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

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

Cong from St Peter's RC School shaded the hexagon grid which helped him look for solutions to this problem.

Proof does have a place in Primary mathematics classrooms, we just need to be clear about what we mean by proof at this level.

This game is known as Pong hau k'i in China and Ou-moul-ko-no in Korea. Find a friend to play or try the interactive version online.