I considered as an introduction to 2D shape, angle games. Angles and shapes can be seen to be very different but angle is so important to the whole interpretation of shape.
And it is the interpretation of shape that brings out the mathematician. Most can see the difference between a regular pentagon and a square - by counting the number of sides. In terms of interpretation there is such a difference in seeing the angles.
Looking at the angles between the sides (or edges). We all know the angles in a square are all 90 degrees but it takes a mathematician to see what the angles in a regular five-sided shape are. We know they are all the same size.
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