James Tanton’s incredible Möbius strip cutting project

Today we revisited one of my all time favorite math projects for kids (also **revisiting**) :

We did this project once before, but I don’t think the kids remembered it:

An absolutely mind blowing project from James Tanton

The project is relatively simple to set up – you have strips of paper and make 5 Möbius strip-like shapes.  If the short descriptions below aren’t clear, don’t worry, the videos have the “picture is worth 1,000 words descriptions

(1) An actual Möbius strip
(2) Same set up as making one Möbius strip, but you start with two strips of paper stacked on top of each other,
(3) A cylinder with a long oval cut out and a half twist on one of the strips left over after removing the oval.
(4) A cylinder with a long oval cut out and a half twist (in the same direction) in both of the strips left over after removing the oval.
(5) Same as (4) but the twists are in opposite directions.

Then you cut the shapes. In (1) and (2) you cut completely along the center line. In (3), (4), and (5) you cut around the oval.

What shape are you left with after the cutting?

(1) Cutting a Möbius strip

(2) Cutting two strips of paper folded into a Möbius strip

(3) Cutting a cylinder with an oval removed with one half twist

(4) Cutting a cylinder with an oval removed with two half twists in the same direction

(5) Cutting a cylinder with an oval removed with two half twists in opposite directions

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