Explaining, convincing and proving

As you come down the ladders of the Tall Tower you collect useful spells. How many can you collect?

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

These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?

How many legs do each of these creatures have? How many pairs is that?

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?

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

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

This game involves addition and subtraction skills combined with some strategic thinking.

How would you create the largest possible two-digit even number using the digit you're given?

In these addition games, you'll need to think strategically to get closest to the target.