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'Tangram Tangle' printed from http://nrich.maths.org/

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The square below has been cut into two pieces:

square cut in two

It is possible to fit the pieces together again to make a new shape.

If you must match whole sides to each other so that the corners meet, how many new shapes can you make?

Watch out for shapes which are really the same but just turned round or flipped over.

You could download this sheet which contains four copies of the square.

Alternatively, experiment with the interactivity below. You can rotate a shape by holding the mouse over a corner. Click on the stars to flip the shapes over.

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