Being collaborative

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?

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

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

Imagine you were given the chance to win some money... and imagine you had nothing to lose...