Primary Numeracy Intervention Program (K–3) FREE
Primary Numeracy Intervention Program
In early elementary education, a gap in math understanding isn't just a temporary hurdle — it's a structural flaw. When a second-grader struggles with multi-digit subtraction, the root cause is rarely the subtraction itself. More often, it's a breakdown in backward counting sequences or number relationships that should have been established in Kindergarten.
The Primary Numeracy Intervention Program (PNIP), developed by Numeracy Consultants, offers a research-informed, diagnostic-first approach to rebuilding these foundations. By targeting the load-bearing skills of early numeracy, PNIP moves students from counting on fingers to true mathematical fluency — and gives educators the tools to make it happen starting day one.
Why Standard Math Curricula Often Fail At-Risk Learners
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 — whether that's numeral identification, spatial pattern recognition, or the inverse relationship between addition and subtraction. From there, instruction becomes targeted, intentional, and measurably effective.
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.
The 4 Pillars of the Primary Numeracy Framework
The Primary Numeracy Diagnostic Assessment
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 below and preview the diagnostic approach before watching the training — no login required.
The 5 Domain Instructional Roadmap
PNIP follows a logical, research-aligned progression across five domains that mirrors cognitive development in early numeracy. Instruction begins with numeral identification, ensuring students can recognize and interpret numbers before operating with them. From there, the program moves into counting by ones and tens, building the mental number line that underpins all future operations.
Part-whole understanding comes next, developing the relational thinking students need to move beyond counting as their primary strategy. Addition and subtraction strategies follow, giving students a repertoire of efficient, conceptually grounded approaches to operations. The progression culminates in place value, where students learn to compose and decompose numbers in ways that support multi-digit thinking and set the stage for everything that follows.
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 →
The CRA Instructional Model
Every lesson in the PNIP eLibrary 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 RTI 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.
Who Is PNIP Designed 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 with built-in progress monitoring and documentation.
What You Get — Free After Completing the Training
After watching the two-hour free training, participants receive immediate access to over 100 ready-to-use resources including the Primary Numeracy Diagnostic Assessment, the Primary Numeracy Framework, the Counting eLibrary (1.0 and 2.0), leveled workbooks, lesson templates, a leveled activities guide, and dozens of printable intervention materials. Additional supplemental lesson libraries and workbooks are available for purchase.
How PNIP Fits Your MTSS 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.
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.