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PAT Rational Number is a low-stakes, formative, standardised assessment for Years 3-10 that focuses specifically on rational number. It sits within the wider PAT Pāngarau, and provides an in-depth examination of this critical aspect of mathematics.
This is a computer-adaptive assessment that is available online-only through NZCER Assist. Ākonga will complete approximately 30 questions that are automatically tailored to ākonga levels of achievement from a larger bank of questions. Most questions are in selected response formats, such as multiple choice or drag and drop. There are also some short constructed response questions.
All questions are scored automatically, with comprehensive reporting available in NZCER Assist to support interpretation and inform next teaching steps.
Like all PATs, Rational Number should be used formatively in a low-stakes environment. It should sit alongside classroom observations, rich learning conversations, and teacher-designed assessments as part of a broad, balanced approach to understanding learners and learning. Kaiako can use this assessment information to:
- Inform classroom programmes and school-wide planning
- Plan targeted teaching
- Guide day-to-day teaching decisions
- Support ākonga learning conversations
- Understand the impact of teaching and interventions
For further information, please see Understanding PATs - for parents and the community, which explains what PATs assess and how they are marked. Or click here for our extensive PLD support for PATs!
Features and benefits of PAT Rational Number
- Standardised, online rational number assessment for Years 3-10
- Locally designed and maintained by NZCER’s assessment experts
- Automated reporting, including individual reports, group / class reports, year level reports and item-level reports
- A robust, reliable measurement scale for student progress over time (including year to year) with regularly updated national norms
- Can be used any time of the year
What is in the Rational Number assessment?
The Rational Number assessment focuses on the big ideas involved in understanding and using rational numbers. It has been carefully designed to reflect the expectations for what ākonga should know, understand, and be able to do, as described in Phases 1 to 4 of the mathematics and statistics learning area of Te Mātaiaho | The New Zealand Curriculum.
Rational number is a domain of knowledge and skills that includes fractions, decimals, percentages, and ratios. According to The New Zealand Curriculum, rational number understanding develops progressively through the phases:
- In Phase 1 (Years 0–3), ākonga develop understanding of fractions as multiplicative part–whole relationships. They represent simple fractions, interpret numerators and denominators, compare and order fractions, and use them to describe parts of sets, regions, and measures. They add and subtract fractions with the same denominator and connect fractions to multiplication and division to find fractional parts and determine wholes.
- In Phase 2 (Years 4–6), ākonga extend multiplicative reasoning across fractions, decimals, and percentages. They understand decimals as base-10 fractions, represent and compare numbers to three decimal places, and convert between forms. They recognise equivalent fractions and mixed numbers, use common fraction–decimal–percentage equivalents, and add and subtract fractions and decimals. They use percentages to compare quantities to a whole, supporting emerging proportional reasoning.
- In Phase 3 (Years 7–8), ākonga strengthen connections between fractions, decimals, and percentages through more complex representations and operations. They work with powers of 10 and expanded form, add and subtract decimals and fractions with different denominators, and use multiple representations to compare, convert, and relate quantities. They apply proportional reasoning in problems involving percentages, ratios, and rates.
- In Phase 4 (Years 9–10), ākonga work flexibly with rational numbers, including recurring decimals, and reason about equivalence, density, and number line representation. They apply proportional reasoning in increasingly complex contexts, including rates and proportional change, and connect rational number understanding to algebraic representations and relationships. They use these ideas to interpret and solve problems across a range of real-world contexts.
How to access PAT Rational Number
As an online-only assessment, Rational Number is only available through our NZCER Assist platform. Schools must sign up and log in to NZCER Assist to subscribe to PAT Rational Number. There are no subscription or per assessment usage fees for PAT Rational Number for Term 3, 2026.
If you have not used NZCER Assist before, you can begin by contacting our Assessment Services team and they will help you get set up.
NZCER Assist also gives schools our comprehensive diagnostic reporting and ongoing support from our Assessment Services team.