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

Concrete

Objects

Children handle objects such as counters, cubes or place-value equipment to explore a concept.

Pictorial

Pictures

Children represent their thinking through drawings, ten frames, part–whole models, arrays or number lines.

Abstract

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.