Maths (Concrete, Pictorial and Abstract (CPA) Model)




The Concrete, Pictorial and Abstract (CPA) Model of learning is one that fully encompasses the way we teach mathematics at Stony Dean. We use this approach to enable our pupils to fully understand and master the maths concepts that we are teaching.

This approach is not about getting the answer quickly or teaching quick fix ‘tricks’. It is about giving our pupils the tools to understand the maths that they are focusing on. We believe if our pupils fully understand the concept they are learning and keep revisiting it, then they will be able to apply the maths independently in the future.

This model is not linear, we use a cyclical approach. For example, even when a pupil has worked out the answer using an abstract method, we may ask them to use concrete manipulatives to convince others that they are correct.


When starting a new concept whatever the year group or ability of our pupils we use concrete apparatus. This is to make the concepts being taught real to our pupils so they can make sense of the maths rather than dealing with ideas that are abstract.

We use a range of concrete resources in teaching all areas of mathematics but specifically with reference to number work.

Please see the document below (Concrete Resources) that details some of the resources we use as part of our everyday teaching of mathematics at Stony Dean.


As our pupils gain understanding of a concept through using concrete materials they move into using pictorial resources to support them moving away from using concrete resources.

The pictorial aspect of this model is a vital step for enabling all our pupils to move from concrete maths to abstract maths.

It includes pictures and diagrams of resources that our pupils are familiar with and are sometimes included in the Fact Files that we provide as part of Additional Learning.


Once we believe our pupils have mastered maths concepts through using concrete and pictorial resources we move into the abstract.

Even when working abstractly in maths our pupils always have access to concrete and pictorial resources to support them.

Please see the document below (CPA in Action – Data) that demonstrates how the CPA model in action.

SD footer banner footer swish