Table of Contents
Getting Started
About this Course
Students Start Here
Quick Start
Using Desmos
Additional Resources
Supporting All Learners
Preparing for Success
Study Tips
Creating Your Best Self
Building Relationships
Unit 1: Linear Equations
Unit 1 Overview and Readiness
Unit 1 Overview: Why Should I Care?
Unit 1 Overview: Am I Ready to Learn This?
Solve Linear Equations: Mini-Lesson Review
Classify Equations: Mini-Lesson Review
Find Coordinates: Mini-Lesson Review
Unit 1 Overview: Wrap Up
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: Additional Resources
1.1.3: Understanding Constraints
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: 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: Additional Resources
1.2.3: Writing Equations to Represent Relationships
1.2.3: Additional Resources
1.2.4: Writing Equations to Represent Relationships with Percentages
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: Writing Equations to Model Relationships, Part 2
1.3.0: Lesson Overview
1.3.1: Finding a Relationship between π and π
1.3.2: Describing Relationships Using Words and Equations
1.3.2: Additional Resources
1.3.3: Identifying and Representing Relationships
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: 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: Additional Resources
1.4.3: Finding the Solution to an Equation in Two Variables
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: 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 Additional Resources
1.5.3: Examining an Equation in Two Variables and Its Graph, Part 1
1.5.3: Additional Resources
1.5.4: Writing, Graphing, and Solving a Linear Equation
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
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: Additional Resources
1.6.3: Exploring Related Equations
1.6.3: Additional Resources
1.6.4: Recognizing Related Equations
1.6.5: Practice
1.6.6: Lesson Summary
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: Additional Resources
1.7.3: Understanding Equations with No Solution or Infinitely Many
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: 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: Additional Resources
1.8.3: Writing Equations and Isolating Variables
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: 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: Additional Resources
1.9.3: Writing and Rearranging Equations in Two Variables
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: 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: Additional Resources
1.10.3: Writing and Graphing Equations in Standard Form
1.10.3: Additional Resources
1.10.4: Matching Equations and Graphs
1.10.5: Practice
1.10.6: Lesson Summary
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: Additional Resources
1.11.3: Reasoning Symbolically and Abstractly about Linear Equations
1.11.3: Additional Resources
1.11.4: Identifying the Features of a Graph
1.11.5: Practice
1.11.6: Lesson Summary
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: Additional Resources
1.12.3: Writing an Equation Given the Slope and a Point
1.12.3: Additional Resources
1.12.4: Writing Equations in Different Forms
1.12.4 Additional Resources
1.12.5: Writing an Equation Given Two Points
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: 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: Additional Resources
1.13.3: Matching Tables, Equations, and Graphs
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: 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 Additional Resources
1.14.3: Writing an Equation of a Line Parallel to a Given Line
1.14.3: Additional Resources
1.14.4: Writing an Equation of a Line Perpendicular to a Given Line
1.14.4: Additional Resources
1.14.5: Writing an Equation of a Line Parallel or Perpendicular to an Axis
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: Direct Variation
1.15.0: Lesson Overview
1.15.1: Solving Proportions
1.15.2: Modeling Equations Using Direct Variation
1.15.2: Additional Resources
1.15.3: Using Direct Variation to Solve Application Problems, Part 1
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: 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 Overview and Readiness
Unit 2 Overview: Why should I care?
Unit 2 Overview: Am I ready to learn this?
Determine the Ordered Pair: Mini-Lesson Review
Find the Slope and y-Intercept: Mini-Lesson Review
Find the x- and y-Intercepts: Mini-Lesson Review
Unit 2 Overview: Wrap Up
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 Additional Resources
2.1.3: Meeting Constraints
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: 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: Additional Resources
2.2.3: Graphs of Systems of Equations
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: 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: Additional Resources
2.3.3: Solving Equations Using Substitution
2.3.3: Additional Resources
2.3.4: Solving More Equations
2.3.5: Practice
2.3.6: Lesson Summary
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: Additional Resources
2.4.3: Adding and Subtracting Systems of Equations and Using Their Graphs
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: 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: Additional Resources
2.5.3: Solving Systems of Linear Equations in Two Variables
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: 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: Additional Resources
2.6.3: Finding Solutions to Unordered Sets of Equivalent Systems
2.6.3: Additional Resources
2.6.4: Building Equivalent Systems
2.6.5: Practice
2.6.6: Lesson Summary
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: Additional Resources
2.7.3: Sorting Systems of Equations Based on Number of Solutions
2.7.3: Additional Resources
2.7.4: Writing Consistent and Inconsistent Systems of Equations
2.7.5: Practice
2.7.6: Lesson Summary
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 Additional Resources
2.8.3: Writing Inequalities to Represent Constraints
2.8.3 Additional Resources
2.8.4: Writing More Inequalities
2.8.5: Practice
2.8.6: Lesson Summary
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: Additional Resources
2.9.3: Understanding the Meaning of an Inequality
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: 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: 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: Additional Resources
2.10.3: Different Ways of Solving an Inequality
2.10.3: Additional Resources
2.10.4: Matching Inequalities and Solutions
2.10.5: Solving Inequalities
2.10.5: Additional Resources
2.10.6: Writing Inequalities to Represent a Situation
2.10.7: Practice
2.10.8: Lesson Summary
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: Additional Resources
2.11.3: Sketching Solutions to Inequalities
2.11.3: Additional Resources
2.11.4: Shading Boundary Line Regions
2.11.5: Practice
2.11.6: Lesson Summary
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: Additional Resources
2.12.3: Graphing Solutions and Interpreting Points
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: 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: Additional Resources
2.13.3: Matching Representations of Inequalities
2.13.3: Additional Resources
2.13.4: Solving Inequality Problems Using Tables
2.13.4 Additional Resources
2.13.5: Graphing Solutions to an Inequality
2.13.6: Practice
2.13.7: Lesson Summary
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: Additional Resources
2.14.3: Writing Systems of Inequalities that Represent Situations
2.14.3: Additional Resources
2.14.4: Graphing Solutions of Systems of Inequalities
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: 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: Additional Resources
2.15.3: Solving Problems to Satisfy Multiple Constraints Simultaneously
2.15.3: Additional Resources
2.15.4: Identifying Graph Regions Included in a Systemβs Solution
2.15.5: Practice
2.15.6: Lesson Summary
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 Overview and Readiness
Unit 3 Overview: Why Should I Care?
Unit 3 Overview: Am I Ready to Learn This?
Distinguish Patterns: Mini-Lesson Review
Identify Positive and Negative Trends: Mini-Lesson Review
Interpret Slope and y-Intercept: Mini-Lesson Review
Unit 3 Overview: Wrap Up
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: Additional Resources
3.1.3: Interpreting the Slope and Vertical Intercept of a Linear Model
3.1.3: Additional Resources
3.1.4: Interpreting the Slope and Vertical Intercept of a Scatter Plot
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: 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: Additional Resources
3.2.3: Writing Linear Models without Technology
3.2.3 Additional Resources
3.2.4: Assessing the Fit of a Linear Model
3.2.4: Additional Resources
3.2.5: Working with Fitted Lines
3.2.6: Practice
3.2.7: Lesson Summary
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: Additional Resources
3.3.3: Matching Residuals Graphs to Scatter Plots
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
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: Additional Resources
3.4.3: Finding the Correlation Coefficient with Technology
3.4.3 Additional Resources
3.4.4: Matching Correlation Coefficients
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: 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: Additional Resources
3.5.3: Using Correlation Coefficient to Describe Relationships between Two Variables
3.5.3: Additional Resources
3.5.4: Interpreting the Correlation Coefficient
3.5.5: Practice
3.5.6: Lesson Summary
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: Additional Resources
3.6.3: Using the Term Causal Relationship
3.6.3: Additional Resources
3.6.4: Determining the Type of Relationship
3.6.5: Practice
3.6.6: Lesson Summary
Project 3: Two-Variable Statistics
Project 3 Overview
Estimate Lengths
Analyze Data
Unit 3 Wrap Up
Unit 4: 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?
Find Slope: Mini-Lesson Review
Describe Graphs: Mini-Lesson Review
Extend a Pattern: Mini-Lesson Review
Unit 4 Overview: Wrap Up
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: Additional Resources
4.1.3: Examining Relations and Functions
4.1.3: Additional Resources
4.1.4: Describing Functional Relationships
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: 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: Additional Resources
4.2.3: Finding a Unique Output for Each Input
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: 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: Additional Resources
4.3.3: Comparing Statements in Function Notation
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: 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: Additional Resources
4.4.3: Using Tables to Find Function Rules
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: 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: Additional Resources
4.5.3: Comparing Functions
4.5.3: Additional Resources
4.5.4: Using Function Notation and Graphing Technology
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
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: Additional Resources
4.6.3: Connecting Graphical and Verbal Representations of a Function
4.6.3: Additional Resources
4.6.4: Key Features of Linear Functions
4.6.4 Additional Resources
4.6.5: Interpreting Graphs
4.6.6: Practice
4.6.7: Lesson Summary
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: Additional Resources
4.7.3: Writing Linear Equations
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: 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: Additional Resources
4.8.3: Finding and Interpreting Average Rates of Change
4.8.3: Additional Resources
4.8.4: Rate of Change of Linear Functions
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: 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: Additional Resources
4.9.3: Sketching Graphs of Functions
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: 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: Additional Resources
4.10.3: Comparing Functions Represented in Separate Graphs
4.10.3: Additional Resources
4.10.4: Comparing Graphs and Statements that Represent Functions without a Context
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: Graphing a Function Using Transformations
4.11.0: Lesson Overview
4.11.1: Graphing Linear Functions
4.11.2: Vertical Shifts
4.11.2: Additional Resources
4.11.3: Horizontal Shifts
4.11.3: Additional Resources
4.11.4: Vertical Stretches and Compressions
4.11.4: Additional Resources
4.11.5: Horizontal Stretches and Compressions
4.11.5: Additional Resources
4.11.6: Graphing Using Transformations
4.11.7: Practice
4.11.8: Lesson Summary
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: Additional Resources
4.12.3: Range: The Output of a Function
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: 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: Additional Resources
4.13.3: Finding Domain and Range Using a Graph
4.13.3: Additional Resources
4.13.4: Real-World Domain and Range
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
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: Additional Resources
4.14.3: The Connection between Sequences and Terms
4.14.3: Additional Resources
4.14.4: Rules for a Sequence
4.14.5: Practice
4.14.6: Lesson Summary
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: Additional Resources
4.15.3: Complete the Sequence
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: 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: Additional Resources
4.16.3: A Sequence Is a Type of Function
4.16.3: Additional Resources
4.16.4: Identify and Generate Sequences
4.16.5: Practice
4.16.6: Lesson Summary
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: Additional Resources
4.17.3: Ways to Represent a Sequence
4.17.3: Additional Resources
4.17.4: Geometric Recursive Definitions
4.17.5: Practice
4.17.6: Lesson Summary
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: Additional Resources
4.18.4: Define a Geometric Sequence by the nth Term
4.18.4: Additional Resources
4.18.5: Interchanging between Formulas
4.18.5: Additional Resources
4.18.6: Different Types of Equations
4.18.7: Practice
4.18.8: Lesson Summary
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 Overview and Readiness
Unit 5 Overview: Why Should I Care?
Unit 5 Overview: Am I Ready to Learn This?
Write Linear Functions from a Graph: Mini-Lesson Review
Interpret Linear Functions: Mini-Lesson Review
Evaluate Exponential Expressions: Mini-Lesson Review
Unit 5 Overview: Wrap Up
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: Additional Resources
5.1.3: Using Zero Exponent Property and Negative Exponents
5.1.3: Additional Resources
5.1.4: Using Power Properties for Exponents
5.1.4: Additional Resources
5.1.5: Simplifying Exponents
5.1.6: Practice
5.1.7: Lesson Summary
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: Additional Resources
5.2.3: Radicals and Rational Exponents
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: 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: Additional Resources
5.3.3: Compare and Contrast Two Patterns
5.3.3: Additional Resources
5.3.4: Match Expressions and Tables with Situations
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: Representing Exponential Growth
5.4.0: Lesson Overview
5.4.1: Exponent Rules
5.4.2: Zero Exponent Rule
5.4.2: Additional Resources
5.4.3: Exponential Change: The Growth Factor
5.4.3: Additional Resources
5.4.4: Graphing Exponential Expressions
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: Representing Exponential Decay
5.5.0: Lesson Overview
5.5.1: Identifying Linear and Exponential Quantities
5.5.2: Exponential Decay
5.5.2: Additional Resources
5.5.3: Using Graphs to Represent Exponential Decay
5.5.3: Additional Resources
5.5.4: Justifying Exponential Models
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: 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: Additional Resources
5.6.3: Interpreting Negative Exponents in Exponential Decay
5.6.3: Additional Resources
5.6.4: Using Scientific Notation
5.6.4: Additional Resources
5.6.5: Applying Scientific Notation
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: Analyzing Graphs
5.7.0: Lesson Overview
5.7.1: Patterns in Real Numbers
5.7.2: Comparing Graphs
5.7.2: Additional Resources
5.7.3: Describing Graphs
5.7.3: Additional Resources
5.7.4: Quantities that Change Exponentially
5.7.5: Practice
5.7.6: Lesson Summary
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: Additional Resources
5.8.3: Using Function Language and Notation
5.8.3: Additional Resources
5.8.4: Function Notation
5.8.5: Practice
5.8.6: Lesson Summary
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: Additional Resources
5.9.3: Graph Equations to Solve Problems
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: 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: Additional Resources
5.10.3: Explore Average Rates of Change in an Exponential Decay Context
5.10.3: Additional Resources
5.10.4: Average Rate of Change
5.10.5: Practice
5.10.6: Lesson Summary
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: Additional Resources
5.11.3: Modeling with Exponential Functions
5.11.4: Examine Exponential Decay in Context
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: 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: Additional Resources
5.12.3: Graphs Representing Exponential Decay
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
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: Additional Resources
5.13.3: Comparing Exponential Functions
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: 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: Additional Resources
5.14.3: Compare Linear Functions with Exponential Functions
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: 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: Additional Resources
5.15.3: Growth Rate of an Exponential Function
5.15.3: Additional Resources
5.15.4: Comparing Linear and Exponential Growth
5.15.5: Practice
5.15.6: Lesson Summary
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
Unit 6: Working with Polynomials
Unit 6 Overview and Readiness
Unit 6 Overview: Why Should I Care?
Unit 6 Overview: Am I Ready to Learn This?
Simplify Expressions Using Properties of Exponents: Mini-Lesson Review
Simplify Expressions Using the Distributive Property: Mini-Lesson Review
Find the Greatest Common Factor: Mini-Lesson Review
Unit 6 Overview: Wrap Up
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
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: Additional Resources
6.1.3: Evaluating a Polynomial Function for a Given Value
6.1.3: Additional Resources
6.1.4: Adding and Subtracting Polynomial Functions
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: Multiplying Polynomials
6.2.0: Lesson Overview
6.2.1: Multiplying Monomials
6.2.2: Multiplying Binomials
6.2.2: Additional Resources
6.2.3: Multiplying a Polynomial by a Polynomial
6.2.3: Additional Resources
6.2.4: Multiplying Special Products
6.2.4: Additional Resources
6.2.5: Multiplying Polynomial Functions
6.2.6: Practice
6.2.7: Lesson Summary
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: Additional Resources
6.3.3: Dividing Polynomials Using Synthetic Division
6.3.3: Additional Resources
6.3.4: Dividing Polynomial Functions and the Remainder Theorem
6.3.4: Additional Resources
6.3.5: Using the Factor Theorem
6.3.6: Practice
6.3.7: Lesson Summary
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: Additional Resources
6.4.3: Factoring the GCF from Polynomials
6.4.3: Additional Resources
6.4.4: Factoring Polynomials by Grouping
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: 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: Additional Resources
6.5.3: Factoring Trinomials Using Trial and Error
6.5.3: Additional Resources
6.5.4: Factoring Trinomials Using the βacβ Method and Substitution
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: 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: Additional Resources
6.6.3: Factoring the Difference of Squares
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: 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: Additional Resources
6.7.3: Implementing General Strategies for Factoring
6.7.3: Additional Resources
6.7.4: Is the Polynomial Completely Factored?
6.7.5: Practice
6.7.6: Lesson Summary
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 Overview and Readiness
Unit 7 Overview: Why Should I Care?
Unit 7 Overview: Am I Ready to Learn This?
Multiply Binomials: Mini-Lesson Review
Factor Trinomials: Mini-Lesson Review
Compare Linear and Exponential Functions: Mini-Lesson Review
Unit 7 Overview: Wrap Up
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: Additional Resources
7.1.3: Plotting Measurements
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: 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: Additional Resources
7.2.3: Quadratic Expressions
7.2.3: Additional Resources
7.2.4: Quadratic Relationships
7.2.5: Practice
7.2.6: Lesson Summary
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: Additional Resources
7.3.3: Quadratic Sequences
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: 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: Additional Resources
7.4.3: Comparing Exponential and Quadratic Functions
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: 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: Additional Resources
7.5.3: Distance as a Quadratic Function of Elapsed Time
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: 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: Additional Resources
7.6.3: Using Quadratic Functions to Describe Height
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: 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: Additional Resources
7.7.3: The Domain, Vertex, and Zero of Quadratic Functions
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
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: Additional Resources
7.8.3: Using Diagrams to Find Equivalent Quadratic Expressions
7.8.3: Additional Resources
7.8.4: Writing Equivalent Expressions
7.8.5: Practice
7.8.6: Lesson Summary
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: Additional Resources
7.9.3: Standard and Factored Forms of Quadratic Expressions
7.9.3: Additional Resources
7.9.4: Expressions in Standard Form
7.9.5: Practice
7.9.6: Lesson Summary
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: Additional Resources
7.10.3: The X- and Y-Intercepts of Quadratic Expressions
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
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: Additional Resources
7.11.3: Sketching a Graph of a Quadratic Function Using at Least Three Identifiable Points
7.11.3: Additional Resources
7.11.4: Using the Vertex and Axis of Symmetry of Quadratics
7.11.4: Additional Resources
7.11.5: Graphs of Quadratic Functions
7.11.6: Practice
7.11.7: Lesson Summary
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: Additional Resources
7.12.3: Understanding the Behaviors of a Graph in Relation to Its Quadratic Expression
7.12.3: Additional Resources
7.12.4: Representations of Quadratic Functions
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: 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: Additional Resources
7.13.3: Writing Equations that Represent a Graph
7.13.3: Additional Resources
7.13.4: Writing Quadratic Equations from Real Solutions
7.13.4 Additional Resources
7.13.5: Graphing Quadratic Equations
7.13.6: Practice
7.13.7: Lesson Summary
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: Additional Resources
7.14.3: Analyzing Functions Using Different Representations
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: Vertex Form
7.15.0: Lesson Overview
7.15.1: Analyzing Two Sets of Equations
7.15.2: The Vertex Form
7.15.2: Additional Resources
7.15.3: The Coordinates of the Vertex
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: 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: Additional Resources
7.16.3: Quadratic Equations and Graphs
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: 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: Additional Resources
7.17.3: Changing the Parameters of a Quadratic Expression
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: Design a Fountain
Project 7 Overview
Introduction to Fountain Design
Design a Fountain
Unit 7 Wrap Up
Unit 8: Quadratic Equations
Unit 8 Overview and Readiness
Unit 8 Overview: Why Should I Care?
Unit 8 Overview: Am I Ready to Learn This?
Write Equivalent Expressions: Mini-Lesson Review
Find Intercepts: Mini-Lesson Review
Match Quadratic Graphs and Their Equations: Mini-Lesson Review
Unit 8 Overview: Wrap Up
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: Additional Resources
8.1.3: Formulating a Quadratic Equation to Represent the Model
8.1.3: Additional Resources
8.1.4: Interpreting a Solution
8.1.5: Practice
8.1.6: Lesson Summary
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: Additional Resources
8.2.3: Solving a Quadratic Equation Set Equal to Zero
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
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: Additional Resources
8.3.3: Solving More Complex Quadratic Equations
8.3.3: Additional Resources
8.3.4: Finding the Solutions
8.3.5: Practice
8.3.6: Lesson Summary
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: Additional Resources
8.4.3: Applying the Zero Product Property to Solve a Real-World Projectile Problem
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: 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: Additional Resources
8.5.3: Choosing an Effective Strategy to Solve Quadratic Equations
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: 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: Additional Resources
8.6.3: Rewriting Quadratic Expressions in Standard Form
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: 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: Additional Resources
8.7.3: Analyzing Factors of 100 and β100
8.7.3: Additional Resources
8.7.4: Finding the Missing Terms
8.7.5: Practice
8.7.6: Lesson Summary
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: Additional Resources
8.8.3: Factoring Quadratic Equations without a Linear Term
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: 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: Additional Resources
8.9.3: Writing an Equation to Represent a Quadratic Function with Only One Solution
8.9.3: Additional Resources
8.9.4: Solving More Quadratic Equations
8.9.5: Practice
8.9.6: Lesson Summary
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: Additional Resources
8.10.3: Using Technology to Find Rational Factors
8.10.3: Additional Resources
8.10.4: Finding the Factors of Quadratic Expressions in Standard Form
8.10.4: Additional Resources
8.10.5: Solving Quadratic Equations by Any Method
8.10.6: Practice
8.10.7: Lesson Summary
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: Additional Resources
8.11.3: Finding a Quadratic Function from Its Zeros and a Point
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: 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: Additional Resources
8.12.3: Making Predictions Using a Quadratic Model
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: 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 Overview and Readiness
Unit 9 Overview: Why Should I Care?
Unit 9 Overview: Am I Ready to Learn This?
Simplifying Radicals: Mini-Lesson Review
Factoring Perfect Square Trinomials: Mini-Lesson Review
Transformations: Mini-Lesson Review
Unit 9 Overview: Wrap Up
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: Additional Resources
9.1.3: Solving Multi Step Quadratic Equations Using Perfect Squares
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: 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: Additional Resources
9.2.3: Completing the Square
9.2.3: Additional Resources
9.2.4: Making a Perfect Square
9.2.5: Practice
9.2.6: Lesson Summary
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: Additional Resources
9.3.3: Solve by Completing the Square
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: 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: Additional Resources
9.4.3: Standard Form and Squared Factors
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: 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: Additional Resources
9.5.3: Finding Irrational Solutions by Completing the Square
9.5.3: Additional Resources
9.5.4: Finding Exact Solutions
9.5.5: Practice
9.5.6: Lesson Summary
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: Additional Resources
9.6.3: The Quadratic Formula
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: 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: Additional Resources
9.7.3: Different Methods of Checking Solutions of Quadratic Equations
9.7.3: Additional Resources
9.7.4: Practice Spotting Calculation Errors
9.7.5: Practice
9.7.6: Lesson Summary
Lesson 9.8: Deriving the Quadratic Formula
9.8.0: Lesson Overview
9.8.1: Deriving the Quadratic Formula, Part 1
9.8.1: Additional Resources
9.8.2: Deriving the Quadratic Formula, Part 2
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
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: Additional Resources
9.9.3: Vertex Form Given a Vertex and Point
9.9.3: Additional Resources
9.9.4: Rewriting Quadratics
9.9.5: Practice
9.9.6: Lesson Summary
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: Additional Resources
9.10.4: Rewriting Expressions in Vertex Form
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: 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: Additional Resources
9.11.3: Comparing Maximums between Quadratics
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: 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
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
8.7.3: Analyzing Factors of 100 and β100
