Cutting Corners


I really feel that it is good to have such an open investigation every now and again. From my experience it will need to be introduced in some enthusiastic way that will capture the pupils' interest and imagination.

The pupils' understanding of the properties of these isosceles triangles will no doubt be enhanced. With some pupils you may get into the whole idea of pythagoras and square numbers and square roots. The concept of area is often challenged in this investigation as our eyes seem to play trick on us and we have to verify things in a more certain way.

Take for example this, where the half triangle has been placed in the bottom right hand corner.

Triangles small-drawfile3
drawfile3

It looks to many people that it does not show a half, and what about putting the smaller triangle in the top corner so that it fits snugly.

There is also a good opportunity in this investigation to consider Infinity, and particularly in respect of fractions.

It's not possible to predict what will happen but I have found these activity to be very rich in what the pupils learn, develop, image and communicate. There's not much more that we would want!