Conjecturing and generalising

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

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

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?

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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

Find a great variety of ways of asking questions which make 8.

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

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?