This is my all-time favourite activity to do with learners of any age and with the teachers that I work with too.
The Mobius strip is named after the mathematician August Mobius who invented the strip in 1858. It is curious because it only has one side and one edge. A Mobius strip is simple to construct. All you need is a long strip of paper, sticky tape and a pair of scissors.
Take the long piece of paper and put the ends together as if you were making a headband. Before you attach the two ends with tape, give one of them a twist and then stick the ends together.
Now try drawing a line along the centre of the strip. What do you notice?
You will end up back where you started, without having to take your pen off the paper. So you have drawn on both sides of the strip of paper in one go, meaning that your original strip of paper, which had two sides, now only has one side!
Now cut along the line that you have drawn. What do you think might happen?
Try it and see!
There are many other interesting things that you can do with this strip. Try making another one, but this time instead of cutting along the middle, cut a third of the way from one edge. What do you think will happen this time?