Your Mathematics Standards Companion, Grades 3-5

Indexes Cross-Referencing Your State Standards Quick Reference Guide Acknowledgments Letter to Grades 3-5 Teachers Letter to Elementary School Principals Introduction A Brief History of Current State Standards College and Career Ready Standards for Mathematics Instructional Shifts Terminology Used in This Book Effective Teaching Practices How to Use This Book Reflection Questions Part 1. Operations and Algebraic Thinking Domain Overview Suggested Materials for This Domain Key Vocabulary Grade 3 Cluster A: Represent and solve problems involving multiplication and division. Cluster B: Understand properties of multiplication and the relationship between multiplication and division. Cluster C: Multiply and divide within 100. Cluster D: Solve problems involving the four operations, and identify and explain patterns in arithmetic. Sample Planning Page: Operations and Algebraic Thinking, Grade 3, Cluster A Planning Pages Grade 4 Cluster A: Use the four operations with whole numbers to solve problems. Cluster B: Gain familiarity with factors and multiples. Cluster C: Generate and analyze patterns. Sample Planning Page: Operations and Algebraic Thinking, Grade 4, Cluster B Planning Pages Grade 5 Cluster A: Write and interpret numerical expressions. Cluster B: Analyze patterns and relationships. Sample Planning Page: Operations and Algebraic Thinking, Grade 5, Cluster A Planning Pages Reflection Questions: Operations and Algebraic Thinking Part 2. Number and Operations in Base Ten Domain Overview Suggested Materials for This Domain Key Vocabulary Grade 3 Cluster A: Use place value understanding and properties of operations to perform multi-digit arithmetic. Sample Planning Page: Number and Operations in Base Ten, Grade 3, Cluster A Planning Page Grade 4 Cluster A: Generalize place value understanding for multi-digit whole numbers. Cluster B: Use place value understanding and properties of operations to perform multi-digit arithmetic. Sample Planning Page: Number and Operations in Base Ten, Grade 4, Cluster B Planning Pages Grade 5 Cluster A: Understand the place value system. Cluster B: Perform operations with multi-digit whole numbers and with decimals to hundredths. Sample Planning Page: Number and Operations in Base Ten, Grade 5, Cluster B Planning Pages Reflection Questions: Number and Operations in Base Ten Part 3. Number and Operations-Fractions Domain Overview Suggested Materials for This Domain Key Vocabulary Grade 3 Cluster A: Develop understanding of fractions as numbers. Sample Planning Page: Number and Operations-Fractions, Grade 3, Cluster A Planning Page Grade 4 Cluster A: Extend understanding of fraction equivalence and ordering. Cluster B: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Cluster C: Understand decimal notation for fractions, and compare decimal fractions. Sample Planning Page: Number and Operations-Fractions, Grade 4, Cluster C Planning Pages Grade 5 Cluster A: Use equivalent fractions as a strategy to add and subtract fractions. Cluster B: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Sample Planning Page: Number and Operations-Fractions, Grade 5, Cluster A Planning Pages Reflection Questions: Number and Operations-Fractions Part 4. Measurement and Data Domain Overview Suggested Materials for This Domain Key Vocabulary Grade 3 Cluster A: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Cluster B: Represent and interpret data. Cluster C: Geometric measurement: Understand concepts of area and relate area to multiplication and to addition. Cluster D: Geometric measurement: Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Sample Planning Page: Measurement and Data, Grade 3, Cluster A Planning Pages Grade 4 Cluster A: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Cluster B: Represent and interpret data. Cluster C: Geometric measurement: Understand concepts of angle and measure angles. Sample Planning Page: Measurement and Data, Grade 4, Cluster A Planning Pages Grade 5 Cluster A: Convert like measurement units within a given measurement system. Cluster B: Represent and interpret data. Cluster C: Geometric measurement: Understand concepts of volume and relate volume to multiplication and to addition. Sample Planning Page: Measurement and Data, Grade 5, Cluster C Planning Pages Reflection Questions: Measurement and Data Part 5. Geometry Domain Overview Suggested Materials for This Domain Key Vocabulary Grade 3 Cluster A: Reason with shapes and their attributes. Sample Planning Page: Geometry, Grade 3, Cluster A Planning Page Grade 4 Cluster A: Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Sample Planning Page: Geometry, Grade 4, Cluster A Planning Page Grade 5 Cluster A: Graph points on the coordinate plane to solve real-world and mathematical problems. Cluster B: Classify two-dimensional figures into categories based on their properties. Sample Planning Page: Geometry, Grade 5, Cluster A Planning Pages Reflection Questions: Geometry Resources Table 1. Addition and Subtraction Situations, Grades 3-5 Table 2. Multiplication and Division Situations, Grades 3-5 Table 3. Standards for Mathematical Practice Table 4. Effective Teaching Practices Reproducibles Reproducible 1. Hundreds Chart Reproducible 2. Place Value Chart to Hundreds Reproducible 3. Grid Paper Reproducible 4. Base-Ten Blocks Reproducible 5. Fraction Area Models (Circular) Reproducible 6. Fraction Area Models (Rectangular) Reproducible 7. Fraction Strips/Bars Reproducible 8. Place Value Chart Reproducible 9. Geoboard Paper Reproducible 10. Dot Paper (Centimeter) Reproducible 11. Pattern Blocks Reproducible 12. Tangram Pattern Additional Resources About the Authors