Your Mathematics Standards Companion, Grades K-2

What They Mean and How to Teach Them
Linda M. Gojak - Mathematics Consultant, NCTM Past-President
Ruth Harbin Miles - Mary Baldwin College, VA
Corwin Mathematics Series
Your Mathematics Standards Companion, Grades K-2
May 2017 | 288 pages | Corwin
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eBook
ISBN: 9781544302348
Available from January 0001
Spiral
ISBN: 9781506382234
Available from January 0001

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.

Contents

Indexes Cross-Referencing Your State Standards

Indexes Cross-Referencing Your State Standards

Quick Reference Guide

Quick Reference Guide

Acknowledgments

Acknowledgments

Letter to Grades K–2 Teachers

Letter to Grades K–2 Teachers

Letter to Elementary School Principals

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. Counting and Cardinality

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Know number names and the count sequence.
  • Cluster B: Count to tell the number of objects.
  • Cluster C: Compare numbers.
  • Sample Planning Page: Counting and Cardinality, Kindergarten, Cluster B
  • Planning Pages
  • Reflection Questions: Counting and Cardinality

Part 2. Operations and Algebraic Thinking

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
  • Sample Planning Page: Operations and Algebraic Thinking, Kindergarten, Cluster A
  • Planning Page
  • Grade 1
  • Cluster A: Represent and solve problems involving addition and subtraction.
  • Cluster B: Understand and apply properties of operations and the relationship between addition and subtraction.
  • Cluster C: Add and subtract within 20.
  • Cluster D: Work with addition and subtraction equations.
  • Sample Planning Page: Operations and Algebraic Thinking, Grade 1, Cluster C
  • Planning Pages
  • Grade 2
  • Cluster A: Represent and solve problems involving addition and subtraction.
  • Cluster B: Add and subtract within 20.
  • Cluster C: Work with equal groups of objects to gain foundations for multiplication.
  • Sample Planning Page: Operations and Algebraic Thinking, Grade 2, Cluster A
  • Planning Pages
  • Reflection Questions: Operations and Algebraic Thinking

Part 3. Number and Operations in Base Ten

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Work with numbers 11–19 to gain foundation for place value.
  • Sample Planning Page: Number and Operations in Base Ten, Kindergarten, Cluster A
  • Planning Page
  • Grade 1
  • Cluster A: Extend the counting sequence.
  • Cluster B: Understand place value.
  • Cluster C: Use place value understanding and properties of operations to add and subtract.
  • Sample Planning Page: Number and Operations in Base Ten, Grade 1, Cluster C
  • Planning Pages
  • Grade 2
  • Cluster A: Understand place value.
  • Cluster B: Use place value understanding and properties of operations to add and subtract.
  • Sample Planning Page: Number and Operations in Base Ten, Grade 2, Cluster B
  • Planning Pages
  • Reflection Questions: Number and Operations in Base Ten

Part 4. Measurement and Data

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Describe and compare measurable attributes.
  • Cluster B: Classify objects and count the number of objects in each category.
  • Sample Planning Page: Measurement and Data, Kindergarten, Cluster A
  • Planning Pages
  • Grade 1
  • Cluster A: Measure lengths indirectly and by iterating length units.
  • Cluster B: Tell and write time.
  • Cluster C: Represent and interpret data.
  • Sample Planning Page: Measurement and Data, Grade 1, Cluster C
  • Planning Pages
  • Grade 2
  • Cluster A: Measure and estimate lengths in standard units.
  • Cluster B: Relate addition and subtraction to length.
  • Cluster C: Work with time and money.
  • Cluster D: Represent and interpret data.
  • Sample Planning Page: Measurement and Data, Grade 2, Cluster D
  • Planning Pages
  • Reflection Questions: Measurement and Data

Part 5. Geometry

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Identify and describe shapes.
  • Cluster B: Analyze, compare, create, and compose shapes.
  • Sample Planning Page: Geometry, Kindergarten, Cluster A
  • Planning Pages
  • Grade 1
  • Cluster A: Reason with shapes and their attributes.
  • Sample Planning Page: Geometry, Grade 1, Cluster A
  • Planning Page
  • Grade 2
  • Cluster A: Reason with shapes and their attributes.
  • Sample Planning Page: Geometry, Grade 2, Cluster A
  • Planning Page
  • Reflection Questions: Geometry

Resources

  • Table 1. Addition and Subtraction Situations
  • Table 2. Addition and Subtraction Fact Strategies
  • Table 3. Scaffolding Addition and Subtraction
  • Table 4. Sample Addition and Subtraction Strategies
  • Table 5. Standards for Mathematical Practice
  • Table 6. Effective Teaching Practices

Reproducibles

  • Reproducible 1. Five Frame
  • Reproducible 2. Ten Frame
  • Reproducible 3. Double Ten Frame
  • Reproducible 4. Hundreds Chart
  • Reproducible 5. Dot Cards
  • Reproducible 6. Numeral Cards
  • Reproducible 7. Number Line to 20
  • Reproducible 8. Open Number Line
  • Reproducible 9. Part-Part-Whole Chart
  • Reproducible 10. Place Value Chart (Tens/Ones)
  • Reproducible 11. Place Value Chart (Hundreds/Tens/Ones)
  • Reproducible 12. Comparison Cards

Additional Resources

Additional Resources

About the Authors

About the Authors

Resources

Companion Website

Additional materials

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.

Contents

Indexes Cross-Referencing Your State Standards

Indexes Cross-Referencing Your State Standards

Quick Reference Guide

Quick Reference Guide

Acknowledgments

Acknowledgments

Letter to Grades K–2 Teachers

Letter to Grades K–2 Teachers

Letter to Elementary School Principals

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. Counting and Cardinality

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Know number names and the count sequence.
  • Cluster B: Count to tell the number of objects.
  • Cluster C: Compare numbers.
  • Sample Planning Page: Counting and Cardinality, Kindergarten, Cluster B
  • Planning Pages
  • Reflection Questions: Counting and Cardinality

Part 2. Operations and Algebraic Thinking

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
  • Sample Planning Page: Operations and Algebraic Thinking, Kindergarten, Cluster A
  • Planning Page
  • Grade 1
  • Cluster A: Represent and solve problems involving addition and subtraction.
  • Cluster B: Understand and apply properties of operations and the relationship between addition and subtraction.
  • Cluster C: Add and subtract within 20.
  • Cluster D: Work with addition and subtraction equations.
  • Sample Planning Page: Operations and Algebraic Thinking, Grade 1, Cluster C
  • Planning Pages
  • Grade 2
  • Cluster A: Represent and solve problems involving addition and subtraction.
  • Cluster B: Add and subtract within 20.
  • Cluster C: Work with equal groups of objects to gain foundations for multiplication.
  • Sample Planning Page: Operations and Algebraic Thinking, Grade 2, Cluster A
  • Planning Pages
  • Reflection Questions: Operations and Algebraic Thinking

Part 3. Number and Operations in Base Ten

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Work with numbers 11–19 to gain foundation for place value.
  • Sample Planning Page: Number and Operations in Base Ten, Kindergarten, Cluster A
  • Planning Page
  • Grade 1
  • Cluster A: Extend the counting sequence.
  • Cluster B: Understand place value.
  • Cluster C: Use place value understanding and properties of operations to add and subtract.
  • Sample Planning Page: Number and Operations in Base Ten, Grade 1, Cluster C
  • Planning Pages
  • Grade 2
  • Cluster A: Understand place value.
  • Cluster B: Use place value understanding and properties of operations to add and subtract.
  • Sample Planning Page: Number and Operations in Base Ten, Grade 2, Cluster B
  • Planning Pages
  • Reflection Questions: Number and Operations in Base Ten

Part 4. Measurement and Data

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Describe and compare measurable attributes.
  • Cluster B: Classify objects and count the number of objects in each category.
  • Sample Planning Page: Measurement and Data, Kindergarten, Cluster A
  • Planning Pages
  • Grade 1
  • Cluster A: Measure lengths indirectly and by iterating length units.
  • Cluster B: Tell and write time.
  • Cluster C: Represent and interpret data.
  • Sample Planning Page: Measurement and Data, Grade 1, Cluster C
  • Planning Pages
  • Grade 2
  • Cluster A: Measure and estimate lengths in standard units.
  • Cluster B: Relate addition and subtraction to length.
  • Cluster C: Work with time and money.
  • Cluster D: Represent and interpret data.
  • Sample Planning Page: Measurement and Data, Grade 2, Cluster D
  • Planning Pages
  • Reflection Questions: Measurement and Data

Part 5. Geometry

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Identify and describe shapes.
  • Cluster B: Analyze, compare, create, and compose shapes.
  • Sample Planning Page: Geometry, Kindergarten, Cluster A
  • Planning Pages
  • Grade 1
  • Cluster A: Reason with shapes and their attributes.
  • Sample Planning Page: Geometry, Grade 1, Cluster A
  • Planning Page
  • Grade 2
  • Cluster A: Reason with shapes and their attributes.
  • Sample Planning Page: Geometry, Grade 2, Cluster A
  • Planning Page
  • Reflection Questions: Geometry

Resources

  • Table 1. Addition and Subtraction Situations
  • Table 2. Addition and Subtraction Fact Strategies
  • Table 3. Scaffolding Addition and Subtraction
  • Table 4. Sample Addition and Subtraction Strategies
  • Table 5. Standards for Mathematical Practice
  • Table 6. Effective Teaching Practices

Reproducibles

  • Reproducible 1. Five Frame
  • Reproducible 2. Ten Frame
  • Reproducible 3. Double Ten Frame
  • Reproducible 4. Hundreds Chart
  • Reproducible 5. Dot Cards
  • Reproducible 6. Numeral Cards
  • Reproducible 7. Number Line to 20
  • Reproducible 8. Open Number Line
  • Reproducible 9. Part-Part-Whole Chart
  • Reproducible 10. Place Value Chart (Tens/Ones)
  • Reproducible 11. Place Value Chart (Hundreds/Tens/Ones)
  • Reproducible 12. Comparison Cards

Additional Resources

Additional Resources

About the Authors

About the Authors

Resources

Companion Website

Additional materials

SAGE Publishing Logo

Your Mathematics Standards Companion, Grades K-2

What They Mean and How to Teach Them

Linda M. Gojak , Ruth Harbin Miles
Cancel Print

May 2017 | 288 pages | Corwin

Format Published Date ISBN Price
Spiral 01/02/2026 9781506382234 $43.95
Lifetime 01/02/2026 9781544302348 $40.00

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.


Table Of Contents:

  • Indexes Cross-Referencing Your State Standards
  • Quick Reference Guide
  • Acknowledgments
  • Letter to Grades K–2 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. Counting and Cardinality
  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Know number names and the count sequence.
  • Cluster B: Count to tell the number of objects.
  • Cluster C: Compare numbers.
  • Sample Planning Page: Counting and Cardinality, Kindergarten, Cluster B
  • Planning Pages
  • Reflection Questions: Counting and Cardinality
  • Part 2. Operations and Algebraic Thinking
  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
  • Sample Planning Page: Operations and Algebraic Thinking, Kindergarten, Cluster A
  • Planning Page
  • Grade 1
  • Cluster A: Represent and solve problems involving addition and subtraction.
  • Cluster B: Understand and apply properties of operations and the relationship between addition and subtraction.
  • Cluster C: Add and subtract within 20.
  • Cluster D: Work with addition and subtraction equations.
  • Sample Planning Page: Operations and Algebraic Thinking, Grade 1, Cluster C
  • Planning Pages
  • Grade 2
  • Cluster A: Represent and solve problems involving addition and subtraction.
  • Cluster B: Add and subtract within 20.
  • Cluster C: Work with equal groups of objects to gain foundations for multiplication.
  • Sample Planning Page: Operations and Algebraic Thinking, Grade 2, Cluster A
  • Planning Pages
  • Reflection Questions: Operations and Algebraic Thinking
  • Part 3. Number and Operations in Base Ten
  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Work with numbers 11–19 to gain foundation for place value.
  • Sample Planning Page: Number and Operations in Base Ten, Kindergarten, Cluster A
  • Planning Page
  • Grade 1
  • Cluster A: Extend the counting sequence.
  • Cluster B: Understand place value.
  • Cluster C: Use place value understanding and properties of operations to add and subtract.
  • Sample Planning Page: Number and Operations in Base Ten, Grade 1, Cluster C
  • Planning Pages
  • Grade 2
  • Cluster A: Understand place value.
  • Cluster B: Use place value understanding and properties of operations to add and subtract.
  • Sample Planning Page: Number and Operations in Base Ten, Grade 2, Cluster B
  • Planning Pages
  • Reflection Questions: Number and Operations in Base Ten
  • Part 4. Measurement and Data
  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Describe and compare measurable attributes.
  • Cluster B: Classify objects and count the number of objects in each category.
  • Sample Planning Page: Measurement and Data, Kindergarten, Cluster A
  • Planning Pages
  • Grade 1
  • Cluster A: Measure lengths indirectly and by iterating length units.
  • Cluster B: Tell and write time.
  • Cluster C: Represent and interpret data.
  • Sample Planning Page: Measurement and Data, Grade 1, Cluster C
  • Planning Pages
  • Grade 2
  • Cluster A: Measure and estimate lengths in standard units.
  • Cluster B: Relate addition and subtraction to length.
  • Cluster C: Work with time and money.
  • Cluster D: Represent and interpret data.
  • Sample Planning Page: Measurement and Data, Grade 2, Cluster D
  • Planning Pages
  • Reflection Questions: Measurement and Data
  • Part 5. Geometry
  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Cluster A: Identify and describe shapes.
  • Cluster B: Analyze, compare, create, and compose shapes.
  • Sample Planning Page: Geometry, Kindergarten, Cluster A
  • Planning Pages
  • Grade 1
  • Cluster A: Reason with shapes and their attributes.
  • Sample Planning Page: Geometry, Grade 1, Cluster A
  • Planning Page
  • Grade 2
  • Cluster A: Reason with shapes and their attributes.
  • Sample Planning Page: Geometry, Grade 2, Cluster A
  • Planning Page
  • Reflection Questions: Geometry
  • Resources
  • Table 1. Addition and Subtraction Situations
  • Table 2. Addition and Subtraction Fact Strategies
  • Table 3. Scaffolding Addition and Subtraction
  • Table 4. Sample Addition and Subtraction Strategies
  • Table 5. Standards for Mathematical Practice
  • Table 6. Effective Teaching Practices
  • Reproducibles
  • Reproducible 1. Five Frame
  • Reproducible 2. Ten Frame
  • Reproducible 3. Double Ten Frame
  • Reproducible 4. Hundreds Chart
  • Reproducible 5. Dot Cards
  • Reproducible 6. Numeral Cards
  • Reproducible 7. Number Line to 20
  • Reproducible 8. Open Number Line
  • Reproducible 9. Part-Part-Whole Chart
  • Reproducible 10. Place Value Chart (Tens/Ones)
  • Reproducible 11. Place Value Chart (Hundreds/Tens/Ones)
  • Reproducible 12. Comparison Cards
  • Additional Resources
  • About the Authors

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