Computer Science and Math

Printable Into Math Table of Contents

Grade K
Visit with your student's classroom teacher for details on which lessons will be used from Into Math.

Unit 1 COUNT SEQUENCE AND NUMBERS TO 5

Module 1: Represent Numbers to 5 with Objects  
Lesson 1.1 Represent 1 and 2
Lesson 1.2 Represent 3 and 4
Lesson 1.3 Represent 5
Lesson 1.4 Represent 0
Lesson 1.5 Ways to Make 5

Module 2: Represent Numbers to 5 with a Written Numeral  
Lesson 2.1 Count and Write 0 and 1
Lesson 2.2 Count and Write 2 and 3
Lesson 2.3 Count and Write 4 and 5
Lesson 2.4 Count and Write Numbers to 5
Lesson 2.5 Count and Order to 5

Module 3: Matching and Counting Numbers to 5  
Lesson 3.1 Identify a Greater Number of Objects Within 5
Lesson 3.2 Identify a Lesser Number of Objects Within 5
Lesson 3.3 Match Equal Groups of Objects Within 5
Lesson 3.4 Compare Groups Within 5 by Counting
Lesson 3.5 Compare Groups Within 5 by Matching
Lesson 3.6 Compare Numbers Within 5

Module 4: Classify, Count, and Sort Objects  
Lesson 4.1 Classify and Count by Color
Lesson 4.2 Classify and Count by Shape
Lesson 4.3 Classify and Count by Size
Lesson 4.4 Classify, Count, and Sort by Count

Module 5: Add To and Take Away From Within 5  
Lesson 5.1 Act Out Addition Problems Within 5
Lesson 5.2 Act Out Subtraction Problems Within 5
Lesson 5.3 Solve Add To Problems Within 5
Lesson 5.4 Solve Take From Problems Within 5
Lesson 5.5 Write Addition Equations Within 5
Lesson 5.6 Write Subtraction Equations Within 5
Lesson 5.7 Solve Result Unknown Word Problems Within 5

Module 6: Put Together and Take Apart Within 5  
Lesson 6.1 Represent Addition Problems Within 5 Using Objects and Drawings
Lesson 6.2 Represent Subtraction Problems Within 5 Using Objects and Drawings
Lesson 6.3 Solve Put Together Problems Within 5
Lesson 6.4 Solve Take Apart Problems Within 5
Lesson 6.5 Represent Addition Using Mental Images
Lesson 6.6 Represent Subtraction Using Mental Images
Lesson 6.7 Solve Word Problems Within 5

GRADE 1
Unit 1 WAYS TO ADD AND SUBTRACT

Module 1: Addition Strategies  
Lesson 1.1 Represent Addition
Lesson 1.2 Count On
Lesson 1.3 Add 10 and More
Lesson 1.4 Make a 10 to Add
Lesson 1.5 Add Doubles
Lesson 1.6 Use Known Sums to Add
Lesson 1.7 Choose a Strategy to Add

Module 2: Subtraction Strategies  
Lesson 2.1 Represent Subtraction
Lesson 2.2 Count Back
Lesson 2.3 Count On to Subtract
Lesson 2.4 Add to Subtract
Lesson 2.5 Use 10 to Subtract
Lesson 2.6 Choose a Strategy to Subtract

Module 3: Properties of Operations  
Lesson 3.1 Represent Addition in Any Order
Lesson 3.2 Add in Any Order
Lesson 3.3 Represent Addition of 3 Numbers
Lesson 3.4 Add 3 Numbers
Lesson 3.5 Add 3 Numbers to Solve Problems
Lesson 3.6 Determine Equal and Not Equal
Lesson 3.7 Develop Fluency in Addition

Module 4: Apply the Addition and Subtraction Relationship  
Lesson 4.1 Think Addition to Subtract
Lesson 4.2 Represent Related Facts
Lesson 4.3 Identify Related Facts
Lesson 4.4 Use Addition to Check Subtraction
Lesson 4.5 Use Subtraction to Find an Unknown Addend
Lesson 4.6 Solve for the Unknown Addend
Lesson 4.7 Develop Fluency in Subtraction

Unit 2 ADDITION AND SUBTRACTION SITUATIONS AND DATA
Module 5: Understand Add To and Take From Problems  
Lesson 5.1 Represent Result Unknown Problems with Objects and Drawings
Lesson 5.2 Represent Change Unknown Problems with Objects and Drawings
Lesson 5.3 Represent Start Unknown Problems with Objects and Drawings
Lesson 5.4 Solve Add To and Take From Problems

Module 6: Understand Put Together and Take Apart Problems  
Lesson 6.1 Represent Total Unknown Problems with Objects and Drawings
Lesson 6.2 Represent Both Addends Unknown Problems with Objects and Drawings
Lesson 6.3 Represent Addend Unknown Problems with Objects and Drawings
Lesson 6.4 Represent Total Unknown Problems with a Visual Model
Lesson 6.5 Represent Addend Unknown and Both Addends Unknown Problems with a Visual Model
Lesson 6.6 Solve Put Together and Take Apart Problems
Lesson 6.7 Solve Addition and Subtraction Problems

Module 7: Understand Compare Problems  
Lesson 7.1 Represent Difference Unknown Problems with Objects and Drawings
Lesson 7.2 Represent Bigger Unknown Problems with Objects and Drawings
Lesson 7.3 Represent Smaller Unknown Problems with Objects and Drawings
Lesson 7.4 Represent Difference Unknown Problems with a Visual Model
Lesson 7.5 Represent Bigger Unknown and Smaller Unknown Problems with a Visual Model
Lesson 7.6 Use Strategies to Solve Compare Problems
Lesson 7.7 Solve Addition and Subtraction Situations

Module 8: Data  
Lesson 8.1 Interpret Picture Graphs
Lesson 8.2 Represent Data with Picture Graphs
Lesson 8.3 Interpret Tally Charts
Lesson 8.4 Represent Data with Tally Charts
Lesson 8.5 Interpret Bar Graphs
Lesson 8.6 Represent Data with Bar Graphs
Lesson 8.7 Use Data to Solve Problems

Unit 3 NUMBERS TO 120
Module 9: Understand Place Value  
Lesson 9.1 Make Tens and Ones
Lesson 9.2 Understand Tens and Ones
Lesson 9.3 Make Tens

Module 10: Count and Represent Numbers  
Lesson 10.1 Count to 120
Lesson 10.2 Represent Numbers as Tens and Ones with Objects
Lesson 10.3 Represent Numbers as Tens and Ones with Drawings
Lesson 10.4 Decompose Numbers in Different Ways
Lesson 10.5 Represent, Read, and Write Numbers from 100 to 110
Lesson 10.6 Represent, Read, and Write Numbers from 110 to 120

Module 11: Compare Numbers  
Lesson 11.1 Understand Greater Than
Lesson 11.2 Understand Less Than
Lesson 11.3 Use Symbols to Compare
Lesson 11.4 Compare Numbers

Unit 4 ADDITION AND SUBTRACTION IN BASE TEN
Module 12: Understand Addition and Subtraction with Tens and Ones  
Lesson 12.1 Represent Adding Tens
Lesson 12.2 Represent Subtracting Tens
Lesson 12.3 Add or Subtract Tens
Lesson 12.4 Use a Hundred Chart to Add
Lesson 12.5 Represent Addition with Tens and Ones
Lesson 12.6 Represent Make Ten to Add
Lesson 12.7 Represent Make Ten to Add with a Visual Model
Lesson 12.8 Use Mental Math to Find 10 Less and 10 More

Module 13: Two-Digit Addition and Subtraction  
Lesson 13.1 Use a Hundred Chart to Show Two-Digit Addition and Subtraction
Lesson 13.2 Understand and Explain Place Value Addition
Lesson 13.3 Understand and Explain Place Value Subtraction
Lesson 13.4 Solve Two-Digit Addition and Subtraction Problems
Lesson 13.5 Practice Facts to 20
Lesson 13.6 Practice Two-Digit Addition and Subtraction

Unit 5 GEOMETRY
Module 14: Three-Dimensional Shapes  
Lesson 14.1 Describe and Draw Three-Dimensional Shapes
Lesson 14.2 Compare Three-Dimensional Shapes
Lesson 14.3 Make New Three-Dimensional Shapes

Module 15: Two-Dimensional Shapes  
Lesson 15.1 Sort Two-Dimensional Shapes by Attribute
Lesson 15.2 Describe and Draw Two-Dimensional Shapes
Lesson 15.3 Compose Two-Dimensional Shapes
Lesson 15.4 Identify Composed Shapes
Lesson 15.5 Make New Two-Dimensional Shapes

Module 16: Fraction Foundations  
Lesson 16.1 Take Apart Two-Dimensional Shapes
Lesson 16.2 Identify Equal or Unequal Shares
Lesson 16.3 Partition Shapes into Halves
Lesson 16.4 Partition Shapes into Fourths

Unit 6 MEASUREMENT
Module 17: Measure Length  
Lesson 17.1 Order Length
Lesson 17.2 Use Indirect Measurement to Compare Length
Lesson 17.3 Use Nonstandard Units to Measure Length
Lesson 17.4 Make a Nonstandard Measuring Tool

Module 18: Measure Time  
Lesson 18.1 Understand Time to the Hour
Lesson 18.2 Understand Time to the Half Hour
Lesson 18.3 Tell Time to the Hour and Half Hour
Lesson 18.4 Practice Time to the Hour and Half Hour

GRADE 2 
Unit 1: NUMBERS TO 20 AND DATA
Module 1: Fluency for Addition and Subtraction Within 20
Lesson 1.1 Use Doubles Facts to Add
Lesson 1.2 Develop Fluency with Addition Using Mental Strategies and Properties
Lesson 1.3 Relate Addition and Subtraction
Lesson 1.4 Develop Fluency with Subtraction Using Mental Strategies
Lesson 1.5 Use the Make a Ten Strategy to Add
Lesson 1.6 Use a Tens Fact to Subtract
Lesson 1.7 Add 3 Numbers Using Mental Strategies and Properties

Module 2: Equal Groups
Lesson 2.1 Identify Even and Odd Numbers
Lesson 2.2 Write Equations to Represent Even Numbers
Lesson 2.3 Represent Equal Groups
Lesson 2.4 Add to Find the Total Number of Objects in Arrays
Lesson 2.5 Practice with Arrays

Module 3: Data
Lesson 3.1 Collect and Record Data
Lesson 3.2 Interpret Picture Graphs
Lesson 3.3 Draw Picture Graphs to Represent Data
Lesson 3.4 Interpret Bar Graphs
Lesson 3.5 Draw Bar Graphs to Represent Data

Unit 2: PLACE VALUE
Module 4: Understand Place Value
Lesson 4.1 Group Tens as Hundreds
Lesson 4.2 Understand Three-Digit Numbers
Lesson 4.3 Represent Three-Digit Numbers
Lesson 4.4 Represent Numbers with Hundreds, Tens, and Ones
Lesson 4.5 Place Value to 1,000

Module 5: Read, Write, and Show Numbers to 1,000
Lesson 5.1 Use Expanded Form
Lesson 5.2 Use Number Names
Lesson 5.3 Different Ways to Write Numbers
Lesson 5.4 Different Ways to Show Numbers
Lesson 5.5 Read, Write, and Show Numbers

Module 6: Use Place Value
Lesson 6.1 Count Within 1,000
Lesson 6.2 Add and Subtract 10 or 100
Lesson 6.3 Identify and Extend Number Patterns
Lesson 6.4 Compare Three-Digit Numbers
Lesson 6.5 Use Symbols to Compare Numbers

Unit 3: MONEY AND TIME
Module 7: Coins
Lesson 7.1 Relate Place Value to Coins
Lesson 7.2 Identify and Find the Value of Coins
Lesson 7.3 Compute the Value of Coin Combinations
Lesson 7.4 Show Amounts in Different Ways

Module 8: Dollar Amounts
Lesson 8.1 Relate the Value of Coins to One Dollar
Lesson 8.2 Compute the Value of Dollar Combinations
Lesson 8.3 Solve Problems Involving Money

Module 9: Time
Lesson 9.1 Tell and Write Time to 5 Minutes
Lesson 9.2 Different Ways to Tell and Write Time
Lesson 9.3 Practice Telling and Writing Time
Lesson 9.4 Tell and Write Time with A.M. and P.M.

Unit 4: ADDITION AND SUBTRACTION IN BASE TEN
Module 10: Addition and Subtraction Counting Strategies
Lesson 10.1 Use a Hundred Chart
Lesson 10.2 Use a Number Line
Lesson 10.3 Use Counting Strategies

Module 11: Addition and Subtraction Grouping Strategies
Lesson 11.1 Decompose Ones to Add
Lesson 11.2 Decompose Ones to Subtract
Lesson 11.3 Decompose Numbers to Add
Lesson 11.4 Decompose Addends as Tens and Ones
Lesson 11.5 Decompose Numbers to Subtract

Module 12: Represent and Record Addition and Subtraction
Lesson 12.1 Represent Regrouping for Addition
Lesson 12.2 Represent Regrouping for Subtraction
Lesson 12.3 Represent and Record Two-Digit Addition
Lesson 12.4 Represent and Record Two-Digit Subtraction
Lesson 12.5 Add Two-Digit Numbers
Lesson 12.6 Subtract Two-Digit Numbers

Module 13: Develop Addition and Subtraction Fluency
Lesson 13.1 Rewrite Addition Problems
Lesson 13.2 Rewrite Subtraction Problems
Lesson 13.3 Use Addition and a Number Line to Subtract
Lesson 13.4 Add 3 Two-Digit Numbers Using Strategies and Properties
Lesson 13.5 Add 4 Two-Digit Numbers Using Strategies and Properties

Module 14: Algebra
Lesson 14.1 Use Drawings to Represent Addition and Subtraction Situations
Lesson 14.2 Use Equations to Represent Addition and Subtraction Situations
Lesson 14.3 Use Drawings and Equations to Represent Two-Digit Addition
Lesson 14.4 Use Drawings and Equations to Represent Two-Digit Subtraction

Module 15: Addition and Subtraction Word Problems
Lesson 15.1 Solve Addition Word Problems
Lesson 15.2 Solve Subtraction Word Problems
Lesson 15.3 Solve Multistep Addition and Subtraction Problems

Unit 5: THREE-DIGIT ADDITION AND SUBTRACTION
Module 16: Three-Digit Addition
Lesson 16.1 Use Drawings to Represent Three-Digit Addition
Lesson 16.2 Decompose Three-Digit Addends
Lesson 16.3 Represent Regrouping for Addition
Lesson 16.4 Add Three-Digit Numbers

Module 17: Three-Digit Subtraction
Lesson 17.1 Represent Three-Digit Subtraction
Lesson 17.2 Represent Regrouping for Subtraction
Lesson 17.3 Subtract Three-Digit Numbers
Lesson 17.4 Represent Regrouping with Zeros
Lesson 17.5 Regrouping with Zeros
Lesson 17.6 Add and Subtract Three-Digit Numbers

Unit 6: MEASUREMENT — LENGTH
Module 18: Length in Inches, Feet, and Yards
Lesson 18.1 Estimate Lengths Using Inches
Lesson 18.2 Make and Use a Ruler
Lesson 18.3 Measure to the Nearest Inch
Lesson 18.4 Make Line Plots to Show Measurement Data
Lesson 18.5 Estimate Lengths Using Feet
Lesson 18.6 Measure in Inches and Feet
Lesson 18.7 Measure to the Nearest Yard
Lesson 18.8 Choose Appropriate Tools

Module 19: Length in Centimeters and Meters
Lesson 19.1 Estimate Lengths Using Centimeters
Lesson 19.2 Measure to the Nearest Centimeter
Lesson 19.3 Estimate Lengths Using Meters
Lesson 19.4 Measure in Centimeters and Meters

Module 20: Relate Addition and Subtraction to Length
Lesson 20.1 Relate Inches to a Number Line
Lesson 20.2 Add and Subtract Lengths in Inches
Lesson 20.3 Relate Centimeters to a Number Line
Lesson 20.4 Add and Subtract Lengths in Centimeters
Lesson 20.5 Measure and Compare Lengths in Centimeters

Unit 7: GEOMETRY AND FRACTIONS
Module 21: Two- and Three-Dimensional Shapes
Lesson 21.1 Identify and Draw Three-Dimensional Shapes
Lesson 21.2 Identify and Draw Two-Dimensional Shapes
Lesson 21.3 Find and Count Angles in Two-Dimensional Shapes
Lesson 21.4 Sort Two-Dimensional Shapes by Sides and Angles

Module 22: Understand Fractions
Lesson 22.1 Partition Rectangles
Lesson 22.2 Identify and Describe Equal Shares
Lesson 22.3 Draw Equal Shares
Lesson 22.4 Show and Describe an Equal Share
Lesson 22.5 Different Ways to Show Equal Shares

GRADE 3 
Unit 1: UNDERSTAND MULTIPLICATION AND AREA
Module 1: Understand Multiplication
Lesson 1.1 Count Equal Groups
Lesson 1.2 Relate Addition and Multiplication
Lesson 1.3 Represent Multiplication with Arrays
Lesson 1.4 Understand the Commutative Property of Multiplication
Lesson 1.5 Represent Multiplication with Number Lines
Lesson 1.6 Represent Multiplication with Bar Models

Module 2: Relate Multiplication and Area
Lesson 2.1 Understand Area by Counting Unit Squares
Lesson 2.2 Measure Area by Counting Unit Squares
Lesson 2.3 Relate Area to Addition and Multiplication
Lesson 2.4 Solve Problems with Area
Lesson 2.5 Find the Area of Combined Rectangles

Unit 2: MULTIPLICATION AND DIVISION
Module 3: Understand Multiplication Strategies
Lesson 3.1 Multiply with 2 and 4
Lesson 3.2 Multiply with 5 and 10
Lesson 3.3 Multiply with 3 and 6

Module 4: Apply Multiplication Properties as Strategies
Lesson 4.1 Understand the Identity and Zero Properties of Multiplication
Lesson 4.2 Understand the Distributive Property
Lesson 4.3 Understand the Associative Property of Multiplication
Lesson 4.4 Multiply with 7
Lesson 4.5 Multiply with 8
Lesson 4.6 Multiply with 9
Lesson 4.7 Identify Number Patterns on the Multiplication Table

Module 5: Read, Write, and Show Numbers to 1,000
Lesson 5.1 Use the Distributive Property
Lesson 5.2 Use the Associative Property of Multiplication
Lesson 5.3 Use Place-Value Strategies to Multiply with Multiples of 10
Lesson 5.4 Multiply Multiples of 10 by 1-Digit Numbers

Module 6: Understand Division
Lesson 6.1 Represent Division
Lesson 6.2 Separate Objects into Equal Groups
Lesson 6.3 Find the Number of Equal Groups
Lesson 6.4 Relate Subtraction and Division
Lesson 6.5 Represent Division with Arrays
Lesson 6.6 Represent Division with Bar Models
Lesson 6.7 Apply Division Rules for 1 and 0

Module 7: Relate Multiplication and Division
Lesson 7.1 Relate Multiplication and Division
Lesson 7.2 Write Related Facts
Lesson 7.3 Multiply and Divide with 2, 4, and 8
Lesson 7.4 Multiply and Divide with 5 and 10
Lesson 7.5 Multiply and Divide with 3 and 6
Lesson 7.6 Multiply and Divide with 7 and 9
Lesson 7.7 Build Fluency with Multiplication and Division

Unit 3: ADDITION AND SUBTRACTION STRATEGIES AND APPLICATIONS
Module 9: Addition and Subtraction Strategies
Lesson 9.1 Identify Number Patterns on the Addition Table
Lesson 9.2 Use Mental Math Strategies for Addition and Subtraction
Lesson 9.3 Use Properties to Add
Lesson 9.4 Use Mental Math to Assess Reasonableness
Lesson 9.5 Round to the Nearest Ten or Hundred
Lesson 9.6 Use Estimation with Sums and Differences

Module 10: Addition and Subtraction Within 1,000
Lesson 10.1 Use Expanded Form to Add
Lesson 10.2 Use Place Value to Add
Lesson 10.3 Combine Place Values to Subtract
Lesson 10.4 Use Place Value to Subtract
Lesson 10.5 Choose a Strategy to Add or Subtract
Lesson 10.6 Model and Solve Two-Step Problems

Module 11: Understand Perimeter
Lesson 11.1 Describe Perimeter
Lesson 11.2 Find Perimeter
Lesson 11.3 Find Unknown Side Lengths
Lesson 11.4 Represent Rectangles with the Same Area and Different Perimeters
Lesson 11.5 Represent Rectangles with the Same Perimeter and Different Areas

Unit 4: FRACTIONS
Module 12: Time Measurement and Intervals
Lesson 12.1 Tell and Write Time to the Minute
Lesson 12.2 Use a.m. and p.m. to Describe Time
Lesson 12.3 Measure Time Intervals
Lesson 12.4 Find Start and End Times
Lesson 12.5 Solve Time Interval Problems

Module 13: Understand Fractions as Numbers
Lesson 13.1 Describe Equal Parts of a Whole
Lesson 13.2 Represent and Name Unit Fractions
Lesson 13.3 Represent and Name Fractions of a Whole
Lesson 13.4 Represent and Name Fractions on a Number Line
Lesson 13.5 Express Whole Numbers as Fractions
Lesson 13.6 Represent and Name Fractions Greater Than 1
Lesson 13.7 Use Fractions to Measure Lengths

Module 14: Relate Shapes, Fractions, and Area
Lesson 14.1 Relate Fractions and Area
Lesson 14.2 Partition Shapes into Equal Areas
Lesson 14.3 Use Unit Fractions to Describe Area

Module 15: Compare Fractions
Lesson 15.1 Compare Fractions Using Concrete and Visual Models
Lesson 15.2 Compare Fractions with the Same Denominator
Lesson 15.3 Compare Fractions with the Same Numerator
Lesson 15.4 Use Reading Strategies to Compare Fractions

Module 16: Understand Equivalent Fractions
Lesson 16.1 Use Drawings to Represent Equivalent Fractions with Smaller Parts
Lesson 16.2 Represent Equivalent Fractions with Larger Parts
Lesson 16.3 Recognize and Generate Equivalent Fractions

Unit 5: MEASUREMENT AND DATA
Module 17: Liquid Volume and Mass
Lesson 17.1 Estimate and Measure Liquid Volume
Lesson 17.2 Estimate and Measure Mass
Lesson 17.3 Solve Problems About Liquid Volume and Mass

Module 18: Represent and Interpret Data
Lesson 18.1 Use Picture Graphs
Lesson 18.2 Make Picture Graphs
Lesson 18.3 Use Bar Graphs
Lesson 18.4 Make Bar Graphs
Lesson 18.5 Use Line Plots to Display Measurement Data
Lesson 18.6 Make Line Plots to Display Measurement Data
Lesson 18.7 Solve One- and Two-Step Problems Using Data

Unit 6: GEOMETRY
Module 19: Define Two-Dimensional Shapes
Lesson 19.1 Describe Shapes
Lesson 19.2 Describe Angles in Shapes
Lesson 19.3 Describe Sides of Shapes
Lesson 19.4 Define Quadrilaterals

Module 20: Categorize Two-Dimensional Shapes
Lesson 20.1 Draw Quadrilaterals
Lesson 20.2 Categorize Quadrilaterals
Lesson 20.3 Categorize Plane Shapes

GRADE 4 
Unit 1: PLACE VALUE AND WHOLE‑NUMBER OPERATIONS
Module 1: Place Value of Whole Numbers
Lesson 1.1 Understand Place Value Relationships
Lesson 1.2 Read and Write Numbers
Lesson 1.3 Regroup and Rename Numbers
Lesson 1.4 Compare and Order Numbers
Lesson 1.5 Use Place Value Understanding to Round Numbers

Module 2: Addition and Subtraction of Whole Numbers
Lesson 2.1 Add Whole Numbers and Assess Reasonableness
Lesson 2.2 Subtract Whole Numbers and Assess Reasonableness
Lesson 2.3 Use Addition and Subtraction to Solve Comparison Problems
Lesson 2.4 Apply the Perimeter Formula for Rectangles

Unit 2: MULTIPLICATION AND DIVISION PROBLEMS
Module 3: Understand Multiplication Strategies
Lesson 3.1 Explore Multiplicative Comparisons
Lesson 3.2 Distinguish Between Multiplicative and Additive Comparisons
Lesson 3.3 Use Division to Solve Multiplicative Comparison Problems
Lesson 3.4 Use Comparisons to Solve Problem Situations
Lesson 3.5 Solve Multistep Problems with Multiplication and Division

Module 4: Mental Math and Estimation Strategies
Lesson 4.1 Explore Multiplication Patterns with Tens, Hundreds, and Thousands
Lesson 4.2 Explore Division Patterns with Tens, Hundreds, and Thousands
Lesson 4.3 Estimate Products by 1‑Digit Numbers
Lesson 4.4 Estimate Quotients Using Compatible Numbers
Lesson 4.5 Use Mental Math Strategies for Multiplication and Division

Module 5: Multiply by 1‑Digit Numbers
Lesson 5.1 Represent Multiplication
Lesson 5.2 Use Area Models and the Distributive Property to Multiply
Lesson 5.3 Multiply Using Expanded Form
Lesson 5.4 Multiply Using Partial Products
Lesson 5.5 Use Place Value to Multiply 2‑Digit Numbers
Lesson 5.6 Multiply 3‑Digit and 4‑Digit Numbers
Lesson 5.7 Use Equations to Solve Multistep Problems

Module 6: Understand Division by 1‑Digit Numbers
Lesson 6.1 Represent Division
Lesson 6.2 Investigate Remainders
Lesson 6.3 Interpret Remainders
Lesson 6.4 Use Area Models and the Distributive Property to Divide
Lesson 6.5 Divide Using Repeated Subtraction
Lesson 6.6 Divide Using Partial Quotients

Module 7: Divide by 1‑Digit Numbers
Lesson 7.1 Represent Division with Regrouping
Lesson 7.2 Use Place Value to Divide
Lesson 7.3 Divide by 1‑Digit Numbers
Lesson 7.4 Solve Multistep Multiplication and Division Problems

Unit 3: EXTEND AND APPLY MULTIPLICATION
Module 8: Multiply by 2‑Digit Numbers
Lesson 8.1 Multiply with Tens
Lesson 8.2 Estimate Products
Lesson 8.3 Relate Area Models and Partial Products
Lesson 8.4 Multiply Using Partial Products
Lesson 8.5 Multiply with Regrouping
Lesson 8.6 Choose a Multiplication Strategy
Lesson 8.7 Solve Multistep Problems and Assess Reasonableness

Module 9: Apply Multiplication to Area
Lesson 9.1 Apply the Area Formula to Rectangles
Lesson 9.2 Find the Area of Combined Rectangles
Lesson 9.3 Find Unknown Measures
Lesson 9.4 Solve Area Problems

Unit 4: FRACTIONS AND DECIMALS
Module 10: Algebraic Thinking — Number Theory
Lesson 10.1 Investigate Factors
Lesson 10.2 Identify Factors
Lesson 10.3 Generate Multiples Using Factors
Lesson 10.4 Identify Prime and Composite Numbers
Lesson 10.5 Generate and Analyze Number Patterns

Module 11: Addition and Subtraction Grouping Strategies
Lesson 11.1 Compare Fractions Using Visual Models
Lesson 11.2 Compare Fractions Using Benchmarks
Lesson 11.3 Explain Fraction Equivalence Using Visual Models
Lesson 11.4 Generate Equivalent Fractions
Lesson 11.5 Use Common Multiples to Write Equivalent Fractions
Lesson 11.6 Compare Fractions Using Common Numerators and Denominators
Lesson 11.7 Use Comparisons to Order Fractions

Module 12: Relate Fractions and Decimals
Lesson 12.1 Represent Tenths as Fractions and Decimals
Lesson 12.2 Represent Hundredths as Fractions and Decimals
Lesson 12.3 Identify Equivalent Fractions and Decimals
Lesson 12.4 Compare Decimals
Lesson 12.5 Relate Fractions, Decimals, and Money
Lesson 12.6 Solve Multistep Money Problems

Module 13: Use Fractions to Understand Angles
Lesson 13.1 Explore Lines, Rays, and Angles
Lesson 13.2 Explore Angles
Lesson 13.3 Relate Angles to Fractional Parts of a Circle
Lesson 13.4 Relate Degrees to Fractional Parts of Circles
Lesson 13.5 Measure and Draw Angles Using a Protractor
Lesson 13.6 Join and Separate Angles
Lesson 13.7 Find Unknown Angle Measures

Module 14: Understand Addition and Subtraction of Fractions with Like Denominators
Lesson 14.1 Decompose Fractions into Sums
Lesson 14.2 Join Parts of the Same Whole
Lesson 14.3 Represent Addition of Fractions
Lesson 14.4 Separate Parts of the Same Whole
Lesson 14.5 Represent Subtraction of Fractions
Lesson 14.6 Add Fractional Parts of 10 and 100

Module 15: Add and Subtract Fractions and Mixed Numbers with Like Denominators
Lesson 15.1 Add and Subtract Fractions to Solve Problems
Lesson 15.2 Rename Fractions and Mixed Numbers
Lesson 15.3 Add and Subtract Mixed Numbers to Solve Problems
Lesson 15.4 Rename Mixed Numbers to Subtract
Lesson 15.5 Apply Properties of Addition to Add Fractions and Mixed Numbers
Lesson 15.6 Practice Solving Fraction Problems

Module 16: Multiply Fractions by Whole Numbers
Lesson 16.1 Understand Multiples of Unit Fractions
Lesson 16.2 Find Multiples of Fractions
Lesson 16.3 Represent Multiplication of a Fraction by a Whole Number
Lesson 16.4 Solve Problems Using Multiplication of a Fraction or Mixed Number by a Whole Number

Unit 6: TWO‑DIMENSIONAL FIGURES AND SYMMETRY
Module 17: Two‑Dimensional Figures
Lesson 17.1 Identify and Draw Perpendicular and Parallel Lines
Lesson 17.2 Identify and Classify Triangles by Angles
Lesson 17.3 Identify and Classify Triangles by Sides
Lesson 17.4 Identify and Classify Quadrilaterals
Lesson 17.5 Measure and Draw Angles of Two-Dimensional Figures

Module 18: Symmetry and Patterns
Lesson 18.1 Recognize Lines of Symmetry
Lesson 18.2 Identify and Draw Lines of Symmetry
Lesson 18.3 Generate and Identify Shape Patterns

Module 19: Relative Sizes of Customary Measurement Units
Lesson 19.1 Identify Customary Measurement Benchmarks
Lesson 19.2 Compare Customary Units of Length
Lesson 19.3 Compare Customary Units of Weight
Lesson 19.4 Compare Customary Units of Liquid Volume
Lesson 19.5 Represent and Interpret Measurement Data in Line Plots

Module 20: Relative Sizes of Metric Measurement Units
Lesson 20.1 Identify Metric Measurement Benchmarks
Lesson 20.2 Compare Metric Units of Length
Lesson 20.3 Compare Metric Units of Mass and Liquid Volume
Lesson 20.4 Solve Problems Using Measurements

Module 21: Solve Problems with Time and Measurement
Lesson 21.1 Compare Units of Time
Lesson 21.2 Solve Problems Involving Elapsed Time
Lesson 21.3 Solve Problems Involving Start Time and End Time
Lesson 21.4 Practice with Mixed Measures

Grade 5

Module 1: Whole Number Place Value and Multiplication
Lesson 1.1 Recognize the 10 to 1 Relationship Among Place-Value Positions
Lesson 1.2 Use Powers of 10 and Exponents
Lesson 1.3 Use a Pattern to Multiply by Multiples of 10, 100, and 1,000
Lesson 1.4 Multiply by 1-Digit Numbers
Lesson 1.5 Multiply by Multi-Digit Numbers
Lesson 1.6 Develop Multiplication Fluency

Module 2: Understand Division of Whole Numbers
Lesson 2.1 Relate Multiplication to Division
Lesson 2.2 Represent Division with 2-Digit Divisors
Lesson 2.3 Estimate with 2-Digit Divisors
Lesson 2.4 Use Partial Quotients

Module 3: Practice Division of Whole Numbers
Lesson 3.1 Divide by 2-Digit Divisors
Lesson 3.2 Interpret the Remainder
Lesson 3.3 Adjust Quotient
Lesson 3.4 Practice with Division

Module 4: Expressions
Lesson 4.1 Write Numerical Expressions
Lesson 4.2 Interpret Numerical Expressions
Lesson 4.3 Evaluate Numerical Expressions
Lesson 4.4 Use Grouping Symbols

Module 5: Volume
Lesson 5.1 Use Unit Cubes to Build Solid Figures
Lesson 5.2 Understand Volume
Lesson 5.3 Estimate Volume
Lesson 5.4 Find Volume of Right Rectangular Prisms
Lesson 5.5 Apply Volume Formulas
Lesson 5.6 Find Volume of Composed Figures

Module 6: Understand Addition and Subtraction of Fractions with Unlike Denominators
Lesson 6.1 Represent Fraction Sums and Differences
Lesson 6.2 Represent Addition with Different-Sized Parts
Lesson 6.3 Represent Subtraction with Different-Sized Parts
Lesson 6.4 Rewrite Fractions with a Common Denominator

Module 7: Understand Compare Problems
Lesson 7.1 Use Benchmarks and Number Sense to Estimate
Lesson 7.2 Assess Reasonableness of Fraction Sums and Differences
Lesson 7.3 Assess Reasonableness of Mixed Number Sums and Differences
Lesson 7.4 Rename Mixed Numbers to Subtract
Lesson 7.5 Apply Properties of Addition
Lesson 7.6 Practice Addition and Subtraction Using Equations

Module 8: Understand Multiplication of Fractions
Lesson 8.1 Explore Groups of Equal Shares to Show Multiplication
Lesson 8.2 Represent Multiplication of Whole Numbers by Fractions
Lesson 8.3 Represent Multiplication with Unit Fractions
Lesson 8.4 Represent Multiplication of Fractions
Lesson 8.5 Use Representation of Area to Develop Procedures
Lesson 8.6 Interpret Fraction Multiplication as Scaling
Lesson 8.7 Multiply Fractions

Module 9: Understand and Apply Multiplication of Mixed Numbers
Lesson 9.1 Explore Area and Mixed Numbers
Lesson 9.2 Multiply Mixed Numbers
Lesson 9.3 Practice Multiplication with Fractions and Mixed Numbers
Lesson 9.4 Apply Fraction Multiplication to Find Area

Module 10: Understand Division with Whole Numbers and Unit Fractions
Lesson 10.1 Interpret a Fraction as Division
Lesson 10.2 Represent and Find the Size of Equal Parts
Lesson 10.3 Use Representations of Division of Unit Fractions by Whole Numbers
Lesson 10.4 Represent and Find the Number of Equal-Sized Parts
Lesson 10.5 Use Representations of Division of Whole Numbers by Unit Fractions

Module 11: Divide with Whole Numbers and Unit Fractions
Lesson 11.1 Relate Multiplication and Division of Fractions
Lesson 11.2 Divide Whole Numbers by Unit Fractions
Lesson 11.3 Interpret and Solve Division of a Whole Number by a Unit Fraction
Lesson 11.4 Divide Unit Fractions by Whole Numbers
Lesson 11.5 Interpret and Solve Division of a Unit Fraction by a Whole Number
Lesson 11.6 Solve Division Problems Using Visual Models and Equations

Module 12: Customary Measurement
Lesson 12.1 Convert Customary Measurements
Lesson 12.2 Solve Multistep Customary Measurement Problems
Lesson 12.3 Represent and Interpret Measurement Data in Line Plots
Lesson 12.4 Convert Time and Find Elapsed Time

Module 13: Decimal Place Value
Lesson 13.1 Understand Thousandths
Lesson 13.2 Read and Write Decimals to Thousandths
Lesson 13.3 Round Decimals
Lesson 13.4 Compare and Order Decimals

Module 14: Add and Subtract Decimals
Lesson 14.1 Represent Decimal Addition
Lesson 14.2 Represent Decimal Subtraction
Lesson 14.3 Assess Reasonableness of Sums and Differences
Lesson 14.4 Add Decimals
Lesson 14.5 Subtract Decimals
Lesson 14.6 Use Strategies and Reasoning to Add and Subtract

Module 15: Multiply Decimals and Whole Numbers
Lesson 15.1 Understand Decimal Multiplication Patterns
Lesson 15.2 Represent Multiplication with Decimals and Whole Numbers
Lesson 15.3 Assess Reasonableness of Products
Lesson 15.4 Multiply Decimals by 1-Digit Whole Numbers
Lesson 15.5 Multiply Decimals by 2-Digit Whole Numbers
Lesson 15.6 Solve Problems Using Bar Models

Module 16: Multiply Decimals
Lesson 16.1 Represent Decimal Multiplication
Lesson 16.2 Multiply Decimals
Lesson 16.3 Multiply Decimals with Zeros in the Product

Module 17: Divide Decimals
Lesson 17.1 Understand Decimal Division Patterns
Lesson 17.2 Represent Division of Decimals by Whole Numbers
Lesson 17.3 Assess Reasonableness of Quotients
Lesson 17.4 Divide Decimals by Whole Numbers
Lesson 17.5 Represent Decimal Division
Lesson 17.6 Divide Decimals
Lesson 17.7 Write Zeros in the Dividend

Module 18: Customary and Metric Measurement
Lesson 18.1 Understand Metric Conversions
Lesson 18.2 Solve Customary and Metric Conversion Problems
Lesson 18.3 Solve Multistep Measurement Problems

Module 19: Graphs and Patterns
Lesson 19.1 Describe a Coordinate System
Lesson 19.2 Understand Ordered Pairs
Lesson 19.3 Use Ordered Pairs to Represent Problems
Lesson 19.4 Generate and Identify Numerical Patterns
Lesson 19.5 Identify and Graph Relationships and Patterns

Module 20: Classify Two-Dimensional Figures
Lesson 20.1 Identify and Classify Polygons
Lesson 20.2 Classify and Organize Triangles
Lesson 20.3 Classify and Organize Quadrilaterals
Lesson 20.4 Use Venn Diagrams to Classify Two-Dimensional Figures

Grade 6

MODULE 1 Integer Concepts
Lesson 1 Identify and Interpret Integers
Lesson 2 Compare and Order Integers on a Number Line
Lesson 3 Find and Apply Absolute Value

Module 2: Understand Division of Whole Numbers
Lesson 1 Interpret Rational Numbers
Lesson 2 Compare Rational Numbers on a Number Line
Lesson 3 Find and Apply LCM and GCF
Lesson 4 Order Rational Numbers

MODULE 3 Fraction Division
Lesson 1 Understand Fraction Division
Lesson 2 Explore Division of Fractions with Unlike Denominators
Lesson 3 Explore Division of Mixed Numbers
Lesson 4 Practice and Apply Division of Fractions and Mixed Numbers
Lesson 5 Practice Fraction Operations

MODULE 4 Fluency with Multi-Digit Decimal Operations
Lesson 1 Add and Subtract Multi-Digit Decimals
Lesson 2 Multiply Multi-Digit Decimals
Lesson 3 Divide Multi-Digit Whole Numbers
Lesson 4 Divide Multi-Digit Decimals
Lesson 5 Apply Operations with Multi-Digit Decimals

MODULE 5 Ratios and Rates
Lesson 1 Understand the Concept and Language of Ratios
Lesson 2 Represent Ratios and Rates with Tables and Graphs
Lesson 3 Compare Ratios and Rates
Lesson 4 Find and Apply Unit Rates
Lesson 5 Solve Ratio and Rate Problems Using Proportional Reasoning

MODULE 6 Apply Ratios and Rates to Measurement
Lesson 1 Use Ratio Reasoning with Circle Graphs
Lesson 2 Use Rate Reasoning to Convert Within Measurement Systems
Lesson 3 Use Rate Reasoning to Convert Between Measurement Systems

MODULE 7 Understand and Apply Percent
Lesson 1 Understand, Express, and Compare Percent Ratios
Lesson 2 Use Strategies to Find a Percent of a Quantity
Lesson 3 Solve a Variety of Percent Problems

MODULE 8 Numerical and Algebraic Expressions
Lesson 1 Understand and Apply Exponents
Lesson 2 Write and Evaluate Numerical Expressions for Situations
Lesson 3 Write Algebraic Expressions to Model Situations
Lesson 4 Interpret and Evaluate Algebraic Expressions
Lesson 5 Identify and Generate Equivalent Algebraic Expressions

MODULE 9 Solve Problems Using Equations and Inequalities
Lesson 1 Write Equations to Represent Situations
Lesson 2 Use Addition and Subtraction Equations to Solve Problems
Lesson 3 Use Multiplication and Division Equations to Solve Problems
Lesson 4 Use One-Step Equations to Solve a Variety of Problems
Lesson 5 Write and Graph Inequalities

MODULE 10 Real-World Relationships Between Variables
Lesson 1 Represent Equations in Tables and Graphs
Lesson 2 Write Equations from Verbal Descriptions
Lesson 3 Write Equations from Tables and Graphs

MODULE 11 Polygons on the Coordinate Plane
Lesson 1 Graph Rational Numbers on the Coordinate Plane
Lesson 2 Graph Polygons on the Coordinate Plane
Lesson 3 Find Distance on the Coordinate Plane
Lesson 4 Find Perimeter and Area on the Coordinate Plane

MODULE 12 Area of Triangles and Special Quadrilaterals
Lesson 1 Develop and Use the Formula for Area of Parallelograms
Lesson 2 Develop and Use the Formula for Area of Triangles
Lesson 3 Develop and Use the Formula for Area of Trapezoids
Lesson 4 Find Area of Composite Figures

MODULE 13 Surface Area and Volume
Lesson 1 Explore Nets and Surface Area
Lesson 2 Find Volume of Rectangular Prisms
Lesson 3 Solve Volume Problems

MODULE 14 Data Collection and Displays
Lesson 1 Explore Statistical Data Collection
Lesson 2 Display Data in Dot Plots
Lesson 3 Make Histograms and Frequency Tables

MODULE 15 Measures of Center
Lesson 1 Explore Mean as Fair Share
Lesson 2 Find Measures of Center
Lesson 3 Choose a Measure of Center

MODULE 16 Variability and Data Distribution
Lesson 1 Explore Patterns of Data
Lesson 2 Display Data in Box Plots
Lesson 3 Find Mean Absolute Deviation
Lesson 4 Explore Measures of Variability
Lesson 5 Describe Distributions

Printable 7th and 8th Grade Reveal Math Table of Contents

COURSE 2 – 7th Grade
Visit with your student's classroom teacher for details on which lessons will be used from Reveal Math.

Module 1: Proportional Relationships
1‑1 Unit Rates Involving Ratios of Fractions — Explore: Find Unit Rates with Fractions
1‑2 Understand Proportional Relationships
1‑3 Tables of Proportional Relationships — Explore: Ratios in Tables
1‑4 Graphs of Proportional Relationships — Explore: Proportional Relationships, Tables, and Graphs; Explore: Analyze Points
1‑5 Equations of Proportional Relationships — Explore: Proportional Relationships and Equations
1‑6 Solve Problems Involving Proportional Relationships

Module 2: Solve Percent Problems
2‑1 Percent of Change — Explore: Percent of Change
2‑2 Tax — Explore: Sales Tax
2‑3 Tips and Markups
2‑4 Discounts
2‑5 Interest — Explore: Interest
2‑6 Commission and Fees
2‑7 Percent Error — Explore: Percent Error

Module 3: Operations with Integers
3‑1 Add Integers — Explore: Use Algebra Tiles to Add Integers
3‑2 Subtract Integers — Explore: Use Algebra Tiles to Subtract Integers; Explore: Find Distance on a Number Line
3‑3 Multiply Integers — Explore: Use Algebra Tiles to Multiply Integers
3‑4 Divide Integers — Explore: Use Algebra Tiles to Divide Integers
3‑5 Apply Integer Operations

Module 4: Operations with Rational Numbers
4‑1 Rational Numbers — Explore: Rational Number Written as Decimals
4‑2 Add Rational Numbers
4‑3 Subtract Rational Numbers
4‑4 Multiply Rational Numbers
4‑5 Divide Rational Numbers
4‑6 Apply Rational Numbers Operations

Module 5: Simplify Algebraic Expressions
5‑1 Simplify Algebraic Expressions — Explore: Simplify Algebraic Expressions
5‑2 Add Linear Expressions — Explore: Add Expressions
5‑3 Subtract Linear Expressions
5‑4 Factor Linear Expressions — Explore: Factor Linear Expressions
5‑5 Combine Operations with Linear Expressions

Module 6: Write and Solve Equations
6‑1 Write and Solve One‑Step Equations — Explore: Solve One‑Step Equations Using Algebra Tiles
6‑2 Solve Two‑Step Equations: px + q = r — Explore: Solve Two‑Step Equations Using Bar Diagrams; Explore: Solve Two‑Step Equations Using Algebra Tiles
6‑3 Write and Solve Two‑Step Equations: px + q = r — Explore: Write Two‑Step Equations
6‑4 Solve Two‑Step Equations: p(x + q) = r — Explore: Solve Two‑Step Equations Using Bar Diagrams; Explore: Solve Two‑Step Equations Using Algebra Tiles
6‑5 Write and Solve Two‑Step Equations: p(x + q) = r — Explore: Write Two‑Step Equations

Module 7: Write and Solve Inequalities
7‑1 Solve One‑Step Addition and Subtraction Inequalities — Explore: Addition and Subtraction Properties of Inequality
7‑2 Write and Solve One‑Step Addition and Subtraction Inequalities
7‑3 Solve One‑Step Multiplication and Division Inequalities with Positive Coefficients — Explore: Multiplication and Division Properties of Inequality
7‑4 Solve One‑Step Multiplication and Division Inequalities with Negative Coefficients — Explore: Multiplying and Dividing Inequalities by Negative Numbers
7‑5 Write and Solve One‑Step Multiplication and Division Inequalities
7‑6 Write and Solve Two‑Step Inequalities

Module 8: Geometric Figures
8‑1 Vertical and Adjacent Angles — Explore: Vertical and Adjacent Angle Pairs
8‑2 Complementary and Supplementary Angles — Explore: Complementary and Supplementary Angle Pairs
8‑3 Triangles — Explore: Create Triangles
8‑4 Scale Drawings — Explore: Scale Drawings
8‑5 Three‑Dimensional Figures

Module 9: Measure Figures
9‑1 Circumference of Circles — Explore: The Distance Around a Circle
9‑2 Area of Circles — Explore: Area of Circles
9‑3 Area of Composite Figures
9‑4 Volume — Explore: Volume of Prisms; Explore: Volume of Pyramids
9‑5 Surface Area — Explore: Surface Area of Prisms and Pyramids
9‑6 Volume and Surface Area of Composite Figures

Module 10: Probability
10‑1 Find Likelihoods — Explore: Chance Events
10‑2 Relative Frequency of Simple Events — Explore: Experiments and Likelihood
10‑3 Theoretical Probability of Simple Events — Explore: Long‑Run Relative Frequencies
10‑4 Compare Probabilities of Simple Events
10‑5 Probability of Compound Events — Explore: Sample Space for Repeated Simple Events
10‑6 Simulate Chance Events — Explore: Simulations

Module 11: Sampling and Statistics
11‑1 Biased and Unbiased Samples
11‑2 Make Predictions
11‑3 Generate Multiple Samples — Explore: Multiple Samples; Explore: Sample Size in Multiple Samples
11‑4 Compare Two Populations — Explore: Compare Means of Two Populations
11‑5 Assess Visual Overlap

COURSE 3 – 8th Grade
Visit with your student's classroom teacher for details on which lessons will be used from Reveal Math.

Module 1: Proportional Relationships
1‑1 Powers and Exponents — Explore: Exponents
1‑2 Multiply and Divide Monomials — Explore: Product of Power; Explore: Quotient of Powers
1‑3 Powers of Monomials — Explore: Power of a Power
1‑4 Zero and Negative Exponents — Explore: Exponents of Zero; Explore: Negative Exponents
1‑5 Scientific Notation — Explore: Scientific Notation
1‑6 Compute with Scientific Notation

Module 2: Real Numbers
2‑1 Terminating and Repeating Decimals — Explore: Terminating Decimals
2‑2 Roots — Explore: Find Square Roots Using a Square Model
2‑3 Real Numbers — Explore: Real Numbers
2‑4 Estimate Irrational Numbers — Explore: Roots of Non‑Perfect Squares
2‑5 Compare and Order Real Numbers

Module 3: Solve Equations with Variables on Each Side
3‑1 Solve Equations with Variables on Each Side — Explore: Equations with Variables on Each Side
3‑2 Write and Solve Equations with Variables on Each Side — Explore: Write and Solve Equations with Variables on Each Side
3‑3 Solve Multi‑Step Equations
3‑4 Write and Solve Multi‑Step Equations — Explore: Translate Problems into Equations
3‑5 Determine the Number of Solutions — Explore: Number of Solutions

Module 4: Linear Relationships and Slope
4‑1 Proportional Relationships and Slope — Explore: Rate of Change
4‑2 Slope of a Line — Explore: Develop Concepts of Slope; Explore: Slope of Horizontal and Vertical Lines
4‑3 Similar Triangles and Slope — Explore: Right Triangles and Slope
4‑4 Direct Variation — Explore: Derive the Equation y = mx
4‑5 Slope‑Intercept Form — Explore: Derive the Equation y = mx + b
4‑6 Graph Linear Equations

Module 5: Functions
5‑1 Identify Functions — Explore: Relations and Functions
5‑2 Function Tables — Explore: An Introduction to Function Rules
5‑3 Construct Linear Functions
5‑4 Compare Functions — Explore: Comparing Properties of Functions
5‑5 Nonlinear Functions — Explore: Linear and Nonlinear Functions
5‑6 Qualitative Graphs — Explore: Interpret Qualitative Graphs

Module 6: Systems of Linear Equations
6‑1 Solve Systems of Equations by Graphing — Explore: Systems of Equations
6‑2 Determine Number of Solutions — Explore: Systems of Equations: Slopes and y‑Intercepts
6‑3 Solve Systems of Equations by Substitution — Explore: Solve Systems of Equations by Substitution
6‑4 Solve Systems of Equations by Elimination — Explore: Solve Systems of Equations by Elimination
6‑5 Write and Solve Systems of Equations

Module 7: Triangles and the Pythagorean Theorem
7‑1 Angle Relationships and Parallel Lines — Explore: Parallel Lines and Transversals
7‑2 Angle Relationships and Triangles — Explore: Angles of Triangles; Explore: Exterior Angles of Triangles
7‑3 The Pythagorean Theorem — Explore: Right Triangle Relationships; Explore: Proof of the Pythagorean Theorem
7‑4 Converse of the Pythagorean Theorem — Explore: Prove the Converse of the Pythagorean Theorem
7‑5 Distance on the Coordinate Plane — Explore: Use the Pythagorean Theorem to Find Distance

Module 8: Transformations
8‑1 Translations — Explore: Translate Using Coordinates
8‑2 Reflections — Explore: Reflect Using Coordinates
8‑3 Rotations — Explore: Rotate Using Coordinates
8‑4 Dilations — Explore: Dilate Figures on the Coordinate Plane

Module 9: Congruence and Similarity
9‑1 Congruence and Transformations — Explore: Congruence and Transformations
9‑2 Congruence and Corresponding Parts
9‑3 Similarity and Transformations
9‑4 Similarity and Corresponding Parts — Explore: Similar Triangles; Explore: Angle‑Angle Similarity
9‑5 Indirect Measurement — Explore: Similar Triangles and Indirect Measurement

Module 10: Volume
10‑1 Volume of Cylinders — Explore: Volume of Cylinders
10‑2 Volume of Cones — Explore: Volume of Cones
10‑3 Volume of Spheres
10‑4 Find Missing Dimensions
10‑5 Volume of Composite Solids

Module 11: Scatter Plots and Two‑Way Tables
11‑1 Scatter Plots — Explore: Scatter Plots
11‑2 Draw Lines of Fit — Explore: Lines of Fit
11‑3 Equations for Lines of Fit
11‑4 Two‑Way Tables
11‑5 Associations in Two‑Way Tables — Explore: Patterns of Association in Two‑Way Tables

Printable EnVision MAth Table of Contents Math i ii iii

enVision Integrated MATHEMATICS 
Visit with your student's classroom teacher for details on which lessons will be used from EnVision Math.

Topic 1: Solving Equations and Inequalities
1‑1 Solving Linear Equations
1‑2 Solving Equations with Variables on Both Sides
1‑3 Literal Equations and Formulas
1‑4 Solving Inequalities in One Variable
1‑5 Compound Inequalities
1‑6 Absolute Value Equations and Inequalities

Topic 2: Linear Equations
2‑1 Slope‑Intercept Form
2‑2 Point‑Slope Form
2‑3 Standard Form
2‑4 Parallel and Perpendicular Lines

Topic 3: Linear Functions
3‑1 Relations and Functions
3‑2 Linear Functions
3‑3 Transforming Linear Functions
3‑4 Arithmetic Sequences
3‑5 Scatter Plots and Lines of Fit
3‑6 Analyzing Lines of Fit

Topic 4: Systems of Linear Equations and Inequalities
4‑1 Solving Systems of Equations by Graphing
4‑2 Solving Systems of Equations by Substitution
4‑3 Solving Systems of Equations by Elimination
4‑4 Linear Inequalities in Two Variables
4‑5 Systems of Linear Inequalities

Topic 5: Exponents and Exponential Functions
5‑1 Rational Exponents and Properties of Exponents
5‑2 Exponential Functions
5‑3 Exponential Growth and Decay
5‑4 Geometric Sequences
5‑5 Transformations of Exponential Functions

Topic 6: Foundations of Geometry
6‑1 Measuring Segments and Angles
6‑2 Basic Constructions
6‑3 Midpoint and Distance
6‑4 Inductive Reasoning
6‑5 Conditional Statements
6‑6 Deductive Reasoning
6‑7 Writing Proofs
6‑8 Indirect Proof

Topic 7: Parallel and Perpendicular Lines
7‑1 Parallel Lines
7‑2 Proving Lines Parallel
7‑3 Parallel Lines and Triangle Angle Sums
7‑4 Slopes of Parallel and Perpendicular Lines

Topic 8: Transformations
8‑1 Reflections
8‑2 Translations
8‑3 Rotations
8‑4 Classification of Rigid Motions
8‑5 Symmetry

Topic 9: Triangle Congruence
9‑1 Congruence
9‑2 Isosceles and Equilateral Triangles
9‑3 Proving and Applying the SAS and SSS Congruence Criteria
9‑4 Proving and Applying the ASA and AAS Congruence Criteria
9‑5 Congruence in Right Triangles
9‑6 Congruence in Overlapping Triangles
9‑7 Polygons in the Coordinate Plane
9‑8 Chords

Topic 10: Statistics
10‑1 Analyzing Data Displays
10‑2 Comparing Data Sets
10‑3 Interpreting the Shapes of Data Displays
10‑4 Standard Deviation
10‑5 Two‑Way Frequency Tables

enVision Integrated MATHEMATICS II
Visit with your student's classroom teacher for details on which lessons will be used from EnVision Math.

Topic 1: Exponents and Roots
1‑1 Operations on Real Numbers
1‑2 Rational Exponents and Properties of Exponents
1‑3 Exponential Models
1‑4 The Square Root Function
1‑5 The Cube Root Function

Topic 2: Polynomials and Factoring
2‑1 Adding and Subtracting Polynomials
2‑2 Multiplying Polynomials
2‑3 Multiplying Special Cases
2‑4 Factoring Polynomials
2‑5 Factoring x² + bx + c
2‑6 Factoring ax² + bx + c
2‑7 Factoring Special Cases

Topic 3: Quadratic Functions
3‑1 Key Features of a Quadratic Function
3‑2 Quadratic Functions in Vertex Form
3‑3 Quadratic Functions in Standard Form
3‑4 Modeling with Quadratic Functions
3‑5 Linear, Exponential, and Quadratic Models

Topic 4: Solving Quadratic Equations
4‑1 Solving Quadratic Equations Using Graphs and Tables
4‑2 Solving Quadratic Equations by Factoring
4‑3 Rewriting Radical Expressions
4‑4 Solving Quadratic Equations Using Square Roots
4‑5 Solving Systems of Linear and Quadratic Equations

Topic 5: Quadratic Equations and Complex Numbers
5‑1 Complex Numbers and Operations
5‑2 Completing the Square
5‑3 The Quadratic Formula
5‑4 Linear‑Quadratic Systems
5‑5 Polynomial Identities
5‑5a The Fundamental Theorem of Algebra

Topic 6: Working With Functions
6‑1 The Absolute Value Function
6‑2 Piecewise‑Defined Functions
6‑3 Step Functions
6‑4 Transformations of Piecewise‑Defined Functions
6‑5 Analyzing Functions Graphically
6‑6 Translations of Functions
6‑7 Compressions and Stretches of Functions
6‑8 Operations With Functions
6‑9 Inverse Functions

Topic 7: Relationships in Triangles
7‑1 Writing Proofs
7‑2 Parallel Lines
7‑3 Perpendicular and Angle Bisectors
7‑4 Bisectors in Triangles
7‑5 Medians and Altitudes
7‑6 Inequalities in One Triangle
7‑7 Inequalities in Two Triangles

Topic 8: Quadrilaterals and Other Polygons
8‑1 The Polygon Angle‑Sum Theorems
8‑2 Kites and Trapezoids
8‑3 Properties of Parallelograms
8‑4 Proving a Quadrilateral Is a Parallelogram
8‑5 Properties of Special Parallelograms
8‑6 Conditions of Special Parallelograms

Topic 9: Similarity and Right Triangles
9‑1 Dilations
9‑2 Similarity Transformations
9‑3 Proving Triangles Similar
9‑4 Similarity in Right Triangles
9‑5 Proportions in Triangles
9‑6 Right Triangles and the Pythagorean Theorem
9‑7 Trigonometric Ratios
9‑7a The Pythagorean Identity

Topic 10: Probability
10‑1 Two‑Way Frequency Tables
10‑2 Probability Events
10‑3 Conditional Probability
10‑4 Permutations and Combinations
10‑5 Probability Distributions
10‑6 Expected Value
10‑7 Probability and Decision Making

Topic 11: Coordinate Geometry
11‑1 Polygons in the Coordinate Plane
11‑2 Proofs Using Coordinate Geometry
11‑3 Circles in the Coordinate Plane
11‑4 Parabolas in the Coordinate Plane

Topic 12: Circles
12‑1 Arcs and Sectors
12‑2 Tangent Lines to a Circle
12‑3 Chords
12‑4 Inscribed Angles
12‑5 Secant Lines and Segments

Topic 13: Two‑ and Three‑Dimensional Models
13‑1 Three‑Dimensional and Cross Sections
13‑2 Volumes of Prisms and Cylinders
13‑3 Pyramids and Cones
13‑4 Spheres

enVision Integrated MATHEMATICS III
Visit with your student's classroom teacher for details on which lessons will be used from EnVision Math.

Topic 1: Linear Functions and Systems
1‑1 Key Features of Functions
1‑2 Transformations of Functions
1‑3 Piecewise‑Defined Functions
1‑4 Arithmetic Sequences and Series
1‑5 Solving Equations and Inequalities by Graphing
1‑6 Linear Systems

Topic 2: Polynomial Functions
2‑1 Graphing Polynomial Functions
2‑2 Adding, Subtracting, and Multiplying Polynomials
2‑3 Polynomial Identities
2‑4 Dividing Polynomials
2‑5 Zeros of Polynomial Functions
2‑6 Theorems About Roots of Polynomial Equations
2‑7 Transformations of Polynomial Functions

Topic 3: Rational Functions
3‑1 Inverse Variation and the Reciprocal Function
3‑2 Graphing Rational Functions
3‑3 Multiplying and Dividing Rational Expressions
3‑4 Adding and Subtracting Rational Expressions
3‑5 Solving Rational Equations

Topic 4: Rational Exponents and Radical Functions
4‑1 nth Roots, Radicals, and Rational Exponents
4‑2 Properties of Exponents and Radicals
4‑3 Graphing Radical Functions
4‑4 Solving Radical Equations
4‑5 Function Operations
4‑6 Inverse Relations and Functions

Topic 5: Exponential and Logarithmic Functions
5‑1 Key Features of Exponential Functions
5‑2 Exponential Models
5‑2a Analyzing Residuals
5‑3 Linear, Exponential, and Quadratic Models
5‑4 Logarithms
5‑5 Logarithmic Functions
5‑6 Properties of Logarithms
5‑7 Exponential and Logarithmic Equations
5‑8 Geometric Sequences and Series

Topic 6: Trigonometric Functions
6‑1 Trigonometric Functions and Acute Angles
6‑2 Angles and the Unit Circle
6‑3 Trigonometric Functions and Real Numbers
6‑4 Graphing Sine and Cosine Functions
6‑5 Graphing Other Trigonometric Functions
6‑6 Translating Trigonometric Functions

Topic 7: Trigonometric Equations and Identities
7‑1 Solving Trigonometric Equations Using Inverses
7‑2 Law of Sines and Law of Cosines
7‑3 Problem Solving With Trigonometry
7‑4 Trigonometric Identities

Topic 8: Data Analysis and Statistics
8‑1 Statistical Questions and Variables
8‑2 Statistical Studies and Sampling Methods
8‑3 Data Distributions
8‑4 Normal Distributions
8‑5 Margin of Error
8‑6 Testing Hypotheses From Testing
8‑7 Probability and Decision Making

Topic 9: Coordinate Geometry
9‑1 Basic Constructions Extension: Constructions in Triangles
9‑1a Constructions in Triangles
9‑2 Slopes of Parallel and Perpendicular Lines
9‑3 Polygons in the Coordinate Plane
9‑4 Proofs Using Coordinate Geometry
9‑4a Partitioning a Line Segment
9‑5 Circles in the Coordinate Plane
9‑6 Parabolas in the Coordinate Plane

Topic 10: Circles
10‑1 Arcs and Sectors
10‑2 Tangent Lines to a Circle
10‑3 Chords
10‑4 Inscribed Angles
10‑5 Secant Lines and Segments

Topic 11: Two‑ and Three‑Dimensional Models
11‑1 Three‑Dimensional Figures and Cross Sections
11‑2 Volumes of Prisms and Cylinders
11‑3 Pyramids and Cones
11‑4 Spheres

Grade Level	Designated Math Instructional Time*
K+-2	60 Minutes (protected time)         +Half day Kindergarten 45 minutes	45 minutes for Tier 1 across the school day   ●        No more than 5-8 minutes (11-18%) of class time is dedicated to direct instruction where teacher-talk dominates (Leinwand & Milou, 2021)
3-6	90 minutes (protected time)	60 minutes for Tier 1 across the school day   ●        No more than 8-12 minutes (13-20%) of class time is dedicated to direct instruction where teacher-talk dominates (Leinwand & Milou, 2021)
6-12	Educators have an average of 60 minutes per school day of uninterrupted Tier 1 instructional time (Leinwand & Milou, 2021)   ●       No more than 12-15 minutes (20-25%) of class time is dedicated to direct instruction where teacher-talk dominates (Leinwand & Milou, 2021)

 

Math Placement for Ninth-Grade Students

Students entering ninth grade are placed into Secondary Math I, which is the state-recommended foundational math course for ninth-grade students.  

Students may request to be placed into Secondary Math II if:

• Evidence is provided that they have satisfactorily completed a Secondary Math I course which is aligned to USBE’s Secondary Math I core standards.  

  • Evidence may include but is not limited to results from a comprehensive final assessment aligned to Secondary Math I standards or 

  • Documentation of successful completion of a Secondary Math I course that has been verified by the district to be aligned to state standards. 

• Students who have not taken a formal Secondary Math I course can be placed into a Secondary Math II course upon successful completion of the approved Secondary Math I competency assessment.

Credit begins to generate when a student enters ninth grade.  Students who complete Secondary Math I before their ninth-grade year are required to earn three math credits in high school that should include Secondary Math II, Secondary Math III, and an additional approved math course.  As per R277-700-6(9) students who complete calculus with a C or better will fulfill all of their math requirements.  It is highly recommended that students enroll in a math course every year to maintain their mathematical knowledge and skills.  Although it is not needed to be on track for graduation, for students contemplating graduating early, credit for Secondary Math I can be earned in the summer prior to their ninth-grade year by taking the approved Secondary Math I competency assessment arranged through the counseling department to be given by the district.