Visualising and representing

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.

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

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

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Sequences of multiples keep cropping up...

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.