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'Twice as Big?' printed from http://nrich.maths.org/

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If we double each side of a small square we get a new enlarged square:

square to square with sides twice as long


The new enlarged square is the size of four of the smaller squares.

This also happens when we enlarge other shapes. Some, like the squares, can be filled with the same smaller shape.

Look at these:

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Can you work out how the four shapes fit to make the enlarged shape each time?
You need to rotate or reflect the smaller shapes to fit them in. (This means that if you make them from squared paper you will need to turn them round or turn them over.)

Please send us pictures of your completed shapes.

In this interactivity the rotation and the reflection of the shapes has been done for you.

If you enjoyed working on this problem, you might like to investigate some more shapes. Have a look at Two Squared or print out this sheet which contains some other examples as well as the shapes above.