Exploring and noticing

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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