As I scrolled through my Twitter feed on Sunday night (October 8th 2017), I came across the following photograph.
Accompanied by the caption “Greater Depth at KS1, making the activity more complex...” I was drawn to the simple but effective nature of the activity. What’s more, it kick started a train of thought around the use of Numicon and other visual representations in activities designed to provide pupils with access to a greater depth of mathematical understanding.
Taking the activity in the picture as a starting point there are quite a few examples of how a few modifications could open up entire worlds of exploration for our pupils.
For instance, instead of totalling 10, why not ask pupils to generate prime numbers in each column/row before opening up a discussion around the nature of the addends required to make said primes.
Not only is this potentially mathematically rich but it may also help a greater number of pupils to reason and conjecture confidently about relatively complex abstract notions.
Perhaps blanking out a square on the grid could help to create missing number problems or provide pupils with support when generating their own. This is something which, if done effectively, could be utilised across many year groups. In Year 6 the colour of the manipulatives could even be used to support the generation of algebraic expression and the description of patterns present on the grid.
It may, however, be the centre square which holds the greatest potential for the provision of greater challenge and depth. Determining the ‘number’ placed at the centre allows the teacher to dial the difficulty up or down at will. For example, when insisting that one line must be double or half of the other or, when generating representations of fractions with the manipulatives, by insisting that each line must be an equivalent fraction to the other.
In keeping with my original prime number example the relationships between addends and odd and even numbers must surely be explored through the use of this activity and if you want to dial it all the way up to 11 we could always introduce the notion of consecutive numbers, their relationships with odd, even, square, cube and prime numbers, patterns and the generalisations which can be made off the back of deep and meaningful exploration of the underlying mathematics.
I don’t for a minute think the suggestions considered here form an exhaustive list and I certainly don’t think they are original in any way but I was struck by the thinking behind this particular activity. In this scenario manipulatives were no longer the domain of pupils struggling with concepts. In this scenario they were the scaffold they were designed to be. Fulfilling the needs of all the pupils in the class and providing pupils, exploring mathematics on a deeper level, with the support they needed to generalise, reason and think like the mathematicians they are. Don’t get me wrong, manipulatives are an effective way of providing access to mathematical concepts. But they are effective at all levels of comprehension.
An idea like this gives me hope. And hope is all we really need.