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?

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

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?

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 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.

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

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

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?

Can you work out how to win this game of Nim? Does it matter if you go first or second?