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At the maths workshop I went to recently, my head of department and I planned an activity around one idea: asking questions of the form 'give me an example of...' There are 3 main ways of using this, and I've been trying them a lot recently.

1. Ask students for an example of something, and keep adding criteria until there is one correct answer (attributed to lots of different people, as far as I can tell). Cute, but I don't like the idea of their first answers being 'wrong', so I want to be careful about how I phrase this. Also, it's less focussed on creativity.
For example: 'Give me an example of an even number.' 'Now see if you can find an example that's a multiple of 3' 'Now see if you can find an example that's a square number' etc. until everyone has, say, 36.

2. Make it really open ended: 'Give me an example of a hard question for this topic. Why is it hard? What would be an easy question?' I like this in really small groups or one-to-one, but in a class of 30+ I find it tricky to have everyone involved in the discussion.

3. Ask for an example of something, then compare. My favourite way of doing this involves everyone thinking of the first thing that comes into their heads. Get it down on paper, get it out of the way. Now the pressure's off, everyone's got someting, think of another example that you don't think anyone else will have got. I did this with 2 classes last week, asking each of them for a shape with an area of 5. After the initial shapes (rectangles, mostly, and a few right triangles), it got interesting. I asked them all to stand, then asked the people with rectangles to sit down. Then the people with triangles, then parallelograms, then trapeziums. Then we looked at what was left. The second time I did this, I talked more about the different categories as the students sat down, or rather, got them to talk about 'how to draw an x with area 5', which allowed them to share expertise and made those ideas seem more valued.

We extended this into another favourite tactic, question swapping, by asking each student to pick an integer between 6 and 20, then draw a shape with that area on a card. Then I paired them up and swapped them, and they had to find the area of the shape drawn on the card they were given, and check their answer with the person who drew it. Paired by ability, this meant I managed to challenge most of them. Incidentally, it also meant I won a bet with my head of department: I said that I was sure at least one of my top set would draw a circle. 'Surely not! What would you even write on it? The radius? Like....root of (5 over pi)?' In fact, I got a circle with a decimal radius, but said I wouldn't accept inaccurate answers, could they write it accurately please? Then they had it! Never underestimate.

The creativity in maths is so often lost, especially when the teacher does all the creative work! What would make a good question here? How did they get that answer? Handing the reins over for a bit was far less work for me in terms of preparation, though harder in terms of generating ideas and think-time. It got some kids involved who rarely volunteer answers in maths, either through anxiety about their ability or general shyness. It was so nice to see the kids who usually think their strengths lie in what they see as 'creative' subjects have a chance to shine in maths, and it gave the 'good-at-maths' rule followers pause for thought. I just wish more lessons could be more like this.