Blog home
The Blog

Fresh Ideas and Inspiration for education

Essential Maths Manipulatives

In this blog we look at how the Concrete, Pictorial, Abstract Approach (CPA) to mathematics is highly effective with essential maths manipulatives that enable pupils develop a deeper understanding of mathematical concepts.

Posted on Wednesday 17th May 2023

Essential Maths Manipulatives

 Concrete, Pictorial, Abstract Approach (CPA)                         

Maths Manipulatives are essential tools and used in CPA. Concrete, Pictorial, Abstract Approach (CPA) is a highly effective way to teach mathematics. Using this method helps pupils develop a deeper understanding of mathematical concepts.

Often people find maths difficult to grasp because it is so abstract. The CPA approach helps them to make sense of the abstract, learn new ideas quicker and build on existing knowledge.

CPA is at the heart of Mastery Maths                                       

The Concrete is the ‘doing’ stage, bringing concepts to life by allowing children to handle physical objects themselves, connecting a physical representation of a number. Providing pupils with a variety of concrete manipulatives gives them a deeper understanding of the quantity.

The Pictorial is the ‘seeing’ stage, to encourage children to make mental connections between physical objects and the abstract, by drawing and looking at pictures or diagrams which represent the quantity. It helps pupils to visualise the problem and make it more accessible.

The Abstract is the ‘symbolic’ stage. Children use abstract symbols to model and solve maths problems. To fully understand this stage we need to have experienced the other two stages.

Children need to be able to go back and forth between these stages to reinforce concepts. To do this they need to be encouraged to represent maths problems in a variety of ways. Using different physical visual aids will help pupils to build an understanding and enable them to make quicker mental connections. Essential Maths Manipulatives are necessary to make sense of mathematics.

Using Manipulatives in Maths

Using manipulatives makes maths more engaging and enables pupils to understand the content in greater depth. Manipulatives enable pupils to become more confident, to view concepts clearly and ensure problems are easier to understand.

Quality Resources

Using good quality resources is a powerful way to teach pupils to work through a problem. Maths concepts can be quickly mastered through firstly using maths manipulatives as these will represent the symbols and numbers in a maths problem and help the reader to make better sense of it.

Place Value Counters                                                         

Place Value Counters are a powerful resource perfect with the CPA (Concrete, Pictorial, Abstract) approach.

The counters can be used to model large number calculations, children able to work with numbers in hundredths and millions!

They enable pupils to understand strategies and make sense of mathematical concepts.

TTS sell different types of counters. Look out for the ones that best suit your needs.

White Rose Maths uses place value counters to develop conceptual understanding, alongside fluency with numbers. TTS sell White Rose Maths Essential Kits that include place value counters and other useful manipulatives.

Vast array of Concrete Manipulatives                         

Manipulatives and pictures should be offered to all students and at TTS we offer resources for every child, bringing mathematics to life with hands-on experiences.

Resources to look out for: