Drawing shapes on squared paper is a great way to work out their area. There are some well-known theorems to discover too...

How to build a kingdom on a mathematical trick.

We started drawing some quadrilaterals - can you complete them?

Draw some shapes on a dotty grid, and explore the relationships between the dots on the edge, the dots inside, and the area. Is there a theorem to describe what's happening?

Is there a quick way to work out the area of a square drawn on a dotty grid? What if the square is tilted?

Cut up a square and rearrange the pieces to make a rectangle. The shapes have a different area - how can this be possible?

Here are some resources to help you explore dotty grids, including some printable grids and an interactive environment.