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An Appearing Act

Age 11 to 16

This resource is part of "Dotty Grids - Exploring Area"

You may wish to print out some dotty paper.

Take an 8 by 8 square, and cut it up like this:

Rearrange the pieces to make a 13 by 5 rectangle:

It seems we can use the same pieces to make two shapes with different areas!
Can you explain why?

Can you perform this “magic trick” by splitting squares of other sizes in a similar way?

Which squares are least obvious?

What patterns are there in the square sizes?