__I Can't Do this! It's Impossible!__**Is this a valid response to a maths question? Is this an appropriate way for any student of mine to speak in class?**

Sure. Particularly when the question being asked was deliberately.....impossible.

__So What Was The Problem?__**The kids were asked to make a square. Then, using one single straight cut, they had to produce an equilateral triangle.**

The results were many and varied.

__What did they do?__**Many kids rushed straight in and went "Snip! - Done it!", holding aloft a beautiful triangle. But was it equilateral? Well, maybe not but the problem was half solved - at least we had produced a triangle.**

__That Beautiful Moment of Confusion and Panic__**Next ensued that period of chaos as kids rethought their initial ideas and tried a variety of different techniques. Not surprisingly, every triangle produced was a right-angled triangle.**

__And then, the Moment of Revelation__**Having battled with the idea for 15 minutes, one student finally sat back and said, "This is impossible!" Whether he meant, "This is impossible**

__for me__." or "The is

__mathematically__impossible." I'm still not sure but it doesn't really matter - he had come to the realisation that maybe there was no solution.

Almost simultaneously another, more mathematical, student observed that the hypotenuse (not her word) would always be longer than the other 2 sides, no matter how much longer you made the sides. Focusing solely on the sides, she realised that she could not get them all to be the same length.

And then the conversation was deftly redirected (by me) to consider the internal angles. To be an equilateral triangle, all angles needed to be 60 degrees. Suddenly, the kids saw that no matter where they cut a line in the square, there was always going to be a 90 degree angle.

__Is it Fair to Ask Impossible Questions?__**Fair? Unfair? Right? Wrong? Is there a moral dimension to this? - I doubt it.**

What I do know is that this provocation produced some good thinking. Kids had to work from what they knew about shapes to think about what they were trying to do. When they exhausted all their possibilities, they were left with a solution - maybe I've proved that it can't be done.

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