Why do this problem?
Knots are a fascinating subject and this problem
is a good way to begin exploring them. It would be well worth watching the video What's a Knot?
with your class in addition to having a go at this problem.
This problem is probably best approached in a very practical way with children - giving them some string to tie the knots for themselves. However, before this, encourage your pupils to predict which knot will be best and why. If they take time to hypothesise they will get a lot more out of the practical task.
Following on from this activity, you might like to look at Turning Granny
which invites learners to look at using symmetry to distinguish between knots.
How do you think you can tie that knot?
If you want to make things secure with a knot, what do you think is important?
Why don't you try tying two things together using each knot to test which knot stays in the same shape?
Do you think that this will make it less likely to slip?
Learners could have a go at this problem
Suggest using this information with real string:
To tie a reef knot you take an end of the string in each hand and do 'right over left, left over right'. A granny knot is 'right over left, right over left again'.