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Shape up to solve the puzzle

For the past six years I have been a member of the Hampshire Leading Mathematics Teachers group. A group of around 20 from Hampshire schools, we meet about three times a year and present ideas which have worked well for us and that we think others might like to try.

I am involved in the gifted and talented group. While many of the ideas we have trialled are quite complex, this is a simple idea which I and my colleagues have been able to use with a variety of different year groups. It's flexible, thought-provoking and provides ample opportunity for discussion.

I call it the Hexagon. Year 7 pupils were asked to pick out as many quadrilaterals as they could from the hexagon and then asked to present reasons why some quadrilaterals were possible and some were not. You can probably see a trapezium and hopefully a rectangle, but can you see a square? The nature of the angles and lengths determine which quadrilaterals are possible.

Year 9 were presented with the hexagon and asked first to find different polygons within the shape and then find what percentage of the whole hexagon each polygon took up. This was then extended to discussing whether it is possible to have a trapezium which takes up 13 of the hexagon.

Year 11 had lots of fun with the shape discussing and trying to prove whether each of the small triangles was congruent and then finding the area of one of them.

If anyone reading this would like to use the hexagon I would be interested to hear of any new and interesting applications.

Debbie Sutch, Head of maths, The Westgate School, Hampshire Email:

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