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Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Square to L

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

Midpoint Triangle

Can you cut up a square in the way shown and make the pieces into a triangle?

Cut and Make

Age 7 to 11
Challenge Level

Why do this problem?

This problem is based on the popular Tangram activities. It may help to extend pupils' concepts of triangles and it will encourage them to use visualisation.


Key questions

How have you done this?
What have you tried so far?
How could you join these two shapes? Where could the third piece go?

Possible extension

Take a large square and cut it up into a variety of shapes, for example:
Tan
These are the classic tangram pieces and there are many interactive tangrams on NRICH in the World of Tan series.

Possible support

Plastic or card shapes would be helpful.