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Table of Contents
About This Course
Quick Start to RAISE Teacher Guide
Course-level Teacher Resources
Overview
STAAR Exam Resources
Vocabulary Resources
Facilitating Group Work and Collaboration
Supporting English Language Learners
Unit 1: Linear Equations, Inequalities, and Systems
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: 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
Unit 1 Project Overview
Activity P.1: Notice and Wonder: Sugar and Flour
Activity P.2: Matching Matching
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 (Optional)
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 (Optional)
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
Activity P2.1: Determining a Solution to Inequalities
Activity P2.2: Interpret a Set of Mathematical Models
Activity P2.3: 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: Casual 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
Activity P3.1: Estimating Lengths
Activity P3.2: 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)
Unit 4 Inquiry Project Teacher Guide: Defining 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 (Optional)
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: Using Verbal Descriptions to Create Graphs of Functions
4.9.5: Representing Quantities in a Situation
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: Vertical Stretches and Compressions
4.11.4: Graphing Using Transformations
4.11.5: Practice
4.11.6: 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 (Optional)
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: Different Types of 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: Sequences are Functions
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 an Arithmetic Sequence
4.18.0: Lesson Overview
4.18.1: Repeated Addition Is Multiplication
4.18.2: Define a Sequence by the nth Term
4.18.3: Identify a Domain for a Function
4.18.4: Interchanging between Formulas
4.18.5: Different Types of Equations
4.18.6: Practice
4.18.7: Lesson Synthesis
Project 4 Teacher Guide: Using Functions to Model Battery Power
Project 4 Overview
Activity: P4.1: Estimate Time to Charge a Battery
Activity: P4.2: Analyze Percent Change Over Time
Activity: P4.3: 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
Activity P5.1: Analyze Data
Activity P5.2: Writing Equations to Model Populations
Activity P5.3: 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)
Unit 6 Inquiry Project Teacher Guide: Area Model Multiplication
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
Activity: P6.1: Areas of Rectangles
Activity: P6.2: Dimensions and Areas of Rectangles
Activity: P6.3: 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: Building Quadratic Functions from Geometric Patterns
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: 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: Designing a Fountain
Project 7 Overview
Activity P7.1: Introduction to Fountain Design
Activity P7.2: Designing 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
Activity P8.1: Relating the Graphs of Quadratic Equations to Their Factored Form by Their Zeros
Activity P8.2: Converting between Factored Form and Standard Form
Activity P8.3: Modeling 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
Activity: P9.1: Equations of Two Lines and a Curve
Activity: P9.2: Analyzing a Dive
Activity: P9.3: A Linear Function and a Quadratic Function
Activity: P9.4: Profit from a River Cruise
Activity: P9.3: A Linear Function and a Quadratic Function
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