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The Foundations of Numeracy:
A PK–5 Math Framework

Download the Framework View the Social Toolkit

Content

The mathematical “what” of elementary learning.

Integers

Know symbols for quantities, place value, the four operations, and estimation.

Fractions

Use rational numbers to represent parts and proportional relationships.

Shapes

Describe and measure the physical world using geometric and quantitative characteristics.

Data

Represent, interpret, and communicate numerical data visually and with words.

Competencies

All four are mutually reinforcing.

Conceptual Understanding​

Demonstrate number sense; comprehend the principles behind mathematical concepts.​

Fact Fluency​

Use math facts with confidence and fluidity.​

Procedural Fluency​

Execute operations accurately and efficiently.​

Application

Use math in real-world situations, such as money, time, and distance.​

ways of thinking

The cognitive approaches that power mathematical reasoning.

Symbolic Understanding

Represent quantities and mathematical ideas using symbols and diagrams.

Pattern Recognition

Notice and use patterns to understand mathematical structure, generalize, and act accordingly.

Explaining

Articulate mathematical and numerical reasoning in words.

Sense-Making

Interpret mathematical problems, understand what is important to consider, and decide what strategies to use.

Motivators

What drives learning: engagement and belief in our potential.

We Are All “Math People”

Believe in the innate ability of humans to understand mathematical ideas.

Persistence Counts

Have a growth mindset and know that effort leads to learning.

Math is Mind-Blowing

Appreciate the power and beauty of mathematics.

Math Is Everywhere

Recognize the relevance and widespread utility of math.

Content

The mathematical “what” of elementary learning.

Integers

Know symbols for quantities, place value, the four operations, and estimation.

Fractions

Use rational numbers to represent parts and proportional relationships.

Shapes

Describe and measure the physical world using geometric and quantitative characteristics.

Data

Represent, interpret, and communicate numerical data visually and with words.

Competencies

All four are mutually reinforcing.

Conceptual Understanding​

Demonstrate number sense; comprehend the principles behind mathematical concepts.​

Fact Fluency​

Use math facts with confidence and fluidity.​

Procedural Fluency​

Execute operations accurately and efficiently.​

Application

Use math in real-world situations, such as money, time, and distance.​

ways of thinking

The cognitive approaches that power mathematical reasoning.

Symbolic Understanding

Represent quantities and mathematical ideas using symbols and diagrams.

Pattern Recognition

Notice and use patterns to understand mathematical structure, generalize, and act accordingly.

Explaining

Articulate mathematical and numerical reasoning in words.

Sense-Making

Interpret mathematical problems, understand what is important to consider, and decide what strategies to use.

Motivators

What drives learning: engagement and belief in our potential.

We Are All “Math People”

Believe in the innate ability of humans to understand mathematical ideas.

Persistence Counts

Have a growth mindset and know that effort leads to learning.

Math is Mind-Blowing

Appreciate the power and beauty of mathematics.

Math Is Everywhere

Recognize the relevance and widespread utility of math.

Why Do We Need A Framework?

Across the country, states and districts are prioritizing math across prekindergarten through grade 5 as student performance falters. Yet despite growing attention, the field lacks a shared definition of what “numeracy” truly means in the elementary grades.

Developed in collaboration with leading experts and grounded in more than 200 research studies, the framework outlines four cornerstones and 16 essential building blocks for PreK–5 math learning. Designed for teachers, leaders, families, and policymakers alike, it offers a shared, research-based roadmap to help every student build strong mathematical foundations.

Decades of Research, One Comprehensive Framework

Research shows that elementary math proficiency is one of the strongest predictors of later school achievement, even more so than reading. Students who develop conceptual understanding, fluency, and reasoning skills by grade five are better prepared for advanced mathematics, better positioned for long-term academic success, and more likely to access future opportunities. Much like Scarborough’s Reading Rope helped teachers align around the essential components of literacy, the Foundations of Numeracy offers a unifying structure to clarify what strong numeracy development requires.

The Science Behind Strong Mathematical Foundations

The Foundations of Numeracy framework identifies exactly what students need by middle school: 16 evidence-backed building blocks organized into four cornerstones. Rather than advancing a single instructional approach, the framework integrates insights from over 200 studies across disciplines.

Competencies

Conceptual Understanding

Fact Fluency

Application

Procedural Fluency

Content

Whole Numbers

Fractions

Shapes

Data

ways of thinking

Abstract Thinking

Sense-making

Pattern Recognition

Explaining

Motivators

We are all “math People”

Persistence Counts

math is mind-blowing!

math is everywhere

A Path to Coherence

Unlike abstract academic theories, this framework offers true alignment; not on how to teach, but on what every elementary student must develop to build lasting mathematical understanding. It provides a clear, research‑grounded structure that brings coherence to instruction, curriculum, and decision‑making across PK–5.

Uniting the Field Around Evidence

The framework brings coherence to a field long marked by fragmentation. It serves multiple stakeholders from education leaders directing resources to policymakers shaping early math priorities by grounding their work in a shared, research‑based understanding of numeracy. With a common evidence‑aligned foundation, the field can now move in the same direction to ensure every student builds the mathematical understanding they need to thrive.

Rethinking What Matters in PK–5 Math

cornerstone
traditional
approach
Framework
approach
classroom
impact
content
Emphasis on coverage
over coherence
Focus on core ideas
that build over time
Strong foundation for
future learning
competencies
Treats fluency and
understanding as
separate
Supports fluency
through deep
understanding
Flexible, confident
problem solvers
ways of thinking
Little reasoning or
explanation required
Encourages sense-
making, strategy, and
justification
Teachers see how
students think
motivators
Math feels abstract
and disconnected
Joyful connections to
the real world
Increased student
engagement and
math identity
cornerstone
traditional approach
content
Emphasis on coverage over coherence
competencies
Treats fluency and understanding as separate
ways of thinking
Little reasoning or explanation required
motivators
Math feels abstract and disconnected
cornerstone
Framework Approach
content
Focus on core ideas that build over time
competencies
Supports fluency through deep understanding
ways of thinking
Encourages sense-making, strategy, and justification
motivators
Joyful connections to the real world
cornerstone
classroom Impact
content
Strong foundation for future learning
competencies
Flexible, confident problem solvers
ways of thinking
Teachers see how students think
motivators
Increased student engagement and math identity

Recognized by Math Leaders

Educators are tasked with meeting the math needs of all students, and many students experience difficulty with math. The Foundations of Numeracy could be used as a tool to help educators think practically about essential math skills for students so educators can provide evidence-based instruction for students.

Sarah R. Powell
Ph.D.
The University of Texas at Austin

The Foundations of Numeracy expands the definition of early math beyond procedures. It invites students into a space for deep thinking, creativity, and exploration. By illuminating the importance of reasoning and mindset, the framework supports lasting understanding and helps students develop a strong, positive mathematics identity.

Dr. Jo Boaler
Cofounder, youcubed and Struggly
Nomellini and Olivier Professor, Stanford University

Numeracy matters as much as literacy. Families and educators know this. The goal in creating the Foundations of Numeracy was to synthesize the vast research base into a memorable, practical framework that could help anyone in the education field improve elementary math outcomes for students.

Gloria Lee
Lead Author, Foundations of Numeracy
Stanford Graduate School of Education