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Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Find the exact difference between the largest ball and the smallest ball on the Hepta Tree and then use this to work out the MAGIC NUMBER!

Find your way through the grid starting at 2 and following these operations. What number do you end on?

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

A practical experiment which will introduce students to tree diagrams, and help them to understand that outcomes may not be equally likely.