Free K–3 Math Intervention | Primary Numeracy Program
The Primary Numeracy Intervention Program (PNIP) is a free K–3 math intervention program that uses one-on-one diagnostic assessment to identify the exact foundational gaps causing math struggles in early learners — and provides leveled instructional materials to address them systematically. Designed for classroom teachers, interventionists, and MTSS coordinators, PNIP gives educators over 100 ready-to-use resources at no cost after completing a free two-hour online training. All core program components are free — including the diagnostic assessment, learning framework, leveled activities guide, and dozens of printable resources. Supplemental lesson libraries and workbooks are available for purchase separately.
Free K–3 Math Intervention Program for MTSS and RTI
Why Standard Math Curricula Often Fail At-Risk Learners
In early elementary education, a gap in math understanding is rarely just a temporary hurdle — it is a structural flaw with a compounding effect. When a second-grader struggles with multi-digit subtraction, the root cause is almost never the subtraction itself. More often it is a breakdown in backward counting sequences or number relationships that should have been established in Kindergarten. One overlooked skill creates a gap. That gap creates another. By the time the deficit is visible in grade-level work, the original cause is several steps back and nearly impossible to identify without a diagnostic lens.
Most Tier 1 math programs move at a relentless pace, prioritizing coverage over mastery. For students in MTSS or RTI frameworks, this creates a snowball effect — each unresolved gap compounds the next, until a child who was only slightly behind in Kindergarten is significantly behind by second grade. PNIP shifts the focus from teaching the grade to teaching the child. Using a clinical interview-style diagnostic assessment, teachers can pinpoint exactly where a student's numerical logic breaks down and target instruction with precision.
Proven Results in the Classroom
The impact of the Primary Numeracy Intervention Program is backed by real classroom data. In a documented case study, students using PNIP demonstrated significant measurable growth in foundational numeracy skills over a single intervention period — results that speak directly to the program's diagnostic-first, research-aligned approach.
How Does the Primary Numeracy Intervention Program Work
What Does the Primary Numeracy Diagnostic Assessment Measure?
This is not a traditional paper-and-pencil test. It is a one-on-one observation tool that uncovers the how behind a student's answer. Does the student count from one? Do they count on? Do they use a known fact? This diagnostic data is then plotted on the Primary Numeracy Framework to identify each student's exact instructional starting point — eliminating guesswork and ensuring that every minute of intervention time is used efficiently.
Unlike standardized assessments that tell you what a student got wrong, the Primary Numeracy Assessment reveals why. It captures the reasoning process behind each response, giving teachers a precise picture of where a student's numerical understanding breaks down and exactly what needs to be taught next. Administered one-on-one in approximately 15–20 minutes, it is designed to be practical for classroom teachers and interventionists alike — not just specialists.
Download the Primary Numeracy Assessment above and preview the diagnostic approach before watching the training — no login required.
What Are the 5 Domains of the Primary Numeracy Framework?
The Primary Numeracy Framework follows a research-aligned progression across five domains that mirrors how number sense actually develops in young children — not how it is sequenced in a textbook. What sets it apart from most intervention tools is its dual focus: it measures both the foundational competencies students need to have automated, such as numeral identification and counting sequences, and the mathematical reasoning that determines whether those skills translate into genuine understanding. Knowing what a student can recall is only half the picture. Knowing how they think about numbers is what makes instruction precise.
Once the diagnostic assessment is complete, teachers plot each student's results directly onto the Primary Numeracy Framework — creating a visual map of exactly where a student's understanding is solid, where it breaks down, and what needs to be taught next. This plotting process transforms raw assessment data into an individualized curriculum path, giving teachers a clear, actionable starting point for every student without guesswork.
The five domains follow a deliberate developmental sequence. Numeral identification comes first — students must be able to recognize and interpret numbers before they can be expected to operate with them meaningfully. Counting by ones and tens follows, building the mental number line that underpins every operation that comes after it. Part-whole understanding develops next, giving students the relational thinking they need to move beyond counting as their primary strategy and begin reasoning about how numbers relate to each other. Addition and subtraction strategies build on that foundation, equipping students with a repertoire of efficient, conceptually grounded approaches to operations rather than a single procedure to memorize. The progression culminates in place value — where students learn to compose and decompose numbers in ways that support multi-digit thinking and establish the groundwork for everything that follows in upper elementary mathematics.
For a full review of the research underlying each domain of the Primary Numeracy Program, including studies by Fuson, Baroody, and Steffe, visit our Research Foundation page →
What Instructional Model Does PNIP Use
Every lesson in the PNIP eLibrary and free Leveled Activities Guide is built around the Concrete-Representational-Abstract instructional sequence — one of the most well-researched frameworks in mathematics education. Students first work with physical manipulatives such as counters and beads, then move to visual representations like sketches and ten frames, before arriving at abstract number sentences and symbolic notation. This progression ensures conceptual understanding is built before procedural fluency is expected — a critical distinction for students who have previously been pushed to abstract work before they were ready.
Progress Monitoring and Documentation
Built-in tracking tools make IEP data collection and MTSS reporting straightforward and consistent. Teachers can document student growth in real time, ensuring interventions remain data-driven and that evidence of progress is always at hand for team meetings, parent conferences, and compliance documentation.
Because the Primary Numeracy Assessment measures discrete, observable skills rather than broad achievement levels, the data it generates is specific enough to inform individualized goals and precise enough to demonstrate movement over short intervention windows — exactly what special education teams and MTSS coordinators need when making placement and programming decisions.
Who is it for, What do i get, How does it fit with mtss
Who Is the Primary Numeracy Intervention Program For?
The Primary Numeracy Intervention Program is built to serve the full range of educators working with struggling K–3 math learners. Classroom teachers can use it to differentiate Tier 1 instruction and identify students who need additional support. Interventionists and specialists will find the diagnostic tools and leveled materials ready to use in small group or one-on-one pull-out settings. Instructional coaches can use the framework to anchor school-wide math intervention conversations, and administrators will find that PNIP integrates cleanly into any existing MTSS structure.
What Do Teachers Get for Free with the Primary Numeracy Program?
Watch the free 2-hour training and get immediate access to over 100 ready-to-use resources, including:
- Primary Numeracy Diagnostic Assessment
- Primary Numeracy Framework
- Leveled Activities Guide
- Counting eLibrary (1.0 & 2.0)
- Leveled workbooks & lesson templates
- Dozens of printable intervention materials
- Free access to our games page, with games designed to align with each level of the program
Looking for more? Additional supplemental lesson libraries and workbooks are available for purchase.
How Does PNIP Fit Into an MTSS or RTI Framework?
PNIP is designed to align with any Multi-Tiered System of Support. The diagnostic assessment functions as a universal screening tool, the leveled materials support differentiated instruction across Tier 1, Tier 2, and Tier 3 settings, and the built-in progress monitoring ensures seamless documentation at every level. Whether you are implementing school-wide intervention or supporting a single student, PNIP scales to meet the need.
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Frequently Asked Questions About the Primary Numeracy Program
Is the Primary Numeracy Intervention Program really free?
Yes. The core program — including the diagnostic assessment, Primary Numeracy Framework, leveled activities guide, and over 100 ready-to-use resources — is completely free after watching a two-hour online training. There are additional supplement lessons and workbooks that can be purchased to support the program, but the core components are all free. No login, subscription, or credit card is required.
What grades is PNIP designed for?
PNIP is designed for Kindergarten through Grade 3. It targets the foundational numeracy skills that must be established in early elementary in order to support success in later mathematics.
How long does the diagnostic assessment take to administer?
The Primary Numeracy Assessment is administered one-on-one and takes approximately 15–20 minutes per student. It is designed to be practical for classroom teachers and interventionists, not just specialists.
How is PNIP different from a standard math curriculum?
Unlike grade-level curricula that prioritize content coverage, PNIP identifies where a student's numerical understanding actually breaks down and targets instruction at that point — regardless of grade level. It is designed to address the root cause of math struggles, not the surface-level symptom.
Does PNIP work within a special education or IEP setting?
Yes. The built-in progress monitoring tools generate the specific, measurable data needed for IEP goals and MTSS documentation. The discrete skill tracking makes it easy to demonstrate growth over short intervention windows.
What is the CRA model used in PNIP lessons?
CRA stands for Concrete-Representational-Abstract. Students first work with physical manipulatives, then visual representations, then abstract number notation. This sequence is one of the most well-researched frameworks in mathematics education and ensures conceptual understanding is built before procedural fluency is expected.
Can PNIP be used for Tier 1, Tier 2, and Tier 3 instruction?
Yes. The diagnostic assessment functions as a universal screener, the leveled materials support differentiated instruction across all three tiers, and the progress monitoring tools provide documentation at every level.
Research Foundation
The Primary Numeracy Intervention Program is grounded in decades of peer-reviewed research in mathematics education and cognitive development. The following studies inform the program's diagnostic approach, instructional sequence, and emphasis on foundational numeracy skills.
Counting and Number Sequence Development Fuson, K. C. (1988). Children's Counting and Concepts of Number. Springer-Verlag. — Foundational research establishing the developmental progression of counting sequences and their relationship to early arithmetic.
Backward Counting as a Predictor of Subtraction Success Lyons, I. M., & Beilock, S. L. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition, 121(2), 256–261. — Documents the critical role of number sequence fluency, including backward counting, in arithmetic development.
The CRA Instructional Model Witzel, B. S., Mercer, C. D., & Miller, M. D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research & Practice, 18(2), 121–131. — Validates the Concrete-Representational-Abstract sequence as an evidence-based approach for students with math learning difficulties.
Diagnostic Assessment and MTSS Fuchs, L. S., & Fuchs, D. (2007). A model for implementing responsiveness to intervention. Teaching Exceptional Children, 39(5), 14–20. — Establishes the framework for using diagnostic data to drive tiered intervention decisions within MTSS.
Place Value and Composing Numbers Ross, S. H. (1989). Parts, wholes, and place value: A developmental view. Arithmetic Teacher, 36(6), 47–51. — Examines how students develop place value understanding and the role of part-whole reasoning in that progression.
Standards-Based Assessment National Council of Teachers of Mathematics. (2014). Principles to Actions: Ensuring Mathematical Success for All. NCTM. — Provides the research-based framework for effective mathematics instruction and assessment aligned to the program's approach.