Math Expressions®

Build deep understanding with this essential inquiry-based mathematics curriculum

Mastering math starts with knowing the numbers. We get students started on the right path in Pre-K, but that's just the beginning. It’s also about looking beyond numbers to understand how and why they work, and learning to ask the questions that lead to a thoughtful, informed approach to solving problems.

Based on research funded by the National Science Foundation (NSF), Math Expressions is a proven Pre-K–6 curriculum that helps children make sense of math by exploring, discussing, and demonstrating their understanding of key concepts. In busy, active lessons, students learn how to look deeper and choose their own path to the answers—skills that will take them far beyond the math classroom.

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Every lesson integrates mathematical processes and practices.

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Students use authentic examples to make sense of mathematics.

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Schools see an average gain of 12–15% on state tests.

Looking deeper produces exceptional results

When children understand math, they’re not relying on memorization. They’re relying on themselves. Dr. Karen Fuson’s comprehensively researched approach to teaching math is based on the way children actually learn and is used across the country because it raises student achievement.

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A yearlong study of success

Students from eight schools across four states showed “statistically significant” improvement.

See what Math Expressions has in store for your classroom.

How to think about math

The deep conceptual understanding that’s the hallmark of the program leads to strong skills fluency and the ability to make generalizations within and among mathematical strands. As students grow and learn to think critically, teachers develop their own richer understanding of math through detailed instruction and embedded support.

Math Expressions is based on NSF-funded research.

  • Contextual Learning
    Students develop an understanding of mathematics through real-world situations and visual supports.
  • Multiple Strategies
    Students learn multiple ways to solve problems, including algorithms based on reasoning.
  • Manageable Instruction
    Teaching materials embody a "learn-while-teaching" style.
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Student Experience

Lessons build understanding through active inquiry.

  • Coherence 
    Students make connections between key topics both within and across grades.
  • Discourse 
    Math Talk gives students the chance to ask questions and use their MathBoards to explain and justify their solutions.
  • Practice 
    The online Student Activity Book gives young learners the tools to explore and deepen their understanding of key math concepts.

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Student technology builds understanding, practice, and problem solving.

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The Math Worlds augmented reality app gives students an amazingly interactive opportunity to apply what they’ve learned.

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Games in the online Math Activity Center develop fluency in math facts and operations.

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Students build concrete and pictorial relationships with digital manipulatives.

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Learners can download and practice working with content offline via HMH Player®.

Making teachers' lives easier by changing the learning landscape

Hear what Dr. Fuson thinks about early learning in mathematics and how it can help close the equity gap.

Early Learning Resources

Research tells us that students who start kindergarten with a high level of math understanding do better in both math and reading after kindergarten. With that in mind, we developed Math Expressions Early Learning Resources to provide early learners with the understanding they need to confidently take the first and subsequent steps of their mathematics journey.

  • Grounded in Research
    Students will benefit from teaching-learning paths and structured, repetitive experiences as recommended in “Mathematics Learning in Early Childhood: Paths toward Excellence and Equity.”
  • Rated as Strong by ESSA
    Early Learning Resources is based on the same ESSA strong foundation and research as the rest of Math Expressions, making it an ideal transitional program for pre-kindergarten early learners.
  • Focused on Numbers and Geometry
    Research guidelines led to a strong focus on numbers and geometry, content areas that are particularly important in early math instruction.
  • Hands-On
    Playful activities help children see, discuss, and use mathematical structures, building understanding and fluency gradually and systematically.
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Classroom Structures Support Understanding and Math Talk

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Students use colorful manipulatives and shape puzzle mats to develop a deep understanding of number and geometry concepts.

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Fun games and puzzle cards engage students and get them excited about mathematics.

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Daily routines include learning the count word sequence and relating to number symbols and quantities through patterns, fingers, and actions.

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Students take turns as student leaders, building confidence over time.

Teacher Experience

Math Expressions facilitates learning while teaching.

Professional development, classroom demonstration, and daily routine videos are at point of use in the Teacher Edition.

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Lessons include teaching and inquiry notes, visual models, and suggestions for Math Talk.

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Mathematical processes, practices, and learning progressions are featured in every lesson.

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Formative assessment reporting helps group students for instruction and identifies appropriate differentiation resources.

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Differentiated support to encourage all students.

  • Differentiated Instruction 

The Math Activity Center supports every child with Practice, Re-teach, and Challenge resources for each lesson.

  • Adaptive Practice

Customize instruction with the Personal Math Trainer® Powered by Knewton™, an online personalized learning and assessment system with real-time reporting and adaptive practice.

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Math Expressions classrooms are collaborative

Hear from a teacher about how Math Talk engages his class.


The instruction keeps students constantly moving forward while providing teachers with explicit support. Learn more about Dr. Fuson’s approach through the samplers below.


Dive deeper into the student components and teaching support.


See an example of a complete lesson from Grade 2 and from Grade 4.


Explore Pre-K, Transitional K, and 4K content.

  • Deepen mathematical understanding

    Students develop an understanding of the concepts behind the math and build connections between concrete, pictorial, and abstract relationships.

  • Develop critical-thinking skills

    Students learn to ask questions and use the answers to devise thoughtful, informed approaches to solving problems.

  • Enhance teacher effectiveness

    Teachers use the program’s extensive, lesson-by-lesson support to supplement and deepen their own mathematical understanding.

  • Increase student participation

    Math Talk classrooms create lively, collaborative environments where children share their ideas and solutions and listen respectfully to the ideas of their classmates.

  • Improve student performance

    Students learn to effectively communicate their mathematical understanding verbally and in writing.

Test drive Math Expressions.

Research & Results

The research driving Math Expressions gives students a full understanding of concepts behind the math and the tools to effectively express what they’ve learned. Learn more about what’s behind the program and its impact on students across the country.

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"All-Green" Rating from EdReports

Math Expressions Grades K-5 has been rated as Meets Expectations at Gateways 1, 2, and 3 by EdReports. Read the full review at

Strong ESSA Rating

Math Expressions received a Strong ESSA rating based on the distinctive amount and quality of professional learning that teachers receive as part of the Math Expressions program.

ESSA Evidence Criteria for Math Expressions


Math Expressions is based on the results of the NSF-funded Children’s Math Worlds research project, a 10-year study led by Dr. Fuson.

Math Expressions: Research Evidence Base

  • Report Type: Research Evidence Base
  • Grade Level: Elementary, Middle
  • Demonstrates a Rationale
  • Math

US Department of Education Institute of Education Sciences (IES): Achievement Effects of Four Early Elementary School Math Curricula: Finding for First and Second Graders (Year 2)

  • Report Type: Efficacy Study, Publication from External Organization, Study Conducted by Third Party
  • Grade Level: Elementary
  • District Urbanicity: Urban, Suburban
  • Strong Evidence
  • Math

Math Expressions: Impact Study, Grades 2 and 4 

  • Report Type: Efficacy Study, Study Conducted by Third Party
  • Grade Level: Elementary
  • Region: Midwest, West
  • District Urbanicity: Suburban, Rural
  • Demonstrates a Rationale
  • Math


See how Math Expressions supports the CCSS Operations and Algebraic Thinking Learning path.


Discover how the eight mathematical practices in the CCSS are supported by Math Expressions.


Learn how Math Expressions progresses from understanding to fluency.


Dr. Karen Fuson is a leading voice in math education today. Dr. Fuson has studied how children understand math ideas for more than 50 years. She designs teaching materials based on how children learn and understand, along with working in schools to help teachers support every child.

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Professor Emerita, Northwestern University

Related Solutions

We know success doesn’t come from one solution, but from a network of support. When you select a program from HMH®, it’s the start of a relationship—one that helps you implement and instruct that program in the ways that work best for your district, school, or classroom.

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Professional Services

Professional learning is included with Math Expressions to help teachers transition to the program’s new instructional model, technology, and teaching strategies.  

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GO Math!®

Students in Grades 6–8 continue to build and reinforce foundational math skills and seamlessly transition to GO Math! Middle School.

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Into AGA

A comprehensive, growth-oriented solution for students ready for Algebra 1, Geometry, and Algebra 2.

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Early Learning

Get students started on solid ground with programs designed to prepare them for learning success.

News & Events

Stay connected to the math community. From exclusive thought leadership to news and upcoming events, learn more about what’s happening in math today.

See how Math Expressions can work in your classroom.

See how Math Expressions can work in your classroom.

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