Being curious

Use properties of numbers to work out whether you can satisfy all these statements at the same time.

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.

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

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

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

There are lots of different methods to find out what the shapes are worth - how many can you find?

Can you find the values at the vertices when you know the values on the edges?