Same Shapes

'Same Shapes' printed from https://nrich.maths.org/

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Same Shapes

Look at this shape. The dotted line shows how it can be cut in half to make two shapes that are the same shape and size.

How can these shapes be cut in half to make two shapes the same shape and size?

Can you find more than one way to do it?

Why do this problem?

This activity will be very useful when wishing to challenge and extend pupils' spatial awareness with 2D shapes. It can also be an exercise in perseverence.

Possible approach

The problem Happy Halving might be suitable to start with, before tackling the shapes in this problem. There are detailed suggestions of an approach in the teachers' notes of Happy Halving.

If you would prefer to tackle this problem as it stands, it would be good to have a large image of one the shapes for all the pupils gathered around to see. This could give a good opportunity for a class discussion.

Key questions

Are you able to show me that your two halves are the same shape and size?

Are there other ways of halving this shape?

Possible extension

Some learners will enjoy inventing some shapes of a similar nature. Make sure they test their own shapes to check they work!

Possible support

Ideally, pupils could work in pairs so they can share ideas with each other.