I wanted to share an example of how ‘What if…’ can be used to open up new ways of exploring concepts that might not appear obviously open to investigation. In this case it is multiplying and dividing by 10, 100 and 1000. Obviously this is an important concept and one that we want children to be able to be fluent in.

I have a few strategies for developing starting points and one of them is to arrange them in some kind of diagram. In this case the idea was to build in multiplying and dividing by 10, 100 and 1000 in a ring. In its simplest form, we can think about just trying to perform operations so that we end back with 324. With some I might give them a range of numbers that they could put in the circles as support. .

Often I’ve used the POG format with this kind of thing (get them to make a **p**eculiar and **o**rdinary example and then think about what needed to be true in **g**eneral). The general being something around that the amount multiplied needs to be the same as the amount divided.

But there is plenty of possibilities for the use of ‘What if…’, to make it more challenging perhaps or just to allow them to go down their own direction.

The obvious one is what if they had more circles in the ring? An odd number makes for an interesting case with the fact that you then can’t have the same number of divisions as multiplications.

We can though be far more creative and perhaps initially it might come from you but soon the children will come up with their own ideas and rules. What if no circle could have the same value? What if we had two rings and the circle in the same position on both rings couldn’t have the same value? A wealth of opportunities present themselves that could be pitched at different levels. I’ve done this idea with both Years 4 (with just integers) and 6 (where we focused a lot more on not allowing the same value more than once) but I see no reason why it wouldn’t be effective in lower Key Stage 3 as well.

This is the power of ‘What if…’, it really allows interesting new areas of exploration to open up.