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Linda M. Gojak & Ruth Harbin Miles 
The Common Core Mathematics Companion: The Standards Decoded, Grades 3-5 
What They Say, What They Mean, How to Teach Them

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Couverture du Linda M. Gojak & Ruth Harbin Miles: The Common Core Mathematics Companion: The Standards Decoded, Grades 3-5 (PDF)

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.

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Table des matières

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

A propos de l’auteur

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.
Langue Anglais ● Format PDF ● Pages 320 ● ISBN 9781483381596 ● Taille du fichier 26.4 MB ● Maison d’édition SAGE Publications ● Lieu Thousand Oaks ● Pays US ● Publié 2015 ● Édition 1 ● Téléchargeable 24 mois ● Devise EUR ● ID 6693311 ● Protection contre la copie Adobe DRM
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