envisions and investigations

Grades K-5

Joint-Usage Master Plan

enVisionMATHTM

Investigations IN NUMBER, DATA, AND SPACE®

First Edition

Plan 1 1 Designed for enVisionMATH users who would like to use some Investigations activities as additional

resources for an enVisonMATH topic

Plan 2 36 Designed for enVisionMATH users who would

like to teach an entire Investigations curriculum unit as

a replacement for some enVisonMATH topics

1

Introduction to Plan 1

Pearson Scott Foresman has developed a two-in-one Joint-Usage Master Plan for

enVisionMATH and Investigations in Number, Data, and Space® First Edition for

teachers who are interested in using both programs.

The Plan 1 section of this Joint-Usage Master Plan has been designed for teachers using

enVisionMATH as their core program who would like to use some Investigations Activities as

additional resources for an enVisionMATH topic.

Using Plan 1

Step 1 Turn to the Plan 1 Contents for your grade level:

_____________________________________________________________

Kindergarten Contents ............................................................. 2

Grade 1 Contents .................................................................... 7

Grade 2 Contents .................................................................... 13

Grade 3 Contents .................................................................... 19

Grade 4 Contents .................................................................... 25

Grade 5 Contents .................................................................... 30

_____________________________________________________________

Step 2 Locate the enVisionMATH topic you are about to teach.

Step 3 Identify the page where the related Investigations resources are listed.

Step 4 Turn to that page and choose the resources that best meet the needs of your students.

GRADE K

2 Grade K, Plan 1 Designed for enVisionMATH users who would like to use Investigations resources with an envisionMATH topic

Kindergarten Contents

Topic 1: Sorting and Classifying...................................................................... 3

Topic 2: Position and Location ........................................................................ 3

Topic 3: Patterns ............................................................................................ 3

Topic 4: Zero to Five ....................................................................................... 3

Topic 5: Six to Ten .......................................................................................... 4

Topic 6: Comparing Numbers.......................................................................... 4

Topic 7: Geometry .......................................................................................... 4

Topic 9: Measurement .................................................................................... 5

Topic 10: Addition........................................................................................... 5

Topic 11: Subtraction...................................................................................... 5

Topic 12: Larger Numbers .............................................................................. 5

Topic 13: Money ............................................................................................. 6

Topic 14: Time ................................................................................................ 6

Topic 15: Calendar.......................................................................................... 6

Topic 16: Graphing ......................................................................................... 6

GRADE K


enVisionMATH Topic 1: Sorting and Classifying Related Investigations Unit Counting Ourselves and Others (Exploring Data) Activities

Choice Time: Self Portraits, p. 25

Focus Time: Favorite Lunch Foods, p. 39

Focus Time: Sorting the Lunch Foods, p. 40 Choice Time: Boxes, Bottles, and Cans, p. 46

Choice Time: The Grocery Store, p. 48

Choice Time: Clothing Sort, p. 51

enVisionMATH Topic 2: Position and Location Related Investigations Unit Counting Ourselves and Others (Exploring Data) Activities

Choice Time: Same and Different, p. 44

Choice Time: Boxes, Bottles, and Cans, p. 46

Choice Time: The Grocery Store, p. 48 Choice Time: Clothing Sort, p. 51

enVisionMATH Topic 3: Patterns Related Investigations Unit Pattern Trains and Hopscotch Paths (Exploring Pattern) Activities

Focus Time: Can You Do What I Do?, p. 4

Choice Time: Making Patterns, p. 14 Choice Time: Patterns on the Pocket Chart, p. 27

Choice Time: Patterns with Color Tiles, p. 28

Choice Time: What Comes Next?, p. 32 Choice Time: Add On, p. 36

Choice Time: Break the Train, p. 38 Choice Time: Make a Train, p. 40

Focus Time: Making Hopscotch Paths, p. 50

Focus Time: Paper Hopscotch Paths, p. 52

enVisionMATH Topic 4: Zero to Five Related Investigations Unit Collecting, Counting, and Measuring (Developing Number Sense) Activities

Focus Time: Anno’s Counting Book, p. 5

Focus Time: Make-Your-Own Counting Books, p. 7

Choice Time: My Counting Book, p. 10

GRADE K


enVisionMATH Topic 5: Six to Ten Related Investigations Units Mathematical Thinking in Kindergarten (Introduction) Activities

Focus Time: Counting Jar, p. 28

Focus Time: Sharing How We Counted, p. 30

Collecting, Counting, and Measuring (Developing Number Sense) Activities

Focus Time: How Many Letters in Your Name?, p. 55 Choice Time: Focus Time: Making Name Towers, p. 57

Choice Time: Collect 10 Together, p. 64 Choice Time: Racing Bears, p. 74

Focus Time: Arranging Six Tiles, p. 81

Focus Time: My Six Tiles, p. 82 Choice Time: Books of Six, p. 86

Counting Ourselves and Others (Exploring Data) Activity

Choice Time: Pattern Block Grab, p. 30

enVisionMATH Topic 6: Comparing Numbers Related Investigations Units Collecting, Counting, and Measuring (Developing Number Sense) Activities

Choice Time: Grab and Count: Which Has More?, p. 44 Choice Time: Compare, p. 46

Focus Time: Grab and Count Compare, p. 62

How Many in All? (Counting and the Number System) Activity

Choice Time: Grab Two Handfuls, p. 40

enVisionMATH Topic 7: Geometry Related Investigations Unit Making Shapes and Building Blocks (Exploring Geometry) Activities

Focus Time: A Book About Shapes, p. 5

Focus Time: Planning a Class Book of Shapes, p. 6 Choice Time: Pattern Block Pictures, p. 14

Choice Time: Shape Mural, p. 17

Choice Time: Pattern Block Puzzles, p. 34 Focus Time: Describing Shapes, p. 62

Focus Time: Making Shapes with Clay, p. 64

Choice Time: Build a Block, p. 73 Focus Time: A Close Look at Geoblocks, p. 84

Choice Time: Geoblock Match-Up, p. 90

GRADE K


enVisionMATH Topic 9: Measurement Related Investigations Unit Collecting, Counting, and Measuring (Developing Number Sense) Activities

Focus Time: Using Towers to Compare and Measure, p. 38

Focus Time: How Did You Compare?, p. 40

Focus Time: Measuring Table, p. 42

enVisionMATH Topic 10: Addition Related Investigations Unit How Many in All? (Counting and the Number System) Activities

Choice Time: Inventory Bags, p. 20

Focus Time: Six Tiles in All, p. 33

Choice Time: Books of Six in All, p. 38 Choice Time: Towers of Six, p. 42

Focus Time: Stories That Involve Combining, p. 55

Focus Time: Acting Our Story Problems, p. 58 Choice Time: Double Compare, p. 63

Focus Time: Five Crayons in All, p. 77

Choice Time: Six Crayons in All, p. 82 Choice Time: Total of Six, p. 84

enVisionMATH Topic 11: Subtraction Related Investigations Unit How Many in All? (Counting and the Number System) Activities

Focus Time: Stories That Involve Separating, p. 56 Focus Time: Acting Our Story Problems, p. 58

enVisionMATH Topic 12: Larger Numbers Related Investigations Units Mathematical Thinking in Kindergarten (Introduction) Activities

Focus Time: How Many Are We?, p. 5 Focus Time: Making an Attendance Stick, p. 7

Counting Ourselves and Others (Exploring Data) Activities

Focus Time: Counting the Class, p. 5

Focus Time: Representing the count, p. 6 Focus Time: How Many Noses?, p. 17

Focus Time: How Many Eyes?, p. 19

Focus Time: Making a Class “Eye Chart”, p. 21 Choice Time: Counting Chairs, p. 28

Focus Time: How Many Are Here Today?, p. 79

How Many in All? (Counting and the Number System) Activity

Choice Time: Collect 15 Together, p. 17

GRADE K


enVisionMATH Topic 13: Money Related Investigations Unit Counting Ourselves and Others (Exploring Data) Activity

Choice Time: The Grocery Store, p. 48

enVisionMATH Topic 14: Time Related Investigations Unit Mathematical Thinking in Kindergarten (Introduction) Activities

Focus Time: Only Six More Days, p. 43

Focus Time: Our Calendar, p. 44

enVisionMATH Topic 15: Calendar Related Investigations Unit Mathematical Thinking in Kindergarten (Introduction) Activities

Focus Time: Only Six More Days, p. 43

Focus Time: Our Calendar, p. 44

enVisionMATH Topic 16: Graphing Related Investigations Unit Mathematical Thinking in Kindergarten (Introduction) Activities

Focus Time: Are You a Boy or a Girl?, p. 54 Focus Time: Looking at Our Data, p. 55

Focus Time: Adding Absent Students, p. 57

GRADE 1

7 Grade 1, Plan 1 Designed for enVisionMATH users who would like to use Investigations resources with an envisionMATH topic

Grade 1 Contents

Topic 1: Numbers to 12................................................................................... 8

Topic 2: Comparing and Ordering Numbers ................................................... 8

Topic 3: Understanding Addition .................................................................... 8

Topic 4: Understanding Subtraction ............................................................... 8

Topic 5: Five and Ten Relationships................................................................ 9

Topic 6: Addition Facts to 12 ......................................................................... 9

Topic 7: Subtraction Facts to 12 .................................................................... 9

Topic 8: Geometry ......................................................................................... 10

Topic 9: Patterns ........................................................................................... 10

Topic 10: Counting and Number Patterns to 100 ............................................ 10

Topic 11: Tens and Ones ................................................................................ 10

Topic 12: Comparing and Ordering Numbers to 100 ...................................... 11

Topic 13: Counting Money............................................................................... 11

Topic 14: Measurement ................................................................................. 11

Topic 15: Time ............................................................................................... 11

Topic 16: Addition Facts to 18 ....................................................................... 12

Topic 17: Subtraction Facts to 18 ................................................................... 12

Topic 18: Data and Graphs.............................................................................. 12

Topic 20: Adding and Subtracting with Tens and Ones ................................... 12

GRADE 1


enVisionMATH Topic 1: Numbers to 12 Related Investigations Units Mathematical Thinking at Grade 1 (Introduction) Activities

Introducing Staircases, p. 34

A Story with a Growing Pattern, p. 100

Building Number Sense (The Number System) Activities

Quick Images, pp. 4 and 18 How Many Dots?, p. 29

Numbers on Our Fingers, p. 32

enVisionMATH Topic 2: Comparing and Ordering Numbers Related Investigations Units Mathematical Thinking at Grade 1 (Introduction) Activity

Compare, p. 26

Building Number Sense (The Number System) Activity

Compare Dots, p. 8

enVisionMATH Topic 3: Understanding Addition Related Investigations Unit Building Number Sense (The Number System) Activities

Making Sense of Combining, p. 116 Recording Combining Strategies, p. 118

Sharing Strategies, p. 120

Choice Time: Story Problems, p. 139 Sharing Story Problem Strategies, p. 142

Assessment Solving Story Problems, p. 160

enVisionMATH Topic 4: Understanding Subtraction Related Investigations Unit Building Number Sense (The Number System) Activities

Making Sense of Separating, p. 128 Recording Separating Strategies, p. 129

Sharing Separating Strategies, p. 130

GRADE 1


enVisionMATH Topic 5: Five and Ten Relationships Related Investigations Units Building Number Sense (The Number System) Activity

Introducing Towers of 10, p. 68

Number Games and Story Problems (Addition and Subtraction) Activities

Quick Image Pictures of 10, p. 5

Introducing Total of 10, p. 17 Ten Crayons, p. 24

Sharing Combinations of 10, p. 37

enVisionMATH Topic 6: Addition Facts to 12 Related Investigations Units Mathematical Thinking at Grade 1 (Introduction) Activities

Seven Peas and Carrots, p. 43 Eleven Fruits: How Many of Each?, p. 92


Twelve Cats and Dogs, p. 38 How Many of Each? Problems About Ten, p. 48

Assessment Three Towers , p. 75


Quick Image Dot Combinations, p. 28

Crayon Puzzles, p. 30

Reading a Number Combination Book, p. 40 Creating Number Combination Stories, p. 42

Introducing Tens Go Fish, pp. 129 and 132

enVisionMATH Topic 7: Subtraction Facts to 12 Related Investigations Unit Building Number Sense (The Number System) Activities

Choice Time: Story Problems, p. 139 Sharing Story Problem Strategies, p. 142

Student Strategies, p. 143


GRADE 1


enVisionMATH Topic 8: Geometry Related Investigations Unit Quilt Squares and Block Towns (2-D and 3-D Geometry) Activities

Drawing Classroom Objects, p. 7

Guess My Rule with Shape Cards, p. 43

Triangles on the Shape Cards, p. 48 Describing Geoblocks, p. 66

Choice Time: Geoblock Footprints, p. 67

Introducing Block Pictures, p. 74 Introducing Blocks in a Sock, p. 80

Looking at Mystery Boxes, p. 85

Hw Many Sides?, p. 86 Making Boxes with Cards, pp. 89 and 90

enVisionMATH Topic 9: Patterns Related Investigations Unit Mathematical Thinking at Grade 1 (Introduction) Activities

Cube Patterns, p. 62

Make Your Own Cube Pattern, p. 64 Clapping Patterns, p. 67

Same or Different, p. 69 Patterns Around Us, p. 73

enVisionMATH Topic 10: Counting and Number Patterns to 100 Related Investigations Units Mathematical Thinking at Grade 1 (Introduction) Activities

Collect 15 Together, p. 85

How Many Are Here Today?, p. 116


Exploring the 100 Chart, p. 82

Introducing Counting Strips, p. 86

Clapping Patterns, pp. 106 and 163 A Counting Story, p. 110


How Many Hands?, p. 50 Patterns in People and Hands, p. 59

Counting by Kangaroos, p. 98

enVisionMATH Topic 11: Tens and Ones Related Investigations Unit Number Games and Story Problems (Addition and Subtraction) Activity

Introducing Roll Tens, p. 88

GRADE 1


enVisionMATH Topic 12: Comparing and Ordering Numbers to 100 Related Investigations Units Building Number Sense (The Number System) Activities

Double Compare, p. 53

Missing Numbers, p. 84


Exploring the 100 Chart, p. 78 Missing Numbers, pp. 79 and 84

enVisionMATH Topic 13: Counting Money Related Investigations Unit Number Games and Story Problems (Addition and Subtraction) Activities

Exploring Coins, p. 64

Collect 25¢Together, p. 65

enVisionMATH Topic 14: Measurement Related Investigations Unit Bigger, Taller, Heavier, Smaller (Measuring) Activities

Introducing the Balance, p. 7

Who Sank the Boat?, p. 11

Introducing Balancing Grocery bags, p. 23 Introducing Balancing Balances, p. 24

How Can We Tell If It’s Balanced?, p. 28 Filling Cups: Experiment 1, p. 34

What Is a Cupful of Sand?, p. 36

Filling Cups: Experiment 2, p. 37 Which Is Longer?, p. 62

Measuring a Strip of Tape, p. 68

enVisionMATH Topic 15: Time Related Investigations Unit Survey Questions and Secret Rules (Collecting and Sorting Data)

Activities

When Is Your Birthday?, p. 56 How Many in Each Month?, p. 58

Whose Birthday Comes Next?, p. 64

Birthday Lineup, p. 66 A House for Hermit Crab, p. 70

Creating a Timeline, p. 72

GRADE 1


enVisionMATH Topic 16: Addition Facts to 18 Related Investigations Unit Number Games and Story Problems (Addition and Subtraction) Activities

Making Sense of Combining, p. 112

Recording Combining Strategies, p. 105

Sharing Combining Strategies, p. 106 Choice Time: Story Problems, pp. 120, 131, and 144

Combining with Unknown Change, p.138


enVisionMATH Topic 17: Subtraction Facts to 18 Related Investigations Unit Number Games and Story Problems (Addition and Subtraction) Activities

Making Sense of Separating, p. 109

Recording Separating Strategies, p. 110

Sharing Separating Strategies, p. 111 Choice Time: Story Problems, pp. 120, 131, and 144


enVisionMATH Topic 18: Data and Graphs Related Investigations Units Mathematical Thinking at Grade 1 (Introduction) Activities

Quick Surveys, p. 119 Ways to get to School, p. 135

Collecting the Data, p. 136

Survey Questions and Secret Rules (Collecting and Sorting Data) Activities

Would You Rather Be an Eagle or a Whale, p. 34

Representations of Eagle and Whale Data, p. 36

When Is Your Birthday?, p. 56 How Many in Each Month?, p. 58

Signing In, p. 90

A Most Unusual Day, p. 92 Representing a Most Unusual Day, p. 94

enVisionMATH Topic 20: Adding and Subtracting with Tens and Ones Related Investigations Unit Number Games and Story Problems (Addition and Subtraction) Activities

Making Sense of Combining, p. 102

Recording Combining Strategies, p. 104 Sharing Combining Strategies, p. 106

Making Sense of Separating, p. 109 Recording Separating Strategies, p. 110

Sharing Separating Strategies, p. 111

Choice Time: Story Problems, pp. 120, 131, and 144 Assessment Solving Story Problems, p. 149

GRADE 2


Grade 2 Contents

Topic 1: Understanding Addition and Subtraction........................................... 14

Topic 2: Addition Strategies ........................................................................... 14

Topic 3: Subtraction Strategies ...................................................................... 14

Topic 4: Place Value: Numbers to 100 ............................................................ 14

Topic 5: Counting Money ................................................................................ 15

Topic 6: Mental Addition ................................................................................ 15

Topic 7: Mental Subtraction ........................................................................... 15

Topic 8: Adding Two-Digit Numbers ............................................................... 16

Topic 9: Subtracting Two-Digit Numbers ....................................................... 16

Topic 10: Using Addition and Subtraction ...................................................... 16

Topic 11: Geometry ....................................................................................... 16

Topic 12: Fractions ........................................................................................ 17

Topic 13: Measurement: Length and Area ...................................................... 17

Topic 15: Time and Temperature ................................................................... 17

Topic 16: Graphs and Probability ................................................................... 17

Topic 17: Numbers and Patterns to 1,000 ...................................................... 18

Topic 18: Three-Digit Addition and Subtraction ............................................. 18

Topic 19: Multiplication Concepts .................................................................. 18

GRADE 2


enVisionMATH Topic 1: Understanding Addition and Subtraction Related Investigations Unit Mathematical Thinking at Grade 2 (Introduction) Activities

Today’s Number: Ways to Make 5, p. 22

Today’s Number, p. 40

Ways to Get to 11, p. 49 Ways to Get to 12, p. 50

enVisionMATH Topic 2: Addition Strategies Related Investigations Unit Coins, Coupons, and Combinations (The Number System) Activities

Ways to Make 10, p. 6

Book of 10, p. 8 Two of Everything, p. 22

Book of Magic Pot Riddles, p. 24

Strategies for Combining Numbers, p. 27

enVisionMATH Topic 3: Subtraction Strategies Related Investigations Unit Putting Together and Taking Apart (Addition and Subtraction) Activities

Solving a Separating Problem, p. 128

The Separating Poster: Comparing Solutions, p. 129

enVisionMATH Topic 4: Place Value: Numbers to 100 Related Investigations Units Mathematical Thinking at Grade 2 (Introduction) Activities

How Many Pockets?, pp. 41 and 113 Counting Strips, p. 92

Class Discussion: Counting Strips, p. 95

Coins, Coupons, and Combinations (The Number System) Activities

Counting Bags, p. 67

Filling in the 100 Chart, p. 110

What Do You Notice About the 100 Chart?, p. 111 100 Chart, p. 116

GRADE 2


enVisionMATH Topic 5: Counting Money Related Investigations Units Mathematical Thinking at Grade 2 (Introduction) Activities

Exploring Coins, p. 86

Collect 25¢, p. 87


Ways to Make 15¢, p. 76 Matching Coins and Coupons, p. 77

Collect 50¢, p. 79

Putting Together and Taking Apart (Addition and Subtraction) Activity

Collect $1, p. 66

enVisionMATH Topic 6: Mental Addition Related Investigations Units Mathematical Thinking at Grade 2 (Introduction) Activity

Today’s Number, p. 115


Today’s Number: Using Number Combinations We Know, p. 45 Counting Pockets, pp. 50 and 83

Putting Together and Taking Apart (Addition and Subtraction) Activities

What’s a Story for This Problem?, p. 9 Get to 100, p. 45

Roll a Square, p. 49

Moving on the 100 Chart, p. 59 Ways to Make 100, p. 88

A Story About 100, p. 89 Equations for 100, p. 93

Class Discussion: Equations for 100, p. 96

Choosing a Story and an Equation, p. 97

enVisionMATH Topic 7: Mental Subtraction Related Investigations Units Coins, Coupons, and Combinations (The Number System) Activities

Start-Up, pp. 99 and 103

Class Discussion: Is It Adding or Subtracting?, p. 106

Today’s Number: How Far from 100?, p. 113


What’s a Story for This Problem?, p. 24

What Was Taken Away?, p. 77

GRADE 2


enVisionMATH Topic 8: Adding Two-Digit Numbers Related Investigations Units Coins, Coupons, and Combinations (The Number System) Activities

Story Problems, p. 116

Class Discussion: Many Ways to Solve a Problem, p. 118


Solving a Combining Problem, p. 118 The Combining Poster: Comparing Solutions, p. 119

enVisionMATH Topic 9: Subtracting Two-Digit Numbers Related Investigations Unit Putting Together and Taking Apart (Addition and Subtraction) Activities

Story Problems, p. 29

Introducing Notation, p. 35 Writing Your Own Story Problems, p. 36

Teacher Checkpoint: Student Strategies, p. 37 Solving Story Problems, p. 80

Solving a Separating Problem, p. 128


enVisionMATH Topic 10: Using Addition and Subtraction Related Investigations Unit Putting Together and Taking Apart (Addition and Subtraction) Activities

Creating Story Problems, p. 81

Understanding Story Problem, p. 83

enVisionMATH Topic 11: Geometry Related Investigations Units Mathematical Thinking at Grade 2 (Introduction) Activities

Find the Block, p. 55 How Many Different Geoblocks?, p. 64

Sorting Geoblocks, p. 68

Mystery Block, p. 70 Opening the Geoblock Count Box, p. 75

Shapes, Halves, and Symmetry (Geometry and Fractions) Activities

Covering Pattern Blocks, p. 14 Introducing Geoblock Buildings, p. 98

Pattern Block Symmetry, p. 98

Mirror Designs, p. 104 Introducing Fold and Cut, p. 109

Class Discussion: Is It Symmetrical?, p. 112

Symmetrical Pictures, p. 113

GRADE 2


enVisionMATH Topic 12: Fractions Related Investigations Unit Shapes, Halves, and Symmetry (Geometry and Fractions) Activities

Introducing Halves of Geoblocks, p. 76

Introducing Shape Halves, p. 82

Fraction Flags, p. 86 Fourths and Thirds of Rectangles, p. 89

Thirds and Fourths Flags, p. 93

enVisionMATH Topic 13: Measurement: Length and Area Related Investigations Unit How Long? How Far? (Measuring) Activities

Measurement Riddles, p. 31 Measuring Our Classroom, p. 37

Class Discussion: Measuring Our Classroom, p. 39

Introducing Paths, p. 48 Walking Paths, p. 48

Walking and Drawing Paths, p. 49

Comparing Lengths of Paths, p. 63 Introducing Paper Paths, p. 64

enVisionMATH Topic 15: Time and Temperature Related Investigations Unit Timelines and Rhythm Patterns (Representing Time) Activities

What Is a Timeline?, p. 5

Creating a Dr. Seuss Timeline, p. 6

enVisionMATH Topic 16: Graphs and Probability Related Investigations Units Mathematical Thinking at Grade 2 (Introduction) Activities

Playing Guess My Rule, p. 102

Collecting and Recording Guess My Rule Data, p. 104 Representing Guess My Rule Data, p. 105

Does It Walk, Crawl, or Swim? (Sorting and Classifying Data) Activities

What Sinks? What Floats?, p. 50

Graphing Our Data, p. 52

How Many Pockets? How Many Teeth? (Collecting and Representing Data) Activities

How Old Are the Kids in Our Class?, p. 5

How Many Siblings Do We Have?, p. 7 How Many Letters in Our Names?, p. 9

Introducing Pocket Towers, p. 13

Creating a Pocket Representation, p. 15

GRADE 2


enVisionMATH Topic 17: Numbers and Patterns to 1,000 Related Investigations Unit Coins, Coupons, and Combinations (The Number System) Activities

How Many Legs Are in Our Class?, p. 56

Looking for Patterns, p. 58

Counting Around the Class, p. 63 Teacher Checkpoint: Counting on Our Fingers, p. 70

How Many Fingers?, p. 71

enVisionMATH Topic 18: Three-Digit Addition and Subtraction Related Investigations Unit Putting Together and Taking Apart (Addition and Subtraction) Activities

Story Problems, p. 29 Introducing Notation, p. 35

Writing Your Own Story Problems, p. 36

Teacher Checkpoint: Student Strategies, p. 37 Solving Story Problems, p. 80

Solving a Combining Problem, p. 118

The Combining Poster: Comparing Solutions, p. 119 Solving a Separating Problem, p. 128


enVisionMATH Topic 19: Multiplication Concepts Related Investigations Unit Coins, Coupons, and Combinations (The Number System) Activities

How Many Legs Are in Our Class?, p. 56 Looking for Patterns, p. 58

Counting Around the Class, p. 63 Counting on Our Fingers, p. 70

How Many Fingers?, p. 71

GRADE 3


Grade 3 Contents

Topic 1: Numeration ...................................................................................... 20

Topic 2: Adding Whole Numbers .................................................................... 20

Topic 3: Subtraction and Number Sense ......................................................... 20

Topic 4: Subtracting Whole Numbers to Solve Problems................................. 20

Topic 5: Multiplication Meanings and Facts .................................................... 21

Topic 6: Multiplication Fact Strategies: Use Known Facts .............................. 21

Topic 7: Division Meanings ............................................................................ 21

Topic 8: Division Facts ................................................................................... 21

Topic 9: Patterns and Relationships ............................................................... 22

Topic 10: Solids and Shapes .......................................................................... 22

Topic 11: Congruence and Symmetry ............................................................. 22

Topic 12: Understanding Fractions ................................................................. 22

Topic 13: Decimals and Money ....................................................................... 23

Topic 14: Customary Measurement ................................................................ 23

Topic 15: Metric Measurement ....................................................................... 23

Topic 16: Perimeter, Area, and Volume .......................................................... 23

Topic 17: Time and Temperature ................................................................... 24

Topic 18: Multiplying Greater Numbers .......................................................... 24

Topic 19: Dividing with 1-Digit Numbers ....................................................... 24

Topic 20: Data, Graphs, and Probability ......................................................... 24

GRADE 3


enVisionMATH Topic 1: Numeration Related Investigations Units Mathematical Thinking at Grade 3 (Introduction) Activities

Making a 100 Chart, p. 10

Introducing Plus, Minus, Stay the Same, p. 11

Counting Money, p. 39

Landmarks in the Hundreds (The Number System) Activities

Making a Thousand, p. 54

Locating Numbers on the 1000 Chart, p. 56 Finding Real Quantities for the 1000 Chart, p. 57

enVisionMATH Topic 2: Adding Whole Numbers Related Investigations Units Mathematical Thinking at Grade 3 (Introduction) Activities

Discussion: Doing Doubles Problems, p. 42

Handfuls of Cubes, p. 60

Landmarks in the Hundreds (The Number System) Activity

Calculating with the 1000 Chart, p. 58

Combining and Comparing (Addition and Subtraction) Activity

Quick Images: How Many Paper Clips?, p. 54

enVisionMATH Topic 3: Subtraction and Number Sense Related Investigations Unit Combining and Comparing (Addition and Subtraction) Activities

Combining, Then Subtracting, p. 55 Paper Clip Problems, p. 56

enVisionMATH Topic 4: Subtracting Whole Numbers to Solve Problems Related Investigations Unit Combining and Comparing (Addition and Subtraction) Activities

Comparing Family Size, p. 4 Days In and Out of School, p. 64

Making International Comparisons, p. 66

GRADE 3


enVisionMATH Topic 5: Multiplication Meanings and Facts Related Investigations Units Things That Come in Groups (Multiplication and Division) Activities

Naming Things That Come in Groups (Multiplication and Division), p. 4

Asking Multiplication Questions, p. 5

Pictures of Things That Come in Groups (Multiplication and Division), p. 8 Writing “Groups of” as Multiplication, p. 9

Writing Riddles for Our Pictures, p. 12

How Many Altogether?, p. 16


What Is a Factor, p. 10

enVisionMATH Topic 6: Multiplication Fact Strategies: Use Known Facts Related Investigations Unit Things That Come in Groups (Multiplication and Division) Activities

Playing Cover 50, p. 37 Arranging Chairs in Rectangular Arrays, p. 43

Arranging More Chairs, p. 44

Making Array Cards, p. 45 Counting Squares in Arrays, p. 48

Playing Array Games, p. 49

Discussing Array Game Strategies, p. 53

enVisionMATH Topic 7: Division Meanings Related Investigations Units Things That Come in Groups (Multiplication and Division) Activities

Writing Story Problems, p. 70

A Class Book of Problems, p. 71

Solving Problems in the Class Book, p. 72


Using Standard Notation, p. 44

Fair Shares (Fractions) Activity

How Many For Each Person?, p.57

enVisionMATH Topic 8: Division Facts Related Investigations Unit Things That Come in Groups (Multiplication and Division) Activity

Acting Out Number Sentences, p. 61

GRADE 3


enVisionMATH Topic 9: Patterns and Relationships Related Investigations Unit Landmarks in the Hundreds (The Number System) Activities

Ways to Count to 10, p. 4

Ten-Minute Math: Counting Around the Class, p. 7

Skip Counting on the 100 Chart, p. 8

enVisionMATH Topic 10: Solids and Shapes Related Investigations Unit Exploring Solids and Boxes (3-D Geometry) Activities

Sorting Solids, p. 4

Thinking About Sorting Schemes, p. 6

Learning the Game: What’s My Shape?, p. 10 Playing the Game in Small Groups, p. 12

Discussion: How the Game Worked, p. 13

Open Boxes for Cubes, p. 28 More Cube Patterns, p. 31

Patterns for Triangular Pyramids, p. 35

enVisionMATH Topic 11: Congruence and Symmetry Related Investigations Unit Flips, Turns, and Area (2-D Geometry) Activities

Creating Different Shapes with Four Squares, p. 4 Covering a Rectangle with One Shape, p. 6

The Perfect Cover-Up, p. 11

Changing the Shape of the Rectangle, p. 23 Covering the New Rectangles, p. 27

enVisionMATH Topic 12: Understanding Fractions Related Investigations Unit Fair Shares (Fractions) Activities

Making Fraction Cards, p. 6 From Smallest to Largest, p. 8

Finding Fraction Facts, p. 9

Sharing Seven Brownies, p. 14 Designs That Are Half Yellow, p. 41

Other Fractions of Yellow, p.41

How Do You Know It Is Half Yellow?, p. 42

GRADE 3


enVisionMATH Topic 13: Decimals and Money Related Investigations Units Mathematical Thinking at Grade 3 (Introduction) Activity

What’s the Little Dot?, p. 75

Landmarks in the Hundreds (The Number System) Activities

Working with Coins, p.24

Dividing a Dollar Among Five People, p. 24 Class Discussion: Six People Paying $1.50 Each, p. 41

Problems Using Money, p. 42

enVisionMATH Topic 14: Customary Measurement Related Investigations Unit From Paces to Feet (Measuring and Data) Activities

Estimating Distance in Giant Steps, p. 4 Measuring in Baby Steps, p. 6

Pacing the Classroom, p. 10 Estimating How Far in Paces, p. 11

Introduction to Measuring Tools, p. 31

Looking at Foot Length, p. 37 Things Longer Than a Foot, p. 39

enVisionMATH Topic 15: Metric Measurement Related Investigations Unit From Paces to Feet (Measuring and Data) Activities

Introducing Centimeters and Meters, p. 52

Looking at How Chairs Fit, p.62 Measuring Ourselves and Our Chairs, p. 64

Making a Clear Picture of the Data, p.65

Making Our Report, p. 66

enVisionMATH Topic 16: Perimeter, Area, and Volume Related Investigations Units Flips, Turns, and Area (2-D Geometry) Activities

Measuring Flat Space, p. 35

Finding Shapes with an Area of Four Square Units, p. 40

Class Discussion: Creating New Shapes, p. 43 Class Discussion: Are These Two Shapes the Same?, p. 44

Finishing the Posters, p. 47

Exploring Solids and Boxes (3-D Geometry) Activities

Predicting the Number of Cubes in a Box, p. 40

Designing Boxes to Hold 12 Cubes, p. 46

Introducing the Problem, p.54 Planning and Building the City, p. 56

Final Plans and Construction, p. 58

GRADE 3


enVisionMATH Topic 17: Time and Temperature Related Investigations Unit Combining and Comparing (Addition and Subtraction) Activities

Planning a Party, p. 35

How Much Longer?, p. 60

How Many Days Until Your Birthday?, p. 61

enVisionMATH Topic 18: Multiplying Greater Numbers Related Investigations Unit Landmarks in the Hundreds (The Number System) Activities

Making a Picture of 100, p. 19

Listing the Factors of 100, p. 22

enVisionMATH Topic 19: Dividing with 1-Digit Numbers Related Investigations Unit Landmarks in the Hundreds (The Number System) Activity

Division Problems, p. 47

enVisionMATH Topic 20: Data, Graphs, and Probability Related Investigations Unit Combining and Comparing (Addition and Subtraction) Activities

Comparing Handfuls of Beans, p. 43

Looking at the Handfuls Data, p. 45

GRADE 4


Grade 4 Contents

Topic 1: Numeration ...................................................................................... 26

Topic 2: Adding and Subtracting Whole Numbers ........................................... 26

Topic 3: Multiplication Meanings and Facts .................................................... 26

Topic 4: Division Meanings and Facts ............................................................. 26

Topic 5: Multiplying by 1-Digit Numbers ......................................................... 27

Topic 6: Patterns and Expressions ................................................................. 27

Topic 7: Multiplying by 2-Digit Numbers ........................................................ 27

Topic 8: Dividing by 1-Digit Numbers ............................................................. 28

Topic 10: Understanding Fractions ................................................................ 28

Topic 13: Operations with Decimals ............................................................... 28

Topic 15: Solids ............................................................................................. 28

Topic 16: Measurement, Time, and Temperature ........................................... 29

Topic 17: Data and Graphs ............................................................................. 29

Topic 18: Equations ....................................................................................... 29

Topic 19: Transformations, Congruence, and Symmetry ................................ 29

Topic 20: Probability ...................................................................................... 29

GRADE 4


enVisionMATH Topic 1: Numeration Related Investigations Units Mathematical Thinking at Grade 4 (Introduction) Activities

Counting Money, p. 35

The Collecting Dollars Game, p. 38

The Hidden Coins Game, p. 40

Landmarks in the Thousands (The Number System) Activities

Making a 1000 Book, p. 38

100 for Every Student, p. 54 Completing the 10,000 Chart, p. 56

What can We See on the 10,000 Chart?, p. 57

Money, Miles, and Large Numbers (Addition and Subtraction) Activity

Ways to Make a Dollar, p. 13

enVisionMATH Topic 2: Adding and Subtracting Whole Numbers Related Investigations Units Mathematical Thinking at Grade 4 (Introduction) Activity

Playing 101 to 200 Bingo, p. 51

Money, Miles, and Large Numbers (Addition and Subtraction) Activity

Class Discussion: Strategies for Adding and Subtracting Large Numbers, p. 49

enVisionMATH Topic 3: Multiplication Meanings and Facts Related Investigations Units Arrays and Shares (Multiplication and Division) Activities

Solving Multiplication Clusters, p. 10 Arranging a Group of 18 People, p. 19

Finding All Possible Arrays For a Number, p. 20 Class Discussion: Looking at All the Arrays, p. 21

Preparing a Personal Set of Array Cards, p. 26

Using the Array Cards, p. 27 Another Array Game, p. 29

How Many Ways Can You Make 8 x 6?, p. 32


What Are All the Factors of 100?, p. 6

Do We Have All the Factors of 100?, p. 6

enVisionMATH Topic 4: Division Meanings and Facts Related Investigations Unit Arrays and Shares (Multiplication and Division) Activities

Making Groups, p. 8 Introducing Division Notation, p. 35

GRADE 4


enVisionMATH Topic 5: Multiplying by 1-Digit Numbers Related Investigations Units Arrays and Shares (Multiplication and Division) Activities

Solving Cluster Problems, p. 44

Writing About Your Strategies, p. 45 Discussing Multiplication Pairs, p. 55

Which Pairs Are Hard for You?, p. 55


Building with 100 Cubes, p. 11

Skip Counting on the 300 Chart, p. 21

Boxes for 200, p. 27

Packages and Groups (Multiplication and Division) Activities

Returning to Multiplication Clusters, p. 18

Making a Cluster of Problems, p. 20

enVisionMATH Topic 6: Patterns and Expressions Related Investigations Units Arrays and Shares (Multiplication and Division) Activities

Multiples on the 100 Chart, p. 4 Highlighting 100 Charts, p. 5


Skip Counting on the 100 Chart by 2’s and 6’s, p. 4 Highlighting 100 Charts, p. 5

enVisionMATH Topic 7: Multiplying by 2-Digit Numbers Related Investigations Units Landmarks in the Thousands (The Number System) Activities

Factors of 1000: Counting with Calculators, p. 41

Counting to 1000, p. 41

Packages and Groups (Multiplication and Division) Activities

Skip Counting by Two-Digit Numbers, p. 11

Making a Multiple Tower, p. 12 Multiple Towers and Working on Difficult Pairs, p. 13

Making Close Estimates, p. 24

GRADE 4


enVisionMATH Topic 8: Dividing by 1-Digit Numbers Related Investigations Unit Packages and Groups (Multiplication and Division) Activities

How Many 4’s in 48?, p. 30

Connecting Division Equations to a Context, p. 31

Dividing by Grouping, p. 42 Another Problem with Cubes, p. 43

Marbles in a Bag, p. 51

Finding Factors of Large Numbers, p. 53 Class Discussion: Making Conjectures About Finding Factors, p. 55

enVisionMATH Topic 10: Understanding Fractions Related Investigations Units Different Shapes, Equal Pieces (Fractions and Area) Activities

Making Fraction Cards, p. 41

Recognizing Equivalent Fractions, p. 43 Playing Fraction Fish, p. 43

Groups Order Fractions with Respect to Landmarks, p. 46

Playing Capture Fractions, p. 49 Making a Fraction Number Line, p. 50

Three Out of Four Like Spaghetti (Data and Fractions) Activities

Fractions to Describe Our class, p. 5 Making a Fraction Strip, p. 10

Estimating Familiar Fractions, p. 11

Using Class Strips to Find Familiar Fractions, p. 12 Using Fractions to Write Word Problems, p. 23

enVisionMATH Topic 13: Operations with Decimals Related Investigations Unit Money, Miles, and Large Numbers (Addition and Subtraction) Activities

Estimating and Finding Totals, p. 4

Adding Money on the Calculator: What Happens to the Cents?, p. 18 Estimating Grocery Receipts, p. 20

Change from $1.00, p. 23 Teacher Checkpoint Spaghetti and Sauce, p. 24

enVisionMATH Topic 15: Solids Related Investigations Unit Seeing Solids and Silhouettes (3-D Geometry) Activities

Building from Quick Images, p. 10

Predicting the Shape of Silhouettes, p. 17 Building the Toy, p. 53

Making the Instruction Booklet, p. 53

Testing the Plans, p. 54

GRADE 4


enVisionMATH Topic 16: Measurement, Time, and Temperature Related Investigations Unit Money, Miles, and Large Numbers (Addition and Subtraction) Activities

Introducing Parts of a Mile, p. 32

City Landmarks, p. 41

Measuring Distance on a Map, p. 51

enVisionMATH Topic 17: Data and Graphs Related Investigations Units The Shape of Data (Statistics) Activities

Measuring Heights in the Class, p. 23

Describing the class Height Data, p. 25

Finding the Median Height for This Class, p. 39 What’s the Median Height of the All-Stars?, p. 40

How Long Do People Sleep?, p. 53

Choosing a Question, p. 55 Working with Preliminary Data, p. 56

Collecting, Organizing, and Describing Data, p. 59

Developing Theories and Publishing Findings, p. 60

Changes Over Time (Graphs) Activities

Graph of Speed, p. 40

Describing a Marathon Graphically, p. 40

enVisionMATH Topic 18: Equations Related Investigations Unit Money, Miles, and Large Numbers (Addition and Subtraction) Activities

Ways to Make a Dollar, p. 13

Class Discussion: Strategies for Adding and Subtracting Large Numbers, p. 49

enVisionMATH Topic 19: Transformations, Congruence, and Symmetry Related Investigations Unit Mathematical Thinking at Grade 4 (Introduction) Activities

Symmetry with Pattern Blocks, p. 67 Symmetry in the Environment, p. 68

Patterns Around Hexagons, p. 73

A Display of Patterns, p. 78 Writing About Our designs, p. 79

Symmetry on the Geoboard, p. 83

Counting Lines of Symmetry, p. 86 Mirror and Rotational Symmetry, p. 87

enVisionMATH Topic 20: Probability Related Investigations Unit Landmarks in the Thousands (The Number System) Activity

Ten Minute Math: What Is Likely?, p. 20

GRADE 5


Grade 5 Contents

Topic 1: Numeration ................................................................................................ 31

Topic 2: Adding and Subtracting Whole Numbers and Decimals .............................. 31

Topic 3: Multiplying Whole Numbers ........................................................................ 31

Topic 4: Dividing by 1-Digit Divisors ........................................................................ 31

Topic 5: Dividing by 2-Digit Divisors ......................................................................... 32

Topic 8: Shapes ....................................................................................................... 32

Topic 9: Fractions and Decimals ............................................................................... 32

Topic 10: Adding and Subtracting Fractions and Mixed Numbers ............................. 33

Topic 11: Multiplying Fractions and Mixed Numbers ................................................ 33

Topic 13: Solids ....................................................................................................... 33

Topic 14: Measurement Units, Time, and Temperature ............................................ 33

Topic 15: Solving and Writing Equations and Inequalities ....................................... 34

Topic 16: Ratio and Percent ..................................................................................... 34

Topic 18: Graphs and Data ....................................................................................... 34

Topic 20: Probability ................................................................................................ 35

GRADE 5


enVisionMATH Topic 1: Numeration Related Investigations Unit Mathematical Thinking at Grade 5 (Introduction) Activities

Numbering Squares in Our Rectangle, p. 44

Displaying 10,000 Squares, p. 46

enVisionMATH Topic 2: Adding and Subtracting Whole Numbers and Decimals Related Investigations Unit Building on Numbers You Know (Computation and Estimation Strategies) Activities

Introducing the Digits Game, p. 29 Playing the Digits Game, p. 30

Strategies for Subtraction, p. 36

Solving Subtraction Problems, p. 37

enVisionMATH Topic 3: Multiplying Whole Numbers Related Investigations Units Mathematical Thinking at Grade 5 (Introduction) Activities

Building Number Rectangles, p. 5

Special Math Words, p. 7

Strategies for Remembering Factor Pairs, p. 31 Factor Pairs of 100, p. 35

Factor Pairs of Multiples of 100, p. 37

Building Rectangles with 1000 Squares, p. 38 What Rectangles Did We Make?, p. 40

Solving Multiplication Clusters, p. 55

Factor Pairs of 10,000, p. 91

Building on Numbers You Know (Computation and Estimation Strategies) Activities

Making Close Multiplication Estimates, p. 75

Reasoning About Multiplication Estimates, p. 76

enVisionMATH Topic 4: Dividing by 1-Digit Divisors Related Investigations Unit Building on Numbers You Know (Computation and Estimation Strategies) Activities

Division Situations, p. 57

Writing a Related Division Situation, p. 64

Making Close Division Estimates, p. 83 Reasoning About Division Estimates, p. 84

Looking at Division Clusters, p. 85

Making a Division Cluster, p. 89

GRADE 5


enVisionMATH Topic 5: Dividing by 2-Digit Divisors Related Investigations Unit Building on Numbers You Know (Computation and Estimation Strategies) Activities

Finding Multiples of 21, p. 18

Making a Tower of Multiples of 21, p. 19

Using Multiples to Solve Problems, p. 21 Practice with Estimating, p. 91

Solving a Problem with the First Step Given, p. 92

Estimating Answers to Difficult Problems, p. 123 Different Paths to 10,000, p. 133

enVisionMATH Topic 8: Shapes Related Investigations Unit Picturing Polygons (2-D Geometry) Activities

Putting Together Power Polygons, p. 10

Identifying Triangles by Their Angles, p. 32 Sorting Triangles, p. 34

All Triangles, Some Triangles, p. 35

Identifying Quadrilaterals, p. 36 Sorting Quadrilaterals, p. 37

Attributes of Quadrilaterals, p. 38 Playing Guess My Rule, p. 39

Following the Rules, p. 47

Finding Angle Sizes, p. 70

enVisionMATH Topic 9: Fractions and Decimals Related Investigations Unit Name That Portion (Fractions, Percents, and Decimals) Activities

What Fraction Do You See?, p. 11

Ordering Fraction Cards, p. 50

Capture Fractions, p. 51 Fractions to Decimals on the Calculator, p. 67

Win/Loss Records, p. 69

Decimals on Grids, p. 73 Capture Decimals, p. 80

Comparing Decimals, p. 84

Assessment: Showing Which Is Larger, p. 95

GRADE 5


enVisionMATH Topic 10: Adding and Subtracting Fractions and Mixed Numbers Related Investigations Unit Name That Portion (Fractions, Percents, and Decimals) Activities

Adding Fractions on the Clock, p. 36

Roll Around the Clock Game, p. 38

Making Fraction Strips, p. 42 Using the Strips for Fraction Sums, p. 44

Halfway Across the Fraction Tracks, p. 46

Labeling the Fraction Tracks, p. 48 Patterns on the Fraction Tracks, p. 48

Counting by Fractions, p. 49

Introducing the Fraction Track Game, p. 55 Playing the Fraction Track Game, p. 56

enVisionMATH Topic 11: Multiplying Fractions and Mixed Numbers Related Investigations Unit Name That Portion (Fractions, Percents, and Decimals) Activities

Introducing the Fraction Track Game, p. 54

Playing the Fraction Track Game, p. 56

enVisionMATH Topic 13: Solids Related Investigations Unit Containers and Cubes (3-D Geometry, Volume) Activities

Building Models of Volume Units, p. 43

Discussion: Which Unit Should We Use?, p. 44

A Plan to Measure Classroom Space, p. 45 How Many Cubic Meters in Our Classroom?, p. 50

Discussion: How We Measured, p. 52 Measuring Another Room, p. 58

Writing a Report on the Volume, p. 59

Sharing Our Findings, p. 59 Comparing Volumes of Containers, p. 63

Comparing Cylinders and Cones, p. 79

enVisionMATH Topic 14: Measurement Units, Time, and Temperature Related Investigations Unit Measurement Benchmarks (Estimating and Measuring) Activities

Reading Measuring Tools, p. 19 Guidelines for Measuring, p. 27

How Long Is 100 Meters?, p. 30

Sharing Our Paths, p. 33 Using a Map Scale, p. 38

Measurements on Grocery Labels, p. 47

Same or Different Weights?, p. 63 Assessment: Describing Measure of Weight and Liquid Quantity, p. 66

Discussion: Units of Time, p. 76 Reading the Second Hand, p. 77

Estimating 30 Seconds, p. 78

GRADE 5


enVisionMATH Topic 15: Solving and Writing Equations and Inequalities Related Investigations Units Building on Numbers You Know (Computation and Estimation Strategies) Activities

Writing a Multiplication Situation, p. 63

Writing a Related Division Situation, p. 64

Making Close Multiplication Estimates, p. 75 Reasoning About Multiplication Estimates, p. 76

Mathematical Thinking at Grade 5 (Introduction) Activities

Solving Multiplication Clusters, p. 55 Making Our Own Problem Clusters, p. 58

enVisionMATH Topic 16: Ratio and Percent Related Investigations Unit Name That Portion (Fractions, Percents, and Decimals) Activities

Fractions, Decimals, and Percents, p. 4

Interpreting Percents, p. 12 Making Grid Patterns, p. 16

Fourths and Eighths on Grids, p. 19

Making a Percent Equivalence Strip, p. 24 Age and Gender Distributions, p. 102

enVisionMATH Topic 18: Graphs and Data Related Investigations Units Name That Portion (Fractions, Percents, and Decimals) Activities

Making Circle Graphs, p. 111

Using Circle Graphs to Represent Data, p. 113

Data: Kids, Cats, and Ads (Statistics) Activities

Describing Cats, p. 26

Representing Cat Data, p. 28 Sharing Our Findings on Cats, p. 29

Asking Questions About Cats, p. 35

Sharing Findings About Associations, p. 37 How Much of the Page Is Ads?, p. 70

Sampling and Collecting Ad Data, p. 73

Putting the Fractions Together, p. 77 Drawing Conclusions from the Sample, p. 79

GRADE 5


enVisionMATH Topic 20: Probability Related Investigations Unit Between Never and Always (Probability) Activities

Spinning a One-Half Spinner, p. 17

Discussing the Spinner Results, p. 21

Testing for Special Guessing Skills, p. 28 Looking at the Guessing Skills Results, p. 33

What Makes a Game Unfair?, p. 48

Making the Game Fair, p. 52 Playing New versions of the Game, p. 53

Who Goes First: What’s Fair?, p. 64

Playing the Unfair Spinner Game, p. 65 Assessment: Judging the Fairness of Games, p. 68

36

Introduction to Plan 2 Pearson Scott Foresman has developed a two-in-one Joint-Usage Master Plan for

enVisionMATH and Investigations in Number, Data, and Space® First Edition for teachers who are interested in using both programs.

The Plan 2 section of this Joint-Usage Master Plan has been designed for teachers using

enVisionMATH as their core program who would like to teach an Investigations curriculum unit

as a replacement for some enVisionMATH lessons. Typically, only one or two Investigations

units are incorporated during the first year a teacher is using enVisionMATH.

Using Plan 2

Step 1 Turn to the Plan 2 Contents for your grade level:

______________________________________________________________________

Kindergarten Contents ................................................................................. 37

Grade 1 Contents ........................................................................................ 47

Grade 2 Contents ........................................................................................ 58

Grade 3 Contents ........................................................................................ 69

Grade 4 Contents ........................................................................................ 83

Grade 5 Contents ........................................................................................ 95

______________________________________________________________________

Step 2 Locate the enVisionMATH topic you are about to teach and the Investigations unit or

units to which it is related. Choose and follow one curriculum plan. (Also note any additional

enVisionMATH topics that are related to the Investigations unit you choose to teach. In some cases, a topic will be taught out of sequence, and you will need to adjust your instructional plan

accordingly.)

Step 3 Identify the page where the instructional plan is located.

Step 4 Turn to that page and follow the comprehensive instructional plan for combining the Investigations unit with one or more enVisionMATH topics. All of the Investigations sessions and

enVisionMATH lessons should be taught in the order indicated. NOTE This plan lists the

individual Investigations sessions in the unit, the enVisionMATH topics and lessons that the sessions replace, and the enVisionMATH lessons you need to teach (or, in most cases, simply

integrate) with the Investigations sessions.

GRADE K

37 Grade K, Plan 2 Designed for enVisionMATH users who would like to use an Investigations unit as a replacement for some enVisionMATH lessons

Kindergarten Contents

Investigations Unit Mathematical Thinking in Kindergarten (Introduction) .................................. 39

Related enVisionMATH topics

Topic 2: Position and Location

Topic 4: Zero to Five

Topic 5: Six to Ten

Topic 15: Calendar

Investigations Unit Pattern Trains and Hopscotch Paths (Exploring Pattern)................................ 40

Related enVisionMATH topic

Topic 3: Patterns

Investigations Unit Collecting, Counting, and Measuring (Developing Number Sense).................. 41

Related enVisionMATH topics Topic 4: Zero to Five

Topic 5: Six to Ten

Topic 6: Comparing Numbers

Topic 8: Fractions and Ordinals

Topic 9: Measurement

Investigations Unit

Counting Ourselves and Others (Exploring Data) ........................................... 43


Topic 1: Sorting and Classifying

Topic 5: Six to Ten

Topic 12: Larger Numbers

Topic 16: Graphing

GRADE K


Investigations Unit

Making Shapes and Building Blocks (Exploring Geometry) ............................ 44


Topic 7: Geometry

Investigations Unit

How Many in All? (Counting and the Number System).................................... 45




Topic 10: Addition

Topic 11: Subtraction

GRADE K


Investigations Unit Mathematical Thinking in Kindergarten (Introduction)

Related enVisionMATH topics Topic 2: Position and Location


Topic 5: Six to Ten

Topic 15: Calendar

____________________________________________________________________________

Start with these enVisionMATH lessons:

2-1 Inside and Outside 2-2 Over, Under, and On

2-3 Top, Middle, and Bottom

2-4 Before and After 2-5 Left and Right

2-6 Problem Solving: Act It Out

Investigation 1: Attendance

Focus Time: Attendance Choice Time: Exploring Color Tiles

Choice Time: Exploring Pattern Blocks

Choice Time: Exploring Geoblocks

Investigation 2: Counting Jar

Focus Time: Counting Jar Choice Time: Counting Jar

enVisionMATH lessons to be taught/incorporated: 4-5 Reading and Writing 0

4-6 Making 4 and 5 4-7 More, Fewer, and Same As

4-8 1 and 2 More

4-9 1 and 2 Fewer 4-10 Problem Solving: Make an Organized List

5-2 Making 6 and 7

5-5 Making 8 and 9 5-8 Making 10

5-10 Ordering Numbers on a Number Line

5-11 Problem Solving: Make a Graph

enVisionMATH lessons replaced:

4-1 Counting 1, 2, and 3 4-2 Reading and Writing 1, 2, and 3

4-3 Counting 4 and 5 4-4 Reading and Writing 4 and 5

5-1 Counting 6 and 7

5-3 Reading and Writing 6 and 7

GRADE K



5-6 Reading and Writing 8 and 9 5-7 Counting 10

5-9 Reading and Writing 10

Investigation 3: Calendar

Focus Time: Calendar Choice Time: Exploring Interlocking Cubes

enVisionMATH lessons to be taught/incorporated: 15-1 Calendar: Months and Seasons

15-6 Calendar: Temperature

15-7 Problem Solving: Draw a Picture

enVisionMATH lessons to replaced:

15-2 Calendar: Days of the Week 15-3 Calendar: Yesterday, Today, and Tomorrow

15-4 Calendar: Numbers on a Calendar 15-5 Calendar: Calendar

Investigation 4: Today’s Question

Focus Time: Today’s Question

____________________________________________________________________________

Investigations Unit

Pattern Trains and Hopscotch Paths (Exploring Pattern)


Topic 3: Patterns

____________________________________________________________________________

Investigation 1: Exploring Patterns

Focus Time: Watching and Looking

Focus Time: Cubes: What Do You Notice? Choice Time: Making Patterns

Choice Time: What’s Missing?

enVisionMATH lesson to replaced:

3-1 Sound and Movement Patterns

Investigation 2: What Comes Next?

Focus Time: Patterns on the Pocket Chart Choice Time: What Comes Next?

Choice Time: Pattern Block Snakes

Choice Time: Add On Choice Time: Break the Train

Choice Time: Make a Train

GRADE K


enVisionMATH lessons to replaced:

3-2 Color Patterns 3-3 Shape Patterns

Investigation 3: Hopscotch Paths

Focus Time: Hopscotch Paths

Choice Time: Hopscotch Paths Choice Time: Tile Paths

Investigation 4: Pattern Borders

Focus Time: Pattern Borders

Choice Time: Color Tile Borders

Choice Time: 12 Chips Choice Time: Staircase Patterns

enVisionMATH lessons to replaced: 3-4 Comparing Patterns

3-5 Problem Solving: Look for a Pattern 3-6 Using Patterns to Predict What Comes Next

3-7 Creating Patterns

____________________________________________________________________________

Investigations Unit

Collecting, Counting, and Measuring (Developing Number Sense)


Topic 5: Six to Ten

Topic 6: Comparing Numbers


____________________________________________________________________________

Investigation 1: Counting Books

Focus Time: Counting Books

Choice Time: My Counting Book Choice Time: Grab and Count

Choice Time: Counting Jar

Investigation 2: Taking Inventory

Focus Time: Taking Inventory Choice Time: Inventory Bags

Investigation 3: Comparing Towers

Focus Time: Measurement Towers

Choice Time: Measuring Table

Choice Time: Grab and Count: Which Has More? Choice Time: Compare

GRADE K


enVisionMATH lessons to be taught/incorporated:

5-1 Counting 6 and 7 5-2 Making 6 and 7

5-3 Reading and Writing 6 and 7

5-4 Counting 8 and 9 5-5 Making 8 and 9

5-6 Reading and Writing 8 and 9 5-7 Counting 10

5-8 Making 10

5-9 Reading and Writing 10 5-10 Ordering Numbers on a Number Line


9-1 Comparing and Ordering by Size 9-4 Measuring Length

9-5 Problem Solving: Try, Check, and Revise

9-6 Comparing Capacities 9-7 Measuring Capacity

9-8 Comparing Weights 9-9 Measuring Weight

enVisionMATH lesson to be replaced: 9-2 Comparing by Length

Investigation 4: Counting and Comparing

Focus Time: Letters in Our Names

Choice Time: Comparing Name

Choice Time: Grab and count: Compare Choice Time: Collect 10 Together

enVisionMATH lessons to be taught/incorporated: 6-4 1 and 2 More and Fewer

6-5 Problem Solving: Use Objects 9-10 Problem Solving: Try, Check, and Revise

enVisionMATH lessons to be replaced: 6-1 Comparing Numbers Through 10

6-2 Comparing Numbers to 5

6-3 Comparing Numbers to 10 9-3 Ordering by Length

Investigation 5: Least to Most

Focus Time: Least to Most

Choice Time: Grab and Count: Least to Most Choice Time: Racing Bears

Investigation 6: Arrangements of Six

Focus Time: Six Tiles

Choice Time: Books of Six

GRADE K


____________________________________________________________________________

Investigations Unit

Counting Ourselves and Others (Exploring Data)


Topic 1: Sorting and Classifying

Topic 12: Larger Numbers

Topic 16: Graphing

____________________________________________________________________________


12-1 Counting, Reading, and Writing 11 and 12 12-2 Counting, Reading, and Writing 13, 14, and 15

12-3 Counting, Reading, and Writing 16 and 17

12-4 Counting, Reading, and Writing 18, 19, and 20

Investigation 1: How Many Are We?

Focus Time: How Many Are We?

Focus Time: Counting Noses, Counting Eyes

Choice Time: Self Portraits Choice Time: Counting Chairs

Choice Time: Pattern Block Grab


12-5 Odd and Even

12-6 Counting to 100 12-7 Counting Groups of Ten

12-8 Patterns on a Hundred Chart

12-9 Skip Counting by 2 and 5 12-10 Problem Solving: Look for a Pattern

Investigation 2: What Did You Eat for Lunch?

Focus Time: What Did You Eat for Lunch?

Choice Time: Same and Different Choice Time: Boxes, Bottles, and Cans

Choice Time: The Grocery Store

Choice Time: Clothing Sort


1-4 Sorting by More Than One Attribute 1-5 Problem Solving: Use Logical Reasoning

16-1 As Many, More, and Fewer

enVisionMATH lessons to be replaced:

1-1 Same and Different 1-2 Sorting by One Attribute

1-3 Sorting the Same Set in Different Ways

GRADE K


Investigation 3: Collecting Data about Our class

Focus Time: Yes/No Surveys Choice Time: Yes/No Surveys

enVisionMATH lessons to be taught/incorporated: 16-3 Real Graphs

16-4 Picture Graphs 16-5 Bar Graphs

16-6 More Likely, Less Likely


enVisionMATH lesson to be replaced:

16-2 Collecting Data

Investigation 4: Who’s Here? Who’s Not?

Focus Time: Who’s Here? Who’s Not?

____________________________________________________________________________

Investigations Unit

Making Shapes and Building Blocks (Exploring Geometry)


Topic 7: Geometry

____________________________________________________________________________

Investigation 1: 2-D Shapes Around Us

Focus Time: Looking at 2-D Shapes

Choice Time: Book of Shapes Choice Time: Pattern Block Pictures

Choice Time: Shape Mural


7-3 Making Shapes from Other Shapes

7-4 Same Size, Same Shape 7-5 Symmetry

enVisionMATH lessons to be replaced: 7-1 Squares and Other Rectangles

7-2 Circles and Triangles

Investigation 2: Exploring Shapes with the Computer

Focus Time: Introducing the MS_Shapes Software Choice Time: Free Explore with MS_Shapes on the Computer

Choice Time: Pattern Block Puzzles

GRADE K


Investigation 3: Looking at 3-D Shapes

Focus Time: 3-D Shapes in the Classroom Choice Time: Shape Hunt

Choice Time: Exploring Geoblocks

Choice Time: The Shape of Things on the Computer

enVisionMATH lessons to be replaced: 7-6 Solid Figures

7-7 Comparing Solid Figures

Investigation 4: Making Shapes and building Blocks

Focus Time: Clay Shapes

Choice Time: Clay Shapes Choice Time: Fill in the Hexagons

Choice Time: Build a Block

Choice Time: Quick Images on the Computer

enVisionMATH lesson to be replaced: 7-3 Making Shapes from Other Shapes

Investigation 5: 2-D Faces on 3-D Blocks

Focus Time: A Close Look at Geoblocks

Choice Time: Matching Faces

Choice Time: Geoblock Match-Up Choice Time: Planning Pictures on the Computer

enVisionMATH lessons to be taught/incorporated: 7-8 Flat Surfaces of Solid Figures

7-9 Problem Solving: Use Objects

_________________________________________________________________________________

Investigations Unit

How Many in All? (Counting and the Number System)



Topic 10: Addition

Topic 11: Subtraction

____________________________________________________________________________

Investigation 1: Combining and Measuring

Focus Time: Counting and Measuring

Choice Time: Measuring with Sticks

Choice Time: Measuring with Cubes Choice Time: Collect 15 Together

Choice Time: Inventory Bag

GRADE K


Investigation 2: Six Tiles

Focus Time: Six Tiles in All

Choice Time: Books of Six in All

Choice Time: Grab Two Handfuls Choice Time: Towers of Six


10-4 Using the Plus Sign

Investigation 3: Story Problems

Focus Time: Story Problems

Choice Time: Double Compare Choice Time: Counters in a Cup

Choice Time: Racing Bears


4-1 Counting 1, 2, and 3 4-2 Reading and Writing 1, 2, and 3


4-4 Reading and Writing 4 and 5 4-5 Reading and Writing 0

4-6 Making 4 and 5

4-7 More, Fewer, and Same As 4-8 1 and 2 More

4-9 1 and 2 Fewer

4-10 Problem Solving: Make An Organized List 10-6 Addition Sentences


11-3 Stories About Comparing 11-4 Using the Minus Sign

11-6 Subtraction Sentences 11-7 Problem Solving: Act It Out

enVisionMATH lessons to be replaced: 10-1 Stories About Joining

10-2 More Joining

10-3 Joining Groups 10-5 Finding Sums

11-1 Stories About Separating

11-2 Stories About Take Away 11-5 Finding Differences

Investigation 4: Blue and Red Crayons

Focus Time: Five Crayons in All

Choice Time: Six Crayons in All Choice Time: Total of Six

GRADE 1

47 Grade 1, Plan 2 Designed for enVisionMATH users who would like to use an Investigations unit as a replacement for some enVisionMATH lessons

Grade 1 Contents

Investigations Unit Mathematical Thinking at Grade 1 (Introduction)........................................... 49


Topic 1: Numbers to 12

Topic 2: Comparing and Ordering Numbers

Investigations Unit

Building Number Sense (The Number System) .............................................. 50


Topic 3: Understanding Addition

Topic 4: Understanding Subtraction

Topic 5: Five and Ten Relationships

Topic 12: Comparing and Ordering Numbers to 100

Investigations Unit

Survey Questions and Secret Rules (Collecting and Sorting Data).................. 52


Topic 18: Data and Graphs

Investigations Unit

Quilt Squares and Block Towns (2-D and 3-D Geometry)................................ 53


Topic 8: Geometry

Topic 19: Fractional Parts

GRADE 1


Investigations Unit

Number Games and Story Problems (Addition and Subtraction)..................... 54


Topic 6: Addition Facts to 12

Topic 7: Subtraction Facts to 12

Topic 10: Counting and Number Patterns to 10

Topic 11: Tens and Ones

Topic 13: Counting Money



Topic 20: Adding and Subtracting with Tens and Ones

Investigations Unit

Bigger, Taller, Heavier, Smaller (Measuring) .................................................. 56

Related enVisionMATH topics Topic 14: Measurement

Topic 15: Time

GRADE 1


____________________________________________________________________________

Investigations Unit

Mathematical Thinking at Grade 1 (Introduction)


Topic 1: Numbers to 12

Topic 2: Comparing and Ordering Numbers

____________________________________________________________________________


1-1 0 to 5

1-2 6 to 10

1-3 10, 11, and 12


Investigation 1: Exploring Materials

Session 1: Getting Started with Materials

Sessions 2, 3, and 4: Exploring Materials

Investigation 2: Exploring Numbers

Session 1: The Game of Compare

Sessions 2 and 3: Introducing Staircases and Choice Time Session 4: Seven Peas and Carrots

Sessions 5 and 6: Number Choices


1-4 Spatial Patterns for Numbers to 9

1-5 Spatial Patterns for Numbers to 10

2-3 Ordering Numbers to 12 with a Number Line

2-4 Problem Solving: Act It Out


2-1 Comparing Two Numbers 2-2 Ordering Three Numbers

Investigation 3: Patterns

Session 1: What Comes Next?

Session 2: Changing Patterns

Sessions 3 and 4: Finding and Making Patterns Sessions 5 and 6: What is a Pattern?

Investigation 4: Counting and Combining

Session 1: Collect 15 Together Sessions 2 and 3: Counting and Combining

Session 4: Eleven Fruits

Session 5: Making Predictions About a Story Session 6: How Many in All?

GRADE 1


Investigation 5: Data About Our Class

Session 1: Kid Pins Session 2: Attendance and Other Surveys

Sessions 3 and 4: Inventing Survey Representations

Sessions 5 and 6: How We Got to School Today

_________________________________________________________________________________

Investigations Unit Building Number Sense (The Number System)


Topic 3: Understanding Addition

Topic 4: Understanding Subtraction

Topic 5: Five and Ten Relationships

Topic 12: Comparing and Ordering Numbers to 100

____________________________________________________________________________

Investigation 1:

Session 1: Quick Images Session 2: Compare Dots

Sessions 3 and 4: Copying Cubes Sessions 5 and 6: Number Shapes

Sessions 7 and 8: Making Dot Pictures

Session 9: How Many Dots?

Investigation 2: Building Numbers in Different Ways

Session 1: Twelve Cats and Dogs Session 2: Problems about Ten

Session 3: The Game of Double Compare

Sessions 4 and 5: Breaking Numbers into Two Parts Sessions 6, 7, and 8: Towers of 10 and Number Choices

Session 9: Three Towers


5-1 Representing Numbers on a Ten-Frame 5-2 Recognizing Numbers on a Ten-Frame

5-5 Problem Solving: Make a Table


4-1 Finding Missing Parts of 6 and 7

4-2 Finding Missing Parts of 8 4-3 Finding Missing Parts of 9

5-3 Parts of 10

5-4 Finding Missing Parts of 10

GRADE 1


Investigation 3: Counting

Sessions 1 and 2: The 100 Chart Sessions 3 and 4: Which Holds More?

Sessions 5, 6, and 7: More Counting and Comparing

Session 8: Clapping Patterns Session 9: (Excursion) Counting Stories


12-1 1 More, 1 Less; 10 More, 10 Less

12-3 Comparing Numbers with >, <, = 12-5 Number Line Estimation

12-6 Before, After, and Between

12-7 Ordering Three Numbers 12-8 Problem Solving: Make an Organized List

enVisionMATH lessons replaced: 12-2 Making Numbers on a Hundred Chart

12-4 Ordering Numbers with a Hundred Chart

Investigation 4: Addition and Subtraction

Session 1: Introducing Combining Situations Session 2: Introducing Separating Situations

Sessions 3, 4, and 5: Five-in-a-Row and Story Problems

Session 6: Dot Addition Sessions 7, 8, and 9: Combining and Separating

Session10: Solving Story Problems


3-6 Adding in Any Order

3-7 Problem Solving: Use Objects 4-6 Stories About Comparing

4-7 Connecting Addition and Subtraction 4-8 Problem Solving: Use Objects

enVisionMATH lessons replaced: 3-1 Making 6 and 7

3-2 Making 8

3-3 Making 9

3-4 Introducing Addition Number Sentences

3-5 Stories About Joining

4-4 Introducing Subtraction Number Sentences 4-5 Stories About Separating

GRADE 1


____________________________________________________________________________

Investigations Unit

Survey Questions and Secret Rules (Collecting and Sorting Data)

Related enVisionMATH topic Topic 18: Data and Graphs

____________________________________________________________________________

Investigation 1: Sorting

Sessions 1 and 2: Sorting Shapes

Session 3: Sorting Session 4: Sorting Buttons

Session 5: Sorting Lids

Session 6: Representations of Sorted Objects

Investigation 2: Survey Questions

Sessions 1 and 2: Would You Rather?

Sessions 3 and 4: More Surveys and Sorting

Sessions 5 and 6: Representing and Sharing Survey Results


18-1 Using Data from Real Graphs 18-2 Using Data from Picture Graphs

enVisionMATH lesson replaced: 18-8 Problem Solving: Make a Graph

Investigation 3: Birthdays

Session 1: When Is Your Birthday?

Session 2: Whose Birthday Comes Next? Session 3: (Excursion) Timeline

enVisionMATH lesson to be taught/incorporated: 18-3 Using Data from Bar Graphs

Investigation 4: Ages and Attendance

Session 1: How Old Are We?

Sessions 2 and 3: Representing Data on Family Ages

Sessions 4 and 5: Attendance Comparisons

enVisionMATH lessons to be taught/incorporated: 18-4 Location on a Grid

18-5 Collecting Data Using Tally Marks

18-6 Making Real Graphs 18-7 Making Picture Graphs

18-9 Certain or Impossible

18-10 Likely or Unlikely

GRADE 1


____________________________________________________________________________

Investigations Unit

Quilt Squares and Block Towns (2-D and 3-D Geometry)

Related enVisionMATH topics Topic 8: Geometry

Topic 19: Fractional Parts

____________________________________________________________________________

Investigation 1: 2-D Shapes and Patterns

Session 1: What Shapes Do You See? Session 2: Same Shape, Different Pieces

Sessions 3, 4, 5, and 6: Describing 2-D Shapes

Session 7: Three Ways to Fill and Outline Sessions 8, 9, and 10: Filling Shapes

Sessions 11 and 12: Sorting 2-D Shapes Sessions 13, 14, and 15: Quilting with Squares and Triangles

enVisionMATH lessons to be taught/incorporated: 8-2 Properties of Plane Shapes

8-4 Breaking Apart Shapes to Make Shapes

8-5 Ways to Move Shapes 8-6 Congruence

8-7 Symmetry

19-1 Making Equal Parts 19-2 Describing Equal Parts of Whole Objects

19-3 Making Parts of a Set

19-4 Describing Parts of Sets 19-5 Problem Solving: Draw a Picture


8-1 Identifying Plane Shapes

8-3 Making New Shapes from Shapes 8-8 Problem Solving: Make an Organized List

Investigation 2: Comparing and Constructing 3-D Shapes

Sessions 1 and 2: Describing and Comparing Shapes

Session 3: Block Pictures

Sessions 4, 5, and 6: Blocks in a Sock Session 7: What Kind of Box Is It?

Sessions 8, 9, and 10: Making Boxes

enVisionMATH lesson to be taught/incorporated:

8-11 Sorting Solid Figures


8-9 Identifying Solid Figures 8-10 Flat Surfaces and Corners

GRADE 1


Investigation 3: Building a Block Town

Sessions 1 and 2: Drawing Geoblocks

Sessions 3 and 4: Planning a Town

Session 5: Building a Town Sessions 6 and 7: Giving Directions

____________________________________________________________________________

Investigations Unit

Number Games and Story Problems (Addition and Subtraction)




Topic 10: Counting and Number Patterns to 10

Topic 11: Tens and Ones




Topic 20: Adding and Subtracting with Tens and Ones

____________________________________________________________________________

Investigation 1: Number Combinations

Session 1: Pictures of Ten Sessions 2 and 3: Number Combinations

Sessions 4 and 5: Total of 10

Session 6: How Many of Each Color? Sessions 7, 8, and 9: Crayon Puzzles

Session 10: (Excursion) Number Combination Stories


6-4 Facts with 5 on a Ten-Frame 6-5 Making 10 on a Ten-Frame

6-1 Adding with 0, 1, 2

6-2 Doubles 6-3 Near Doubles

7-1 Subtracting with 0, 1, 2

7-2 Thinking Addition 7-3 Thinking Addition to 8 to Subtract

7-4 Thinking Addition to 12 to Subtract


6-6 Problem Solving: Draw a Picture and Write a Number Sentence 7-5 Problem Solving: Draw a Picture and Write a Number Sentence

GRADE 1


Investigation 2: Twos, Fives, and Tens

Session 1: How Many Hands? Session 2: Twos and Fours

Session 3: Collect 25¢ Together

Sessions 4 and 5: Counting and Combining Sessions 6, 7, and 8: Numbers to 100

Session 9: Patterns of Fives and Tens Sessions 10, 11, and 12: Twos, Fives, and Tens

Session 13: (Excursion) Counting by Kangaroos


10-1 Making Numbers 11 to 20

10-2 Using Numbers 11 to 20 10-3 Counting by 10s to 100

10-6 Odd and Even Numbers

10-7 Ordinals Through Twentieth 10-9 Problem Solving: Look for a Pattern

13-4 Value of Half Dollar and Dollar 13-6 Problem Solving: Try, Check, and Revise

11-2 Numbers Made with Tens

11-3 Tens and Ones 11-4 Expanded Form

11-5 Ways to Make Numbers

11-6 Problem Solving: Make an Organized List


10-4 Counting Patterns on a Hundred Chart 10-5 Using Skip Counting

10-8 Patterns in Tables

11-1 Counting with Groups of 10 and Leftovers 13-1 Values of Penny and Nickel

13-2 Values of Penny, Nickel, and Dime 13-3 Value of Quarter

13-5 Counting Sets of Coins

Investigation 3: Addition and Subtraction

Session 1: Combining Situations

Session 2: Separating Situations Sessions 3, 4, and 5: Five-in-a-Row and story Problems

Sessions 6, 7, and 8: Tens Go Fish

Session 9: Combining with Unknown Change Sessions 10, 11, and 12: Addition and Subtraction

Session 13: Solving Story Problems


16-1 Doubles 16-2 Doubles Plus 1

16-3 Doubles Plus 2

16-4 Problem Solving: Two-Question Problems 16-5 Making 10 to Add 9

16-6 Making 10 to Add 8

GRADE 1


16-7 Adding Three Numbers

16-8 Problem Solving: Make a Table 17-1 Using Related Facts

17-2 Fact Families

17-3 Using Addition to Subtract 17-4 Subtraction Facts

20-1 Adding Groups of 10 20-2 Adding Tens on a Hundred Chart

20-3 Adding Tens to Two-Digit Numbers

20-4 Adding to a Two-Digit Number 20-5 Subtracting Tens on a Hundred Chart

20-6 Subtracting Tens from Two-Digit Numbers

20-7 Subtracting from a Two-Digit Number 20-8 Problem Solving: Extra Information

enVisionMATH lesson replaced: 17-5 Problem Solving: Draw a Picture and Write a Number Sentence

____________________________________________________________________________

Investigations Unit Bigger, Taller, Heavier, Smaller (Measuring)

Related enVisionMATH topics Topic 14: Measurement

Topic 15: Time

____________________________________________________________________________

Investigation 1: Weighing and Balancing

Sessions 1 and 2: Exploring Weight

Sessions 3 and 4: Comparing Two Objects

Sessions 5 and 6: Balancing Groups of Objects


14-11 Pounds 14-12 Grams and Kilograms

enVisionMATH lesson replaced:

14-10 Comparing and Ordering by Weight

Investigation 2: Filling

Session 1: A Cupful of Sand

Sessions 2, 3, and 4: Filling Space Sessions 5, 6, and 7: Comparing Containers

GRADE 1



14-8 Cups, Pints, and Quarts 14-9 Liters

14-13 Comparing and Ordering by Temperature


14-7 Comparing and Ordering by Capacity

Investigation 3: Measuring Length

Session 1: Longer Than, Shorter Than Session 2: Measuring with Hands and feet

Session 3: Feet Lengths

Sessions 4 and 5: Measuring with Cubes


14-2 Using Units to Estimate and Measure Length 14-3 Problem Solving: Use Reasoning

14-4 Feet and Inches 14-5 Centimeters

14-6 Understanding Perimeter

15-1 Understanding the Hour and Minute Hands 15-2 Telling and Writing Time to the Hour

15-3 Telling and Writing Time to the Half Hour

15-4 Estimating and Ordering Lengths of Time 15-5 Using the Calculator

15-6 Problem Solving: Use Data from a Table


14-1 Comparing and Ordering by Length

GRADE 2


Grade 2 Contents




Investigations Unit Coins, Coupons, and Combinations (The Number System).............................. 61

Related enVisionMATH topics Topic 2: Addition Strategies

Topic 4: Place Value: Numbers to 100

Investigations Unit

Does It Walk, Crawl, or Swim? (Sorting and Classifying Data) ....................... 62


Topic 16: Graphs and Probability

Investigations Unit Shapes, Halves, and Symmetry (Geometry and Fractions) ............................. 63


Topic 11: Geometry

Topic 12: Fractions

Investigations Unit

Putting Together and Taking Apart (Addition and Subtraction) ...................... 64


Topic 1: Understanding Addition and Subtraction

Topic 3: Subtraction Strategies

Topic 6: Mental Addition

Topic 7: Mental Subtraction

Topic 8: Adding Two-Digit Numbers

GRADE 2


Investigations Unit

How Long? How Far? (Measuring) .................................................................. 66


Topic 13: Measurement: Length and Area

Topic 14: Measurement: Capacity and Weight

Investigations Unit How Many Pockets? How Many Teeth? (Collecting and Representing Data) ... 67

Related enVisionMATH topic Topic 16: Graphs and Probability

Investigations Unit

Timelines and Rhythm Patterns (Representing Time)..................................... 68


Topic 15: Time and Temperature

GRADE 2


____________________________________________________________________________

Investigations Unit




____________________________________________________________________________

Investigation 1: Exploring Materials

Session 1: Exploring Cubes and Arrangements of 10

Sessions 2 and 3: Exploring Cubes, Pattern Blocks, and Geoblocks Session 4: Building and Sorting Cube Things

Investigation 2: Looking at Numbers

Session 1: How Many Days Have We Been in School?

Sessions 2 and 3: Card Games Sessions 4 and 5: Mystery Photos

Session 6: Today’s Number and Counting Pockets

Session 7:Revealing Mystery Photos Session 8: Ways to Get to 12

Investigation 3: Geometric Counts

Sessions 1 and 2: Geoblock Faces and Pattern Block Puzzles

Sessions 3 and 4: Counting Geoblocks and Pattern Blocks

Session 5: Sorting Geoblocks Session 6: Pattern Block Counts

Investigation 4: Counting

Session 1: Enough for the Class?

Session 2: Counting Coins, Counting Choices Sessions 3 and 4: Counting Strips and Counting Choices

Session 5: Enough for the Class? Revisited


5-2 Quarter and Half-Dollar

5-3 Counting Collections of Coins 5-4 Ways to Show the Same Amount

5-5 One Dollar


enVisionMATH lessons replaced: 5-1 Dime, Nickel, and Penny

Investigation 5: Collecting Data about Ourselves

Session 1: Collecting and Representing Data about Ourselves

Session 2: Collecting Pocket Data

Sessions 3 and 4: Taking Inventories Session 5: Representing Inventory Data

GRADE 2


____________________________________________________________________________

Investigations Unit

Coins, Coupons, and Combinations (The Number System)

Related enVisionMATH topics Topic 2: Addition Strategies

Topic 4: Place Value: Numbers to 100

____________________________________________________________________________

Investigation 1: 10s and Doubles

Session 1: Combinations of 10

Sessions 2 and 3: Card Games Sessions 4 and 5: Doubles

Session 6: Number Strings

Session 7: Exploring Calculators Sessions 8 and 9: Close to 20 and Beat the Calculator

Session 10: Today’s Number and the Magic Pot Session 11: Counting Pockets

enVisionMATH lessons to be taught/incorporated: 2-1 Adding 0, 1, 2

2-3 Near Doubles

2-4 Adding in Any Order 2-6 Making 10 to Add 9

2-7 Making 10 to Add 8

2-8 Problem Solving: Draw a Picture and Write a Number Sentence


2-2 Doubles 2-5 Adding Three Numbers

Investigation 2: Grouping by 2s, 5s, and 10s

Session 1: Using Groups of 2

Session 2: Exploring Multiples of 5 Session 3: Counting by Different groups

Sessions 4 and 5: Counting Choices

Session 6: Ways to make 15¢ Sessions 7, 8, and 9: Coins and Coupons

Session 10: Collecting Pocket Data

Investigation 3: Introducing Addition and Subtraction Situations

Session 1: Introducing Combining Situations Session 2: Addition Notation

Session 3: Introducing Separating Situations

Sessions 4 and 5: Making Sense of Addition and Subtraction

Investigation 4: One Hundred

Session 1: Exploring the 100 Chart Sessions 2, 3, and 4: Working with 100

Session 5: Penny-a-Pocket

GRADE 2


enVisionMATH lessons to be taught/incorporated: 4-1 Models for Tens

4-2 Models for Tens and Ones

4-3 Reading and Writing Numbers 4-4 Using Models to Compare Numbers

4-5 Using Symbols to Compare Numbers 4-6 Before, After, and Between

4-7 Order Numbers

4-8 Number Patterns on a Hundred Chart 4-9 Even and Odd Numbers

4-10 Problem Solving: Use Data from a Chart

____________________________________________________________________________

Investigations Unit Does It Walk, Crawl, or Swim? (Sorting and Classifying Data)



____________________________________________________________________________

Investigation 1: Sorting People and Yekttis

Sessions 1 and 2: Collecting and Representing Data About Ourselves

Session 3: Working with Two Attributes

Sessions 4 and 5: Looking at Yekttis Session 6: Introducing Venn Diagrams

Investigation 2: Collections: What Goes Together?

Sessions 1 and 2: Exploring Thing Collections

Sessions 3 and 4: Sink and Float

Investigation 3:

Session 1: How Animals Move Sessions 2 and 3: Representing Data in More Than One Way

enVisionMATH lessons replaced: 16-1 Organizing Data

16-2 Pictographs

Investigation 4:

Session 1: What Scares Us? Sessions 2 and 3: Comparing Scary Things Data

enVisionMATH lesson to be taught/incorporated: 16-3 Bar Graphs

16-4 Coordinate Graphs

16-5 Likely and Unlikely 16-6 Certain, Probable, and Impossible

16-7 Problem Solving: Use a Graph

GRADE 2


____________________________________________________________________________

Investigations Unit

Shapes, Halves, and Symmetry (Geometry and Fractions)

Related enVisionMATH topics Topic 11: Geometry

Topic 12: Fractions

____________________________________________________________________________

Investigation 1: Composing and Decomposing Shapes

Session 1: Shapes Around Us

Sessions 2 and 3: Seeing Shapes Within Shapes

Sessions 4 and 5: Shape Puzzles Sessions 6, 7, and 8: Building Buildings


11-1 Flat Surfaces, Vertices, and Edges

11-2 Relating Plane Shapes to Solid Figures


11-3 Making New Shapes 11-4 Cutting Shapes Apart

Investigation 2: What Is a Rectangle?

Session 1: Investigating Quadrilaterals

Session 2: Which Rectangle Is Biggest?

Session 3: Building Rectangles Sessions 4 and 5: Describing Rectangles

Session 6: Picturing Rectangles

Investigation 3: Fractions of Geometric Shapes

Sessions 1 and 2: Halves of Rectangles and Solids Sessions 3, 4, and 5: Cutting Congruent Halves

Session 6: Fraction Flags

Sessions 7 and 8: (Excursion) Fourths and Thirds of Rectangles


12-3 Non-Unit Fractions and Regions 12-4 Estimating Fractional Parts of a Whole

12-5 Fractions of a Set 12-6 Problem Solving: Use Objects

enVisionMATH lessons replaced: 11-5 Congruence

12-1 Wholes and Equal Parts

12-2 Unit Fractions and Regions

GRADE 2


Investigation 4: Symmetry

Sessions 1 and 2: Symmetrical Designs Sessions 3 and 4: Reflecting Blocks and Tiles

Sessions 5 and 6: Paper Folding and Cutting

Session 7: Symmetrical Pictures

enVisionMATH lessons to be taught/incorporated: 11-6 Ways to Move Shapes

11-8 Problem Solving: Use Reasoning


11-7 Symmetry

____________________________________________________________________________

Investigations Unit Putting Together and Taking Apart (Addition and Subtraction)

Related enVisionMATH topics Topic 1: Understanding Addition and Subtraction

Topic 3: Subtraction Strategies

Topic 6: Mental Addition

Topic 7: Mental Subtraction

Topic 8: Adding Two-Digit Numbers

____________________________________________________________________________

Investigation 1:

Session 1: Introducing Combining Situations

Session 2: Introducing Separating Situations Sessions 3 and 4: Making Sense of addition and Subtraction

Sessions 5 and 6: Writing Stories for Numerical Problems


1-1 Writing Addition Number Sentences

1-3 Writing Subtraction Number Sentences 1-5 Stories About Comparing

1-6 Connecting Addition and Subtraction

3-1 Subtracting 0, 1, 2 3-2 Thinking Addition to Subtract Doubles

3-3 Thinking Addition to 10 to Subtract 3-4 Thinking Addition to 18 to Subtract

3-6 Problem Solving: Two-Question Problems


1-2 Stories About Joining

1-4 Stories About Separating 1-7 Problem Solving: Use Objects

GRADE 2


Investigation 2:

Session 1: Exploring the 100 Chart Session 2: Games on the 100 Chart

Sessions 3 and 4: Working with 100

Sessions 5 and 6: Collect $1 Session 7: How Many Paper Clips?


6-5 Problem Solving: Look for a Pattern

7-3 Subtracting on a Hundred Chart 7-5 Problem Solving: Missing or Extra Information

enVisionMATH lessons replaced: 6-1 Adding Tens

6-2 Adding Ones

6-3 Adding Tens and Ones 6-4 Adding on a Hundred Chart

7-1 Subtracting Tens 7-2 Finding Parts of 100

Investigation 3:

Session 1: Parts and Wholes

Session 2: Problems with a Missing Part

Sessions 3, 4, and 5: Separating and Combining Choices


3-5 Finding the Missing Part

Investigation 4:

Session 1: Emma’s Animals Session 2: Ways to Make 100

Sessions 3 and 4: Stories About 100


7-4 Adding On to Subtract

Investigation 5:

Session 1: Introducing Comparing Situations Sessions 2 and 3: Capture 5

Sessions 4 and 5: Strategies for Combining

Session 6: Capture 5 Strategies Session 7: Strategies for Separating

Session 8: How Far?

GRADE 2



8-1 Regrouping 10 Ones for 1 Ten 8-2 Models to Add Two- and One-Digit Numbers

8-3 Adding Two- and One-Digit Numbers

8-4 Models to Add Two-Digit Numbers 8-5 Adding Two-Digit Numbers

8-6 Adding Three Numbers 8-7 Problem Solving: Draw a Picture and Write a Number Sentence

___________________________________________________________________________

Investigations Unit

How Long? How Far? (Measuring)


Topic 13: Measurement: Length and Area

Topic 14: Measurement: Capacity and Weight

____________________________________________________________________________

Investigation 1:

Session 1: Scavenger Hunt

Sessions 2, 3, and 4: A Scavenger Hunt Choice Time

Sessions 5, 6, and 7: Choices About Measurement Session 8: Measuring Our Classroom

enVisionMATH lessons replaced: 13-1 Thinking About Attributes

13-2 Exploring Length

13-3 Measuring Length Using Nonstandard Units

Investigation 2:

Session 1: Walking, Visualizing, and Representing Paths

Sessions 2 and 3: Investigating Turns

Sessions 4 and 5: Measuring Paths Sessions 6, 7, and 8: Moving on a Grid

enVisionMATH lessons to be taught/incorporated: 13-4 Inches, Feet, and Yards

13-5 Centimeters and Meters

13-6 Exploring Perimeter 13-7 Exploring Area

13-8 Problem Solving: Use Objects 14-1 Exploring Capacity

14-2 Measuring Capacity Using Nonstandard Units

14-3 Cups, Pints, and Quarts 14-4 Liters

14-5 Exploring Weight

14-6 Ounces and Pounds 14-7 Grams and Kilograms


GRADE 2


____________________________________________________________________________

Investigations Unit

How Many Pockets? How Many Teeth? (Collecting and Representing Data)



____________________________________________________________________________

Investigation 1:

Session 1: Quick Data Collections

Sessions 2 and 3: Pocket Towers Sessions 4 and 5: Class Surveys

Investigation 2:

Sessions 1 and 2: How Many Teeth Have You Lost?

Session 3: Comparing Lost Teeth Among Other Grades Sessions 4 and 5: Collecting Teeth Data

Session 6: Mystery Teeth Data

Investigation 3:

Session 1: Choosing a Question to Investigate

Sessions 2, 3, and 4: Collecting, Organizing, and Representing Data Session 5: Data Projects: What Does This Graph Tell Us?

enVisionMATH lessons to be taught/incorporated: 16-1 Organizing Data

16-2 Pictographs

16-3 Bar Graphs 16-4 Coordinate Graphs

16-5 Likely and Unlikely 16-6 Certain, Probable, and Impossible

16-7 Problem Solving: Use a Graph

GRADE 2


____________________________________________________________________________

Investigations Unit

Timelines and Rhythm Patterns (Representing Time)

Related enVisionMATH topics Topic 15: Time and Temperature

____________________________________________________________________________

Investigation 1:

Sessions 1 and 2: What Is a Timeline? Session 3: Timeline of My Life

Sessions 4 and 5: Special Day Timelines

Session 6: Acting Out Timelines

enVisionMATH lessons to be taught/incorporated: 15-1 Telling Time to Five Minutes

15-2 Telling Time Before and After the Hour

15-3 Estimating Time 15-4 Using a Calendar

15-5 Temperature: Fahrenheit and Celsius

15-6 Problem Solving: Multiple-Step Problems

Investigation 2:

Session 1: Follow the Leader Rhythm Game Sessions 2 and 3: Codes and Conventions

Session 4: Guess my Three Rhythms

Session 5: Timing and Rhythms

GRADE 3


Grade 3 Contents



Topic 1: Numeration

Topic 20: Data, Graphs, and Probability

Investigations Unit Things That Come in Groups (Multiplication and Division) ............................. 72

Related enVisionMATH topics Topic 5: Multiplication Meanings and Facts

Topic 8: Division Facts

Topic 9: Patterns and Relationships

Investigations Unit

Flips, Turns, and Area (2-D Geometry) ........................................................... 73


Topic 11: Congruence and Symmetry

Topic 16: Perimeter, Area, and Volume

Investigations Unit From Paces to Feet (Measuring and Data) ...................................................... 74


Topic 14: Customary Measurement

Topic 15: Metric Measurement

Investigations Unit Landmarks in the Hundreds (The Number System) ........................................ 75

Related enVisionMATH topics Topic 1: Numeration

Topic 5: Multiplication Meanings and Facts

Topic 6: Multiplication Fact Strategies: Use Known Facts

Topic 18: Multiplying Greater Numbers

Topic 19: Dividing with 1-Digit Numbers

GRADE 3


Investigations Unit

Up and Down the Number Line (Changes) ...................................................... 77


Topic 2: Adding Whole Numbers

Investigations Unit Combining and Comparing (Addition and Subtraction) ................................... 78

Related enVisionMATH topics Topic 2: Adding Whole Numbers

Topic 4: Subtracting Whole numbers to Solve Problems



Investigations Unit

Turtle Paths (2-D Geometry) .......................................................................... 79



Investigations Unit Fair Shares (Fractions) ................................................................................... 80

Related enVisionMATH topics Topic 12: Understanding Fractions

Topic 13: Decimals and Money

Investigations Unit Exploring Solids and Boxes (3-D Geometry) ................................................... 81

Related enVisionMATH topic Topic 10: Solids and Shapes

GRADE 3


____________________________________________________________________________

Investigations Unit



Topic 1: Numeration

Topic 20: Data, Graphs, and Probability

____________________________________________________________________________

Investigation 1: What Is 100?

Session 1: How Much Is 100? Sessions 2 and 3: Working with 100

Investigation 2: Doubles and Halves

Session 1: Pattern Blocks

Session 2: Strategies for Addition Sessions 3 and 4: Finding Doubles and Halves

Sessions 5, 6, and 7: Doubling with Money


1-1 Hundreds

1-2 Thousands 1-3 Greater Numbers

1-4 Ways to Name Numbers

1-5 Comparing Numbers 1-6 Ordering Numbers

1-8 Making Change


enVisionMATH lesson replaced: 1-7 Counting Money

Investigation 3: Data and Handfuls

Sessions 1 and 2: Collecting and Representing Data

Sessions 3 and 4: Handfuls of Cubes and Other Objects


20-5 Ordered Pairs and Line Graphs

20-6 How Likely? 20-7 Outcomes and Experiments

20-8 Line Plots and Probability 20-9 Problem Solving: Use Tables and Graphs to Draw Conclusions

enVisionMATH lessons replaced: 20-1 Organizing Data

20-2 Reading Pictographs and Bar Graphs

20-3 Making Pictographs 20-4 Making Bar Graphs

GRADE 3


Investigation 4: Exploring Odds and Evens

Session 1: Adding Odds and Evens Session 2: Odds and Evens on the Calculator

Session 3: What We’ve Learned about Odds and Evens

____________________________________________________________________________

Investigations Unit Things That Come in Groups (Multiplication and Division)

Related enVisionMATH topics Topic 5: Multiplication Meanings and Facts

Topic 8: Division Facts

Topic 9: Patterns and Relationships

____________________________________________________________________________

Investigation 1: Things That Come in Groups

Session 1: How Many Things Come in Groups?

Session 2: How Many in Several Groups? Session 3: Writing and Solving Riddles

Session 4: (Excursion): Each Orange Had 8 Slices


5-5 Problem Solving: Writing to Explain

5-6 2 and 5 as Factors 5-7 10 as a Factor

5-8 9 as a Factor

5-9 Multiplying with 0 and 1

enVisionMATH lesson replaced: 5-1 Multiplication as Repeated Addition

Investigation 2: Skip Counting and 100 Charts

Session 1: Highlighting Multiples in 100 Charts

Session 2: Using the Calculator to Skip Count

Sessions 3 and 4: More Practice with Multiples Sessions 5 and 6: Discussing Number Patterns

enVisionMATH lessons to be taught/incorporated: 9-3 Extending Tables

9-4 Writing Rules for Situations 9-5 Translating Words to Expressions

9-6 Geometric Patterns

9-7 Equal or Unequal 9-8 Problem Solving: Act It Out and Use Reasoning

enVisionMATH lessons replaced: 9-1 Repeating Patterns

9-2 Number Sequences

GRADE 3


Investigation 3: Arrays and Skip Counting

Sessions 1 and 2: Arranging Chairs Sessions 3 and 4: Array Games

Session 5: The Shapes of Arrays


5-2 Arrays and Multiplication 5-3 Using Multiplication to Compare

5-4 Writing Multiplication Stories

Investigation 4: The Language of Multiplication and Division

Sessions 1 and 2: Multiply or Divide?

Sessions 3 and 4: Writing and Solving Story Problems


8-1 Relating Multiplication and Division 8-2 Fact Families with 2, 3, 4, and 5

8-3 Fact Families with 6 and 7 8-4 Fact Families with 8 and 9

8-5 Dividing with 0 and 1



Investigation 5: Problems with Larger Numbers

Session 1: Calculating Savings

Session 2: Many, Many Legs Session 3: Data Tables and Line Plots

Session 4: A Riddle with 22 Legs



________________________________________________________________________________

Investigations Unit

Flips, Turns, and Area (2-D Geometry)


Topic 11: Congruence and Symmetry


____________________________________________________________________________

Investigation 1: Motions with Tetrominoes

Session 1: Tetrominoes

Sessions 2 and 3: Slides, Flips, and Turns

Session 4: Rectangles with Different shapes Session 5: Final Challenges

GRADE 3



11-2 Line Symmetry 11-3 Drawing Shapes with Lines of Symmetry



11-1 Congruent Figures and Motion

Investigation 2: Finding Area

Session 1: Triangles and Squares Sessions 2 and 3: A Poster of Four-Unit Shapes

Sessions 4 and 5: Writing About Area



16-2 Perimeter of Common Shapes 16-3 Different Shapes with the Same Perimeter

16-4 Problem Solving: Try, Check, and Revise 16-6 Estimating and Measuring Area

16-7 Volume

16-8 Problem Solving: Solve a Simpler Problem


16-5 Understanding Area

____________________________________________________________________________

Investigations Unit From Paces to Feet (Measuring and Data)




____________________________________________________________________________

Start with these enVisionMATH lessons: 14-1 Understanding Measurement

Investigation 1: Measuring with Paces and Steps

Session 1: Giant Steps and Baby steps

Session 2: Pacing and Comparing Sessions 3 and 4: Robot Directions

Sessions 5 and 6: Finding the Middle-sized Pace

GRADE 3


Investigation 2: From Paces to Feet

Session 1: The Need for a Standard Measure Session 2: Kids’ Feet and Adults’ Feet

Sessions 3 and 4: Measuring Centers

Session 5: Moving to Metric Sessions 6 and 7: Metric Measurement


14-2 Fractions of an Inch

14-3 Using Inches, Feet, Yards, and Miles 14-4 Customary Units of Capacity

14-5 Units of Weight

14-6 Problem Solving: Act It Out 15-1 Using Centimeters and Decimeters

15-2 Using Meters and Kilometers

15-3 Metric Units of Capacity 15-4 Units of Mass

15-5 Problem Solving: Make a Table and Look for a Pattern

Investigation 3: Measuring Project

Session 1: What’s a Good Fit? Sessions 2 and 3: Do Our Chairs Fit Us?

Investigation 4: Measuring Project: Balobbyland

Sessions 1, 2, and 3: Making a Small World

____________________________________________________________________________

Investigations Unit

Landmarks in the Hundreds (The Number System)


Topic 1: Numeration


Topic 6: Multiplication Fact Strategies: Use Known Facts

Topic 18: Multiplying Greater Numbers

Topic 19: Dividing with 1-Digit Numbers

____________________________________________________________________________

Investigation 1: Finding Factors

Session 1: Skip Counting with Cubes Sessions 2 and 3: Factors of 24, 36, and 48

Sessions 4 and 5: Factors of 100

Sessions 6 and 7:Dividing a Dollar


5-1 Multiplication as Repeated Addition 5-2 Arrays and Multiplication

5-3 Using Multiplication to Compare

GRADE 3


5-4 Writing Multiplication Stories

5-5 Problem Solving: Writing to Explain 5-6 2 and 5 as Factors

5-7 10 as a Factor

5-8 9 as a Factor 5-9 Multiplying with 0 and 1

5-10 Problem Solving: Two-Question Problems 6-1 3 as a Factor

6-2 4 as a Factor

6-3 6 and 7 as Factors 6-4 8 as a Factor

6-5 11 and 12 as Factors

6-6 Multiplying with 3 Factors 6-7 Problem Solving: Multiple-Step Problems

Investigation 2: Using Landmarks to Solve Problems

Sessions 1, 2, and 3: Moving Beyond 100

Session 4: Solving Problems with Money Sessions 5 and 6: Real-World Multiplying and Dividing

enVisionMATH lessons to be taught/incorporated: 18-1 Using Mental Math to Multiply

18-2 Estimating Products

18-3 Multiplication and Arrays 18-4 Breaking Apart to Multiply

18-5 Using an Expanded Algorithm

18-6 Multiplying 2- and 3-Digit by 1-Digit Numbers 19-1 Mental Math

19-2 Estimating Quotients

19-3 Connecting Models and Symbols 19-4 Dividing 2-Digit Numbers

19-5 Dividing with Remainders 19-6 Problem Solving: Multiple-Step Problems

enVisionMATH lessons replaced: 1-1 Hundreds


Investigation 3: Constructing a 1000 Chart

Session 1: A 1000 Chart

Sessions 2 and 3: Mental Math: Multiplication Problems

enVisionMATH lessons to be taught/incorporated: 1-2 Thousands

1-3 Greater Numbers

1-4 Ways to Name Numbers 1-5 Comparing Numbers

1-6 Ordering Numbers

1-7 Counting Money 1-8 Making Change


GRADE 3


_________________________________________________________________________________

Investigations Unit

Up and Down the Number Line (Changes)



____________________________________________________________________________

Investigation 1: Net Change

Sessions 1 and 2: Elevator Trips Up and Down

Sessions 3 and 4: Many Ways to Make One Net Change

Session 5: Thirty Changes Sessions 6 and 7: Missing Information Problems

Session 8: (Excursion) Stopping at Many Floors


2-1 Addition Meaning and Properties 2-2 Adding on a Hundred Chart

2-3 Using Mental Math to Add

2-4 Rounding 2-5 Estimating Sums

2-6 Adding 2-Digit Numbers

2-7 Models for Adding 3-Digit Numbers 2-8 Adding 3-Digit Numbers

2-9 Adding 3 or More Numbers 2-10 Problem Solving: Draw a Picture

Investigation 2: Representing Elevator Trips

Session 1: Graphing Elevator Trips

Sessions 2 and 3: Repeating Elevator Trips

Session 4: Plus and Minus Graphs

Investigation 3: Inventing Board Games

Session 1: Playing a Board Game Sessions 2 and 3: Creating a Board Game

GRADE 3


____________________________________________________________________________

Investigations Unit

Combining and Comparing (Addition and Subtraction)



Topic 4: Subtracting Whole numbers to Solve Problems



____________________________________________________________________________

Investigation 1: Comparisons with Record Numbers

Sessions 1 and 2: How Many Children in Your Family?

Session 3: More Record Comparisons

Investigation 2: How Much Heavier or Lighter?

Session 1: Weighing Fruits and Vegetables

Session 2: Comparing the Weights

enVisionMATH lessons to be taught/incorporated: 14-1 Understanding Measurement

14-2 Fractions of an Inch

14-3 Using Inches, Feet, Yards, and Miles 14-4 Customary Units of Capacity

14-5 Units of Weight

14-6 Act It Out and Use Reasoning 15-1 Using Centimeters and Decimeters

15-2 Using Meters and Kilometers

15-3 Metric Units of Capacity 15-4 Units of Mass


Investigation 3: Adding with Money, Inches, and Time

Sessions 1 and 2: Heights and Coupons Session 3: Planning a Party

Investigation 4: Working with Hundreds

Session 1: Handfuls of Beans

Session 2: More Handfuls

Sessions 3 and 4: Handfuls of Paper Clips

enVisionMATH lessons to be taught/incorporated: 2-1 Addition Meaning and Properties

2-2 Adding on a Hundred Chart

2-3 Using Mental Math to Add 2-4 Rounding

2-5 Estimating Sums

2-7 Models for Adding 3-Digit Numbers 2-8 Adding 3-Digit Numbers

2-9 Adding 3 or More Numbers

GRADE 3



4-1 Models for Subtracting 2-Digit Numbers 4-2 Subtracting 2-Digit Numbers

4-3 Models for Subtracting 3-Digit Numbers

4-4 Subtracting 3-Digit Numbers 4-5 Subtracting Across Zero



2-6 Adding 2-Digit Numbers

Investigation 5: Calendar Comparisons

Session 1: How Much Longer? Sessions 2 and 3: School Days

_________________________________________________________________________________

Investigations Unit Turtle Paths (2-D Geometry)


Topic 10: Solids and Shapes


____________________________________________________________________________

Investigation 1: Paths and Lengths of Paths

Session 1: Walking Paths

Session 2: Commanding the Turtle

Sessions 3 and 4: Mazes and Maps

Investigation 2: Turns in Paths

Sessions 1 and 2: Turns Session 3: Turns, Turtles, and Triangles

Session 4: Equilateral Triangles Sessions 5 and 6: Missing Measures

Investigation 3: Paths with the Same Length

Sessions 1 and 2: The 200 Steps

Sessions 3, 4, and 5: Facing Problems

Sessions 6 and 7: (Excursion) Designing a Geo-Logo Project


10-1 Solid Figures 10-2 Relating Solids and Shapes

10-5 Polygons 10-6 Triangles

10-7 Quadrilaterals

10-8 Problem Solving: Make and Test Generalizations

GRADE 3


16-2 Perimeter of Common Shapes

16-3 Different Shapes with the Same Perimeter 16-4 Problem Solving: Try, Check, and Revise

16-5 Understanding Area

16-6 Estimating and Measuring Area 16-7 Volume

16-8 Problem Solving: Solve a Simpler Problem


10-3 Lines and Line Segments 10-4 Angles


_________________________________________________________________________________

Investigations Unit

Fair Shares (Fractions)


Topic 12: Understanding Fractions

Topic 13: Decimals and Money

____________________________________________________________________________

Investigation 1: Sharing Brownies

Sessions 1 and 2: Making Fair Shares

Sessions 3 and 4: More Brownies to Share


12-4 Benchmark Fractions


12-1 Dividing Regions Into Equal Parts 12-2 Fractions and Regions

12-5 Finding Equivalent Fractions 12-6 Using Models to Compare Fractions

12-7 Fractions on the Number Line

Investigation 2: Pattern-Block Cookies

Sessions 1 and 2: Making Cookie Shares

Session 3: Comparing Shares Session 4: The Fraction Cookie Game

Sessions 5 and 6: Backward Sharing

Session 7: (Excursion) Half Yellow

enVisionMATH lessons to be taught/incorporated: 12-9 Using Models to Subtract Fractions


GRADE 3



12-8 Using Models to Add Fractions

Investigation 3: Other Things to Share

Sessions 1 and 2: How Can We Split Balloons? Session 3: Sharing Many Things


13-1 Fractions and Decimals

13-2 Using Money to Understand Decimals 13-3 Adding and Subtracting Money


13-5 Problem Solving: Missing or Extra Information


12-3 Fractions and Sets

____________________________________________________________________________

Investigations Unit

Exploring Solids and Boxes (3-D Geometry)


Topic 10: Solids and Shapes

____________________________________________________________________________

Investigation 1: Sorting and Describing Solids

Session 1: Sorting Polyhedra Session 2: What’s My Shape?


10-2 Relating Solids and Shapes

10-3 Lines and Line Segments 10-4 Angles

enVisionMATH lesson replaced: 10-1 Solid Figures

Investigation 2: Building Polygons and Polyhedra

Sessions 1 and 2: Building Polygons

Session 3: Building Polyhedra Sessions 4 and 5: Building Polyhedra from Descriptions

enVisionMATH lessons to be taught/incorporated: 10-7 Quadrilaterals

10-8 Problem Solving: Make and Test Generalizations

GRADE 3



10-5 Polygons 10-6 Triangles

Investigation 3: Making Boxes

Session 1: Making Boxes for a Cube

Session 2: Patterns for Other Solids

Investigation 4: How Many Cubes in a Box?

Session 1: Finding the Number of Cubes in a Box Session 2: Twelve-Cube Boxes

Session 3: Patterns from the Bottom Up

Investigation 5: Building a City

Sessions 1, 2, 3, and 4: Making a Box City

GRADE 4


Grade 4 Contents



Topic 19: Transformations, Congruence, and Symmetry

Investigations Unit

Arrays and Shares (Multiplication and Division) ............................................. 86



Topic 4: Division Meanings and Facts

Topic 5: Multiplying by 1-Digit Numbers

Investigations Unit Seeing Solids and Silhouettes (3-D Geometry) ............................................... 87

Related enVisionMATH topic Topic 15: Solids

Investigations Unit

Landmarks in the Thousands (The Number System)....................................... 88


Topic 1: Numeration

Topic 2: Adding and Subtracting Whole Numbers

Investigations Unit

Different Shapes, Equal Pieces (Fractions and Area) ...................................... 89



Topic 11: Adding and Subtracting Fractions

Investigations Unit

The Shape of Data (Statistics) ........................................................................ 90



GRADE 4


Investigations Unit

Money, Miles, and Large Numbers (Addition and Subtraction) ....................... 91


Topic 12: Understanding Decimals

Topic 13: Operations with Decimals

Investigations Unit

Changes Over Time (Graphs).......................................................................... 92



Investigations Unit Packages and Groups (Multiplication and Division) ........................................ 93



Topic 8: Dividing by 1-Digit Numbers

Investigations Unit Sunken Ships and Grid Patterns (2-D Geometry)............................................ 94

Related enVisionMATH topic Topic 9: Lines, Angles and Shapes

GRADE 4


____________________________________________________________________________

Investigations Unit



Topic 19: Transformations, Congruence, and Symmetry

____________________________________________________________________________

Investigation 1: How Many Hundreds?

Session 1: Getting Started with Interlocking Cubes

Sessions 2 and 3: How Many Hundreds?

Session 4: Close to 100

Investigation 2: How Many Dollars?

Sessions 1 and 2: How Much Money? Sessions 3 and 4: Number Sense and Coins

Investigation 3: Using Number Patterns

Sessions 1 and 2: The 300 Chart

Session 3: Related Problem Sets Sessions 4 and 5: Addition and Subtraction Strategies

Investigation 4: Making Geometric Patterns

Session 1: Patterns with Mirror Symmetry

Session 2: Patterns with Rotational Symmetry

Sessions 3 and 4: Patterns and Nonpatterns Sessions 5 and 6: Symmetrical Geoboard Patterns

enVisionMATH lessons to be taught/incorporated: 19-1 Translations

19-2 Reflections 19-3 Rotations

19-4 Congruent Figures



19-5 Line Symmetry 19-6 Rotational Symmetry

GRADE 4


____________________________________________________________________________

Investigations Unit

Arrays and Shares (Multiplication and Division)



Topic 4: Division Meanings and Facts


____________________________________________________________________________

Investigation 1: Multiples on the 100 Chart

Sessions 1 and 2: Multiples on the 100 Chart Session 3: Skip Counting and Multiplying

enVisionMATH lesson replaced: 3-1 Meanings of Multiplication

Investigation 2: Arrays

Session 1: Things That Come in Arrays

Sessions 2 and 3: Making Arrangements Session 4: Preparing a Set of Arrays

Sessions 5 and 6: Array Games

Sessions 7 and 8: Looking at Division


3-2 Patterns for Facts 3-3 Multiplication Properties

3-4 3 and 4 as Factors

3-5 6, 7, and 8 as Factors 3-6 10, 11, and 12 as Factors

4-2 Relating Multiplication and Division 4-3 Special Quotients

4-4 Using Multiplication Facts to Find Division Facts

4-5 Problem Solving: Draw a Picture and Write an Equation


3-7 Problem Solving: Draw a Picture and Write an Equation 4-1 Meanings of Division

Investigation 3: Multiplication and Division with Two-Digit Numbers

Session 1: Multiplication Clusters

Sessions 2, 3, and 4: Multiplication and Division Choices Session 5: Problems That Look Hard But Aren’t

enVisionMATH lessons to be taught/incorporated: 5-1 Multiplying by Multiples of 10 and 100

5-3 Using Rounding to Estimate

5-5 Using an Expanded Algorithm 5-7 Multiplying 3-Digit by 1-Digit Numbers


GRADE 4


enVisionMATH lessons replaced: 5-2 Using Mental Math to Multiply

5-4 Problem Solving: Reasonableness

5-6 Multiplying 2-Digit by 1-Digit Numbers

____________________________________________________________________________

Investigations Unit

Seeing Solids and Silhouettes (3-D Geometry)


Topic 15: Solids

____________________________________________________________________________

Investigation 1: Making and Visualizing Cube Buildings

Session 1: Building with Cubes

Session 2: Making Mental Pictures


15-4 Volume 15-5 Problem Solving: Look for a Pattern

Investigation 2: Exploring Geometric Silhouettes

Sessions 1 and 2: (Excursion) Silhouettes of Geometric Solids

Sessions 3 and 4: Silhouettes of Cube Buildings

Session 5: (Excursion) Different Views of a City


15-1 Solids 15-2 Views of Solids: Nets


15-3 Views of Solids: Perspective

Investigation 3: “How-To” Instructions for Cube Building

Session 1: Writing “How-To” Instructions

Sessions 2 and 3: Which Instructions Are Best?

Investigation 4: The Cube Toy Project

Sessions 1, 2, 3, and 4: Making Plans for a Cube Toy

GRADE 4


____________________________________________________________________________

Investigations Unit

Landmarks in the Thousands (The Number System)


Topic 1: Numeration

Topic 2: Adding and Subtracting Whole Numbers

____________________________________________________________________________

Investigation 1: Working with 100

Session 1: Ways to Count to 100

Session 2: 100 in a Box Session 3: Moving Around on the 100 Chart

Investigation 2: Exploring Multiples of 100

Session 1: Factors of 100, 200, 300

Sessions 2, 3, and 4: Using Landmarks to Add and Subtract Session 5: Solving Problems in the Hundreds

enVisionMATH lessons to be taught/incorporated: 2-1 Using Mental Math to Add and Subtract

2-3 Problem Solving: Missing or Extra Information

Investigation 3: How Much Is 1000?

Session 1: Numbers to 1000

Session 2: Moving Around in the 1000 Book Sessions 3, 4, and 5: Estimating, Adding, and Subtracting to 1000

enVisionMATH lessons to be taught/incorporated: 2-6 Subtracting Across Zeros



2-2 Estimating Sums and Differences of Whole Numbers 2-4 Adding Whole Numbers

2-5 Subtracting Whole Numbers

Investigation 4: Making a 10,000 Chart

Sessions 1, 2, and 3: Squares on the Wall


1-2 Millions 1-3 Comparing and Ordering Whole Numbers

1-4 Rounding Whole Numbers

1-5 Using Money to Understand Decimals 1-6 Counting Money and Making Change



1-1 Thousands

GRADE 4


____________________________________________________________________________

Investigations Unit

Different Shapes, Equal Pieces (Fractions and Area)



Topic 11: Adding and Subtracting Fractions

____________________________________________________________________________

Investigation 1: Parts of Squares: Halves, Fourths, and Eighths

Session 1: Finding Halves of Crazy Cakes

Sessions 2, 3 and 4 Halves, Fourths, and Eighths with Geoboards Session 5: Combining Fractions in a Design

enVisionMATH lesson to be taught/incorporated: 10-2 Fractions and Division

10-3 Estimating Fractional Amounts


10-1 Regions and Sets

Investigation 2: Parts of Rectangles: Thirds, Sixths, and Twelfths

Sessions 1 and 2: Thirds, Sixths, and Twelfths Session 3: More Fraction Designs

Session 4: Working with 2/3, 3/4, 5/6, and 7/8


11-1 Adding and Subtracting Fractions with Like Denominators

11-2 Adding Fractions with Unlike Denominators 11-3 Subtracting Fractions with Unlike Denominators



Investigation 3: Ordering Fractions

Sessions 1 and 2: Making Fraction Cards

Session 3: Ordering Fractions with Respect to Landmarks Sessions 4 and 5: Making a Fraction Number Line

enVisionMATH lessons to be taught/incorporated: 10-5 Fractions in Simplest Form

10-6 Improper Fractions and Mixed Numbers


10-4 Equivalent Fractions 10-7 Comparing Fractions

10-8 Ordering Fractions

10-9 Problem Solving: Writing to Explain

GRADE 4


____________________________________________________________________________

Investigations Unit

The Shape of Data (Statistics)



____________________________________________________________________________

Investigation 1: Introduction to Data Analysis

Session 1: How Many Raisins in a Box?

Sessions 2 and 3: How Many People in a Family?


17-4 Ordered Pairs

17-5 Line Graphs

enVisionMATH lessons replaced: 17-3 Line Plots


Investigation 2: Landmarks in the Data

Session 1: How Tall Are Fourth Graders?

Sessions 2 and 3: Fourth and First Graders: How Much Taller? Session 4: Looking at Mystery Data

Session 5: Finding the Median

Sessions 6 and 7: Using Landmarks in the Data


17-6 Mean 17-7 Median, Mode, and Range

Investigation 3: A Data Project: Investigating Sleep

Sessions 1 and 2: What Do We Want to Find Out?

Sessions 2, 3 and 4: The Research Team at Work


17-8 Stem-and-Leaf Plots 17-9 Reading Circle Graphs

enVisionMATH lessons replaced: 17-1 Data From Surveys

17-2 Interpreting Graphs

GRADE 4


____________________________________________________________________________

Investigations Unit

Money, Miles, and Large Numbers (Addition and Subtraction)


Topic 12: Understanding Decimals

Topic 13: Operations with Decimals

____________________________________________________________________________


12-1 Decimal Place Value

12-2 Comparing and Ordering Decimals 12-3 Fractions and Decimals

12-4 Fractions and Decimals on the Number Line

12-5 Mixed Numbers and Decimals on the Number Line 12-6 Problem Solving: Draw a Picture

13-1 Rounding Decimals

Investigation 1: Everyday Uses of Money

Sessions 1 and 2: Groceries, Lunch, and Book Orders Session 3: Making a Dollar

Sessions 4 and 5: Making Sense (Cents) of Money on the Calculator

Session 6: Making Change Sessions 7 and 8: Shopping Smart

enVisionMATH lessons to be taught/incorporated: 13-3 Modeling Addition and Subtraction of Decimals

13-4 Adding and Subtracting Decimals

13-5 Multiplying a Whole Number by a Decimal 13-6 Dividing a Decimal by a Whole Number



13-2 Estimating Sums and Differences of Decimals

Investigation 2: How Far? Measuring in Miles and Tenths

Sessions 1 and 2: Miles and Tenths of a Mile Session 3: (Excursion) How Far Is 1/10 of a Mile?

Session 4: A Tour of Our Town

Investigation 3: Calculating Longer Distances

Session 1: Close to 1000 Sessions 2, 3 and 4: A Trip Around the United States

GRADE 4


____________________________________________________________________________

Investigations Unit

Changes Over Time (Graphs)



____________________________________________________________________________

Investigation 1: Graphing Population Changes

Sessions 1 and 2: Graphing Home Population Over Time

Sessions 3 and 4: Making Group Graphs

Sessions 5 and 6: Ins and Outs Number Problems

Investigation 2: Ways to Show Change Over Time

Sessions 1 and 2: Showing Change Over Time

Investigation 3: Telling Stories from Line Graphs

Sessions 1 and 2: Making Graph Sketches

Session 3: Graphing and Predicting Plant Growth

Session 4: Using Line Graphs to Prepare Growth Session 5: Graphs, Stories, and Number

Session 6: Sequences Interpreting Graphs

Sessions 7 and 8: Mystery Graphs


17-1 Data from Surveys 17-2 Interpreting Graphs

17-3 Line Plots

17-4 Ordered Pairs 17-6 Mean

17-7 Median, Mode, and Range 17-8 Stem-and-Leaf Plots

17-9 Reading Circle Graphs



17-5 Line Graphs

GRADE 4


____________________________________________________________________________

Investigations Unit

Packages and Groups (Multiplication and Division)



Topic 8: Dividing by 1-Digit Numbers

____________________________________________________________________________

Investigation 1: Multiplication Tables

Sessions 1 and 2: Making a Multiplication Table

Session 3: (Excursion) Multiple Plaids Sessions 4 and 5: Multiples of Larger Numbers

Investigation 2: Double-Digit Multiplication

Session 1: Multiplying Two-Digit Numbers

Sessions 2 and 3: Solving and Creating Cluster Problems


7-1 Using Mental Math to Multiply 2-Digit Numbers 7-2 Estimating Products

7-3 Arrays and an Expanded Algorithm

7-4 Multiplying 2-Digit Numbers by Multiples of Ten 7-5 Multiplying 2-Digit by 2-Digit Numbers

7-6 Special Cases


Investigation 3: Multiplication and Division Choices

Sessions 1 and 2: Division Notation and Situations Session 3: Looking More Closely at Division Problems

Sessions 4, 5, and 6: Choice Time Sessions 7 and 8: What Are Numbers Divisible Visible By?

Session 9: Division Bingo

Session 10: Assessing Students’ Understanding of Division


8-1 Using Mental Math to Divide 8-2 Estimating Quotients

8-3 Dividing with Remainders

8-4 Connecting Models and Symbols 8-5 Dividing 2-Digit by 1-Digit Numbers

8-6 Dividing 3-Digit by 1-Digit Numbers 8-7 Deciding Where to Start Dividing

8-8 Factors

8-9 Prime and Composite Numbers 8-10 Problem Solving: Multiple-Step Problems

GRADE 4


____________________________________________________________________________

Investigations Unit

Sunken Ships and Grid Patterns (2-D Geometry)


Topic 9: Lines, Angles, and Shapes

____________________________________________________________________________

Investigation 1: Locating Houses and Ships on a Grid

Session 1: Coordinates and Distances on a Grid

Session 2: Introducing Negative Coordinates

Sessions 3 and 4: Playing Sunken Ships Sessions 5 and 6: Distances On and Off the Computer

Investigation 2: Rectangles, Turns, and Coordinates

Session 1: Making Rectangles

Sessions 2 and 3: Rectangles, Coordinates, and Symmetry Session 4: Properties of Rectangles

Session 5: Turns

Sessions 6 and 7: Turning and Repeating Rectangles Sessions 8 and 9: Designing Rectangle Patterns

enVisionMATH lessons to be taught/incorporated: 9-1 Points, Lines, and Planes

9-2 Line Segments, Rays, and Angles

9-3 Measuring Angles 9-4 Polygons

9-5 Triangles

9-6 Quadrilaterals 9-7 Problem Solving: Make and Test Generalizations

GRADE 5


Grade 5 Contents



Topic 1: Numeration

Topic 3: Multiplying Whole Numbers

Investigations Unit Picturing Polygons (2-D Geometry) ................................................................ 98

Related enVisionMATH topic Topic 8: Shapes

Investigations Unit

Name That Portion (Fractions, Percents, and Decimals) ................................. 99


Topic 9: Fractions and Decimals

Topic 10: Adding and Subtracting Fractions and Mixed Numbers

Topic 11: Multiplying Fractions and Mixed Numbers

Topic 16: Ratio and Percent

Topic 18: Graphs and Data

Investigations Unit

Between Never and Always (Probability) ....................................................... 101


Topic 20: Probability

Investigations Unit Building on Numbers You Know (Computation and Estimation Strategies)..... 101

Related enVisionMATH topics Topic 2: Adding and Subtracting Whole Numbers and decimals


Topic 4: Dividing by 1-Digit Divisors


Investigations Unit

Measurement Benchmarks (Estimating and Measuring) ................................. 103


Topic 14: Measurement Units, Time, and Temperature

GRADE 5


Investigations Unit

Patterns of Change (Tables and Graphs) ........................................................ 104


Topic 6: Variables and Expressions

Topic 15: Solving and Writing Equations and Inequalities

Investigations Unit

Containers and Cubes (3-D Geometry, Volume).............................................. 105


Topic 13: Solids

Investigations Unit

Data: Kids, Cats, and Ads (Statistics) ............................................................ 106



GRADE 5


____________________________________________________________________________

Investigations Unit



Topic 1: Numeration


____________________________________________________________________________


1-1 Place Value

1-2 Comparing and Ordering Whole Numbers

Investigation 1: Exploring Numbers and Number Relationships

Sessions 1, 2, and 3: Rectangles and Factor Puzzles Sessions 4, 5, and 6: Number Puzzles


1-3 Decimal Place Value

1-4 Comparing and Ordering Decimals 1-5 Problem Solving: Look for a Pattern

Investigation 2: Multiples and Factors Up to 1000

Session 1: Skip Counting and Other Ways to Multiply

Sessions 2, 3, and 4: Factor Pairs from 100 to 1000

Session 5: Exploring Rectangles of 1000 squares


3-1 Multiplication Properties 3-2 Using Mental Math to Multiply

3-3 Estimating Products 3-4 Multiplying by 1-Digit Numbers

3-5 Multiplying 2-Digit by 2-Digit Numbers

3-6 Multiplying Greater Numbers 3-7 Exponents


Investigation 3: Multiples and Factors Up to 10,000

Session 1: Comparing Factors of 100, 1000, and 10,000

Sessions 2, 3, and 4: Multiplication and Division Clusters Session 5: Factor Pairs of 1100

Investigation 4: Reasoning About Landmarks up to 10,000

Session 1: Close to 1000 and Close to 0

Sessions 2, 3, and 4: Using Landmarks Up to 10,000 Session 5: Reasoning About Landmarks Up to 10,000

GRADE 5


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Investigations Unit

Picturing Polygons (2-D Geometry)


Topic 8: Shapes

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Investigation 1: Identifying Polygons

Session 1: Is It a Polygon?

Session 2: Making Polygons

Session 3: Polygon Pictures with Coordinate Geometry Session 4: Coordinate Geometry with Geo-Logo


8-1 Basic Geometric Ideas

8-3 Polygons

Investigation 2: Triangles and Quadrilaterals

Sessions 1, 2, and 3: Sorting Polygons Sessions 4 and 5: Making Shapes That Follow Rules

Sessions 6 and 7: Using Move and Turn Commands

Session 8: Finding Angle Sizes Session 9: Angles and Turns Together


8-4 Triangles

8-5 Quadrilaterals 8-6 Problem Solving: Make and Test Generalizations

Investigation 3: Regular Polygons

Sessions 1 and 2: Regular Polygons

Session 3: Patterns of Angles and Turns

Session 4: Building Similar Shapes Sessions 5 and 6: Similarity activities


8-2 Measuring and Classifying Angles

GRADE 5


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Investigations Unit

Name That Portion (Fractions, Percents, and Decimals)


Topic 9: Fractions and Decimals

Topic 10: Adding and Subtracting Fractions and Mixed Numbers

Topic 11: Multiplying Fractions and Mixed Numbers

Topic 16: Ratio and Percent


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Investigation 1: Exploring Percents and Fractions

Session 1: Connecting Fractions, Decimals, and Percents

Session 2: Percent Grid Patterns

Sessions 3 and 4: Fraction and Percent Grids Sessions 5 and 6: Percent Equivalence Strips

Session 7: Fraction and Percent Problems


9-3 Mixed Numbers and Improper Fractions 9-5 Comparing and Ordering Fractions and Mixed Numbers

9-6 Common Factors and Greatest Common Factor 9-7 Fractions in Simplest Form

16-1 Understanding Ratios

16-4 Finding Percent of a Whole Number 16-5 Problem Solving: Make a Table and Look for a Pattern

enVisionMATH lessons replaced: 9-1 Meanings of Fractions

9-4 Equivalent Fractions

16-2 Understanding Percent 16-3 Percents, Fractions, and Decimals

Investigation 2: Models for Fractions

Sessions 1 and 2: Fractions on Clocks

Session 3: Fraction Strips Sessions 4 and 5: Fraction Tracks

Session 6: The fraction Track Game

Sessions 7 and 8: Fraction Games Session 9: Problems with Fractions

enVisionMATH lessons to be taught/incorporated: 10-2 Common Multiples and Least Common Multiple

10-3 Adding Fractions with Unlike Denominators

10-4 Subtracting Fractions with Unlike Denominators 10-5 Adding Mixed Numbers

GRADE 5


10-6 Subtracting Mixed Numbers

11-1 Multiplying Fractions and Whole Numbers 11-2 Multiplying Two Fractions

11-3 Multiplying Mixed Numbers

11-4 Relating Division to Multiplication of Fractions 11-5 Problem Solving: Draw a Picture and Write an Equation


10-1 Adding and Subtracting Fractions with Like Denominators


Investigation 3: Exploring Decimals

Session 1: Interpreting Decimals Session 2: Decimals on Grids

Sessions 3 and 4: Decimal Games

Sessions 5 and 6: Fractions to Decimals Session 7: Fraction, Percent, and Decimal Problems

Session 8: Comparing Fraction Amounts

enVisionMATH lessons to be taught/incorporated: 9-10 Fractions and Decimals on the Number Line

enVisionMATH lessons replaced: 9-2 Fractions and Division

9-8 Tenths and Hundredths

9-9 Thousandths 9-11 Problem Solving: Writing to Explain

Investigation 4: Data and Percents in Circle Graphs (Excursion)

Session 1: Planning Age or Gender Surveys

Session 2: Circle Graphs Sessions 3 and 4: Interpreting Percents

Sessions 5 and 6: Survey Reports

Session 7: Two Days in My Life


18-2 Bar Graphs and Picture Graphs 18-3 Line Graphs

18-4 Stem-and-Leaf Plots

18-5 Histograms 18-7 Mean

18-8 Median, Mode, and Range 18-9 Problem Solving: Make a Graph

enVisionMATH lessons replaced: 18-1 Data from Surveys

18-6 Circle Graphs

GRADE 5


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Investigations Unit

Between Never and Always (Probability)


Topic 20: Probability

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Investigation 1: Finding and Comparing Probabilities

Sessions 1 and 2: Creating a Likelihood Line

Sessions 3 and 4: Using Spinners

Session 5: Testing Guessing Skills Session 6: Guessing Skills Distribution

Session 7: The Scoring Options Game


20-2 Writing Probability as a Fraction 20-4 Problem Solving: Solve a Simpler Problem

enVisionMATH lessons replaced: 20-1 Outcomes

20-3 Experiments and Predictions

Investigation 2: Fair and Unfair Games

Sessions 1 and 2: Rock, Paper, Scissors

Session 3: Does a Fair Game Always Look Fair? Sessions 4 and 5: The Unfair Spinner Game

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Investigations Unit

Building on Numbers You Know (Computation and Estimation Strategies)


Topic 2: Adding and Subtracting Whole Numbers and Decimals




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Investigation 1: Exploring Distance Between Numbers

Session 1: Reasoning About Multiples

Session 2: Counting Puzzles Sessions 3 and 4: Exploring Patterns of Multiples

Session 5: Multiple Towers

Sessions 6 and 7: The Digits Game Session 8: Subtraction Strategies

GRADE 5



2-2 Rounding Whole Numbers and Decimals 2-3 Estimating Sums and Differences


2-6 Adding Decimals 2-7 Subtracting Decimals

2-8 Problem Solving: Multiple-Step Problems


2-1 Mental Math 2-5 Adding and Subtracting

Investigation 2: Multiplication and Division Situations

Sessions 1 and 2: Multiplication and Division Strategies

Session 3: Division Strategies

Session 4: What Should We Do with the Extras? Sessions 5 and 6: Relating Multiplication to Division

Session 7: (Excursion) Problems About Our School


3-1 Multiplication Properties 3-2 Using Mental Math to Multiply

3-3 Estimating Products

3-4 Multiplying by 1-Digit Numbers 4-2 Estimating Quotients

4-3 Problem Solving: Reasonableness

4-6 Zeros in the Quotient 4-7 Understanding Factors

4-8 Prime and Composite Numbers


3-5 Multiplying 2-Digit by 2-Digit Numbers 4-1 Dividing Multiples of 10 and 100

4-4 Connecting Models and Symbols

4-5 Dividing by 1-Digit Divisors 4-9 Problem Solving: Draw a Picture and Write an Equation

Investigation 3: Ways to Multiply and Divide

Sessions 1, 2, and 3: Multiplication Clusters

Sessions 4, 5, and 6: Division Clusters

Sessions 7, 8, and 9: How Did I Solve It? Session 10: Ways to Multiply and Divide


3-6 Multiplying Greater Numbers

5-2 Estimating Quotients with 2-Digit Divisors 5-3 Problem Solving: Multiple-Step Problems

5-6 2-Digit Quotients

5-7 Estimating and Dividing with Greater Numbers 5-8 Problem Solving: Missing or Extra Information

GRADE 5



5-1 Using Patterns to Divide 5-4 Dividing by Multiples of 10

5-5 1-Digit Quotients

Investigation 4: (Excursion) A Million Dots

Session 1: Arrays of Dots Session 2: How Big Is a Million?

enVisionMATH lessons to be taught/incorporated: 3-7 Exponents


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Investigations Unit Measurement Benchmarks (Estimating and Measuring)

Related enVisionMATH topics Topic 14: Measurement Units, Time, and Temperature

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Investigation 1: Measures of Length and Distance

Session 1: Exploring Measurement

Session 2: Using Length Benchmarks Session 3: Using Measuring Tools

Session 4: Measuring and comparing

Sessions 5 and 6: Mapping 100 Meters Sessions 7 and 8: (Excursion)How Far Do Products Travel?

Investigation 2: Measures of Weight and Liquid Volume

Sessions 1 and 2: Grocery Package Contents

Session 3: Working with Units of Weight Session 4: Working with Units of Liquid Volume

Session 5: Comparing Weight and Quantity

Session 6: Writing About Weight and Liquid Measure Sessions 7 and 8: (Excursion) Ordinary and Amazing Vegetables

enVisionMATH lessons to be taught/incorporated: 14-4 Converting Customary Units

14-5 Converting Metric Units


14-1 Customary Units of Capacity 14-2 Metric Units of Capacity

14-3 Units of Weight and Mass

Investigation 3: It’s About Time

Session 1: Estimating Half a Minute

GRADE 5


Session 2: Commercial Minutes

Session 3: Making Sense of Years


14-6 Elapsed Time 14-7 Elapsed Time in Other Units

14-8 Temperature Change

14-9 Problem Solving: Make a Table

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Investigations Unit Patterns of Change (Tables and Graphs)

Related enVisionMATH topics Topic 6: Variables and Expressions

Topic 15: Solving and Writing Equations and Inequalities

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Investigation 1: Number Patterns in Changing Shapes

Sessions 1 and 2: Analyzing Tile Patterns

Sessions 3 and 4: Four growing Tile Patterns


6-1 Variables and Expressions

6-2 Patterns and Expressions 6-3 More Patterns and Expressions

6-4 Distributive Property

6-5 Order of Operations 6-6 Problem Solving: Act It Out and Use Reasoning

15-1 Solving Addition and Subtraction Equations 15-2 Solving Multiplication and Division Equations

15-3 Inequalities and the Number Line

15-4 Patterns and Equations 15-5 Problem Solving: Draw a Picture and Write an Equation

Investigation 2: Motion Stories, Graphs and Tables

Session 1: Describing Changing Speeds

Session 2: From Beanbags to Tables

Session 3: Tables for Stories Session 4: Graphs for Tables

Session 5: Stories, Tables, and Graphs

Investigation 3: Computer Trips on Two Tracks

Session 1: Ways of Making Trips Session 2: Trips on Two Tracks

Session 3: Different Kinds of Trips

Session 4: More Match-Ups Sessions 5 and 6: Two Types of Graphs

Session 7: (Excursion) Animation

GRADE 5


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Investigations Unit

Containers and Cubes (3-D Geometry, Volume)


Topic 13: Solids

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Investigation 1: The Packaging Factory

Sessions 1 and 2: How Many Cubes?

Sessions 3 and 4: Doubling and Halving Boxes of Cubes


13-3 Surface Area


13-5 Volume

Investigation 2: Packing Problems

Sessions 1 and 2: Packing Packages of Different Sizes Sessions 3 and 4: Designing Boxes

Session 5: More Packing Problems

Investigation 3: Measuring the Space in Our Classroom

Sessions 1 and 2: Measuring the Space in a Box

Session 3: The Space Inside Our Classroom Session 4: (Excursion) Measuring the Space in Other Rooms

Investigation 4: Prisms, Pyramids, Cylinders, and Cones

Session 1: Comparing Volumes

Sessions 2 and 3: Comparing Volumes of Related Shapes Sessions 4 and 5: Using Standard Volume Units

Session 6: (Excursion) How Do the Heights Compare?

Sessions 7, 8, and 9: Building Models


13-6 Irregular Shapes and Solids 13-7 Problem Solving: Use Objects and Solve a Simpler Problem

enVisionMATH lessons replaced: 13-1 Solids

13-2 Relating Shapes and Solids 13-4 Views of Solids

GRADE 5


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Investigations Unit

Data: Kids, Cats, and Ads (Statistics)



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Investigation 1: Balancing Act

Session 1: Standing on One Foot

Sessions 2 and 3: Comparing Student and Adult Data

Session 4: Mystery Balancers


18-1 Data from Surveys 18-2 Bar Graphs and Picture Graphs

18-3 Line Graphs 18-5 Histograms


Investigation 2: Examining Cats

Session 1: A Set of Cats

Session 2: Associations: Are Female cats Shorter? Session 3: (Excursion) Using the Computer to Investigate Cats

Investigation 3: Sampling Ourselves

Session 1: Review: Fractions, decimals, Percents

Sessions 2 and 3: Sampling the Classroom

Session 4: The Classroom as a Sample

enVisionMATH lessons to be taught/incorporated: 18-4 Stem-and-Leaf Plots

18-6 Circle Graphs

18-7 Mean 18-8 Median, Mode, and Range

Investigation 4: A Sample of Ads

Session 1: Fractions of Newspaper Ads

Session 2: Collecting Data from Ten Days

Session 3: Combining Ad Data Across Pages

Investigation 5: Researching Play Injuries

Session 1: Issues of Playground Safety

Session 2: Collecting Playground Data

Sessions 3, 4, and 5: Analyzing and Presenting Data

envisions and investigations

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