The Carey Federation


Our Mathematics Intent

Our 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 nonroutine 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. Our curriculum overview, by necessity, is 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. Pupils who grasp concepts rapidly will be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material will be offered opportunities to consolidate their understanding, before moving on.  

Mathematical subject knowledge and conceptual understanding 

Our curriculum overview describes a sequence of knowledge and concepts that also incorporates the 5 Big Ideas of Teaching for Mastery, namely  ‘Mathematical Thinking’, ‘Variation’, ‘Fluency’, ‘Representation and Structure’ and ‘Coherence’. To develop pupils’ reasoning and deeper conceptual understanding, problems are usually set in real life contexts. Carefully chosen representations (manipulatives and images) are available for the children to explore concepts and understand them in more depth. These representations may appear in books as children show their understanding, rather than answers to a series of calculations. For example, the use of practical ‘Concrete’ resources may be photographed, ‘Pictorial’ representations may be drawn (such as Base 10) along with their numerical recording in the ‘Abstract’. This is referred to as ‘Concrete – Pictorial –Abstract’ (CPA) approach.   


While it is important that pupils make progress, we believe that they need to ‘master’ the key concepts by acquiring a deep, long-term, secure and adaptable understanding of the subject. Pupils are taken on a coherent journey through the mathematics and our planning of ‘small steps’ supports the design of lessons which allows us to take all of our children to an end learning point by a progression of small, incremental steps.  

Spoken language 

We believe in the importance of spoken language in pupils’ development across the whole curriculum – cognitively, socially and linguistically. We also believe that 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. We will support them to make their thinking clear to themselves as well as others and ensure that pupils build secure foundations by using discussion and questioning to probe and remedy their misconceptions. The national curriculum for science reflects  

Promoting our school motto and The Carey Qualities 

Our curriculum encourages children to see the mathematics that surrounds them every day by providing real-life contexts that are meaningful to them both inside the classroom and the outside environment. We provide opportunities for children to challenge themselves to   ‘Aim High’ as well as supporting them to ‘Be Resilient’ and keep going when they get stuck on a problem or calculation.  We Take care of each other’ by nurturing pupils’ confidence, being supportive and fostering a sense of curiosity about the subject. Children will also have the opportunity to ‘Be Resourceful’ and use the manipulatives available to support their conceptual understanding of the structure of the mathematical concepts.  

Our Mathematics Implementation

We implement the curriculum through carefully planned sequences which enable children to learn new skills and knowledge , whilst consolidating previous learning. Mapping what is taught in each year group, allows teachers to plan for progression. Please see our progression grid below

Planning for progression Mathematics