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Your Mathematics Standards Companion, Grades 3-5

What They Mean and How to Teach Them

By: Linda M. Gojak, Ruth Harbin Miles

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

This expansion of the popular Common Core Mathematics Companions provides indexes for states implementing state-specific mathematics standards and shows which are the same as CCSS-M, which differ and how.

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Product Details

Grade Level: PreK-12
ISBN: 9781506382241
Published By: Corwin
Series: Corwin Mathematics Series
Year: 2017
Page Count: 360
Publication date: June 22, 2017

Available As:

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Description

Transforming the standards into learning outcomes just got a lot easier

In this resource, 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, allowing you to see and understand 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.

Author(s)

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

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

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

Other Titles in: Curriculum & Content | Elementary Maths

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Related Resources

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