# Types of number with a kinaesthetic approach

This post may not surprise experienced maths teachers, those used to working with kids who find maths difficult, or our primary colleagues. However, whilst none of this is revolutionary in the slightest, it has been a new world for me and something I’d like to share.

I have a small year 10 class who find maths challenging. They show many signs of discalculia and many have a phobia of numbers. I have recently had to teach them the topic of ‘types of number’ (squares, cubes, factors, multiples, primes etc) and have had a few breakthroughs by trying to make it as kinaesthetic as possible. When I thought about it, I realised that multi-link cubes can be used for so many parts of this topic:

Square numbers-Make squares out of a single layer of multi-link cubes with side lengths of 1, 2, 3 and 4 cubes etc. Pupils soon realised in my class that when calculating the number of cubes they needed that they just had to multiply the side lengths of the square. They understood where the square numbers came from and have a mental image of what the pattern looked like out of multi-link cubes, rather than it being an abstract concept.

Cube numbers- Same as above, but get them building cubes. They realised a large cube with sides of length 3 was made up of 3 X 3 X 3 = 27 multi-link cubes.

Multiples- If we want multiples of 6 then pupils group cubes into piles of six and count the total in all groups as they go.

Factors- If pupils need to find the factors of 12 they get 12 cubes then see what rectangles they can make by rearranging the cubes. They realise they can make a 1 X 12, a 2 X 6 or a 3 X 4 rectangle, and they have found the factors…

Primes- Primes are those rectangles which could only be 1 row high.

I do think there is mileage in trying to make links to tangible concrete things that pupils can remember, particularly for kids who find taking in abstract concepts difficult. By my own self admission I need to improve my own practice in this area. I thoroughly enjoy breakthroughs like this as it is something I shall look forward to in the future when I have a similar class. Little victories! I’m still learning every day…

I can’t agree more!! As a primary teacher in a school with a hugely kinaesthetic approach it pains me to hear our kids go to secondary school n have all resources taken away in favour of textbooks!! My advice…..multilink……cuisennaire rods and numicon!!! Must haves!!! X

This is true, and is one of the reasons Singapore Math is so successful. Every lesson and concept should be taught with a concrete understanding first, to build fundamental understanding that doesn’t go away like memorization does.

For more on the role of working with blocks in math, see this article:

http://susanmidlarsky.com/fun-with-blocks-foundational-geometry/

And regarding dyscalculia, I’m concerned that it may be over-diagnosed when the real problem is not a learning disability, but the prevalence of poor math teaching. For more on dyscalculia, please see these articles:

http://susanmidlarsky.com/?s=dyscalculia

I have used these blocks to teach sequences and series, one class became quite expert at finding the general term using them. I’ve also used them to help a class discover prime numbers.

Has anyone else found that when handing out the. Cubes that the. It’s always seem to make guns or is it just me?

Guns and robots…!