Mathematics

Vision Statement

At Shaw Wood Academy we want children to see themselves as mathematicians who: are curious learners; can learn from mistakes; can make mathematical links with the real world; can rapidly recall mathematical facts and skills mentally; have built up confidence and an ambition to succeed; and achieve their full potential through determination and resilience.

Rationale

• We believe that every child can achieve.
• Concepts are broken down into progressive steps to build a solid foundation of deep mathematical understanding.
• Pupils’ mathematical fluency should be built without the need for rote learning.
• New concepts will be introduced using the Concrete-Pictorial- Abstract (CPA) approach
• Pupils learn to think mathematically to find patterns, connections and relationships between different concepts.

Intent

Our intent is for every pupil to develop a deep, secure and connected understanding of mathematics, enabling them to become confident, fluent and resilient mathematicians who can calculate efficiently, reason mathematically and apply their knowledge to solve problems.

This policy has been developed with reference to the NCETM Curriculum Prioritisation and National Curriculum (2014), alongside the principles of teaching for mastery. We recognise that mathematical fluency is built over time through carefully sequenced learning, where pupils develop a secure understanding of fundamental concepts before moving on to more complex ideas.

We aim to develop pupils’ conceptual understanding and procedural fluency alongside one another. In calculation, this means developing a range of efficient mental strategies, using informal methods of recording as an important bridge towards formal written methods, and ensuring that pupils understand the mathematical structures and relationships underpinning formal algorithms. Particular emphasis is placed on place value, so that pupils understand why written methods work rather than simply following a set of procedures.

Our approach embraces the concrete–pictorial–abstract (CPA) progression. Pupils will experience mathematical ideas through practical resources, visual representations and abstract notation, making connections between these representations and developing the confidence to move flexibly between them. This enables pupils to make sense of mathematical symbols and procedures and supports the development of long-term fluency.

We intend for pupils to become increasingly efficient and flexible in their choice of calculation methods. They will be taught to select an appropriate mental, informal or formal method for addition, subtraction, multiplication and division, and to explain and justify their choices. Automatic recall of key additive and multiplicative facts will be developed systematically, providing pupils with the foundational knowledge they need to focus their attention on reasoning, problem-solving and new mathematical concepts.

Our curriculum will reflect the principles of teaching for mastery, with pupils progressing through small, carefully connected steps and having sufficient time to develop and secure understanding. Key mathematical knowledge and concepts will be prioritised and revisited so that learning is retained and built upon across the primary years.

We also recognise that mathematical language and oracy are central to learning mathematics. Pupils will be encouraged to articulate their thinking, explain their methods, use precise mathematical vocabulary and listen and respond to the ideas of others. Through structured mathematical discussion and reasoning, pupils will develop the ability to communicate their understanding as well as demonstrate it.

Ultimately, we want every pupil to leave primary school with a secure mathematical foundation, strong number sense, fluent calculation skills and the confidence to reason, communicate and solve problems. We aim to develop learners who understand mathematics rather than simply perform it, and who can apply their knowledge flexibly and confidently in unfamiliar contexts.

Implementation

Our mathematics curriculum is implemented through a carefully sequenced approach that draws on the NCETM Curriculum Prioritisation, the National Curriculum, the DfE Ready to Progress Criteria, Mastering Number and selected resources and materials from Oak Academy. These sources are used alongside the principles of teaching for mastery to ensure that learning is coherent, progressive and appropriately challenging.

Teachers use the NCETM curriculum prioritisation to identify and sequence the most important mathematical knowledge and concepts, ensuring that key learning is revisited and secured over time. The National Curriculum provides the statutory framework for the knowledge and skills pupils are expected to develop, while the Ready to Progress Criteria support teachers in identifying the essential knowledge and understanding that pupils need to secure at each stage.

Lessons are structured around small, connected steps, with opportunities for pupils to develop conceptual understanding, procedural fluency, reasoning and problem-solving. Teachers make purposeful use of concrete resources, pictorial representations and abstract notation, selecting representations and models that help pupils understand mathematical structures and make connections between ideas.

Oak Academy materials may be used selectively to complement the curriculum, provide additional explanations and representations, support lesson planning, or address particular learning needs. Resources are adapted and combined by teachers rather than followed as a standalone scheme, ensuring that teaching remains responsive to the needs of our pupils and consistent with our curriculum priorities.

Assessment is used formatively to identify misconceptions, inform subsequent teaching and ensure that pupils have secured key knowledge before moving forward. Where pupils require additional support or further challenge, teaching is adapted to enable all pupils to make progress while maintaining high expectations.

Through this approach, we aim to ensure that mathematics is taught consistently across the school while allowing teachers the professional flexibility to respond to their pupils. The curriculum is therefore not dependent on a single scheme, but is underpinned by clear mathematical principles, carefully prioritised content and a shared understanding of effective mathematics teaching.

Calculation Policy

The progression of calculation across addition, subtraction, multiplication and division is aligned with the National Curriculum. Calculations are taught using a combination of mental and written methods, informed by NCETM guidance and supported by clear concrete and pictorial representations.

The consistent use of the Concrete–Pictorial–Abstract (CPA) approach supports children in developing a deep conceptual understanding of calculation and enables them to progress towards efficient and reliable methods. This approach also helps to develop children’s confidence and fluency in both mental and written calculation.

The following section has been taken from the Formal Written Methods Policy for Shaw Wood Academy. This document also provides teachers with clear examples as well as links to video guidance of how to model each method to ensure consistency in the teaching and recording of written calculation methods across the school.

Mastering Number

In Reception and Key Stage 1, we use the NCETM’s Mastering Number programme alongside our mathematics curriculum to develop strong foundations in number. Through short, regular sessions, pupils develop fluency and flexibility with number, including subitising, counting, composition, comparison and additive structures.

From September 2027, Mastering Number will become embedded in KS2. At KS2, Mastering Number is essentially about keeping the focus on strong number sense, rather than children simply learning procedures.

It helps pupils to:

• secure and recall important number facts;
• understand place value and how numbers are composed;
• make connections between different mathematical ideas;
• choose efficient calculation strategies;
• explain their thinking and reason mathematically;
• address gaps in foundational knowledge that may hold them back.

In simple terms: it helps children become more fluent and flexible with number, so they can use their knowledge to tackle more complex KS2 mathematics.

The programme uses concrete resources, visual representations and mathematical discussion to help pupils understand the relationships between numbers and develop efficient strategies for calculation. It supports the development of secure number sense and automatic recall of key facts, providing a strong foundation for later mathematical learning.

As a result, pupils become increasingly confident and efficient when working with number, are able to make connections between known and unknown facts, and develop the reasoning and calculation skills needed to access the wider mathematics curriculum.

Concrete, Pictorial and Abstract (C-P-A)

Research shows that all children, when introduced to a new concept, should have the opportunity to build competency by following the CPA approach. This features   throughout our schemes of learning.

• Concrete - Children should have the opportunity to work with physical objects/concrete resources, in order to bring the maths to life and to build understanding of what they are doing
• Pictorial - Alongside concrete resources, children should work with pictorial representations, making links to the concrete. Visualising a problem in this way can help children to reason and to solve problems
• Abstract - With the support of both the concrete and pictorial representations, children can develop their understanding of abstract methods

Impact

As a result of our mathematics curriculum, pupils develop secure mathematical knowledge, strong number sense and increasing fluency in calculation. They can explain their thinking using precise mathematical language, reason logically and apply their knowledge to solve problems in familiar and unfamiliar contexts.

Pupils retain and build upon key concepts over time, making connections between different areas of mathematics and choosing efficient methods with increasing independence. By the end of primary school, pupils are confident, resilient and flexible mathematicians who understand the mathematics they are doing and can use it effectively.

Whole School Long Term Sequence

Please see the link to NCETM where you can access more information and specific year group curriculum maps:

https://www.ncetm.org.uk/classroom-resources/cp-curriculum-prioritisation-in-primary-maths/