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Möbius Strips

1. An Activity

What was it that day? Maybe there was a planned fire alarm. Or maybe a lot of kids were out testing. Whatever it was, we didn’t have a lesson. We had an activity, instead.

In the morning, I had cut strips of blue paper for the in-person students — two inches wide, 11 inches long. Three strips for each. For those on Zoom, I had posted instructions on what tools they’d need, how to make their own strips, how to get ready for what we were going to do.

“Do this,” I said. They followed what I was doing under the light of the document camera. We made a loop out of one of the strips, taping it together at the end. Then we drew a pencil line down the strip until they got back to where they started.

We agreed to the non-controversial conclusion that the paper had two sides: one side with the line, the other without it.

“Now do this.” We made a different kind of loop from another strip, twisting it just before taping the ends together. “And draw another line.”

“No way!” someone in the back of the room said. We had arrived at the odd conclusion that the paper no longer had two sides. Without picking up their pencils, they had drawn a single unbroken 22 inch line that somehow traversed what used to be the two sides of the paper: a Möbius strip.

2. Scissors

With a spritz of disinfectant and a paper towel, the kids grabbed scissors from a basket as I walked around the room. (They’re high school kids, but they still love using scissors.)

Together, we cut down the middle of the Möbius strip. Again, someone in the back got it: “Cool!” One big twisted loop.

Finally, we made a third strip but this time cut it not down the middle but off to one side. It pushed the limits of their scissor-hand dexterity. 

I was asking them to tell me what they thought was going to happen when voice in the back of the room shouted, “Wow!” and held up their result: two twisted, interlocked loops. A Möbius chain?

3. Feedback

Who knows what the Zoom kids thought.

I can never tell whether they’re even really there. Some obviously aren’t, since they don’t sign off at the end of class. And some seem to be. But how can you tell what they really think — of the lessons, of the problems, of today’s activity?

Then at the end of the day, a student email showed up in my inbox.

“Hi Mr. Hasan. I want you to know that I participated today.” And they attached this picture. “This was fun.”

A student's mobius strip