Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

How many possible necklaces can you find? And how do you know you've found them all?