Mathematics and problem-solving skills

Maths manipulatives

I promised to share some simple ideas about how manipulatives, physical props and visuals can support maths learning beyond early years in a previous blog. Here are a few of the tools I use regularly:

Cuisenaire rods

The uses for these are limited only by our imagination and the cost of owning an inexhaustible supply.


Each differently coloured rod represents a number from 1 to 10 – or 10 to 100, 100 to 1000 if working on place value (or even to visualise numbers using a non-decimal base, but that’s getting a bit ahead of ourselves). The numbers are not written onto the rods, but they could be added to aid familiarisation or if colour vision is impaired.

Use them to to reinforce number bonds


I’ve made number bonds to 10 here, but you could use them to find different ways of making 7, e.g.

1+6 / 2+5 / 3+4 / 4+3 / 5+2 / 6+1

The same technique can be adapted for subtraction: 7 – 3 = 4


And multiplication

3 x 4 = 4 x 3
2 x 5 = 5 x 2
5 x 3 = 3 x 5

Base 10 blocks

These are great for reinforcing place value and are available with numbered and unnumbered 100 square bases, as well as 1000 cubes.



The geoboard is fun for creating patterns and provides a good opportunity to develop fine motor skills. It can be used for copying and creating geometric shapes using elastic bands, and is also a great opportunity to talk through what is happening at each stage:


First model and say what you are going to do, right down to selecting the pegs you are going to attach the elastic bands to, describing what you are doing as you do it. Get the learner to do the same – it won’t feel natural to begin with, but it’s an important step in training for later problem-solving skills. Once they are able to copy a shape independently, insist they tell you what they are going to do before they do it. Verbalising the trial and error process helps to develop critical thinking skills that will make maths easier and that are really useful in all areas of life. More on that here.

Place value props


These are home-made (you can find some to download via the link at the bottom of this blog).

Laminated numbers


I’ve colour coded these to make it easier for me to sort! I have units to 20,  multiples of 5 to 100 and multiples of 10 to 100.

100 square

Such a simple prop, but again, almost unlimited possibilities. I’ve talked before about the maths that goes on for fun in our house – eldest home from first term at uni this weekend and within an hour he and his father are heads together puzzling out a problem I cannot begin to fathom. When my husband saw me snapping my home made 100 square, he asked if I was demonstrating the Sieve of Erastosthenes (look it up if you like). I wasn’t.


I’ve used counters to mark out the 4 x tables. You can support addition (counting on), subtraction (counting back), multiplication and division as above. There are so many possibilities, I’ve decided to dedicate a whole blog to it. (There’s a 100 square to download via the link at the bottom, too).

A collection of infographics related to maths can be found here

A collection of downloadable maths-based resources for printing can be found here

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2 thoughts on “Maths manipulatives

  1. Please contact me back.
    I would like to have a training about dyscalculia teaching strategy.


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