Maths Calculation Policy
The White Rose Maths Calculation Policy sets the expectation in progress through the teaching of addition, subtraction, multiplication, and division. The policy supports teachers to plan progressively, from Reception to Year 6, using the models and images provided. The document also provides guidance and expectations for the delivery of teaching of each operation for each year group.
Click here for the Calculation Policy
The policy introduces key concepts using a Concrete, pictorial, and abstract (CPA) approach.
Concrete – Concrete is the “doing” stage.
During this stage, children use concrete objects to model problems. Unlike traditional maths teaching methods where teachers demonstrate how to solve a problem, the CPA approach brings concepts to life by allowing children to experience and handle physical (concrete) objects. For example, if a problem involves adding pieces of fruit, children can first handle actual fruit. From there, they can progress to handling abstract counters or cubes which represent the fruit.
Pictorial – 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 object they just handled and the abstract pictures, diagrams or models that represent the objects from the problem.
Building or drawing a model makes it easier for children to grasp difficult abstract concepts (for example, fractions). Simply put, it helps students visualise abstract problems and make them more accessible.
Abstract – Abstract is the “symbolic” stage.
Only once children are secure with the use of concrete and pictorial approaches to their calculation, reasoning and problem solving, they move on to use abstract symbols to model problems. They will not progress to this stage until they have demonstrated that they have a solid understanding of the concrete and pictorial stages of the problem, which they can still use to demonstrate their depth of fluency and understanding as they develop to consistently use standard written methods.