Visualising and representing

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Have you ever wondered what it would be like to race against Usain Bolt?

Which numbers can we write as a sum of square numbers?

Follow this recipe for sieving numbers and see what interesting patterns emerge.

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

Can you work out which processes are represented by the graphs?

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.

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?