Cavendish Church of England Primary School

“Mathematics is a creative and highly interconnected discipline… A high-quality mathematics education therefore provides a foundation for understanding the world.”
National Curriculum for Mathematics

At Cavendish Church of England Primary School, we want every child to see themselves as a capable and confident mathematician.

We believe that mathematics is about much more than getting an answer. Children need secure knowledge and fluency, but they also need to understand why mathematics works, recognise connections, explain their thinking and apply what they know to increasingly challenging problems.

Our curriculum therefore develops three closely connected aspects of mathematics: fluency, reasoning and problem solving. These reflect the aims of the National Curriculum and enable children to build secure foundations while developing curiosity and confidence.

Mathematics reflects our school vision: We Learn. We Love. We Belong. Children learn to think carefully and persevere; they work collaboratively and listen to different mathematical ideas; and they develop confidence that mathematics is something in which everyone can participate and succeed.

Our Mathematics Curriculum

Our curriculum has been carefully designed for the mixed-age structure of Cavendish.

We use White Rose Education mixed-age schemes of learning as the main curriculum spine from Year 1 to Year 6. These provide a carefully sequenced progression through the National Curriculum using small steps that allow children to build secure understanding before moving on.

Alongside this, NCETM Mastering Number provides an important fluency spine. It is used in Reception, Years 1 and 2 and Years 4 and 5, while Year 3 follows a carefully planned Cavendish Ready-to-Progress fluency bridge to secure the essential knowledge needed for later Key Stage 2 mathematics.

We also use I See Reasoning resources selectively to strengthen mathematical talk, reasoning and depth once the central concept has been explicitly taught.

Together, these approaches provide a curriculum in which children know more, remember more and become increasingly able to use their mathematics flexibly.

Our Mixed-Age Class Structure

Robins – Reception, Year 1 and Year 2

Although children learn within one mixed-age class, their mathematical entitlement remains appropriate to their age and stage.

Reception follows NCETM Mastering Number as its core number curriculum. Children develop strong foundations in subitising, counting, comparison, composition, number patterns and early fluency.

Importantly, we do not use White Rose as the Reception mathematics scheme.

Because Mastering Number focuses predominantly on number, other essential areas of EYFS mathematics — including shape, space, pattern, positional language, measures and spatial reasoning — are deliberately planned through continuous provision, routines, adult interaction and short enhancements.

Years 1 and 2 follow the White Rose mixed-age curriculum for their main mathematics teaching while also receiving daily Mastering Number fluency. This strengthens number sense, composition, number facts and calculation fluency alongside the wider mathematics curriculum.

Wrens – Year 3 and Year 4

Wrens follow the White Rose Year 3/4 mixed-age curriculum, developing knowledge across place value, calculation, multiplication and division, fractions, decimals, measurement, geometry and statistics.

Year 3 pupils also follow our Cavendish Ready-to-Progress fluency bridge. This deliberately strengthens important additive and multiplicative facts, place value, calculation and mathematical relationships before children enter the formal Year 4/5 Mastering Number programme.

Year 4 pupils use NCETM Mastering Number at Key Stage 2, with a particular emphasis on multiplication facts, multiplicative structures and flexible thinking. This also supports children's readiness for the Year 4 Multiplication Tables Check.

Owls – Year 5 and Year 6

Owls follow the White Rose Year 5/6 mixed-age curriculum, developing increasingly sophisticated understanding of place value, the four operations, fractions, decimals, percentages, ratio, algebra, measurement, geometry and statistics.

Year 5 pupils continue with NCETM Mastering Number, deepening multiplicative understanding through scaling, divisibility, remainders, fractions as division and increasingly flexible use of known facts.

By Year 6, children increasingly draw upon this secure foundation to select efficient methods, explain relationships, solve multi-step problems and apply mathematics with greater independence.

Across all mixed-age classes, children may explore a shared mathematical concept, while numbers, representations, questioning, scaffolding and expectations are carefully adapted to each year group's curriculum.

Mastering Number and Fluency

Fluency is essential because children need secure mathematical knowledge available to them if they are to reason and solve problems successfully.

Our use of Mastering Number is therefore not an additional mathematics curriculum running separately from classroom teaching. It provides a short, regular fluency spine alongside the main curriculum.

Children develop:

secure number sense;
automatic recall of important facts;
understanding of number composition;
additive and multiplicative relationships;
flexible calculation; and
confidence in manipulating numbers.

The emphasis is not simply upon speed. We want pupils to become flexible and efficient, able to recognise relationships and use known facts to derive new ones. Our LTP explicitly maps how this develops from Reception through Year 5.

Concrete, Pictorial and Abstract Mathematics

Children develop secure mathematical understanding when they can connect practical experiences, visual representations and mathematical symbols.

Teachers therefore use carefully selected representations such as:

fingers and practical objects → five and ten frames → rekenreks → bead strings → part-whole models → bar models → place-value equipment → number lines → abstract notation

The aim is not for children to remain dependent upon equipment, but for representations to help them see mathematical structure.

As understanding becomes secure, children move increasingly confidently towards abstract mathematics while still selecting representations when these help them reason or explain. The LTP deliberately expects consistency in the representations children encounter across school.

Mathematical Reasoning

We want children to be able to explain how they know, not simply tell us an answer.

Reasoning is therefore woven through everyday mathematics rather than being saved for a separate challenge at the end of a lesson.

Teachers use questions and prompts such as:

What do you notice?
What is the same and what is different?
Which answer could be correct?
Explain the mistake.
Convince me.
How else could you represent this?

We use I See Reasoning to support this work, particularly for guided reasoning, same-day deepening, mathematical talk, retrieval and exploring misconceptions. In mixed-age classes, children may begin from the same visual prompt while the numbers, representations or sentence stems are adjusted according to year-group expectations.

Problem Solving

Mathematical knowledge becomes powerful when children can recognise when and how to use it.

Children therefore encounter both routine and non-routine problems throughout the curriculum.

Teachers explicitly model how to:

understand what a problem is asking;
identify relevant information;
choose an appropriate operation or strategy;
represent the mathematics;
break more complex problems into manageable steps;
check whether an answer is reasonable; and
explain and justify a solution.

As children's knowledge grows, they are increasingly expected to select methods independently and make connections between different areas of mathematics.

The Cavendish 5 in Mathematics

Our Cavendish 5 are particularly visible within mathematics.

Retrieval
Previously learned facts, vocabulary and representations are revisited frequently so that essential knowledge remains available and new concepts connect securely with prior learning.

I Do, We Do, You Do
Teachers explicitly model mathematical thinking and representations, work through examples with pupils and gradually move children towards independent application.

Purposeful Practice
Children practise sufficiently to develop fluency, but practice is carefully chosen to expose mathematical structure and connections rather than simply repeating large numbers of identical questions.

High-Quality Questioning
Teachers ask children to explain, compare, predict, justify and generalise. Questions are used both to identify misconceptions and to deepen understanding.

Feedback
Live marking and responsive feedback enable misconceptions to be addressed quickly, often while children are still working on the concept.

Mathematics in the Early Years

Mathematical learning in Reception is practical, playful and carefully planned.

NCETM Mastering Number provides the daily number spine. Through this, children develop deep understanding of numbers to 10, subitising, counting, comparison, composition, number bonds and numerical patterns.

However, mathematics happens throughout the Reception environment.

Continuous provision deliberately provides experiences involving:

repeating patterns;
sorting and matching;
2D and 3D shape;
construction;
spatial reasoning;
positional language;
length, height, mass and capacity;
time and sequencing; and
mathematical recording and explanation.

Children might compare quantities at snack time, explore capacity with water, use balance scales, create patterns with natural objects, build with three-dimensional shapes or follow routes and maps.

Adults use these experiences to introduce precise vocabulary and encourage children to notice, explain, predict and prove their thinking.

Mathematical Talk and Vocabulary

Mathematics has its own precise language.

Children are explicitly taught mathematical vocabulary and encouraged to use complete sentences when explaining their thinking.

Teachers model appropriate language and use stem sentences where these help pupils articulate mathematical relationships.

We want children to move beyond statements such as “I just know” towards explanations such as:

“I know this because…”
“I noticed that…”
“This representation shows…”
“The relationship stays the same because…”

Pupil talk is important evidence of understanding. Our planning therefore expects teachers to consider whether children can explain the mathematics, not simply complete the task.

Inclusion and High Expectations

Mathematics is for every child.

Where pupils have gaps in prerequisite knowledge, teachers use retrieval, additional modelling, carefully chosen representations, smaller steps and targeted practice to help them access new learning.

In our mixed-age classes, support may include adjusted number ranges, practical equipment, worked examples, vocabulary prompts and guided practice.

However, support does not mean reducing the mathematical ambition.

Children who grasp concepts quickly are encouraged to explore greater depth through reasoning, connections and increasingly sophisticated problems, rather than simply being accelerated onto new content. This reflects the National Curriculum expectation that depth should come before unnecessary acceleration.

Our aim is to adapt access while preserving the important mathematical thinking.

Assessment and Responsive Teaching

Assessment is an everyday part of mathematics.

Teachers use live marking, questioning, observation, pupils' explanations and work in books to understand what children know during lessons.

End-of-block checks and wider school assessment points provide additional information about what has been secured and where gaps remain. In Reception, assessment draws particularly upon observation, provision and children's mathematical talk and activity.

The long-term plan sets out our curriculum entitlement, but teaching remains responsive. Teachers may adjust timings when assessment shows that children require additional consolidation or when a mixed-age cohort has particular needs.

The key question is not simply “Have we taught it?” but “Do the children understand it securely enough to build upon it?”

Mathematics Across the Curriculum and Everyday Life

Mathematics helps children make sense of the world.

Children use mathematical knowledge in Science, Computing, Geography, Design and Technology and many aspects of everyday school life.

Measurement, money, time, data, scale, pattern and number provide opportunities for pupils to recognise that mathematics has a purpose beyond the mathematics lesson.

The National Curriculum describes mathematical confidence as essential to everyday life and important for science, technology, engineering and financial literacy.

We want children to notice mathematics around them, not simply within a workbook.

Mathematics and Our Christian Vision

Mathematics offers children opportunities to experience curiosity, perseverance, wonder and growth.

Learning mathematics sometimes involves uncertainty. A problem may not yield its solution immediately; a first approach may not work; another person's representation may reveal something we had not noticed.

We want children to develop the confidence to keep thinking, ask for help, listen to others and try another approach.

This reflects our Christian vision. Every child is valued, and mathematical ability is not something reserved for a small number of pupils who are simply “good at maths”.

We want our classrooms to be places where children feel safe to make mistakes, where different ways of thinking are respected and where success is celebrated as understanding grows.