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The Common Core Mathematics Companion: The Standards Decoded, Grades 3-5

What They Say, What They Mean, How to Teach Them

This book is modeled after Jim Burke’s successful Common Core Companion Series. It is the second of two books (K-2, 3-5) in the series. The book will include a clear explanation of the mathematics within each domain, cluster, and standard and suggested grade level appropriate visual models and representations. It is a book for math teachers who may or may not be math specialists. As teachers plan and develop their curriculum, this book will help them determine important mathematics in a cluster and how that mathematics connects from one grade to the next as well as within a grade.

Full description

Product Details
  • Grade Level: PreK-12
  • ISBN: 9781483381602
  • Published By: Corwin
  • Series: Corwin Mathematics Series
  • Year: 2015
  • Page Count: 320
  • Publication date: July 01, 2015

Price: $39.95

Description

Description

Your user’s guide to the mathematics standards

In the 12 short months since the ELA versions of The Common Core Companions, Grades K-2 and 3-5, burst on the scene, they’ve already assisted tens of thousands of teachers with the day-to-day “what you do.” Teachers’ one big criticism: what about mathematics? Luckily NCTM past-president Linda Gojak and mathematics coach Ruth Harbin Miles stepped up to the task. The result? That version of the mathematics standards you wish you had.

Page by page, The Common Core Mathematics Companions clearly lay out:

  • 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

Don’t spend another minute poring over the mathematics standards. Gojak and Miles have already done the heavy-lifting for you. Focus instead on how to teach them, using The Common Core Mathematics Companion as your one-stop guide for teaching, planning, assessing, collaborating, and designing powerful mathematics curriculum.

Winner of the Presidential Award for Excellence in Science and Mathematics Teaching, and director of John Carroll University’s Center for Mathematics and Science Education, Linda Gojak has spent 28 years teaching elementary and middle school mathematics and 15 years working with K–8 teachers. She has served as the president of the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM), and the Ohio Council of Teachers of Mathematics.

Ruth Harbin Miles is a mathematics coach, with special expertise in developing teachers’ content knowledge and strategies for engaging students to achieve high standards in mathematics. She has served on the Board of Directors for the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM), and both the Virginia Council of Teachers of Mathematics and the Kansas Association of Teachers of Mathematics.

Also From Corwin:

  • Gojak & Miles/Common Corwin Mathematics Companion, Grades 3-5
  • Taberski/The Common Core Companion, K-2
  • Hull/The Common Core Mathematics Standards


Key features

  • Offers direct explanation of the standards and their instructional intent
  • Aims to help teachers more deeply understand the mathematics of the common core
  • Includes practical classroom examples and visual aides that teachers can adapt and use in their classrooms
  • Includes connections between the standards
  • Includes connections to the standards of mathematical practice
  • Author(s)

    Author(s)

    Linda M. Gojak photo

    Linda M. Gojak

    Winner of the Presidential Award for Excellence in Science and Mathematics Teaching, Linda M. Gojak directed the Center for Mathematics and Science Education, Teaching, and Technology (CMSETT) at John Carroll University for 16 years. She has spent 28 years teaching elementary and middle school mathematics, and has served as the president of the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM), and the Ohio Council of Teachers of Mathematics.
    Ruth Harbin Miles photo

    Ruth Harbin Miles

    Ruth Harbin Miles coaches rural, suburban, and inner-city school mathematics teachers. Her professional experiences include coordinating the K-12 Mathematics Teaching and Learning Program for the Olathe, Kansas, Public Schools for more than 25 years; teaching mathematics methods courses at Virginia’s Mary Baldwin College; and serving on the Board of Directors for the National Council of Teachers of Mathematics, the National Council of Supervisors of Mathematic, and both the Virginia Council of Teachers of Mathematics and the Kansas Association of Teachers of Mathematics. Ruth is a co-author of five Corwin books including A Guide to Mathematics Coaching, A Guide to Mathematics Leadership, Visible Thinking in the K-8 Mathematics Classroom, The Common Core Mathematics Standards, and Realizing Rigor in the Mathematics Classroom. As co-owner of Happy Mountain Learning, Ruth specializes in developing teachers’ content knowledge and strategies for engaging students to achieve high standards in mathematics.

    Table of Contents

    Table of Contents

    Acknowledgments


    Letter to Grades 3–5 Teachers


    Letter to Elementary School Principals


    Introduction


    A Brief History of the Common Core

    The Common Core State Standards for Mathematics

    Instructional Shifts

    Major Work of Grades 3¬–5

    Common Core Word Wall

    The Common Core Standards for Mathematical Practice

    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

    CCSS Where to Focus Grade 3 Mathematics

    CCSS Where to Focus Grade 4 Mathematics

    CCSS Where to Focus Grade 5 Mathematics

    Reproducibles


    Additional Resources


    About the Authors


    Reviews

    Reviews


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