What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
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?
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?