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Follow the diagrams to make this patchwork piece, based on an octagon in a square.

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

How many different sets of numbers with at least four members can you find in the numbers in this box?

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?

There are nasty versions of this dice game but we'll start with the nice ones...

Investigate different ways of making £5 at Charlie's bank.

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?