Problem Teachers' Notes Hint Solution

This problem offers a novel way of exploring connections between Mathematics and Art. It is important for learners to have plenty of opportunity to discuss with others and to verify ideas.

Some groups of children may need a demonstration by an adult, particularly to ensure good folding and creasing as you work through the instructions given. Encouraging them to work in pairs will mean they can help each other produce the folds and they also have someone with whom to talk.

(For checking purposes, this image shows the progression in folds from the third to the eighth.)

In fact, this series of folds produces what is known as a 'dragon curve'. It will be interesting to see whether any children observe the dragon shape. They are likely to be fascinated and amused by the fact that it has been investigated by several mathematicians!

What do you see?

Does it look like anything?

What could you try now?

Try slightly different alternatives like folding right over left and then left over right etc. Ask pupils to predict whether the result will be the same or different and why.

Drawing on a computer may be enhanced by producing a curved turn rather a right angle. Five folds using right over left then left over right produced the following:

Some pupils may like to go further by looking at the successive mid-points:

Some pupils may require adult help with the manipulative skills of folding and creasing.