Why do this problem?

This problem is useful for getting learners to visualise and predict outcomes which are entirely non-threatening and easy to check. It starts in a way which is easy for all, but can get as difficult and complicated as you want!

You will need plenty of scrap paper, sharp scissors and some hole punches.

Key questions

Can you predict how many pieces you will have now?

What do you think it is going to look like when you unfold it?

Have you made a rule about how you fold/place the paper?

How many times did you fold it?

How many holes did you make?

So how many holes do you think there will be when you unfold it?

Tell me about your pattern.

Can you find a different way of doing it?

Can you explain these results?

Possible extension

Learners could combine the first two sections of the problem (A and B). This will involve folding, cutting and punching holes, and then sketching what they predict they will get when the paper is unfolded.

Possible support

Suggest starting on the third part of the activity (C), successively cutting paper in half and arranging the pieces in a pattern such as the one shown in the problem.