Draw an eight by eight square on dotty paper. You can print some here.

Cut it up to make the four pieces shown in the diagram:

Now rearrange the pieces to make the shape below:

**It seems that the same pieces can make two shapes with different areas!**

Can you explain where the extra area comes from?

Here are some questions you might like to consider:

**Can other squares be split up and rearranged to make rectangles with a different area?**

**Are there other square/rectangle pairs where the areas differ by 1 square unit?**

**Is there a pattern in the sizes of squares that can be arranged in this way?**