Words Their Way Vocabulary for Elementary Mathematics

This practical guide gives mathematics teachers vocabulary-rich activities and strategies that target the important content objectives they already teach, and reflect the expectations of their state or the Common Core standards. The book’s 12 hands-on teaching units address three areas of study covered in a typical mathematics class or textbook–geometry, measurement, and numbers and operations–and cover such topics as lines, angles, and polygons; properties of quadrilaterals; measurement area, perimeter, and volume and fractions. Each unit provides specific directions, language, reproducible materials, supporting activities, and assessments to help teachers effectively and efficiently target the different types of vocabulary needed for academic success–domain-specific and general academic vocabulary and language–all centered on the content that teachers already teach. Aimed at fourth and fifth grade teachers, but also useful to others who teach units on geometry, measurement, or fractions, Words Their Way: Vocabulary for Elementary Mathematics does not seek to replace the classroom mathematics text, but instead serves to explicitly support the learning of academic vocabulary so that students will do better when they work in their basal or other materials.

Lori Helman, PhD, is Associate Professor in literacy education in the Department of Curriculum and Instruction at the University of Minnesota and Director of the Minnesota Center for Reading Research. Her research investigates literacy learning and academic language development for elementary students. She works with teachers and administrators to implement continuous improvement in schoolwide literacy approaches. Dr. Helman is lead author of the Words Their Way with English Learners series. She also publishes books and articles related to literacy instruction and literacy development with multilingual students such as Literacy Development with English Learners (Guilford) and Literacy Instruction in Multilingual Classrooms and Dilemmas and Opportunities: Close Looks into Language and Literacy Learning for Linguistically-Diverse Elementary Students (Teachers College Press).

Kathleen Cramer, PhD, is Associate Professor in Mathematics and Elementary Education in the Department of Curriculum and Instruction at the University of Minnesota and Co-Executive Director of the STEM Education Center.

Francine Johnston, PhD, is Associate Professor Emerita from the School of Education at the University of North Carolina, Greensboro. She is a core author of the Words Their Way series.

Donald R. Bear, PhD, is Professor in the School of Education at Iowa State University and Director of the Duffelmeyer Reading Clinic. He is a core author of the Words Their Way series.

Brief Table of Contents

Introduction

Unit 1 Naming Triangles Part

Unit 2 Naming Triangles Part

Unit 3 Properties of Quadrilaterals

Unit 4 Rectangles, Rhombi, or Squares

Unit 5 Contexts for Area and Perimeter

Unit 6 Comparing Areas and Perimeters of Rectangles

Unit 7 Finding the Volume of Rectangular Prisms

Unit 8 Problems Involving Volume

Unit 9 Fractions

Unit 10 Comparing Fractions with Like and Unlike Denominators

Unit 11 Equivalent Fractions

Unit 12 Fractions Greater than One

Detailed Table of Contents

Introduction

Part 1 The Crucial Role of Vocabulary Knowledge in Mathematics i

Three Essential Types of Vocabulary Knowledge ii

Principles of Vocabulary Instruction iv

Vocabulary Support for Multilingual Learners v

Part 2 Mathematics Units: Organization and Core Activities and Strategies vii

Domain-Specific Vocabulary viii

Step 1: Engaging with Vocabulary and Building Conceptual Knowledge viii

1. Math in My World viii

2. Anticipation Guides ix

3. Telling Math Stories x

4. Concept Maps xi

Step 2: Thinking Like a Mathematician — Finding the Patterns in Mathematics xii

1. Seeing the Big Picture in Mathematics Graphic Organizer xiv

2. Concept Sorts xv

Step 3: Connecting Vocabulary to Context xvi

1. Text Frames xvi

2. Sentence Combining xvii

3. Working with Graphic Displays xvii

Step 4: Assessing Content Vocabulary xviii

1. Basic Assessments xviii

2. Extended Assessments xix

3. Vocabulary Self-Assessment xix

Generative Vocabulary xx

1. Analyzing Words xx

2. Generating Words xx

Moving on to the Mathematics Units xxii

Mathematics Units

Unit 1 Naming Triangles Part 1 1

Vocabulary Overview for the Unit 2

Spanish Cognate Connections 2

Contents

Domain-Specific Vocabulary 3

Step 1: Engaging with Vocabulary and Building Conceptual Knowledge 3

Anticipation Guide 3

Step 2: Thinking Like a Mathematician — Finding the Patterns in Mathematics 3

Name the Pattern 3

Signal the Pattern 3

Verbalize the Pattern 4

Visualize the Pattern 4

Step 3: Connecting Vocabulary to Context 4

Working with Graphic Displays 4

Step 4: Assessing Content Vocabulary 5

Generative Vocabulary 5

Analyzing Words 5

Part 1 5

Part 2 6

Generating Words 7

Unit 2 Naming Triangles Part 2 13

Vocabulary Overview for the Unit 14

Spanish Cognate Connections 14

Domain-Specific Vocabulary 15

Step 1: Engaging with Vocabulary and Building Conceptual Knowledge 15

Math in My World 15

Step 2: Thinking Like a Mathematician — Finding the Patterns in Mathematics 16

Name the Pattern 16

Signal the Pattern 16

Verbalize the Pattern 16

Visualize the Pattern 16

Step 3: Connecting Vocabulary to Context 16

Text Frames 16

Step 4: Assessing Content Vocabulary 17

Generative Vocabulary 17

Analyzing Words 17

Generating Words 18

Unit 3 Properties of Quadrilaterals 23

Vocabulary Overview for the Unit 24

Spanish Cognate Connections 24

Domain-Specific Vocabulary 25

Step 1: Engaging with Vocabulary and Building Conceptual Knowledge 25

Mathematics Hunt 25

Step 2: Thinking Like a Mathematician — Finding the Patterns in Mathematics 26

Name the Pattern 26

Signal the Pattern 26

Verbalize the Pattern 26

Visualize the Pattern 26

Step 3: Connecting Vocabulary to Context 27

Working with Graphic Displays 27

Step 4: Assessing Content Vocabulary 28

Generative Vocabulary 28

Analyzing Words 28

Generating Words 29

Unit 4 Rectangles, Rhombi, or Squares 35

Vocabulary Overview for the Unit 36

Spanish Cognate Connections 36

Domain-Specific Vocabulary 37

Step 1: Engaging with Vocabulary and Building Conceptual Knowledge 37

Anticipation Guide 37

Dot Paper Sketches 37

Step 2: Thinking Like a Mathematician — Finding the Patterns in Mathematics 37

Name the Pattern 37

Signal the Pattern 37

Verbalize the Pattern 38

Visualize the Pattern 38

Step 3: Connecting Vocabulary to Context 38

Working with Graphic Displays 38

Step 4: Assessing Content Vocabulary 39

Generative Vocabulary 41

Analyzing Words 41

Part 1 41

Part 2 41

Generating Words 41

Unit 5 Contexts for Area and Perimeter 48

Vocabulary Overview for the Unit 49

Spanish Cognate Connections 49

Domain-Specific Vocabulary 50

Step 1: Engaging with Vocabulary and Building Conceptual Knowledge 50

Telling Math Stories 50

Step 2: Thinking Like a Mathematician — Finding the Patterns in Mathematics 51

Name the Pattern 51

Signal the Pattern 51

Verbalize the Pattern 51

Visualize the Pattern 52

Step 3: Connecting Vocabulary to Context 52

Working with Graphic Displays 52

Step 4: Assessing Content Vocabulary 53

Generative Vocabulary 53

Analyzing Words 53

Generating Words 54

Unit 6 Comparing Areas and Perimeters of Rectangles 60

Vocabulary Overview for the Unit 61

Spanish Cognate Connections 61

Domain-Specific Vocabulary 62

Step 1: Engaging with Vocabulary and Building Conceptual Knowledge 62

Math in My World 62

Step 2: Thinking Like a Mathematician — Finding the Patterns in Mathematics 62

Name the Pattern 62

Signal the Pattern 63

Verbalize the Pattern 63

Visualize the Pattern 63

Step 3: Connecting Vocabulary to Context 63

Working with Graphic Displays 63

Step 4: Assessing Content Vocabulary 64

Extended Assessment 64

Generative Vocabulary 65

Analyzing Words 65

Generating Words 65

Unit 7 Finding the Volume of Rectangular Prisms 69

Vocabulary Overview for the Unit 70

Spanish Cognate Connections 70

Domain-Specific Vocabulary 71

Step 1: Engaging with Vocabulary and Building Conceptual Knowledge 71

Telling Math Stories 71

Building Model Basements 71

Step 2: Thinking Like a Mathematician — Finding the Patterns in Mathematics 72

Name the Pattern 72

Signal the Pattern 72

Visualize the Pattern 73

Step 3: Connecting Vocabulary to Context 73

Working with Graphic Displays 73

Step 4: Assessing Content Vocabulary 74

Basic Assessment 74

Generative Vocabulary 74

Analyzing Words 74

Generating Words 75

Part 1 75

Part 2 75

Unit 8 Problems Involving Volume 81

Vocabulary Overview for the Unit 82

Spanish Cognate Connections 82

Domain-Specific Vocabulary 83

Step 1: Engaging with Vocabulary and Building Conceptual Knowledge 83

Vocabulary Map 83

Step 2: Thinking Like a Mathematician — Finding the Patterns in Mathematics 83

Name the Pattern 83

Signal the Pattern 84

Verbalize the Pattern 84

Visualize the Pattern 84

Step 3: Connecting Vocabulary to Context 84

Working with Graphic Displays 84

Step 4: Assessing Content Vocabulary 86

Extended Assessment 86

Generative Vocabulary 86

Analyzing Words 86

Generating Words 87

Unit 9 Fractions 93

Vocabulary Overview for the Unit 94

Spanish Cognate Connections 94

Domain-Specific Vocabulary 95

Step 1: Engaging with Vocabulary and Building Conceptual Knowledge 95

Math in My World 95

Step 2: Thinking Like a Mathematician — Finding the Patterns in Mathematics 96

Name the Pattern 96

Signal the Pattern 96

Verbalize the Pattern 97

Visualize the Pattern 97

Step 3: Connecting Vocabulary to Context 97

Working with Graphic Display 97

Step 4: Assessing Content Vocabulary 98

Generative Vocabulary 98

Analyzing Words 98

Generating Words 98

Unit 10 Comparing Fractions with Like and Unlike Denominators 102

Vocabulary Overview for the Unit 103

Spanish Cognate Connections 103

Domain-Specific Vocabulary 104

Step 1: Engaging with Vocabulary and Building Conceptual Knowledge 104

Math in My World 104

Step 2: Thinking Like a Mathematician — Finding the Patterns in Mathematics 105

Name the Pattern 105

Signal the Pattern 105

Verbalize the Pattern 105

Visualize the Pattern 105

Step 3: Connecting Vocabulary to Context 106

Working with Graphic Displays 106

Step 4: Assessing Content Vocabulary 107

Basic Assessment 107

Generative Vocabulary 107

Analyzing Words 107

Generating Words 107

Unit 11 Equivalent Fractions 111

Vocabulary Overview for the Unit 112

Spanish Cognate Connections 112

Domain-Specific Vocabulary 113

Step 1: Engaging with Vocabulary and Building Conceptual Knowledge 113

Anticipation Guide 113

Step 2: Thinking Like a Mathematician — Finding the Patterns in Mathematics 113

Name the Pattern 113

Signal the Pattern 115

Verbalize the Pattern 115

Visualize the Pattern 115

Step 3: Connecting Vocabulary to Context 115

Step 4: Assessing Content Vocabulary 116

Generative Vocabulary 116

Analyzing Words 116

Generating Words 117

Unit 12 Fractions Greater than One 122

Vocabulary Overview for the Unit 123

Spanish Cognate Connections 123

Domain-Specific Vocabulary 124

Step 1: Engaging with Vocabulary and Building Conceptual Knowledge 124

Math in My World 124

Step 2: Thinking Like a Mathematician — Finding the Patterns in Mathematics 126

Name the Pattern 126

Signal the Pattern 126

Verbalize the Pattern 127

Visualize the Pattern 127

Step 3: Connecting Vocabulary to Context 127

Working with Graphic Displays 127

Step 4: Assessing Content Vocabulary 128

Generative Vocabulary 128

Analyzing Words 128

Generating Words 128

Appendix

Templates and Resources 133

References 140

Index 00

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