I have just spent a lesson this week with my class discussing how we might know that there are only 11 nets of a cube.
The problem was that we could find 11 nets, we knew they were all different, and we couldn’t find anymore.
But is the lack of another solution proof enough that you have them all?
Last night, I came across this article from NRich…

To Prove or Not to Prove by David Tall.
In the article he discusses the question:
Into how many squares can you cut a square?'
What a superbly simple question, and perhaps one you could try out with younger children.
However, there’s still quite a bit of thinking to do.
 Can you spot patterns which give lots of answers quickly?
 How do you know when you have got all the solutions?
 Just because you can’t find a solution, does that mean it doesn’t exist?
Perhaps one to try out on a GeoBoard…