Manipulatives – the ‘power’ tool of the maths classroom

How can manipulatives boost understanding in maths?

Author

Grace Coker

Content and Engagement Specialist (Mathematics)

Grace Coker is the EEF’s specialist for Mathematics. In this blog, she explains the importance of manipulatives and how they are a vital tool in supporting children’s mathematical thinking and encouraging high quality talk.

Blogs •3 minutes •5 March, 2025

A good tool improves the way you work. A great tool improves the way you think.

Jeff Duntemann

We know delivering high-quality teaching is essential to achieving the best outcomes for all pupils, particularly the most disadvantaged among them. Extensive research evidence has shown that manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). can be powerful tools for supporting pupils to engage with mathematical ideas as part of high-quality mathematical teaching.

But just like any other tool – it’s how they are used which is most important. They need to be used purposefully and appropriately to have the desired impact.

The nuts and bolts

Manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). aren’t a means to an end. They shouldn’t merely be seen as a tool to help children in ‘getting the right answer’. Instead, a well-used manipulative should develop and improve a pupil’s thinking, helping them make sense of a concept and deepening their mathematical understanding by illuminating underlying general relationships.

Darren Partington, Director of Maths at Three Saints Academy

When used effectively, manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). can help improve the way pupils think. With improved thinking, can come:

improved talking,

better explaining,

greater justifying and

more mathematical connections being made.

A talking tool

“It’s common for ratio problems to have two sets of information. Using double-sided counters can create a dynamic model which helps students to understand and explain what happens as the counters transition between the start and end of the question.“

Tom has 5 times as many chocolates from a tub of Celebrations as Andy.

If Tom gives 24 of his chocolates to Andy, they both have the same amount.

How many chocolates were in the tub initially?

“The counters could initially be placed in a similar way to the image below.”

BEFORE

“Once the counters have been arranged in that ratio, a think, pair, share strategy could be used to establish what must happen if Tom and Andy end up with the same amount of chocolates. Students can replicate Tom giving some chocolates to Andy by physically moving the counters to show that both people have an equal amount like the image below:”

AFTER

Andy Burton, School Improvement Advisor for Maths, Stour Vale Academy Trust

Adding to your toolbox

If you’d like to enhance your knowledge and dip into relevant resources around using manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods)., you may find the following of interest:

Education Endowment Foundation:Manipulatives – the ​‘power’ tool of the maths classroom