Take a dotty grid. Draw a few lines. What can you draw? What can you discover? The more you explore, the deeper you are drawn in...

We have suggested some starting points to stimulate your curiosity. We hope you will be playful, pose some questions of your own, and make some unexpected discoveries.

Coordinates and vectors are very useful tools for working out properties of lines and shapes drawn on a dotty grid. Have a look at the problems and see how you can use these tools to understand what's going on.

We usually measure distance as the crow flies. These problems explore the mathematics that emerges when we express distance in different ways, using ideas from taxi-cab geometry.