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Maths Concrete Resources At Home


In school, we use concrete resources to support pupils in their maths understanding and learning.


What is a concrete resource?

Concrete resources are physical, manipulative apparatus that can be used to support learning in maths. These are for all pupils to enable them to grasps key concepts.


Using manipulatives like money, counters, cubes, base ten blocks and dice to explore and solve problems enable concepts to be grasped and secured.


How are concrete resources used in the CPA approach to maths mastery?

Concrete Pictorial Abstract (known as the CPA approach) is a key feature of the maths mastery approach. In a nutshell, the CPA approach uses concrete manipulatives to eventually gain a secure understanding of more abstract mathematical concepts.

The CPA approach has three clear stages:

Stage 1: Concrete and action-based representation using manipulatives like money, counters, cubes, base ten blocks and dice to explore and solve problems — think of it as the ‘doing’ stage.

Stage 2: Pictorial representations of concrete objects such as bar models are used to model problems — the ‘seeing’ stage.

Stage 3: Abstract notations using mathematical symbols — the symbolic stage.


5 gets the CPA treatment first as Unifix cubes, then a bar model and lastly, as an abstract representation of 3 plus 2


What’s the difference between concrete and abstract thinking?

At each stage of the CPA journey, learners build on their knowledge and deepen their understanding.


The concrete stage helps to bring concepts to life. As they move to the pictorial stage, the concrete stage helps learners make connections between the objects they just handled and pictorial representations. The final abstract stage stands on the shoulders of the concrete and pictorial exploration.


Let’s look at an example: to solve a multiplication problem, children must first understand what multiplication means.


Here are some ways to introduce the concept of multiplication:

  • Making groups of counters, cubes, and other manipulatives
  • Exploring words that mean the same as ‘multiply’
  • Seeing and making pictures of cubes, blocks, and other objects in groups and arrays


Then, when they see the symbol for multiplication, they have a deeper understanding of the core idea.



What can be used as a concrete resource to support my child's maths understanding at home?  

Anything you have around your home can be used as a concrete resource: pasta, rice, Lego/construction bricks, straws, toy cars, board game pieces, playing cards and sweets.


Check out the following images to show how this can be achieved.

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Check out some of the concrete resources our Year 4 pupils have been using to support them in their maths home learning.