At Harrow Shanghai, Primary Mathematics helps children become confident learners who can calculate accurately, explain their thinking and apply their knowledge to solve problems. Learning develops progressively across the year groups, from practical exploration of numbers and shapes to increasingly complex calculations, reasoning and problem-solving.
Making understanding visible
Our skills overviews make this progression visible to families. Classroom resources support children in discussing mathematical ideas, checking their understanding and reflecting on their next steps.
We use the Concrete–Pictorial–Abstract (CPA) approach to help children understand mathematical ideas, and they can revisit objects and pictures whenever these help them explain or solve a problem.
The CPA approach
Objects
Children handle objects such as counters, cubes or place-value equipment to explore a concept.
Pictures
Children represent their thinking through drawings, ten frames, part–whole models, arrays or number lines.
Numbers & symbols
Children connect this understanding to numerals, symbols and equations.
Language, vocabulary and deeper thinking
Mathematical talk and vocabulary. Precise language helps children communicate their ideas. Bilingual sentence stems support pupils as they explain, agree, challenge, clarify, build on an idea and evaluate their learning.
Reasoning and deeper thinking. Questioning prompts and reflection tools encourage pupils to explain their strategies, spot errors and justify answers.
Higher-order thinking ladder
- Remember
- Understand
- Apply
- Analyse
- Evaluate
- Create
- These are thinking processes, not labels for pupils’ ability.
Assessment and homework
Assessment | When / purpose |
|---|---|
NTS Mathematics | Three times a year: review attainment and progress, identify next steps. |
White Rose end-of-unit | At the end of a unit: check understanding and identify gaps in that topic. |
Entry tickets | At the start of learning: check current understanding and inform teaching. |
My NTS Targets sheet | Record targets and planned actions for Assessment Points 1, 2 and 3. |
Homework combines written practice with IXL. Our homework booklets are differentiated using chilli levels, so children can consolidate their learning and encounter an appropriate level of challenge.
Mathematics across the Primary School
Year 1
Number through counting, exploration and pictures.
Year 2
Fluency to 100 and the beginnings of explanation.
Year 3
Three-digit numbers and written methods.
Year 4
Larger numbers, fractions and decimals.
Year 5
Efficient methods and multi-step problems.