Using resources to help our maths

For some children, maths can be a tricky subject to fully understand as it is filled with abstract concepts, which are sometimes difficult to vision. The most powerful way to help a child with their maths is to provide resources which they can use and move around to aid understanding. CAP (concrete, pictorial, abstract) is a highly effective approach which deepens and sustains the understanding in maths.  

This approach works in three parts and can support any area of maths. Concrete is the first stage which basically means the ‘doing’ part. Children use objects, such as fruit, or counters to represent the object. They can then move these around to help make abstract concepts interactive.

The second stage is pictorial, whereby children use visual representations of the concrete objects to model problems. The children make the connections between physically handling objects to drawing them.

The final stage is abstract. The is the ‘symbolic’ stage; the knowledge of objects and pictures is applied to symbols and numbers. For example, 3 balloons and 2 balloons put together creates the number sentence 3 + 2 = 5. 

In year 3, the children are becoming increasingly confident to use the resources to support their knowledge and understanding. For the last few weeks, the children have been learning about fractions. This is usually deemed as a topic which confuses people and is less favoured. However, the children of year 3 have a solid understanding of fractions and this is largely due to the support of concrete resources and pictorial diagrams used in the initial section of the lessons, which lead to abstract numbers. 

An example of this approach used in action took place during the lesson on subtracting fractions. The children started off with 10 counters and all these counters were red (10/10). The children turned 4/10 of these counters over to the yellow side. From this, the children can clearly see that 6/10 counters were still red. This is then modelled using pictures of these counters (10 red blobs, four of which are turned to yellow). Alongside of this, the children can write this in the abstract form of fractions: 10/10 – 4/10 = 6/10.

Ms. Nicola Lloyd

Year 3 Leader