Being collaborative

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

Can you work out what step size to take to ensure you visit all the dots on the circle?

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.

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Explore the effect of reflecting in two intersecting mirror lines.

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...