If you cut a square diagonally from corner to corner you get four right-angled isosceles triangles.
How many different shapes can you make by fitting the four triangles back together?
You may only fit long sides to long sides and short sides to short sides.
The whole length of the side must be joined.
You might like to record what you do.
You could use this interactivity to try out your ideas:
Click on the grey triangles to make new pieces.
You can rotate them by dragging the corners.
Printable NRICH Roadshow