Written Calculation Policy

Concrete, Pictorial, Abstract (CPA) is a highly effective approach to teaching that develops a deep and sustainable understanding of maths in pupils. Our calculation policy reflects this approach.


Children (and adults!) can find maths difficult because it is abstract. The CPA approach builds on children’s existing knowledge by introducing abstract concepts in a concrete and tangible way. It involves moving between concrete materials, pictorial representations, and abstract symbols and problems.



Concrete is the “doing” stage. During this stage, students use concrete objects to model problems.



Pictorial is the “seeing” stage. Here, visual representations of concrete objects are used to model problems. This stage encourages children to make a mental connection between the physical objects and the abstract pictures, diagrams or models that represent the objects from the problem.



Abstract is the “symbolic” stage, where children use abstract symbols to model problems. The abstract stage involves the teacher introducing abstract concepts (for example, mathematical symbols). Children are introduced to the concept using numbers, notation, and mathematical symbols (for example, +, –, x, ÷) to indicate addition, multiplication or division.