Cutting a double Möbius strip

Saw this sequence of tweets last week and thought that the paper cutting examples from the video in video linked by Patrick Honner would make for a great activity to go through with kids. I even recruited a few kids besides my own to try out the exercise.

.@Mythagon @dandersod A very nice progression of such cutting activities shown here: https://t.co/RojNhrqMdE #math #mathchat

— Patrick Honner (@MrHonner) May 26, 2015

Here are the four shapes that we cut in half:

The main purpose of the exercise was to hear kids talking about the shapes, and especially what they thought the shapes would turn into when cut. So, not as much discussion as usual, just ideas.

First up – my kids going through the four exercises:

 

 

 

 

Next up – a 2nd grade son of one of our friends:

 

 

 

 

I goofed up the construction of the double Möbius strip (you have to twist the strips the opposite way to make this work), so the 4th video is really our second time through, though 1st time with the correct shape.

Finally – a 4th grade daughter of one of our friends:

 

 

 

 

I loved hearing what all the kids had to say, and all of them seemed to really love these activities. Would love to go through this exercise with a larger group of kids – it would be amazing to hear all of their ideas about what shapes they thought they would see, and well as their descriptions of the shapes after we cut them. Lots of fun and lots of great opportunities to talk and share math ideas with kids here!