Fold and Cut Theorem and Walking Through an Index Card

http://www.origamiplayer.com/orimath/embed560.php?ori=betsyrossstarfroma4

Yesterday, I threw my lesson plan out the window. It doesn't (can't) often happen in my Algebra 2 Honors or Pre-Calculus classes, as we have a lot to cover in those classes. But it does happen in my Honors Problem Solving Seminar, and those normally tend to be the best lessons.

I try to show students great videos, and this on The Fold and Cut Theoremone popped in my inbox. I didn't watch it, but planned to. Then, one of my Mu Alpha Theta members forwarded it to me, raving about it. So the next morning, we watched it together. It turns out that you can take a piece of paper and fold it several times and may ANY shape with just one cut, as long as the shape is made of straight lines. What???

erikdemaine.org

Check out this video to watch Katie Steckles cut out the entire alphabet and more with one snip of the scissors.

What was very cool for me is that I LOVE to watch these videos with my students without previewing much so I can discover along with them. As soon as she started mentioning the 5 pointed star, I stopped the video and told students that I played the role of Betsy Ross in 5th grade and found out how she impressed George Washington by cutting a 5 pointed star in one snip. I continued the video, and that was exactly the history lesson that was taught...so of course, we had to try it!

I was shocked at how "folding challenged" my students are. I am, too, so this is why I was so shocked. I pulled up this diagram from http://www.ushistory.org/betsy/flagstar.html and we had a lot of fun cutting stars (and recutting when they did something wrong.)

This reminded me of a different activity where you can cut an index card in such a way that you can literally walk through it. I gave my students some time to think about how to do this on their own. They were so funny and cute when they thought they had it, but then they realized it was actually open on each end. I think it's important to let them try it on their own. One student actually had seen this before and demonstrated the right way to the rest of the class (remember I told you that this class, as brilliant as they are--so smart!--are self-claimed craft-challenged), and most finally got it...it was very cool. Below is the video.

Finally, we did go back to the lesson, which was to work on a Speed Math challenge from famat.org. Here is a copy in case you would like to try it!