#MathArtChallenge Day 53: Origami Firework from ONE piece of paper

The Challenge: Make the Origami Firework, but this time, only use ONE PIECE OF PAPER.

Materials Needed: A long piece of paper, patience, and the knowledge that I BELIEVE IN YOU.
Math concepts you could explore with this challenge: angles, origami, symmetry

This is going to be a bit of a divergence from my regular posts. I want to talk about a bit about learning, about leaps of faith, and full disclosure, it’s going to get mushy.

If you’d like to skip all that, head on over to Paula Beardell Krieg’s  post, which explains how to make the origami firework from a single piece of paper.

I had originally thought about doing this as a 2 day post, starting with Paula’s fantastic accordion folds, but I have faith, you can all do this in one. Or ten! Doesn’t matter, you play when you want to with any and all of these. I don’t know, but I think it’ll be helpful if you do the original origami firework before this. By all means, prove me wrong!

I spent most of the week trying to figure out what I had around the house that would work for this. A paper bag? Maybe. A piece of poster paper? Probably too thick? I finally settled on a piece of unicorn paper because the idea of unicorn paper becoming a firework was just too wonderful. It did mean that my firework was a bit smaller and thus a touch harder to work with.

As Paula states in her blog, you need a piece of paper that is at least 6.5 times longer than it is wide. Or, if you’re folding her accordion way, you want paper that is 8 times longer. I wanted to follow Paula’s lead, so I promptly divided my paper length: 27 inches by 8, to get 3.75 in. (You’re right, that is incorrect. I was too excited and went too quickly. Attend to precision Annie! But hey, it was a quick fix to get the proper length – 3.375 in – after I’d folded the accordion. Added bonus was this scrap curled really fabulously.)

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This brought me to the first challenge. Allow me to say, friends, contrary to what I’m sure you all believe, I am a rule follower. At least, certainly when it comes to origami. I like to see the next step, and even if it’s obvious, I want to know that I’m supposed to fold this like this and that like that. Paula, having faith in her audience, just said:

Which… okay. I can see that the diagonals of squares must be folded, and… huh. Okay. I looked around for more instruction to confirm that I should do what my eyes could clearly tell me I should do, and reassuring myself that it was only paper, I let myself fold.

Overjoyed to have succeeded, I turned to the next bit and cursed.

I love Paula, though, and I had faith that I could figure it out. I was convinced that there was no way those vertical edges would happen and was preparing to have to reach out and beg her help. But, again, reminding myself that paper is bendy and it’s just paper and I am lucky enough to have more (unicorn) paper so it was going to be okay, I attempted to figure it out and it… worked. The vertical edges feel magical to me, and I don’t really want to dive too deeply to figure out why they’re vertical, because it’s okay for some things to remain magical.

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This next step is the one where I think it may be helpful to have done the other, 12 paper-fold, first. It was helpful to me to recall what it felt like folding those folds, and I had to take a leap of faith that Paula’s instructions were sufficient for the fold I didn’t see (they are). If you get stuck, though, here’s what I figured out, and perhaps this would help nudge you along (again, YOU CAN DO THIS).

Again, the last step took a lot of patience and finicky folding and refolding. I kept reminding myself that paper has memory – assuring myself that it could find the folds again after I had clearly bent it out of shape irreparably (it wasn’t. It worked out).

Allow me to say it again: YOU CAN DO THIS. You might have to walk away for a while and come back when your emotions aren’t so high, and that’s just fine. You might have to start over. That’s okay too. I promise you, the finished product is worth it.

Also, If you need help, let me know, and we’ll set up a google meet or something. I will happily help you if you decide that’s what you need.

Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments! 

1.) Make sense of problems and persevere in solving them. When you’ve finished, what values do you see? What angle measures and what polygons?

6.) Attend to precision. This is a wonderful task to practice this. It is clear early on whether or not your folds are uniform enough to make this work.