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Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Can you find out which 3D shape your partner has chosen before they work out your shape?

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

Using only six straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).