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Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?

After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?

How many sets of three consecutive odd numbers can you find, in which all three numbers are prime?

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

How many pieces of string have been used in these patterns? Can you describe how you know?

How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.