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?

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

How many trains can you make which are the same length as Matt's, using rods that are identical?

Can you hang weights in the right place to make the equaliser balance?

Use the number weights to find different ways of balancing the equaliser.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

How many different rhythms can you make by putting two drums on the wheel?

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

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?