Words Their Way

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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.

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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

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.

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