Access the student version
Table of Contents
Getting Started
Teachers 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
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 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 1.2 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 1.3 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 1.4 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 1.5 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
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 1.7 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 1.8 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 1.9 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 1.10 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 1.11 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
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 1.13 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 1.14 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 1.15 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
Project 1 Teacher Guide: Slopes and Intercepts
Project 1 Overview
Notice and Wonder Graph Features
Matching Graphs and Equations
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)
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 2.2 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 2.3 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 2.4 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 2.5 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 2.6 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 2.7 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
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 2.9 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 2.10 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
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 2.12 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 2.13 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
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 2.15 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
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
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 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 3.2 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 3.3 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
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 3.5 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 3.6 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
Project 3 Teacher Guide: Two-Variable Statistics
Project 3 Overview
Estimate Lengths
Analyze Data
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
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 4.2 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 4.3 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 4.4 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 4.5 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
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 4.7 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 4.8 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 4.9 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 4.10 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 4.11 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
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 4.13 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
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 4.15 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 4.16 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 4.17 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 4.18 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
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
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 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 5.2 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 5.3 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 5.4 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 5.5 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 5.6 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 5.7 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
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 5.9 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 5.10 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 5.11 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 5.12 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
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 5.14 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 5.15 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
Project 5 Teacher Guide: Introduction to Exponential Functions
Project 5 Overview
Analyze Data
Write Equations to Model Populations
Open-ended Modeling with Data Investigation
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)
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
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 6.2 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 6.3 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
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 6.5 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 6.6 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 6.7 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
Project 6 Teacher Guide: Polynomials and Rectangles
Project 6 Overview
Areas of Rectangles
Dimensions and Areas of Rectangles
Create Your Own Rectangles
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 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 7.2 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
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 7.4 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 7.5 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 7.6 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 7.7 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
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 7.9 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 7.10 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
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 7.12 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 7.13 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 7.14 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 7.15 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 7.16 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 7.17 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
Project 7 Teacher Guide: Design a Fountain
Project 7 Overview
Introduction to Fountain Design
Design a Fountain
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 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 8.2 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
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 8.4 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 8.5 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 8.6 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 8.7 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 8.8 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 8.9 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 8.10 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
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 8.12 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
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
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 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 9.2 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 9.3 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 9.4 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 9.5 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
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 9.7 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 9.8 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
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 9.10 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 9.11 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
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
Appendix
Implementing This Course
Pacing Guides
Implementation Guides
Coaching Guides
Progress Monitoring
Reports and Measuring Progress
Analyzing and Responding to Data
1.4.3 Finding the Solution to an Equation in Two Variables
Access the student version
Access the student version