NumDrum
The NumDrum is an ingeniously simple but effective tool. It consists of a sturdy hollow plastic tube with a list of numbers from 0 to 139 going up in a helix around it. As there are 10 numbers in one rotation the even numbers are vertically aligned. The tube is approximately 3.5 cm in diameter and 10 cm tall, so it fits comfortably in the palm of a hand. It was designed to replace the number square.
The number square, familiar to all those in primary and basic skills education, has a number of drawbacks: what happens when a student get to the end of a line, where does she go? The numdrum overcomes this with the helix; there is no discontinuity with the numbers as they slowly wind up round the tube. It is certainly more appealing that a two-dimensional number square and this in itself is a good reason to use it!
The NumDrum comes with a number of worksheets giving ideas for its use. It also has a plastic sheet that fits over the tube with circles that fit over the numbers; this facilitates a number of low-level investigations into adding and subtracting.
It will be of use to Key Stage 1 and 2 children as well as basic skills classes. It’s ingenious, simple and I wish I’d thought of it!
Steve Bishop, Maths Lecturer, City of Bristol College, Bristol
I have been teaching for over a quarter of a century and I have seen a lot of ‘whiz’ educational ideas and the number that have failed to live up to exaggerated promises have left me rather sceptical. Nevertheless, I looked forward to seeing if the class set of Numdrums would be a useful tool in the classroom. At the time, I had a mixed y5 class that included children with severe limitations in arithmetic. I was certainly encouraged by the initial response: you can’t put a Numdrum in front of a child without him/her wanting to pick it up and ‘play’ with it. Number lines, squares, even the interactive whiteboard do not have that wonderful, child-friendly tactile appeal. The first time the pupils used the Numdrums they spent the time manipulating them, imagining and describing many ways they could be used. I challenged them to tell me four different things about the Numdrum; I stopped them after 10!
Over the next couple of terms and several sessions the pupils and I discovered different ideas we could explore with the Numdrums and different ways of working with them. After a while I found I was using them in two main ways. One way was as the whole class mental maths starter. We would look at such things as patterns (using coloured white-board markers directly onto the Numdrum - very effective and they wipe off easily), multiplication tables, serial additions and subtractions. Using the clear sleeve marked with two appropriately spaced windows the pupils would quickly recognise, for instance, patterns of units and tens in the eight times table, or the addition/subtraction of eight to 43, 53, 103, etc. Once the patterns were becoming established and I wished to develop speed through practice and competition, I noticed that by allowing the less fluent to continue to use the Numdrums they could find answers at a similar speed to the more able mental mathematicians: I had found a way of facilitating differentiation during mental maths starters.
I also used the Numdrums to support my very low ability group who were having great difficulty adding and subtracting single-digit numbers; particularly, of course, when crossing 10s. I realised that they had not then internalised a continuous mental number line but, rather like the traditional 100 number square, it was fragmented. They could manage moving horizontally across the number square but the vertical jumps were problematic. I found that after a few lessons using the Numdrums these pupils were crossing 10s confidently and were also transferring this skill to their mental number line.
The Numdrum is not just a device for increasing variety and maintaining interest within the classroom. It helps to develop and consolidate concepts and establish number patterns that give mathematics its meaning. I found with my y5 class that all of the pupils enjoyed and benefited from the opportunities for using the Numdrums, though, in particular, the lower ability pupils achieved the more dramatic progress. But then, I am still finding ways of using the Numdrum myself.
John Leversedge
NumDrum by John Harrison
Unit 10
Woodgates Farm
Broxted, Essex
CM6 2BN
