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?