 5.5.5: Writing Equations to Represent Exponential Decay
    • 5.5.6: Practice
    • 5.5.7: Lesson Summary
  • Lesson 5.6 Teacher Guide: Negative Exponents and Scientific Notation
    • 5.6.0: Lesson Overview
    • 5.6.1: Checking Exponent Rules
    • 5.6.2: Interpreting Negative Exponents in Exponential Growth
    • 5.6.3: Interpreting Negative Exponents in Exponential Decay
    • 5.6.4: Using Scientific Notation
    • 5.6.5: Applying Scientific Notation
    • 5.6.6: Interpreting Negative Exponents and Scientific Notation
    • 5.6.7: Practice
    • 5.6.8: Lesson Synthesis
  • Lesson 5.6: Negative Exponents and Scientific Notation
    • 5.6.0: Lesson Overview
    • 5.6.1: Checking Exponent Rules
    • 5.6.2: Interpreting Negative Exponents in Exponential Growth
    • 5.6.2: Self Check
    • 5.6.2: Additional Resources
    • 5.6.3: Interpreting Negative Exponents in Exponential Decay
    • 5.6.3: Self Check
    • 5.6.3: Additional Resources
    • 5.6.4: Using Scientific Notation
    • 5.6.4: Self Check
    • 5.6.4: Additional Resources
    • 5.6.5: Applying Scientific Notation
    • 5.6.5: Self Check
    • 5.6.5: Additional Resources
    • 5.6.6: Interpreting Negative Exponents and Scientific Notation
    • 5.6.7: Practice
    • 5.6.8: Lesson Summary
  • Lesson 5.7 Teacher Guide: Analyzing Graphs
    • 5.7.0: Lesson Overview
    • 5.7.1: Patterns in Real Numbers
    • 5.7.2: Comparing Graphs
    • 5.7.3: Describing Graphs
    • 5.7.4: Quantities that Change Exponentially
    • 5.7.5: Practice
    • 5.7.6: Lesson Synthesis
  • Lesson 5.7: Analyzing Graphs
    • 5.7.0: Lesson Overview
    • 5.7.1: Patterns in Real Numbers
    • 5.7.2: Comparing Graphs
    • 5.7.2: Self Check
    • 5.7.2: Additional Resources
    • 5.7.3: Describing Graphs
    • 5.7.3: Self Check
    • 5.7.3: Additional Resources
    • 5.7.4: Quantities that Change Exponentially
    • 5.7.5: Practice
    • 5.7.6: Lesson Summary
  • Unit 5 Section B Overview: Exponential Functions
  • Lesson 5.8 Teacher Guide: Exponential Situations as Functions
    • 5.8.0: Lesson Overview
    • 5.8.1: Meaning of a Function Presented Graphically
    • 5.8.2: Represent a Function as a Table of Values, Graph, and Equation
    • 5.8.3: Using Function Language and Notation
    • 5.8.4: Function Notation
    • 5.8.5: Practice
    • 5.8.6: Lesson Synthesis
  • Lesson 5.8: Exponential Situations as Functions
    • 5.8.0: Lesson Overview
    • 5.8.1: Meaning of a Function Presented Graphically
    • 5.8.2: Represent a Function as a Table of Values, Graph, and Equation
    • 5.8.2: Self Check
    • 5.8.2: Additional Resources
    • 5.8.3: Using Function Language and Notation
    • 5.8.3: Self Check
    • 5.8.3: Additional Resources
    • 5.8.4: Function Notation
    • 5.8.5: Practice
    • 5.8.6: Lesson Summary
  • Lesson 5.9 Teacher Guide: Interpreting Exponential Functions
    • 5.9.0: Lesson Overview
    • 5.9.1: Evaluating Expressions for Different Values of x
    • 5.9.2: Analyze Underlying Relationship in a Graph of a Function
    • 5.9.3: Graph Equations to Solve Problems
    • 5.9.4: Deciding on Graphing Window
    • 5.9.5: Interpret Graphs to find Approximate Values
    • 5.9.6: Practice
    • 5.9.7: Lesson Synthesis
  • Lesson 5.9: Interpreting Exponential Functions
    • 5.9.0: Lesson Overview
    • 5.9.1: Evaluating Expressions for Different Values of x
    • 5.9.2: Analyze Underlying Relationship in a Graph of a Function
    • 5.9.2: Self Check
    • 5.9.2: Additional Resources
    • 5.9.3: Graph Equations to Solve Problems
    • 5.9.3: Self Check
    • 5.9.3: Additional Resources
    • 5.9.4: Deciding on Graphing Window
    • 5.9.5: Interpret Graphs to Find Approximate Values
    • 5.9.6: Practice
    • 5.9.7: Lesson Summary
  • Lesson 5.10 Teacher Guide: Looking at Rates of Change
    • 5.10.0: Lesson Overview
    • 5.10.1: Calculate an Average Rate of Change from Two Points
    • 5.10.2: Explore Average Rates of Change in an Exponential Growth Function
    • 5.10.3: Explore Average Rates of Change in an Exponential Decay Context
    • 5.10.4: Average Rate of Change
    • 5.10.5: Practice
    • 5.10.6: Lesson Synthesis
  • Lesson 5.10: Looking at Rates of Change
    • 5.10.0: Lesson Overview
    • 5.10.1: Calculate an Average Rate of Change from Two Points
    • 5.10.2: Explore Average Rates of Change in an Exponential Growth Function
    • 5.10.2: Self Check
    • 5.10.2: Additional Resources
    • 5.10.3: Explore Average Rates of Change in an Exponential Decay Context
    • 5.10.3: Self Check
    • 5.10.3: Additional Resources
    • 5.10.4: Average Rate of Change
    • 5.10.5: Practice
    • 5.10.6: Lesson Summary
  • Lesson 5.11 Teacher Guide: Modeling Exponential Behavior
    • 5.11.0: Lesson Overview
    • 5.11.1: Changing the Graphing Window
    • 5.11.2: Choosing an Appropriate Model
    • 5.11.3: Modeling with Exponential Functions
    • 5.11.4: Examine Exponential Decay in Context
    • 5.11.5: Using Relationship Models to Answer Questions
    • 5.11.6: Practice
    • 5.11.7: Lesson Synthesis
  • Lesson 5.11: Modeling Exponential Behavior
    • 5.11.0: Lesson Overview
    • 5.11.1: Changing the Graphing Window
    • 5.11.2: Choosing an Appropriate Model
    • 5.11.2: Self Check
    • 5.11.2: Additional Resources
    • 5.11.3: Modeling with Exponential Functions
    • 5.11.4: Examine Exponential Decay in Context
    • 5.11.4: Self Check
    • 5.11.4: Additional Resources
    • 5.11.5: Using Relationship Models to Answer Questions
    • 5.11.6: Practice
    • 5.11.7: Lesson Summary
  • Lesson 5.12 Teacher Guide: Reasoning about Exponential Graphs, Part 1
    • 5.12.0: Lesson Overview
    • 5.12.1: Modeling Exponential Decay
    • 5.12.2: Equations and Their Graphs
    • 5.12.3: Graphs Representing Exponential Decay
    • 5.12.4: Possible Equation for a Function on a Graph
    • 5.12.5: Practice
    • 5.12.6: Lesson Synthesis
  • Lesson 5.12: Reasoning about Exponential Graphs, Part 1
    • 5.12.0: Lesson Overview
    • 5.12.1: Modeling Exponential Decay
    • 5.12.2: Equations and Their Graphs
    • 5.12.2: Self Check
    • 5.12.2: Additional Resources
    • 5.12.3: Graphs Representing Exponential Decay
    • 5.12.3: Self Check
    • 5.12.3: Additional Resources
    • 5.12.4: Possible Equation for a Function on a Graph
    • 5.12.5: Practice
    • 5.12.6: Lesson Summary
  • Unit 5 Section C Overview: Comparing Linear and Exponential Functions
  • Lesson 5.13 Teacher Guide: Reasoning about Exponential Graphs, Part 2
    • 5.13.0: Lesson Overview
    • 5.13.1: Comparing Functions
    • 5.13.2: Creating Exponential Functions from Graphs
    • 5.13.3: Comparing Exponential Functions
    • 5.13.4: Interpreting Features of an Exponential Graph
    • 5.13.5: Practice
    • 5.13.6: Lesson Synthesis
  • Lesson 5.13: Reasoning about Exponential Graphs, Part 2
    • 5.13.0: Lesson Overview
    • 5.13.1: Comparing Functions
    • 5.13.2: Creating Exponential Functions from Graphs
    • 5.13.2: Self Check
    • 5.13.2: Additional Resources
    • 5.13.3: Comparing Exponential Functions
    • 5.13.3: Self Check
    • 5.13.3: Additional Resources
    • 5.13.4: Interpreting Features of an Exponential Graph
    • 5.13.5: Practice
    • 5.13.6: Lesson Summary
  • Lesson 5.14 Teacher Guide: Which One Changes Faster?
    • 5.14.0: Lesson Overview
    • 5.14.1: Distinguish Linear and Exponential Growth
    • 5.14.2: Using Tables to Compare Linear and Exponential Growth Functions
    • 5.14.3: Compare Linear Functions with Exponential Functions
    • 5.14.4: Using Function Notation to Compare Linear and Exponential Functions
    • 5.14.5: Practice
    • 5.14.6: Lesson Synthesis
  • Lesson 5.14: Which One Changes Faster?
    • 5.14.0: Lesson Overview
    • 5.14.1: Distinguish Linear and Exponential Growth
    • 5.14.2: Using Tables to Compare Linear and Exponential Growth Functions
    • 5.14.2: Self Check
    • 5.14.2: Additional Resources
    • 5.14.3: Compare Linear Functions with Exponential Functions
    • 5.14.3: Self Check
    • 5.14.3: Additional Resources
    • 5.14.4: Using Function Notation to Compare Linear and Exponential Functions
    • 5.14.5: Practice
    • 5.14.6: Lesson Summary
  • Lesson 5.15 Teacher Guide: Changes Over Equal Intervals
    • 5.15.0: Lesson Overview
    • 5.15.1: Writing Equivalent Expressions
    • 5.15.2: Linear Function Constant Rate of Change
    • 5.15.3: Growth Rate of an Exponential Function
    • 5.15.4: Comparing Linear and Exponential Growth
    • 5.15.5: Practice
    • 5.15.6: Lesson Synthesis
  • Lesson 5.15: Changes Over Equal Intervals
    • 5.15.0: Lesson Overview
    • 5.15.1: Writing Equivalent Expressions
    • 5.15.2: Linear Function Constant Rate of Change
    • 5.15.2: Self Check
    • 5.15.2: Additional Resources
    • 5.15.3: Growth Rate of an Exponential Function
    • 5.15.3: Self Check
    • 5.15.3: Additional Resources
    • 5.15.4: Comparing Linear and Exponential Growth
    • 5.15.5: Practice
    • 5.15.6: Lesson Summary
  • Project 5 Teacher Guide: Introduction to Exponential Functions
    • Project 5 Overview
    • Analyze Data
    • Write Equations to Model Populations
    • Open-ended Modeling with Data Investigation
  • Project 5: Introduction to Exponential Functions
    • Project 5 Overview
    • Analyze Data
    • Write Equations to Model Populations
    • Open-ended Modeling with Data Investigation
  • Unit 5 Wrap Up
• Fall STAAR Review
• Unit 6: Working with Polynomials
  • Unit 6 Teacher Guide
    • Unit 6 Overview and Readiness
    • Unit 6 Narrative
    • Unit 6 Family Support Materials
    • Building Character: Judgment
    • Supporting English Language Proficiency Standards (ELPS)
  • Unit 6 Overview and Readiness
    • Unit 6 Overview: Why Should I Care?
    • Unit 6 Overview: Am I Ready to Learn This?
    • Question #1: Simplify Expressions Using Properties of Exponents
    • Simplify Expressions Using Properties of Exponents: Mini-Lesson Review
    • Question #2: Simplify Expressions Using the Distributive Property
    • Simplify Expressions Using the Distributive Property: Mini-Lesson Review
    • Question #3: Find the Greatest Common Factor
    • Find the Greatest Common Factor: Mini-Lesson Review
    • Unit 6 Overview: Wrap Up
  • Inquiry Project Teacher Guide: Area Model Multiplication
    • Inquiry Project Overview
    • Discovering an Area Model
    • Understanding an Area Model
    • Using an Area Model
    • Applying an Area Model to Polynomials
  • Inquiry Project: Area Model Multiplication
    • Inquiry Project Overview
    • Discovering an Area Model
    • Understanding an Area Model
    • Using an Area Model
    • Applying an Area Model to Polynomials
  • Unit 6 Section A Overview: Operations with Polynomials
  • Lesson 6.1 Teacher Guide: Add and Subtract Polynomials
    • 6.1.0: Lesson Overview
    • 6.1.1: Understanding Polynomials
    • 6.1.2: Adding and Subtracting Polynomials
    • 6.1.3: Evaluating a Polynomial Function for a Given Value
    • 6.1.4: Adding and Subtracting Polynomial Functions
    • 6.1.5: Reviewing Polynomial Addition and Subtraction
    • 6.1.6: Practice
    • 6.1.7: Lesson Synthesis
  • Lesson 6.1: Add and Subtract Polynomials
    • 6.1.0: Lesson Overview
    • 6.1.1: Understanding Polynomials
    • 6.1.2: Adding and Subtracting Polynomials
    • 6.1.2: Self Check
    • 6.1.2: Additional Resources
    • 6.1.3: Evaluating a Polynomial Function for a Given Value
    • 6.1.3: Self Check
    • 6.1.3: Additional Resources
    • 6.1.4: Adding and Subtracting Polynomial Functions
    • 6.1.4: Self Check
    • 6.1.4: Additional Resources
    • 6.1.5: Reviewing Polynomial Addition and Subtraction
    • 6.1.6: Practice
    • 6.1.7: Lesson Summary
  • Lesson 6.2 Teacher Guide: Multiplying Polynomials
    • 6.2.0: Lesson Overview
    • 6.2.1: Multiplying Monomials
    • 6.2.2: Multiplying Binomials
    • 6.2.3: Multiplying a Polynomial by a Polynomial
    • 6.2.4: Multiplying Special Products
    • 6.2.5: Multiplying Polynomial Functions
    • 6.2.6: Practice
    • 6.2.7: Lesson Synthesis
  • Lesson 6.2: Multiplying Polynomials
    • 6.2.0: Lesson Overview
    • 6.2.1: Multiplying Monomials
    • 6.2.2: Multiplying Binomials
    • 6.2.2: Self Check
    • 6.2.2: Additional Resources
    • 6.2.3: Multiplying a Polynomial by a Polynomial
    • 6.2.3: Self Check
    • 6.2.3: Additional Resources
    • 6.2.4: Multiplying Special Products
    • 6.2.4: Self Check
    • 6.2.4: Additional Resources
    • 6.2.5: Multiplying Polynomial Functions
    • 6.2.6: Practice
    • 6.2.7: Lesson Summary
  • Lesson 6.3 Teacher Guide: Dividing Polynomials
    • 6.3.0: Lesson Overview
    • 6.3.1: Dividing by Monomials
    • 6.3.2: Dividing Polynomials Using Long Division
    • 6.3.3: Dividing Polynomials Using Synthetic Division
    • 6.3.4: Dividing Polynomial Functions and the Remainder Theorem
    • 6.3.5: Using the Factor Theorem
    • 6.3.6: Practice
    • 6.3.7: Lesson Synthesis
  • Lesson 6.3: Dividing Polynomials
    • 6.3.0: Lesson Overview
    • 6.3.1: Dividing by Monomials
    • 6.3.2: Dividing Polynomials Using Long Division
    • 6.3.2: Self Check
    • 6.3.2: Additional Resources
    • 6.3.3: Dividing Polynomials Using Synthetic Division
    • 6.3.3: Self Check
    • 6.3.3: Additional Resources
    • 6.3.4: Dividing Polynomial Functions and the Remainder Theorem
    • 6.3.4: Self Check
    • 6.3.4: Additional Resources
    • 6.3.5: Using the Factor Theorem
    • 6.3.6: Practice
    • 6.3.7: Lesson Summary
  • Unit 6 Section B Overview: Factoring Polynomials
  • Lesson 6.4 Teacher Guide: Greatest Common Factor and Factor by Grouping
    • 6.4.0: Lesson Overview
    • 6.4.1: Finding Factors
    • 6.4.2: Finding the GCF of Two or More Expressions
    • 6.4.3: Factoring the GCF from Polynomials
    • 6.4.4: Factoring Polynomials by Grouping
    • 6.4.5: Can You Factor the Polynomial?
    • 6.4.6: Practice
    • 6.4.7: Lesson Synthesis
  • Lesson 6.4: Greatest Common Factor and Factor by Grouping
    • 6.4.0: Lesson Overview
    • 6.4.1: Finding Factors
    • 6.4.2: Finding the GCF of Two or More Expressions
    • 6.4.2: Self Check
    • 6.4.2: Additional Resources
    • 6.4.3: Factoring the GCF from Polynomials
    • 6.4.3: Self Check
    • 6.4.3: Additional Resources
    • 6.4.4: Factoring Polynomials by Grouping
    • 6.4.4: Self Check
    • 6.4.4: Additional Resources
    • 6.4.5: Can You Factor the Polynomial?
    • 6.4.6: Practice
    • 6.4.7: Lesson Summary
  • Lesson 6.5 Teacher Guide: Factor Trinomials
    • 6.5.0: Lesson Overview
    • 6.5.1: Undoing FOIL
    • 6.5.2: Factoring Trinomials with Leading Coefficients of 1
    • 6.5.3: Factoring Trinomials Using Trial and Error
    • 6.5.4: Factoring Trinomials Using the “ac” Method and Substitution
    • 6.5.5: Choosing Your Own Method to Factor Trinomials
    • 6.5.6: Practice
    • 6.5.7: Lesson Synthesis
  • Lesson 6.5: Factor Trinomials
    • 6.5.0: Lesson Overview
    • 6.5.1: Undoing FOIL
    • 6.5.2: Factoring Trinomials with Leading Coefficients of 1
    • 6.5.2: Self Check
    • 6.5.2: Additional Resources
    • 6.5.3: Factoring Trinomials Using Trial and Error
    • 6.5.3: Self Check
    • 6.5.3: Additional Resources
    • 6.5.4: Factoring Trinomials Using the “ac” Method and Substitution
    • 6.5.4: Self Check
    • 6.5.4: Additional Resources
    • 6.5.5: Choosing Your Own Method to Factor Trinomials
    • 6.5.6: Practice
    • 6.5.7: Lesson Summary
  • Lesson 6.6 Teacher Guide: Factor Special Products
    • 6.6.0: Lesson Overview
    • 6.6.1: Identifying Perfect Square Trinomials
    • 6.6.2: Factoring Perfect Square Trinomials
    • 6.6.3: Factoring the Difference of Squares
    • 6.6.4: Sorting Polynomials by Factoring Methods
    • 6.6.5: Practice
    • 6.6.6: Lesson Synthesis
  • Lesson 6.6: Factor Special Products
    • 6.6.0: Lesson Overview
    • 6.6.1: Identifying Perfect Square Trinomials
    • 6.6.2: Factoring Perfect Square Trinomials
    • 6.6.2: Self Check
    • 6.6.2: Additional Resources
    • 6.6.3: Factoring the Difference of Squares
    • 6.6.3: Self Check
    • 6.6.3: Additional Resources
    • 6.6.4: Sorting Polynomials by Factoring Methods
    • 6.6.5: Practice
    • 6.6.6: Lesson Summary
  • Lesson 6.7 Teacher Guide: General Strategy for Factoring Polynomials
    • 6.7.0: Lesson Overview
    • 6.7.1: Factoring Strategies for Polynomials
    • 6.7.2: Reviewing General Strategies to Factor a Polynomial
    • 6.7.3: Implementing General Strategies for Factoring
    • 6.7.4: Is the Polynomial Completely Factored?
    • 6.7.5: Practice
    • 6.7.6: Lesson Synthesis
  • Lesson 6.7: General Strategy for Factoring Polynomials
    • 6.7.0: Lesson Overview
    • 6.7.1: Factoring Strategies for Polynomials
    • 6.7.2: Reviewing General Strategies to Factor a Polynomial
    • 6.7.2: Self Check
    • 6.7.2: Additional Resources
    • 6.7.3: Implementing General Strategies for Factoring
    • 6.7.3: Self Check
    • 6.7.3: Additional Resources
    • 6.7.4: Is the Polynomial Completely Factored?
    • 6.7.5: Practice
    • 6.7.6: Lesson Summary
  • Project 6 Teacher Guide: Polynomials and Rectangles
    • Project 6 Overview
    • Areas of Rectangles
    • Dimensions and Areas of Rectangles
    • Create Your Own Rectangles
  • Project 6: Polynomials and Rectangles
    • Project 6 Overview
    • Areas of Rectangles
    • Dimensions and Areas of Rectangles
    • Create Your Own Rectangles
  • Unit 6 Wrap Up
• Unit 7: Introduction to Quadratic Functions
  • Unit 7 Teacher Guide
    • Unit 7 Overview and Readiness
    • Unit 7 Narrative
    • Unit 7 Family Support Materials
    • Building Character: Proactivity
    • Supporting English Language Proficiency Standards (ELPS)
  • Unit 7 Overview and Readiness
    • Unit 7 Overview: Why Should I Care?
    • Unit 7 Overview: Am I Ready to Learn This?
    • Question #1: Multiply Binomials
    • Multiply Binomials: Mini-Lesson Review
    • Question #2: Factor Trinomials
    • Factor Trinomials: Mini-Lesson Review
    • Question #3: Compare Linear and Exponential Functions
    • Compare Linear and Exponential Functions: Mini-Lesson Review
    • Unit 7 Overview: Wrap Up
  • Unit 7 Section A Overview: A Different Kind of Change
  • Lesson 7.1 Teacher Guide: Patterns of Change
    • 7.1.0: Lesson Overview
    • 7.1.1: Noticing New Patterns of Change
    • 7.1.2: The Relationship between Length and Area
    • 7.1.3: Plotting Measurements
    • 7.1.4: The Input and Output of a Function
    • 7.1.5: Practice
    • 7.1.6: Lesson Synthesis
  • Lesson 7.1: Patterns of Change
    • 7.1.0: Lesson Overview
    • 7.1.1: Noticing New Patterns of Change
    • 7.1.2: The Relationship between Length and Area
    • 7.1.2: Self Check
    • 7.1.2: Additional Resources
    • 7.1.3: Plotting Measurements
    • 7.1.3: Self Check
    • 7.1.3: Additional Resources
    • 7.1.4: The Input and Output of a Function
    • 7.1.5: Practice
    • 7.1.6: Lesson Summary
  • Lesson 7.2 Teacher Guide: Introduction to Quadratic Relationships
    • 7.2.0: Lesson Overview
    • 7.2.1: Squares in a Geometric Pattern
    • 7.2.2: Constant and Exponential Change
    • 7.2.3: Quadratic Expressions
    • 7.2.4: Quadratic Relationships
    • 7.2.5: Practice
    • 7.2.6: Lesson Synthesis
  • Lesson 7.2: Introduction to Quadratic Relationships
    • 7.2.0: Lesson Overview
    • 7.2.1: Squares in a Geometric Pattern
    • 7.2.2: Constant and Exponential Change
    • 7.2.2: Self Check
    • 7.2.2: Additional Resources
    • 7.2.3: Quadratic Expressions
    • 7.2.3: Self Check
    • 7.2.3: Additional Resources
    • 7.2.4: Quadratic Relationships
    • 7.2.5: Practice
    • 7.2.6: Lesson Summary
  • Unit 7 Section B Overview: Quadratic Functions
  • Lesson 7.3 Teacher Guide: Determining if a Function is Quadratic
    • 7.3.0: Lesson Overview
    • 7.3.1: Quadratic Expressions and Area
    • 7.3.2: Writing Equations for Patterns with Squares
    • 7.3.3: Quadratic Sequences
    • 7.3.4: Is the Pattern a Quadratic Function?
    • 7.3.5: Practice
    • 7.3.6: Lesson Synthesis
  • Lesson 7.3: Determining if a Function is Quadratic
    • 7.3.0: Lesson Overview
    • 7.3.1: Quadratic Expressions and Area
    • 7.3.2: Writing Equations for Patterns with Squares
    • 7.3.2: Self Check
    • 7.3.2: Additional Resources
    • 7.3.3: Quadratic Sequences
    • 7.3.3: Self Check
    • 7.3.3: Additional Resources
    • 7.3.4: Is the Pattern a Quadratic Function?
    • 7.3.5: Practice
    • 7.3.6: Lesson Summary
  • Lesson 7.4 Teacher Guide: Comparing Quadratic and Exponential Functions
    • 7.4.0: Lesson Overview
    • 7.4.1: Comparing Expressions
    • 7.4.2: Exploring Linear, Exponential, and Quadratic Growth
    • 7.4.3: Comparing Exponential and Quadratic Functions
    • 7.4.4: Comparing Exponential and Quadratic Expressions
    • 7.4.5: Practice
    • 7.4.6: Lesson Synthesis
  • Lesson 7.4: Comparing Quadratic and Exponential Functions
    • 7.4.0: Lesson Overview
    • 7.4.1: Comparing Expressions
    • 7.4.2: Exploring Linear, Exponential, and Quadratic Growth
    • 7.4.2: Self Check
    • 7.4.2: Additional Resources
    • 7.4.3: Comparing Exponential and Quadratic Functions
    • 7.4.3: Self Check
    • 7.4.3: Additional Resources
    • 7.4.4: Comparing Exponential and Quadratic Expressions
    • 7.4.5: Practice
    • 7.4.6: Lesson Summary
  • Lesson 7.5 Teacher Guide: Building Quadratic Functions to Describe Situations, Part 1
    • 7.5.0: Lesson Overview
    • 7.5.1: Numerical Patterns
    • 7.5.2: A Time-Distance Quadratic Model
    • 7.5.3: Distance as a Quadratic Function of Elapsed Time
    • 7.5.4: A Quadratic Expression that Represents the Relationship between Distance and Time
    • 7.5.5: Practice
    • 7.5.6: Lesson Synthesis
  • Lesson 7.5: Building Quadratic Functions to Describe Situations, Part 1
    • 7.5.0: Lesson Overview
    • 7.5.1: Numerical Patterns
    • 7.5.2: A Time-Distance Quadratic Model
    • 7.5.2: Self Check
    • 7.5.2: Additional Resources
    • 7.5.3: Distance as a Quadratic Function of Elapsed Time
    • 7.5.3: Self Check
    • 7.5.3: Additional Resources
    • 7.5.4: A Quadratic Expression that Represents the Relationship between Distance and Time
    • 7.5.5: Practice
    • 7.5.6: Lesson Summary
  • Lesson 7.6 Teacher Guide: Building Quadratic Functions to Describe Situations, Part 2
    • 7.6.0: Lesson Overview
    • 7.6.1: Using Linear Functions to Describe Constant Speed
    • 7.6.2: The Force of Gravity Change in Quadratic Functions
    • 7.6.3: Using Quadratic Functions to Describe Height
    • 7.6.4: Interpreting Graphs of Quadratic Functions
    • 7.6.5: Practice
    • 7.6.6: Lesson Synthesis
  • Lesson 7.6: Building Quadratic Functions to Describe Situations, Part 2
    • 7.6.0: Lesson Overview
    • 7.6.1: Using Linear Functions to Describe Constant Speed
    • 7.6.2: The Force of Gravity Change in Quadratic Functions
    • 7.6.2: Self Check
    • 7.6.2: Additional Resources
    • 7.6.3: Using Quadratic Functions to Describe Height
    • 7.6.3: Self Check
    • 7.6.3: Additional Resources
    • 7.6.4: Interpreting Graphs of Quadratic Functions
    • 7.6.5: Practice
    • 7.6.6: Lesson Summary
  • Lesson 7.7 Teacher Guide: Domain, Range, Vertex, and Zeros of Quadratic Functions
    • 7.7.0: Lesson Overview
    • 7.7.1: Comparing Graphs of Functions
    • 7.7.2: Modeling Real-World Data with Quadratic Functions
    • 7.7.3: The Domain, Vertex, and Zero of Quadratic Functions
    • 7.7.4: Relate the Domain of a Function to Its Graph
    • 7.7.5: Practice
    • 7.7.6: Lesson Synthesis
  • Lesson 7.7: Domain, Range, Vertex, and Zeros of Quadratic Functions
    • 7.7.0: Lesson Overview
    • 7.7.1: Comparing Graphs of Functions
    • 7.7.2: Modeling Real-World Data with Quadratic Functions
    • 7.7.2: Self Check
    • 7.7.2: Additional Resources
    • 7.7.3: The Domain, Vertex, and Zero of Quadratic Functions
    • 7.7.3: Self Check
    • 7.7.3: Additional Resources
    • 7.7.4: Relate the Domain of a Function to Its Graph
    • 7.7.5: Practice
    • 7.7.6: Lesson Summary
  • Unit 7, Section C Overview: Working with Quadratic Expressions
  • Lesson 7.8 Teacher Guide: Equivalent Quadratic Expressions
    • 7.8.0: Lesson Overview
    • 7.8.1: Area Diagrams
    • 7.8.2: Using the Distributive Property to Write Equivalent Expressions
    • 7.8.3: Using Diagrams to Find Equivalent Quadratic Expressions
    • 7.8.4: Writing Equivalent Expressions
    • 7.8.5: Practice
    • 7.8.6: Lesson Synthesis
  • Lesson 7.8: Equivalent Quadratic Expressions
    • 7.8.0: Lesson Overview
    • 7.8.1: Area Diagrams
    • 7.8.2: Using the Distributive Property to Write Equivalent Expressions
    • 7.8.2: Self Check
    • 7.8.2: Additional Resources
    • 7.8.3: Using Diagrams to Find Equivalent Quadratic Expressions
    • 7.8.3: Self Check
    • 7.8.3: Additional Resources
    • 7.8.4: Writing Equivalent Expressions
    • 7.8.5: Practice
    • 7.8.6: Lesson Summary
  • Lesson 7.9 Teacher Guide: Standard Form and Factored Form
    • 7.9.0: Lesson Overview
    • 7.9.1: Solving Equations Using Opposite Operations
    • 7.9.2: Finding Products of Differences
    • 7.9.3: Standard and Factored Forms of Quadratic Expressions
    • 7.9.4: Expressions in Standard Form
    • 7.9.5: Practice
    • 7.9.6: Lesson Synthesis
  • Lesson 7.9: Standard Form and Factored Form
    • 7.9.0: Lesson Overview
    • 7.9.1: Solving Equations Using Opposite Operations
    • 7.9.2: Finding Products of Differences
    • 7.9.2: Self Check
    • 7.9.2: Additional Resources
    • 7.9.3: Standard and Factored Forms of Quadratic Expressions
    • 7.9.3: Self Check
    • 7.9.3: Additional Resources
    • 7.9.4: Expressions in Standard Form
    • 7.9.5: Practice
    • 7.9.6: Lesson Summary
  • Lesson 7.10 Teacher Guide: Graphs of Functions in Standard and Factored Forms
    • 7.10.0: Lesson Overview
    • 7.10.1: Graphs of Linear Equations
    • 7.10.2: Quadratic Forms and Their Graphs
    • 7.10.3: The X- and Y-Intercepts of Quadratic Expressions
    • 7.10.4: Using the Standard Form of an Equation to Find the X- and Y-Intercepts
    • 7.10.5: Practice
    • 7.10.6: Lesson Synthesis
  • Lesson 7.10: Graphs of Functions in Standard and Factored Forms
    • 7.10.0: Lesson Overview
    • 7.10.1: Graphs of Linear Equations
    • 7.10.2: Quadratic Forms and Their Graphs
    • 7.10.2: Self Check
    • 7.10.2: Additional Resources
    • 7.10.3: The X- and Y-Intercepts of Quadratic Expressions
    • 7.10.3: Self Check
    • 7.10.3: Additional Resources
    • 7.10.4: Using the Standard Form of an Equation to Find the X- and Y-Intercepts
    • 7.10.5: Practice
    • 7.10.6: Lesson Summary
  • Unit 7 Section D Overview: Features of Graphs of Quadratic Functions
  • Lesson 7.11 Teacher Guide: Graphing from the Factored Form
    • 7.11.0: Lesson Overview
    • 7.11.1: Finding Coordinates
    • 7.11.2: The Factored Form of a Quadratic Expression and the X-Intercepts of Its Graph
    • 7.11.3: Sketching a Graph of a Quadratic Function Using at Least Three Identifiable Points
    • 7.11.4: Using the Vertex and Axis of Symmetry of Quadratics
    • 7.11.5: Graphs of Quadratic Functions
    • 7.11.6: Practice
    • 7.11.7: Lesson Synthesis
  • Lesson 7.11: Graphing from the Factored Form
    • 7.11.0: Lesson Overview
    • 7.11.1: Finding Coordinates
    • 7.11.2: The Factored Form of a Quadratic Expression and the X-Intercepts of Its Graph
    • 7.11.2: Self Check
    • 7.11.2: Additional Resources
    • 7.11.3: Sketching a Graph of a Quadratic Function Using at Least Three Identifiable Points
    • 7.11.3: Self Check
    • 7.11.3: Additional Resources
    • 7.11.4: Using the Vertex and Axis of Symmetry of Quadratics
    • 7.11.4: Self Check
    • 7.11.4: Additional Resources
    • 7.11.5: Graphs of Quadratic Functions
    • 7.11.6: Practice
    • 7.11.7: Lesson Summary
  • Lesson 7.12 Teacher Guide: Graphing the Standard Form, Part 1
    • 7.12.0: Lesson Overview
    • 7.12.1: Using Coefficients and Constant Terms to Identify Graphs of Linear Equations
    • 7.12.2: Transformations with Quadratic Functions
    • 7.12.3: Understanding the Behaviors of a Graph in Relation to Its Quadratic Expression
    • 7.12.4: Representations of Quadratic Functions
    • 7.12.5: Identifying Graphs of Quadratic Equations
    • 7.12.6: Practice
    • 7.12.7: Lesson Synthesis
  • Lesson 7.12: Graphing the Standard Form, Part 1
    • 7.12.0: Lesson Overview
    • 7.12.1: Using Coefficients and Constant Terms to Identify Graphs of Linear Equations
    • 7.12.2: Transformations with Quadratic Functions
    • 7.12.2: Self Check
    • 7.12.2: Additional Resources
    • 7.12.3: Understanding the Behaviors of a Graph in Relation to Its Quadratic Expression
    • 7.12.3: Self Check
    • 7.12.3: Additional Resources
    • 7.12.4: Representations of Quadratic Functions
    • 7.12.4: Self Check
    • 7.12.4: Additional Resources
    • 7.12.5: Identifying Graphs of Quadratic Equations
    • 7.12.6: Practice
    • 7.12.7: Lesson Summary
  • Lesson 7.13 Teacher Guide: Graphing the Standard Form, Part 2
    • 7.13.0: Lesson Overview
    • 7.13.1: Equivalent Expressions
    • 7.13.2: The Linear Term in a Quadratic Expression
    • 7.13.3: Writing Equations that Represent a Graph
    • 7.13.4: Writing Quadratic Equations from Real Solutions
    • 7.13.5: Graphing Quadratic Equations
    • 7.13.6: Practice
    • 7.13.7: Lesson Synthesis
  • Lesson 7.13: Graphing the Standard Form, Part 2
    • 7.13.0: Lesson Overview
    • 7.13.1: Equivalent Expressions
    • 7.13.2: The Linear Term in a Quadratic Expression
    • 7.13.2: Self Check
    • 7.13.2: Additional Resources
    • 7.13.3: Writing Equations that Represent a Graph
    • 7.13.3: Self Check
    • 7.13.3: Additional Resources
    • 7.13.4: Writing Quadratic Equations from Real Solutions
    • 7.13.4 Self Check
    • 7.13.4 Additional Resources
    • 7.13.5: Graphing Quadratic Equations
    • 7.13.6: Practice
    • 7.13.7: Lesson Summary
  • Lesson 7.14 Teacher Guide: Graphs That Represent Situations
    • 7.14.0: Lesson Overview
    • 7.14.1: Evaluating Quadratic Functions in the Real World
    • 7.14.2: Interpreting a Functional Relationship between Two Quantities
    • 7.14.3: Analyzing Functions Using Different Representations
    • 7.14.4: Using Quadratic Functions to Solve Problems
    • 7.14.5: Identifying Key Features of Graphed Functions
    • 7.14.6: Practice
    • 7.14.7: Lesson Synthesis
  • Lesson 7.14: Graphs That Represent Situations
    • 7.14.0: Lesson Overview
    • 7.14.1: Evaluating Quadratic Functions in the Real World
    • 7.14.2: Interpreting a Functional Relationship between Two Quantities
    • 7.14.2: Self Check
    • 7.14.2: Additional Resources
    • 7.14.3: Analyzing Functions Using Different Representations
    • 7.14.3: Self Check
    • 7.14.3: Additional Resources
    • 7.14.4: Using Quadratic Functions to Solve Problems
    • 7.14.5: Identifying Key Features of Graphed Functions
    • 7.14.6: Practice
    • 7.14.7: Lesson Summary
  • Lesson 7.15 Teacher Guide: Vertex Form
    • 7.15.0: Lesson Overview
    • 7.15.1: Analyzing Two Sets of Equations
    • 7.15.2: The Vertex Form
    • 7.15.3: The Coordinates of the Vertex
    • 7.15.4: The Graph of a Function in Vertex Form
    • 7.15.5: Practice
    • 7.15.6: Lesson Synthesis
  • Lesson 7.15: Vertex Form
    • 7.15.0: Lesson Overview
    • 7.15.1: Analyzing Two Sets of Equations
    • 7.15.2: The Vertex Form
    • 7.15.2: Self Check
    • 7.15.2: Additional Resources
    • 7.15.3: The Coordinates of the Vertex
    • 7.15.3: Self Check
    • 7.15.3: Additional Resources
    • 7.15.4: The Graph of a Function in Vertex Form
    • 7.15.5: Practice
    • 7.15.6: Lesson Summary
  • Lesson 7.16 Teacher Guide: Graphing from the Vertex Form
    • 7.16.0: Lesson Overview
    • 7.16.1: Three Forms of Quadratic Expressions
    • 7.16.2: Graph Functions in Vertex Form
    • 7.16.3: Quadratic Equations and Graphs
    • 7.16.4: Sketching A Graph of an Equation
    • 7.16.5: Practice
    • 7.16.6: Lesson Synthesis
  • Lesson 7.16: Graphing from the Vertex Form
    • 7.16.0: Lesson Overview
    • 7.16.1: Three Forms of Quadratic Expressions
    • 7.16.2: Graph Functions in Vertex Form
    • 7.16.2: Self Check
    • 7.16.2: Additional Resources
    • 7.16.3: Quadratic Equations and Graphs
    • 7.16.3: Self Check
    • 7.16.3: Additional Resources
    • 7.16.4: Sketching A Graph of an Equation
    • 7.16.5: Practice
    • 7.16.6: Lesson Summary
  • Lesson 7.17 Teacher Guide: Changing the Vertex
    • 7.17.0: Lesson Overview
    • 7.17.1: Quadratic Expressions in Different Forms
    • 7.17.2: Modify Expressions to Translate Graphs
    • 7.17.3: Changing the Parameters of a Quadratic Expression
    • 7.17.4: Transforming the Parent Function
    • 7.17.5: Equations of Graph Translations
    • 7.17.6: Practice
    • 7.17.7: Lesson Synthesis
  • Lesson 7.17: Changing the Vertex
    • 7.17.0: Lesson Overview
    • 7.17.1: Quadratic Expressions in Different Forms
    • 7.17.2: Modify Expressions to Translate Graphs
    • 7.17.2: Self Check
    • 7.17.2: Additional Resources
    • 7.17.3: Changing the Parameters of a Quadratic Expression
    • 7.17.3: Self Check
    • 7.17.3: Additional Resources
    • 7.17.4: Transforming the Parent Function
    • 7.17.5: Equations of Graph Translations
    • 7.17.6: Practice
    • 7.17.7: Lesson Summary
  • Project 7 Teacher Guide: Design a Fountain
    • Project 7 Overview
    • Introduction to Fountain Design
    • Design a Fountain
  • Project 7: Design a Fountain
    • Project 7 Overview
    • Introduction to Fountain Design
    • Design a Fountain
  • Unit 7 Wrap Up
• Unit 8: Quadratic Equations
  • Unit 8 Teacher Guide
    • Unit 8 Overview and Readiness
    • Unit 8 Narrative
    • Unit 8 Family Support Materials
    • Building Character: Curiosity
    • Supporing English Language Proficiency Standards (ELPS)
  • Unit 8 Overview and Readiness
    • Unit 8 Overview: Why Should I Care?
    • Unit 8 Overview: Am I Ready to Learn This?
    • Question #1: Write Equivalent Expressions
    • Write Equivalent Expressions: Mini-Lesson Review
    • Question #2: Find Intercepts
    • Find Intercepts: Mini-Lesson Review
    • Question #3: Match Quadratic Graphs and Their Equations
    • Match Quadratic Graphs and Their Equations: Mini-Lesson Review
    • Unit 8 Overview: Wrap Up
  • Unit 8 Section A Overview: Finding Unknown Inputs
  • Lesson 8.1 Teacher Guide: Finding Unknown Inputs
    • 8.1.0: Lesson Overview
    • 8.1.1: Understanding a Situation with Quadratic Equations
    • 8.1.2: Modeling a Quadratic Problem
    • 8.1.3: Formulating a Quadratic Equation to Represent the Model
    • 8.1.4: Interpreting a Solution
    • 8.1.5: Practice
    • 8.1.6: Lesson Synthesis
  • Lesson 8.1: Finding Unknown Inputs
    • 8.1.0: Lesson Overview
    • 8.1.1: Understanding a Situation with Quadratic Equations
    • 8.1.2: Modeling a Quadratic Problem
    • 8.1.2: Self Check
    • 8.1.2: Additional Resources
    • 8.1.3: Formulating a Quadratic Equation to Represent the Model
    • 8.1.3: Self Check
    • 8.1.3: Additional Resources
    • 8.1.4: Interpreting a Solution
    • 8.1.5: Practice
    • 8.1.6: Lesson Summary
  • Lesson 8.2 Teacher Guide: When and Why Do We Write Quadratic Equations?
    • 8.2.0: Lesson Overview
    • 8.2.1: Interpreting Equations in Context
    • 8.2.2: Exploring Non-Graphing Strategies to Solve Quadratic Equations
    • 8.2.3: Solving a Quadratic Equation Set Equal to Zero
    • 8.2.4: Solving a Real-World Problem Using Quadratic Equations
    • 8.2.5: Practice
    • 8.2.6: Lesson Synthesis
  • Lesson 8.2: When and Why Do We Write Quadratic Equations?
    • 8.2.0: Lesson Overview
    • 8.2.1: Interpreting Equations in Context
    • 8.2.2: Exploring Non-Graphing Strategies to Solve Quadratic Equations
    • 8.2.2: Self Check
    • 8.2.2: Additional Resources
    • 8.2.3: Solving a Quadratic Equation Set Equal to Zero
    • 8.2.3: Self Check
    • 8.2.3: Additional Resources
    • 8.2.4: Solving a Real-World Problem Using Quadratic Equations
    • 8.2.5: Practice
    • 8.2.6: Lesson Summary
  • Unit 8 Section B Overview: Solving Quadratic Equations
  • Lesson 8.3 Teacher Guide: Solving Quadratic Equations by Reasoning
    • 8.3.0: Lesson Overview
    • 8.3.1: Determining the Number of Solutions
    • 8.3.2: Recognizing Pairs of Solutions
    • 8.3.3: Solving More Complex Quadratic Equations
    • 8.3.4: Finding the Solutions
    • 8.3.5: Practice
    • 8.3.6: Lesson Synthesis
  • Lesson 8.3: Solving Quadratic Equations by Reasoning
    • 8.3.0: Lesson Overview
    • 8.3.1: Determining the Number of Solutions
    • 8.3.2: Recognizing Pairs of Solutions
    • 8.3.2: Self Check
    • 8.3.2: Additional Resources
    • 8.3.3: Solving More Complex Quadratic Equations
    • 8.3.3: Self Check
    • 8.3.3: Additional Resources
    • 8.3.4: Finding the Solutions
    • 8.3.5: Practice
    • 8.3.6: Lesson Summary
  • Lesson 8.4 Teacher Guide: Solving Quadratic Equations with the Zero Product Property
    • 8.4.0: Lesson Overview
    • 8.4.1: Introducing the Zero Product Property
    • 8.4.2: Solving Equations of Increasing Complexity Using Reasoning
    • 8.4.3: Applying the Zero Product Property to Solve a Real-World Projectile Problem
    • 8.4.4: Solving Equations Using the Zero Product Property and Reasoning
    • 8.4.5: Practice
    • 8.4.6: Lesson Synthesis
  • Lesson 8.4: Solving Quadratic Equations with the Zero Product Property
    • 8.4.0: Lesson Overview
    • 8.4.1: Introducing the Zero Product Property
    • 8.4.2: Solving Equations of Increasing Complexity Using Reasoning
    • 8.4.2: Self Check
    • 8.4.2: Additional Resources
    • 8.4.3: Applying the Zero Product Property to Solve a Real-World Projectile Problem
    • 8.4.3: Self Check
    • 8.4.3: Additional Resources
    • 8.4.4: Solving Equations Using the Zero Product Property and Reasoning
    • 8.4.5: Practice
    • 8.4.6: Lesson Summary
  • Lesson 8.5 Teacher Guide: How Many Solutions?
    • 8.5.0: Lesson Overview
    • 8.5.1: Reviewing Zero Product Property
    • 8.5.2: Interpreting Graphs to Solve Quadratic Equations
    • 8.5.3: Choosing an Effective Strategy to Solve Quadratic Equations
    • 8.5.4: Analyzing Errors When Solving Quadratic Equations
    • 8.5.5: Practice
    • 8.5.6: Lesson Synthesis
  • Lesson 8.5: How Many Solutions?
    • 8.5.0: Lesson Overview
    • 8.5.1: Reviewing Zero Product Property
    • 8.5.2: Interpreting Graphs to Solve Quadratic Equations
    • 8.5.2: Self Check
    • 8.5.2: Additional Resources
    • 8.5.3: Choosing an Effective Strategy to Solve Quadratic Equations
    • 8.5.3: Self Check
    • 8.5.3: Additional Resources
    • 8.5.4: Analyzing Errors When Solving Quadratic Equations
    • 8.5.5: Practice
    • 8.5.6: Lesson Summary
  • Lesson 8.6 Teacher Guide: Rewriting Quadratic Expressions in Factored Form, Part 1
    • 8.6.0: Lesson Overview
    • 8.6.1: Finding and Reasoning Unknown Factors
    • 8.6.2: Using Diagrams to Understand Equivalent Expressions
    • 8.6.3: Rewriting Quadratic Expressions in Standard Form
    • 8.6.4: Finding the Missing Numbers in Pairs of Equivalent Expressions
    • 8.6.5: Practice
    • 8.6.6: Lesson Synthesis
  • Lesson 8.6: Rewriting Quadratic Expressions in Factored Form, Part 1
    • 8.6.0: Lesson Overview
    • 8.6.1: Finding and Reasoning Unknown Factors
    • 8.6.2: Using Diagrams to Understand Equivalent Expressions
    • 8.6.2: Self Check
    • 8.6.2: Additional Resources
    • 8.6.3: Rewriting Quadratic Expressions in Standard Form
    • 8.6.3: Self Check
    • 8.6.3: Additional Resources
    • 8.6.4: Finding the Missing Numbers in Pairs of Equivalent Expressions
    • 8.6.5: Practice
    • 8.6.6: Lesson Summary
  • Lesson 8.7 Teacher Guide: Rewriting Quadratic Expressions in Factored Form, Part 2
    • 8.7.0: Lesson Overview
    • 8.7.1: Understanding Sums and Products of Integers
    • 8.7.2: Interpreting Negative Constant Terms When Factoring Quadratic Expressions
    • 8.7.3: Analyzing Factors of 100 and –100
    • 8.7.4: Finding the Missing Terms
    • 8.7.5: Practice
    • 8.7.6: Lesson Synthesis
  • Lesson 8.7: Rewriting Quadratic Expressions in Factored Form, Part 2
    • 8.7.0: Lesson Overview
    • 8.7.1: Understanding Sums and Products of Integers
    • 8.7.2: Interpreting Negative Constant Terms When Factoring Quadratic Expressions
    • 8.7.2: Self Check
    • 8.7.2: Additional Resources
    • 8.7.3: Analyzing Factors of 100 and –100
    • 8.7.3: Self Check
    • 8.7.3: Additional Resources
    • 8.7.4: Finding the Missing Terms
    • 8.7.5: Practice
    • 8.7.6: Lesson Summary
  • Lesson 8.8 Teacher Guide: Rewriting Quadratic Expressions in Factored Form, Part 3
    • 8.8.0: Lesson Overview
    • 8.8.1: Evaluating Expressions Using Mental Math
    • 8.8.2: Recognizing the Expanded Product of the Difference of Two Squares
    • 8.8.3: Factoring Quadratic Equations without a Linear Term
    • 8.8.4: Determining if an Expression Can Be Rewritten in Factored Form
    • 8.8.5: Practice
    • 8.8.6: Lesson Synthesis
  • Lesson 8.8: Rewriting Quadratic Expressions in Factored Form, Part 3
    • 8.8.0: Lesson Overview
    • 8.8.1: Evaluating Expressions Using Mental Math
    • 8.8.2: Recognizing the Expanded Product of the Difference of Two Squares
    • 8.8.2: Self Check
    • 8.8.2: Additional Resources
    • 8.8.3: Factoring Quadratic Equations without a Linear Term
    • 8.8.3: Self Check
    • 8.8.3: Additional Resources
    • 8.8.4: Determining if an Expression Can Be Rewritten in Factored Form
    • 8.8.5: Practice
    • 8.8.6: Lesson Summary
  • Lesson 8.9 Teacher Guide: Solving Quadratic Equations by Using Factored Form
    • 8.9.0: Lesson Overview
    • 8.9.1: Finding a Solution through Substitution
    • 8.9.2: Using Factored Form and the Zero Product Property to Solve Quadratic Equations
    • 8.9.3: Writing an Equation to Represent a Quadratic Function with Only One Solution
    • 8.9.4: Solving More Quadratic Equations
    • 8.9.5: Practice
    • 8.9.6: Lesson Synthesis
  • Lesson 8.9: Solving Quadratic Equations by Using Factored Form
    • 8.9.0: Lesson Overview
    • 8.9.1: Finding a Solution through Substitution
    • 8.9.2: Using Factored Form and the Zero Product Property to Solve Quadratic Equations
    • 8.9.2: Self Check
    • 8.9.2: Additional Resources
    • 8.9.3: Writing an Equation to Represent a Quadratic Function with Only One Solution
    • 8.9.3: Self Check
    • 8.9.3: Additional Resources
    • 8.9.4: Solving More Quadratic Equations
    • 8.9.5: Practice
    • 8.9.6: Lesson Summary
  • Lesson 8.10 Teacher Guide: Rewriting Quadratic Expressions in Factored Form, Part 4
    • 8.10.0: Lesson Overview
    • 8.10.1: Analyzing Various Quadratic Expressions
    • 8.10.2: Working with Quadratic Factored Form with Leading Coefficient Other Than One
    • 8.10.3: Using Technology to Find Rational Factors
    • 8.10.4: Finding the Factors of Quadratic Expressions in Standard Form
    • 8.10.5: Solving Quadratic Equations by Any Method
    • 8.10.6: Practice
    • 8.10.7: Lesson Synthesis
  • Lesson 8.10: Rewriting Quadratic Expressions in Factored Form, Part 4
    • 8.10.0: Lesson Overview
    • 8.10.1: Analyzing Various Quadratic Expressions
    • 8.10.2: Working with Quadratic Factored Form with Leading Coefficient Other Than One
    • 8.10.2: Self Check
    • 8.10.2: Additional Resources
    • 8.10.3: Using Technology to Find Rational Factors
    • 8.10.3: Self Check
    • 8.10.3: Additional Resources
    • 8.10.4: Finding the Factors of Quadratic Expressions in Standard Form
    • 8.10.4: Self Check
    • 8.10.4: Additional Resources
    • 8.10.5: Solving Quadratic Equations by Any Method
    • 8.10.6: Practice
    • 8.10.7: Lesson Summary
  • Unit 8 Section C Overview: Working with Quadratic Equations and Graphs
  • Lesson 8.11 Teacher Guide: Writing Quadratic Equations Given Real Solutions
    • 8.11.0: Lesson Overview
    • 8.11.1: Relating a Quadratic Function and Its Zeros
    • 8.11.2: Finding a Quadratic Function from Its Zeros
    • 8.11.3: Finding a Quadratic Function from Its Zeros and a Point
    • 8.11.4: Writing Quadratics When Given Any Format
    • 8.11.5: Practice
    • 8.11.6: Lesson Synthesis
  • Lesson 8.11: Writing Quadratic Equations Given Real Solutions
    • 8.11.0: Lesson Overview
    • 8.11.1: Relating a Quadratic Function and Its Zeros
    • 8.11.2: Finding a Quadratic Function from Its Zeros
    • 8.11.2: Self Check
    • 8.11.2: Additional Resources
    • 8.11.3: Finding a Quadratic Function from Its Zeros and a Point
    • 8.11.3: Self Check
    • 8.11.3: Additional Resources
    • 8.11.4: Writing Quadratics When Given Any Format
    • 8.11.5: Practice
    • 8.11.6: Lesson Summary
  • Lesson 8.12 Teacher Guide: Using Technology to Find the Quadratic Regression
    • 8.12.0: Lesson Overview
    • 8.12.1: Graphing a Quadratic Data Set Using Technology
    • 8.12.2: Finding the Curve of Best Fit
    • 8.12.3: Making Predictions Using a Quadratic Model
    • 8.12.4: Finding the Missing Data in the Set
    • 8.12.5: Practice
    • 8.12.6: Lesson Synthesis
  • Lesson 8.12: Using Technology to Find the Quadratic Regression
    • 8.12.0: Lesson Overview
    • 8.12.1: Graphing a Quadratic Data Set Using Technology
    • 8.12.2: Finding the Curve of Best Fit
    • 8.12.2: Self Check
    • 8.12.2: Additional Resources
    • 8.12.3: Making Predictions Using a Quadratic Model
    • 8.12.3: Self Check
    • 8.12.3: Additional Resources
    • 8.12.4: Finding the Missing Data in the Set
    • 8.12.5: Practice
    • 8.12.6: Lesson Summary
  • Project 8 Teacher Guide: Modeling Rocket Flight
    • Project 8 Overview
    • Relate Zeros to the Factored Form of Quadratic Equations
    • Convert between Factored Form and Standard Form
    • Model a Rocket Flight Using a Quadratic Equation
  • Project 8: Modeling Rocket Flight
    • Project 8 Overview
    • Relate Zeros to the Factored Form of Quadratic Equations
    • Convert between Factored Form and Standard Form
    • Model a Rocket Flight Using a Quadratic Equation
  • Unit 8 Wrap Up
• Unit 9: More Quadratic Equations
  • Unit 9 Teacher Guide
    • Unit 9 Overview and Readiness
    • Unit 9 Narrative
    • Unit 9 Family Support Materials
    • Building Character: Intellectual Humility
    • Supporting English Language Proficiency Standards (ELPS)
  • Unit 9 Overview and Readiness
    • Unit 9 Overview: Why Should I Care?
    • Unit 9 Overview: Am I Ready to Learn This?
    • Question #1: Simplifying Radicals
    • Simplifying Radicals: Mini-Lesson Review
    • Question #2: Factoring Perfect Square Trinomials
    • Factoring Perfect Square Trinomials: Mini-Lesson Review
    • Question #3: Transformations
    • Transformations: Mini-Lesson Review
    • Unit 9 Overview: Wrap Up
  • Unit 9 Section A Overview: Completing the Square
  • Lesson 9.1 Teacher Guide: What Are Perfect Squares?
    • 9.1.0: Lesson Overview
    • 9.1.1: Equations with Quadratic Expressions on Both Sides of the Equal Sign
    • 9.1.2: Recognizing Structure in Perfect-Square Expressions
    • 9.1.3: Solving Multi Step Quadratic Equations Using Perfect Squares
    • 9.1.4: Explain Why an Expression Is a Perfect Square
    • 9.1.5: Practice
    • 9.1.6: Lesson Synthesis
  • Lesson 9.1: What Are Perfect Squares?
    • 9.1.0: Lesson Overview
    • 9.1.1: Equations with Quadratic Expressions on Both Sides of the Equal Sign
    • 9.1.2: Recognizing Structure in Perfect-Square Expressions
    • 9.1.2: Self Check
    • 9.1.2: Additional Resources
    • 9.1.3: Solving Multi Step Quadratic Equations Using Perfect Squares
    • 9.1.3: Self Check
    • 9.1.3: Additional Resources
    • 9.1.4: Explain Why an Expression Is a Perfect Square
    • 9.1.5: Practice
    • 9.1.6: Lesson Summary
  • Lesson 9.2 Teacher Guide: Completing the Square, Part 1
    • 9.2.0: Lesson Overview
    • 9.2.1: Different Forms of Perfect Squares
    • 9.2.2: Standard and Factored Forms of Perfect Squares
    • 9.2.3: Completing the Square
    • 9.2.4: Making a Perfect Square
    • 9.2.5: Practice
    • 9.2.6: Lesson Synthesis
  • Lesson 9.2: Completing the Square, Part 1
    • 9.2.0: Lesson Overview
    • 9.2.1: Different Forms of Perfect Squares
    • 9.2.2: Standard and Factored Forms of Perfect Squares
    • 9.2.2: Self Check
    • 9.2.2: Additional Resources
    • 9.2.3: Completing the Square
    • 9.2.3: Self Check
    • 9.2.3: Additional Resources
    • 9.2.4: Making a Perfect Square
    • 9.2.5: Practice
    • 9.2.6: Lesson Summary
  • Lesson 9.3 Teacher Guide: Completing the Square, Part 2
    • 9.3.0: Lesson Overview
    • 9.3.1: Solving Equations with Fractions
    • 9.3.2: Using Completing the Square to Solve Equations
    • 9.3.3: Solve by Completing the Square
    • 9.3.4: Completing the Square with Fractions
    • 9.3.5: Practice
    • 9.3.6: Lesson Synthesis
  • Lesson 9.3: Completing the Square, Part 2
    • 9.3.0: Lesson Overview
    • 9.3.1: Solving Equations with Fractions
    • 9.3.2: Using Completing the Square to Solve Equations
    • 9.3.2: Self Check
    • 9.3.2: Additional Resources
    • 9.3.3: Solve by Completing the Square
    • 9.3.3: Self Check
    • 9.3.3: Additional Resources
    • 9.3.4: Completing the Square with Fractions
    • 9.3.5: Practice
    • 9.3.6: Lesson Summary
  • Lesson 9.4 Teacher Guide: Completing the Square, Part 3
    • 9.4.0: Lesson Overview
    • 9.4.1: Perfect Squares with Coefficients Other than 1
    • 9.4.2: Rewrite Squared Expressions
    • 9.4.3: Standard Form and Squared Factors
    • 9.4.4: Three Different Methods for Solving an Equation
    • 9.4.5: Perfect Square and Squared Factors
    • 9.4.6: Practice
    • 9.4.7: Lesson Synthesis
  • Lesson 9.4: Completing the Square, Part 3
    • 9.4.0: Lesson Overview
    • 9.4.1: Perfect Squares with Coefficients Other than 1
    • 9.4.2: Rewrite Squared Expressions
    • 9.4.2: Self Check
    • 9.4.2: Additional Resources
    • 9.4.3: Standard Form and Squared Factors
    • 9.4.3: Self Check
    • 9.4.3: Additional Resources
    • 9.4.4: Three Different Methods for Solving an Equation
    • 9.4.5: Perfect Square and Squared Factors
    • 9.4.6: Practice
    • 9.4.7: Lesson Summary
  • Lesson 9.5 Teacher Guide: Quadratic Equations with Irrational Solutions
    • 9.5.0: Lesson Overview
    • 9.5.1: Roots of Squares
    • 9.5.2: Solutions Written as Square Roots
    • 9.5.3: Finding Irrational Solutions by Completing the Square
    • 9.5.4: Finding Exact Solutions
    • 9.5.5: Practice
    • 9.5.6: Lesson Synthesis
  • Lesson 9.5: Quadratic Equations with Irrational Solutions
    • 9.5.0: Lesson Overview
    • 9.5.1: Roots of Squares
    • 9.5.2: Solutions Written as Square Roots
    • 9.5.2: Self Check
    • 9.5.2: Additional Resources
    • 9.5.3: Finding Irrational Solutions by Completing the Square
    • 9.5.3: Self Check
    • 9.5.3: Additional Resources
    • 9.5.4: Finding Exact Solutions
    • 9.5.5: Practice
    • 9.5.6: Lesson Summary
  • Unit 9 Section B Overview: The Quadratic Formula
  • Lesson 9.6 Teacher Guide: The Quadratic Formula
    • 9.6.0: Lesson Overview
    • 9.6.1: Evaluating Expressions
    • 9.6.2: Choosing the Best Method to Solve an Equation
    • 9.6.3: The Quadratic Formula
    • 9.6.4: Solving Equations Using the Quadratic Formula
    • 9.6.5: Practice
    • 9.6.6: Lesson Synthesis
  • Lesson 9.6: The Quadratic Formula
    • 9.6.0: Lesson Overview
    • 9.6.1: Evaluating Expressions
    • 9.6.2: Choosing the Best Method to Solve an Equation
    • 9.6.2: Self Check
    • 9.6.2: Additional Resources
    • 9.6.3: The Quadratic Formula
    • 9.6.3: Self Check
    • 9.6.3: Additional Resources
    • 9.6.4: Solving Equations Using the Quadratic Formula
    • 9.6.5: Practice
    • 9.6.6: Lesson Summary
  • Lesson 9.7 Teacher Guide: Applying the Quadratic Formula
    • 9.7.0: Lesson Overview
    • 9.7.1: Evaluating Variable Expressions
    • 9.7.2: Common Calculation Errors When Using the Quadratic Formula
    • 9.7.3: Different Methods of Checking Solutions of Quadratic Equations
    • 9.7.4: Practice Spotting Calculation Errors
    • 9.7.5: Practice
    • 9.7.6: Lesson Synthesis
  • Lesson 9.7: Applying the Quadratic Formula
    • 9.7.0: Lesson Overview
    • 9.7.1: Evaluating Variable Expressions
    • 9.7.2: Common Calculation Errors When Using the Quadratic Formula
    • 9.7.2: Self Check
    • 9.7.2: Additional Resources
    • 9.7.3: Different Methods of Checking Solutions of Quadratic Equations
    • 9.7.3: Self Check
    • 9.7.3: Additional Resources
    • 9.7.4: Practice Spotting Calculation Errors
    • 9.7.5: Practice
    • 9.7.6: Lesson Summary
  • Lesson 9.8 Teacher Guide: Deriving the Quadratic Formula
    • 9.8.0: Lesson Overview
    • 9.8.1: Deriving the Quadratic Formula, Part 1
    • 9.8.2: Deriving the Quadratic Formula, Part 2
    • 9.8.3: Understanding That the Quadratic Formula Is the Combined Steps of Completing the Square
    • 9.8.4: Practice
    • 9.8.5: Lesson Synthesis
  • Lesson 9.8: Deriving the Quadratic Formula
    • 9.8.0: Lesson Overview
    • 9.8.1: Deriving the Quadratic Formula, Part 1
    • 9.8.1: Self Check
    • 9.8.1: Additional Resources
    • 9.8.2: Deriving the Quadratic Formula, Part 2
    • 9.8.2: Self Check
    • 9.8.2: Additional Resources
    • 9.8.3: Understanding That the Quadratic Formula Is the Combined Steps of Completing the Square
    • 9.8.4: Practice
    • 9.8.5: Lesson Summary
  • Unit 9 Section C Overview: Vertex Form Revisited
  • Lesson 9.9 Teacher Guide: Writing Quadratics in Different Forms
    • 9.9.0: Lesson Overview
    • 9.9.1: Finding the Vertex in Vertex Form
    • 9.9.2: Different Forms of Quadratics
    • 9.9.3: Vertex Form Given a Vertex and Point
    • 9.9.4: Rewriting Quadratics
    • 9.9.5: Practice
    • 9.9.6: Lesson Synthesis
  • Lesson 9.9: Writing Quadratics in Different Forms
    • 9.9.0: Lesson Overview
    • 9.9.1: Finding the Vertex in Vertex Form
    • 9.9.2: Different Forms of Quadratics
    • 9.9.2: Self Check
    • 9.9.2: Additional Resources
    • 9.9.3: Vertex Form Given a Vertex and Point
    • 9.9.3: Self Check
    • 9.9.3: Additional Resources
    • 9.9.4: Rewriting Quadratics
    • 9.9.5: Practice
    • 9.9.6: Lesson Summary
  • Lesson 9.10 Teacher Guide: Rewriting Quadratic Expressions in Vertex Form
    • 9.10.0: Lesson Overview
    • 9.10.1: The Vertex and Intercepts of a Function
    • 9.10.2: Expanding from Factored Form to Standard Form
    • 9.10.3: Converting from Standard Form to Vertex Form
    • 9.10.4: Rewriting Expressions in Vertex Form
    • 9.10.5: Different Forms of Quadratic Expressions
    • 9.10.6: Vertex Form and Coordinates of the Vertex
    • 9.10.7: Practice
    • 9.10.8: Lesson Synthesis
  • Lesson 9.10: Rewriting Quadratic Expressions in Vertex Form
    • 9.10.0: Lesson Overview
    • 9.10.1: The Vertex and Intercepts of a Function
    • 9.10.2: Expanding from Factored Form to Standard Form
    • 9.10.3: Converting from Standard Form to Vertex Form
    • 9.10.3: Self Check
    • 9.10.3: Additional Resources
    • 9.10.4: Rewriting Expressions in Vertex Form
    • 9.10.4: Self Check
    • 9.10.4: Additional Resources
    • 9.10.5: Different Forms of Quadratic Expressions
    • 9.10.6: Vertex Form and Coordinates of the Vertex
    • 9.10.7: Practice
    • 9.10.8: Lesson Summary
  • Lesson 9.11 Teacher Guide: Using Quadratic Expressions in Vertex Form to Solve Problems
    • 9.11.0: Lesson Overview
    • 9.11.1: Maximum and Minimum Value of a Function
    • 9.11.2: Does the Vertex Represent the Minimum or Maximum Value?
    • 9.11.3: Comparing Maximums between Quadratics
    • 9.11.4: Maximum, Minimum, and Analyzing the Vertex
    • 9.11.5: Practice
    • 9.11.6: Lesson Synthesis
  • Lesson 9.11: Using Quadratic Expressions in Vertex Form to Solve Problems
    • 9.11.0: Lesson Overview
    • 9.11.1: Maximum and Minimum Value of a Function
    • 9.11.2: Does the Vertex Represent the Minimum or Maximum Value?
    • 9.11.2: Self Check
    • 9.11.2: Additional Resources
    • 9.11.3: Comparing Maximums between Quadratics
    • 9.11.3: Self Check
    • 9.11.3: Additional Resources
    • 9.11.4: Maximum, Minimum, and Analyzing the Vertex
    • 9.11.5: Practice
    • 9.11.6: Lesson Summary
  • Project 9 Teacher Guide: Using Quadratic Equations to Model Situations and Solve Problems
    • Project 9 Overview
    • Equations of Two Lines and a Curve
    • Analyze a Dive
    • A Linear Function and a Quadratic Function
    • Profit from a River Cruise
  • Project 9: Using Quadratic Equations to Model Situations and Solve Problems
    • Project 9 Overview
    • Equations of Two Lines and a Curve
    • Analyze a Dive
    • A Linear Function and a Quadratic Function
    • Profit from a River Cruise
  • Unit 9 Wrap Up
• Spring STAAR Review
• Research in Practice
  • Productive Struggle
    • Productive Failure
  • Cooperative Learning and Productive Discourse
    • Classroom Discussion
  • Motivation in the Classroom
    • Growth Mindset
    • Goal Setting
  • Metacognition
    • Spaced Retrieval Practice
  • Multimedia Learning Principle
    • Multimedia Principle
    • Generative Learning Principle
• Appendix
  • Course Design
    • Unit Sequence and Resources
    • Lesson Structure and Resources
    • Assessment Types and Resources
  • Implementing This Course
    • Pacing Guides
    • Implementation Guides
    • Coaching Guides
  • Progress Monitoring
    • Reports and Measuring Progress
    • Analyzing and Responding to Data