Category Archives: Origami

Origami in Japan!

John Montroll's Grasshopper
John Montroll’s Grasshopper

Origami is one of the primary reasons I have devoted my life to mathematics. When I was 5, my parents gave me my first Origami books and I was immediately hooked. I can remember waking up early every morning to fold all sorts of models. The geometry, logic,  necessary dexterity, and focus were all mesmerizing.

Origami has been a constant in just about all of my math courses. We have constructed specific angles in Geometry,  studied complex surface area and volume questions with the help of modular Origami in Multivariable Calculus, and worked on edge connectivity problems in Algebra 2. There are seemingly infinite numbers of ways to work Origami into just about any math lesson! You can read about a recent class module right here: Star Project Part 1, Part 2, Part 3, and Part 4.

Star folding!
Star folding!

Not only can Origami be applied almost anywhere in math, it’s incredibly fun. We’re only a few weeks into class and I’ve already had several students approach me to ask about when we’ll be folding. I can’t wait to get started with this year’s students!

Last fall, as part of my quest to learn as much as I can about Origami, I sat down with one of the world leaders of Math and Origami, Dr. Thomas Hull, Associate Professor at Western New England University and author of Project Origami: Activities for Exploring Mathematics. Dr. Hull was, as expected, provided an absolute wealth of information! We spoke about how to best design Origami lessons, how to choose topics, as well as his recent sabbatical trip to Japan. His input was invaluable in helping me design my Williston professional development application to travel to Japan and study Origami!

screen-shot-2016-09-28-at-11-04-02-amWilliston accepted my proposal and  I was able to travel to Japan in August to attend the Origami Tanteidan in Tokyo. Needless to say, I had an incredible time!

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The Star Project Continues

Star folding!
Star folding!

After my BC Calculus students rocked the 2016 AP exam (check out their custom answer keys!), we started working on the Star Project.

The learned how to fold a 60-piece star, and then I asked them two straight-forward questions:

What’s the surface area of the star in terms of the side length of one of the pieces of paper?

What’s the volume of the star in terms of the side length of one of the piece of paper?

Here are some of their video solutions. The complete playlist of videos is online here.

Surface Area

Volume

Star Project Update 1

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All of my students now know how to fold the building block piece that can be used to make a 60-piece star, or many other shapes. Here are the three stars I’ve built from the pieces my students have folded.

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Their homework over winter break is to experiment with putting the pieces together and to see if they can construct their own 60-piece star!

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The Star Project

The next layer is complete

Over the past week my BC & Multivariable Calculus class has begun their journey working through the wonderful land of three dimensional space. In order to get my students to think more deeply about the dimensions they are now operating within, I have been working Origami into my lessons. I started with hyperbolic paraboloids and now have just taught them the first few skills they will need to create their own 60-piece stars.

Voila!
Voila!

They now know how to make the pieces and over the next few days I will be helping them figure out how to fit them together into a closed, 60-piece star! Here’s what the whole process looks like:

Hyperbolic Paraboloids

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One of my favorite surfaces is the hyperbolic paraboloid. So, of course, all of my students need to know how to fold one from a square sheet of paper. Last night my BC & Multi students practiced their folding skills and today in class their quiz was to fold one on their own without the instructions. They certainly impressed me with their folding skills!

Here are the instruction (PDF). Try folding one!

Their homework creations:

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Folding quiz:

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The hyperbolic paraboloid lineup!

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A family:

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The hallway bulletin board:

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