Being resourceful

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?

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

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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

Can you find the pairs that represent the same amount of money?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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

Can you decide whether these short statistical statements are always, sometimes or never true?