Math in Practice: A Grade-by-Grade Guide for Teachers

Math in Practice, the new resource from Susan O’Connell and colleagues, is a comprehensive, grade-by-grade resource designed to fit with any math program or resource you are using. It is not a curriculum. It identifies the big ideas of both math content and math teaching and shares key instructional strategies—and why those strategies matter. Math in Practice will support teachers, administrators, and entire school communities as they rethink the effective teaching of mathematics in grades K–5.

  • Overview

    Math in Practice

    Math in Practice is a comprehensive, grade-by-grade professional learning resource flexibly designed to fit with any math program you are using. It's not another curriculum or set of math worksheets—it's professional development in a book. Enhance your content knowledge and confidence teaching math with a resource designed with classroom teachers in mind.

    Practical, accessible, and classroom-tested, Math in Practice will help you:

    • Guide students into deeper math understanding
    • Respond to the challenges of your math curriculum
    • Support students who are struggling, excelling, and anywhere in between

    Download a Sampler  Preview Six K-5 Modules

  • Grade-Level Books

    Each grade-level book is organized into modules that carefully unpack the specific math content taught at each grade, K–5. Rather than being used in order, teachers can select modules as needed based on their curriculum map, areas of instructional focus, or reteaching needs.

    Every module provides:

    • insights about the key math ideas
    • teacher notes highlighting approaches for promoting student understanding
    • a wealth of classroom tasks and activities illustrating the specific strategies
    • an extensive collection of corresponding online resources

    Preview Six K-5 Modules

    Click below to see the full list of modules in each grade-level book:

    Kindergarten Modules

    Counting and Cardinality: Numbers 1–5
    Counting and Cardinality: Numbers 0–10
    Counting and Cardinality and Place Value: Numbers 0–20
    Counting Numbers
    Comparing Numbers 1–10
    Decomposing Numbers
    Understanding Addition
    Understanding Subtraction
    Understanding Facts
    Exploring Measurement
    Sorting and Classifying Objects
    Introducing Geometry
    Exploring Geometry

    Grade 1 Modules

    Addition Word Problems with Sums to 20
    Connecting Subtraction and Addition to Solve Word Problems
    Math Fact Understanding and Fluency: Expanding on +/-1, +/-0
    Math Fact Understanding and Fluency: +/-2
    Add and Subtract +/-10
    Add and Subtract Doubles
    Making Ten
    Counting and Understanding Place Value
    Exploring Addition and Subtraction with a Two-Digit Number
    Measuring Lengths with Indirect Comparisons
    Telling Time to the Hour and Half Hour
    Working with Money
    Represent and Interpret Data
    Understanding and Describing Shapes and Defining Attributes
    Partitioning Shapes into Halves and Fourths

    Grade 2 Modules

    Problem Solving
    Math Fact Understanding and Fluency
    Foundations for Multiplication: Equal Groups
    Place Value
    Compare Two Three-digit Numbers
    Understand Multi-digit Addition
    Understand Multi-digit Subtraction
    Extend Understanding of Multi-digit Addition
    Extend Understanding of Multi-Digit Subtraction
    Length Measurement
    Represent and Interpret Data
    Describing Geometric Shapes
    Partition Shapes

    Grade 3 Modules

    Understanding Multiplication and Division
    Understanding Properties of Multiplication and Division
    Fluently Multiply and Divide
    Solving One- and Two-Step Problems with All Four Operations
    Rounding Numbers to the Nearer Ten or Hundred
    Fluently Add Within 1,000
    Fluently Subtract within 1,000
    Understanding Fractions and Fraction Notation
    Fraction Equivalence
    Comparing Fractions
    Mass and Volume
    Represent and Interpret Data
    Understand the Concept of Area
    Understanding and Describing Shapes

    Grade 4 Modules

    Understanding and Solving Problems with Multiplicative Comparison
    Factors, Multiples, and Prime and Composite Numbers
    Understand the Place Value System
    Fluently Add and Subtract Multi-digit Numbers Using the Standard Algorithm
    Use Place Value to Perform Multi-digit Multiplication
    Use Place Value to Perform Multi-digit Division
    Equivalence and Ordering of Fractions
    Adding and Subtracting Fractions with Like Denominators
    Multiplying Fractions by Whole Numbers
    Understand Decimal Notation for Fractions
    Measurement and Measurement Conversions
    Area and Perimeter
    Represent and Interpret Data
    Geometry and Geometric Measurement
    Solving Complex Problems

    Grade 5 Modules

    Place Value
    Write and Interpret Numerical Expressions
    Multiplying with Multi-Digit Numbers
    Division with Multi-Digit Whole Numbers
    Addition and Subtraction of Decimals
    Multiplication and Division with Decimals
    Adding and Subtracting Fractions with Unlike Denominators
    Fractions as Division
    Multiplication of Fractions by Fractions and Whole Numbers
    Division with Whole Numbers and Unit Fractions
    Converting Like Measurement Units
    Represent and Interpret Data
    Geometric Measurement: Exploring Volume
    The Coordinate System
    Classify Two Dimensional Figures

  • Guide for Teachers

    The Guide for Teachers lays out big ideas in best-practice math instruction, including topics such as math talk, modeling, and differentiation.

    Topics addressed include:

    • Asking questions that stimulate student thinking
    • Making sense of and connections between mathematical ideas
    • Using representations and models effectively
    • Helping students communicate about math
    • Learning from meaningful formative assessment
  • Guide for Administrators

    The Guide for Administrators helps principals, coaches, and other leaders know what to look for in effective math classrooms and how to support teacher growth.

    Topics addressed include:

    • The importance of ongoing professional development
    • What to look for in the “new” math classroom
    • How to support teachers and promote effective instruction
    • Ideas for intervention and assessment across an entire school
    • Support for working with parents


Crosswalks and Standards Alignments

Alignments and crosswalks are organized by grade level (K-5) so you can see and study—by unit, lesson plan, or standard—where Math in Practice supports teachers and students.

Praise for Math in Practice

These materials are like Reading Strategies for math! As a literacy-oriented person, math concept development isn't second nature. Sue O’Connell's materials make it feel do-able. From her well-organized lesson examples, grade-by-grade learning progressions, and her accessible writing style coaching the reader through the thinking behind the lessons, every teacher will feel like they can pick up these materials, spend a few minutes getting oriented, and then jump into action in the classroom. My only complaint: Where was this when I was a classroom teacher?

Jen Serravallo Author of The Reading Strategies Book

What a wonderful resource! There is clear and helpful guidance on the core elements of math teaching—reasoning, connections, representations, and discourse. There is practical and powerful information on what to do and how to do it. In other words, Sue has written a great primer on what we need to know and be able to do in our elementary classrooms to be far more effective teachers of mathematics. What more could a teacher of K–5 math ask for?

Steve LeinwandAmerican Institutes for Research, author of Accessible Mathematics

I grew to believe I stunk at math. I couldn’t memorize times-tables or geometric equations. Math, it seemed, was about knowing—not understanding. This is where Sue O’Connell’s Math in Practice offers an important opportunity for change. The pages of this collection ring with a student-centered, teacher-empowering heart. Sue, as a friendly and knowledgeable mentor, models differentiated approaches for truly understanding key grade-level mathematical concepts. You then leave each section feeling empowered to do the same for students.

Chris LehmanFounding Director of The Education Collaborative, coauthor of Falling in Love with Close Reading

What a resource! The tone of each module in every grade-level book is helpful, supportive, and should make any teacher feel it was written for them—and it was. There is no doubt that classroom teachers will want to take their grade-level book home with them every night! They are that helpful. The mathematics content presented is continuously connected to problem-based contexts throughout each grade-level book and regular use of important representations—visual or manipulative—is another key feature of the Math in Practice materials. Each module’s attention to “Ideas for Instruction and Assessment” is particularly important as a way to recognize and value, regularly, that instruction and assessment are linked, not apart

Francis (Skip) Fennell L. Stanley Bowlsbey Professor of Education Emeritus;
Project Director, Elementary Mathematics Specialists and Teacher Leaders Project, McDaniel College; Past President of NCTM