Cutting and Pasting Gets Mathy…and Moebiusy

This activity starts out feeling crafty, and then gets a little unexpected. Prep ahead of time by cutting out long strips of paper. Colored construction paper would probably be best in terms of flexibility and fun. I started with some extra pieces of water color paper that I had lying around. They worked, but were a little stiff.

Take one strip of paper and tape it into a cylindrical shape. Then take the second strip and tape it into a Moebius strip shape. To make the Moebius strip, hold both ends of the paper strip, make one twist, then tape the ends flat together.

Already your kids should be getting curious. I mean, how cool is it to have a twist in the loop! And maybe the cylinder makes a great hat. Go ahead and entertain those thoughts.

When your child is ready to try something new, get a marker or a crayon and pretend you are drawing a racetrack on the outside of the cylinder. You could make it a story…”Little Bunny Foo Foo was chasing a field mouse…” Or maybe your kid wants to do the drawing himself. However you choose to engage your child, the point of it is to note that if you draw a racetrack on the outside of the cylinder, you will always be on the outside of the cylinder. There’s no way to get to the inside without crossing a boundary (the edge of the paper.) You can also draw a line on the inside of the cylinder to note that you will never get to the outside.

Now ask your child what she thinks would happen if you cut this cylinder in half (along the long axis of the strip of paper.) Then do it.

Now repeat this whole process with the Moebius strip. Ask your child to predict what’s going to happen. Draw the racetrack. Oooh…interesting! Cut down the long axis of the strip of paper. Huh! That’s cool! What’s the difference?

If your child is still interested, find out what happens when you cut along the strip’s center axis again. The result is trivial for the cylinder, but what about the Moebius strip?

(Mathematically…a Moebius strip is a surface with only one side and only one boundary (edge). Yes, wrap your head around that. I’ve always thought that description made it sound impossible in 3 dimensions. But there it is, lying on my kitchen table. In this activity, you are exploring a little bit of topology. Topology is the study of shapes and surfaces as they deform. It’s an area of study that extends from geometry and set theory. That may be TMI for the purposes of cutting and pasting with your child, but it is interesting because it is a reminder that math is MUCH more interesting than the standard school progression, and our young children can and should explore more than just counting numbers. And we should, too. Did YOU know what was going to happen to the Moebius strip when it was cut? I didn’t. I knew it would be different than the cylinder, but I struggled with imagining it. So, maybe your teenager would be a little bit delighted with this activity, too! And maybe the kids are better at imagining than we are.)