Triangle Inequalities

On Saturday we went to see a show by this company (amazing tap dancing) and here's some footage from a past show. And as I was sitting in my seat fidgeting with the ticket stub, I got what I think was a great idea. Then I thought, oh surely other people already do this, and I just missed the boat. And now, maybe I'll never sail on that boat again for a while because I may not be teaching geometry next year. And then I went back to fiddling and thinking with my ticket stub.

I was thinking about the lesson on the restrictions on the 3 side lengths that can potentially make a triangle - how any 2 sides of the triangle have to sum up to more than the length of the 3rd. I've taught it various ways. We always explore with a variety of things. BUT. I've never used anything I'm completely satisfied with:
- spaghetti: messy, hard to measure, the thickness may allow students to think it's still possible, hard to get the situation where 2 of the shapes EXACTLY add to the 3rd.

- linking cubes: too thick, and sometimes students would still think they could make a triangle when they couldn't.

- cut strips of paper: see above

- drawing the triangles using compasses set at various lengths: too cumbersome.

PAPER SHOW TICKET to the rescue! Here's my idea. Cut some long strips of thickish paper (cardboard/stock paper?), or have them cut them. Maybe give one or a few to each student. Then have the students experiment with laying it flat on the desk and folding in from the two ends. They can write down all the situations they tried and measure the three resulting sides in centimeters and see what sorts of situations allow them to make a triangle from the resulting 3 sections of the strip. You may even have guiding questions about: "what 3 lengths are not even in the running and why not?" .... "what 3 lengths ALMOST look like they'll make it, but don't?" ... something to that effect.

I think this will be much better than my old props: easy, able to try a variety of cases, cheap, effective.