Working systematically

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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?

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.

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?