James Tanton’s Solve This book is full of incredible math projects to do with kids:

Today we went back to do a project that we’ve looked at a few times before – cutting various versions of a Möbius Strip.

We started with a cylinder just to get going with an easy shape:

Next we moved on to a Möbius strip – but when we made this one we didn’t notice that we’d made a full twist rather than a half twist. So we sort of got two surprises. I’ve included this mistake to show that you do have to be a little careful when you do this project – it is easy to accidentally make the wrong shape:

Here’s the correction and the actual Möbius Strip:

Next was a shape where we had a 2nd little error – this time the tape held the final shape together a bit too much. In our video you can sort of guess what the actual shape will be, but I definitely encourage everyone to try this one out for yourself!

The 4th shape is where things really get interesting. For this and the next two shapes we are making a circular cut through a cylinder with a hole cut out of it. Each of the shapes has a interest set of twists in it – the shape in this video has a single half twist on one of the “arms”:

The 5th shape has half twists (going the same direction) in each of the arms:

The 6th shape has half twists going in different directions in each of the arms:

This really is an amazing project for kids. As our version of the project here shows (accidentally!), you do have to be careful with the preparation, but even with the couple of errors we had, it was still an incredibly fun morning.