Put math manipulatives to work in your classroom and make teaching and learning math both meaningful and productive. Mastering Math Manipulatives includes everything you need to integrate math manipulatives-both concrete and virtual-into math learning. Each chapter of this richly illustrated, easy-to-use guide focuses on a different powerful tool, such as two-color counters, linking cubes, base ten blocks, fraction manipulatives, pattern blocks, tangrams, geometric solids, and others, and includes a set of activities that demonstrate the many ways teachers can leverage manipulatives to model and reinforce math concepts for all learners. It features:      Classroom strategies for introducing math manipulatives, including commercial, virtual, and hand-made manipulatives, into formal math instruction.   Step-by-step instructions for 75 activities that work with any curriculum, including four-color photos, printable work mats, and demonstration videos. Handy charts that sort activities by manipulative type, math topic, domains aligned with standards, and grade-level appropriateness.

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Cover -- Contents -- Activities (by Topic) -- Video List (by Activity Number) -- About the Authors -- Preface -- Acknowledgments -- Introduction: We Know Manipulatives Matter, but . . . -- What Are Manipulatives? -- Why Are Manipulatives Important for Students? -- Attributes of Manipulatives -- Considerations for Distance Learning -- Preparing to Use Manipulatives Effectively -- Managing Your Manipulatives -- Frequently Asked Questions -- Let's Go! -- Chapter 1: Two-Color Counters -- Activity 1.1: One-to-One Correspondence -- Activity 1.2: Cardinality -- Activity 1.3: More and Less -- Activity 1.4: Sorting and Counting -- Activity 1.5: Decomposing Numbers Into Pairs in More Than One Way -- Activity 1.6: Make a Ten -- Activity 1.7: Commutative Property of Addition With Two Colors -- Activity 1.8: Ten Ones and Some More Ones and One Group of Ten and Some More Ones -- Activity 1.9: Even and Odd -- Activity 1.10: Building Equal Groups for Multiplication -- Activity 1.11: Building Arrays for Multiplication -- Activity 1.12: Distributive Property of Multiplication Over Addition With Two-Color Counters -- Activity 1.13: Data Collection and Graphing -- Closing Reflection -- Chapter 2: Linking Cubes -- Activity 2.1: Linking Cubes as Counters -- Activity 2.2: Comparing Quantities (More and Less) -- Activity 2.3: Connecting Models to Number Lines Using Addition -- Activity 2.4: Representing Compare Problems With a Bar Model -- Activity 2.5: Associative Property of Addition With Three Towers -- Activity 2.6: "Groups Of" Multiplication -- Activity 2.7: Commutative Property of Multiplication (3 × 9 vs. 9 × 3) -- Activity 2.8: Division With Grouping -- Activity 2.9: Graphing Towers (Include Scaled Bar Graphs) -- Activity 2.10: Measuring Trains -- Closing Reflection -- Chapter 3: Cuisenaireª Rods -- Activity 3.1: Addend Pairs. Activity 3.2: Creating Bar Models for Addition -- Activity 3.3: Creating Bar Models for Subtraction -- Activity 3.4: Exploring Multiplication -- Activity 3.5: Creating Bar Models for Equal Groups Multiplication and Division -- Activity 3.6: Commutative Property of Multiplication (2 × 3 vs. 3 × 2) -- Activity 3.7: Associative Property of Multiplication With 2 × 3 × 4 -- Activity 3.8: Reasoning About Fractions -- Activity 3.9: Unit Fractions (Three One-Fourths Is the Same as Three-Fourths) -- Closing Reflection -- Chapter 4: Unit Squares -- Activity 4.1: Unit Squares as Counters -- Activity 4.2: Repeated Addition With Unit Squares -- Activity 4.3: Iterating Unit Squares to Find Area -- Activity 4.4: Connecting Iterated Unit Squares and Multiplication as Ways to Find Area -- Activity 4.5: Area Is Additive: Finding Areas of Rectilinear Figures -- Activity 4.6: Distributive Property of Multiplication Over Addition -- Activity 4.7: Same Area and Different Perimeters -- Closing Reflection -- Chapter 5: Base-Ten Blocks -- Activity 5.1: "Ten Ones and Some More Ones" vs. "One Ten and Some More Ones" -- Activity 5.2: Counting and Grouping to One Hundred -- Activity 5.3: Representing Two- and Three-Digit Numbers -- Activity 5.4: Representing Numbers as Quick Images -- Activity 5.5: Comparing Two-Digit Numbers -- Activity 5.6: Counting Up and Down by One, Ten, or One Hundred -- Activity 5.7: Adding With Base-Ten Blocks -- Activity 5.8: Subtracting With Base-Ten Blocks -- Activity 5.9: Multiplying by Multiples of Ten -- Closing Reflection -- Chapter 6: Pattern Blocks -- Activity 6.1: How Many Ways to Compose a Hexagon? -- Activity 6.2: Composing and Decomposing Larger Figures With Pattern Blocks -- Activity 6.3: How Many Ways to Compose a Given Value? -- Activity 6.4: Finding the Perimeter of Pattern-Block Shapes. Activity 6.5: Equivalent Fractions With Pattern Blocks -- Activity 6.6: Attending to the "Whole" When Comparing Fractions -- Closing Reflection -- Chapter 7: Fraction Manipulatives (Towers, Circles, Tiles/Bars, and Squares) -- Activity 7.1: Whole Numbers as Fractions With Circles and Rectangles -- Activity 7.2: "One" as a Fraction -- Activity 7.3: Representing and Counting Unit Fractions -- Activity 7.4: Iterating Unit Fractions to Make a Whole -- Activity 7.5: Fraction Equivalence -- Activity 7.6: Comparing Fractions With Like Numerators -- Activity 7.7: Comparing Fractions With Like Denominators -- Activity 7.8: Building a Set of Fraction Bars -- Activity 7.9: Fractions on the Clock (Quarters and Halves) -- Closing Reflection -- Chapter 8: Tangrams and Geoboards -- Activity 8.1: Composing and Decomposing Shapes With Tangrams -- Activity 8.2: Examining Geometric Relationships by Building a Tangram Set -- Activity 8.3: Finding Relative Values of Tangram Pieces -- Activity 8.4: Finding Halves, Thirds, and Fourths on a Geoboard -- Activity 8.5: Same-Sized Parts Need Not Be the Same Shape -- Activity 8.6: Comparing Polygons on the Geoboard -- Activity 8.7: Finding the Area of a Rectilinear Figure on a Geoboard -- Closing Reflection -- Chapter 9: Geometric Solids -- Activity 9.1 Identifying Faces of Geometric Solids as Two-Dimensional Figures -- Activity 9.2: Describing Geometric Solids -- Activity 9.3: Composing Geometric Solids -- Activity 9.4: Solids With Curved Surfaces -- Activity 9.5: Attributes of Geometric Solids -- Closing Reflection -- Chapter 10: Continuing the Journey -- Glossary -- References -- Index.