Being collaborative

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.

Can you describe this route to infinity? Where will the arrows take you next?

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

Here's a chance to work with large numbers...

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

Which countries have the most naturally athletic populations?