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Your Mathematics Standards Companion, Grades 3-5
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Your Mathematics Standards Companion, Grades 3-5
What They Mean and How to Teach Them

A Joint Publication of Corwin Mathematics and the National Council of Teachers of Mathematics, NCTM Stock Number 15462



June 2017 | 360 pages | Corwin

Transforming the standards into learning outcomes just got a lot easier

In this expansion of the original popular Common Core Mathematics Companions, you can see in an instant how teaching to your state standards should look and sound in the classroom. Under the premise that math is math, the authors provide a Cross-Referencing Index for states implementing their own specific mathematics standards, showing which of your standards are the same as CCSS-M, which differ and how—and which page number to turn to for standards-based teaching ideas.

It’s all here, page by page:

  • The mathematics embedded in each standard for a deeper understanding of the content
  • Examples of what effective teaching and learning look like in the classroom  
  • Connected standards within each domain so teachers can better appreciate how they relate
  • Priorities within clusters so teachers know where to focus their time
  • The three components of rigor: conceptual understanding, procedural skills, and applications
  • Vocabulary and suggested materials for each grade-level band with explicit connections to the standards
  • Common student misconceptions around key mathematical ideas with ways to address them
  • Sample lesson plans and lesson planning templates
  • Cross-referenced index listing the standards in the following states, explaining what is unique to the standards of each state

Your Mathematics Standards Companion is your one-stop guide for teaching, planning, assessing, collaborating, and designing powerful mathematics curriculum.

 
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

Sample Materials & Chapters

At a Glance

Part 3


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