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Purpose of study

Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.



The national curriculum for mathematics aims to ensure that all pupils:

  • become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately
  • reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
  • can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions


Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.

The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.


Spoken language

The national curriculum for mathematics reflects the importance of spoken language in pupils’ development across the whole curriculum – cognitively, socially and linguistically. The quality and variety of language that pupils hear and speak are key factors in developing their mathematical vocabulary and presenting a mathematical justification, argument or proof. They must be assisted in making their thinking clear to themselves as well as others, and teachers should ensure that pupils build secure foundations by using discussion to probe and remedy their misconceptions.


At Middleton

At Middleton we use an AFL approach to maths ensuring that the children are being taught the concept they need. We consolidate and challenge the children's mathematical ability and use a range of strategies to support the children's next steps: White Rose Scheme, Calculation policy, CPA to name a few. Our curriculum is designed to support a mastery approach to teaching and learning and is to support the aims and objectives of the new National Curriculum. The overviews:

  • have number at their heart. A large proportion of time is spent reinforcing number to build competency
  • ensure teachers stay in the required key stage and support the ideal of depth before breadth
  • ensure students have the opportunity to stay together as they work through the schemes as a whole group
  • provide plenty of opportunities to build reasoning and problem solving elements into the curriculum.

White Rose Maths believe that all children, when introduced to a new concept, should have the opportunity to build competency by taking a 'concrete, pictorial and abstract' approach:

  • concrete – children should have the opportunity to use concrete objects and manipulatives to help them understand what they are doing.
  • pictorial – alongside this children should use pictorial representations. These representations can then be used to help reason and solve problems.
  • abstract – both concrete and pictorial representations should support children’s understanding of abstract methods.


Calculation Policy

To support the teaching of number, Middleton have developed a calculation policy which builds on the interconnectedness of mathematics and outlines the progression of the written methods and concrete, pictorial and abstract approach for addition, subtraction, multiplication and division.