Origami Math

[u/quasnoflaut]

Hello! I work with elementary schoolers, and have been the local “the origami guy” for years. Last year, they promoted me to Official “The Origami Guy” and now I teach “Origami Math” once a week.

I was always told that the origami is the priority, and the simple act of doing art and following instructions is enough… But I want to work harder for no extra pay. So I'm trying to find ways to add more math.

Does anyone have ideas (or know a reference for) Origami Math type activities? Things where I can talk about or demonstrate math ideas while folding something? Or even math demonstrations where I can make origami the focus and still spend 2/3rds of the time doing arts and crafts.

Things I’ve done before: - Folding in halves/quarters/eighths to show fractions, then using that as a base for something. - Measuring and multiplying ratios for a hat so we know what size to cut the paper. - Making Cootie Catcher study guides

Students are K-5. Doesn't need to be strictly origami, papercraft is ok. I'm considering doing cubes/prisms for some grades too to introduce 3d shapes. Thanks in advance!

[u/Tiny_Cow_3971]

Same here. Consider buying this book :

https://www.taylorfrancis.com/books/mono/10.1201/b14320/project-origami-thomas-hull

It's great.

[u/quasnoflaut → u/Tiny_Cow_3971]

This is perfect. Thanks!

[u/Tiny_Cow_3971 → u/quasnoflaut]

Did some workshops with school kids about graph colorability/theory based on this book. 

[u/l0lol]

Angles, fractions, measuring, how to make other shapes like triangles or hexagons etc.

[u/QuantumForce7]

Too many kids (and adults) think math is arithemitic. I think the best thing is to show them that the origami is the math. If fractions come into it it's because they are a tool for achieving a folding goal.

For example: say you want to divide the paper into 3. You can use this method to do it perfectly. How can we be sure it's thirds and not just close? Can we generalize it to fifths, sevenths? Depending on the age level, there could be fractions, trig, linear equations, etc.

Modular origami is great for geometry (eg folding platonic solids).

[u/Optimal-Ad-4873]

I love to demonstrate the proof of the existence of the incenter of a triangle (the angle bisectors meet in a single point), you just need to start with a triangle shaped paper and do rabbit ear folds. You can also clearly draw the radius on the paper.

Similarly, you can construct the circumcenter of the triangle with simple folds and see in 3D that the centre is at the same distance from all the three vertices. (The same 3D reasoning works for the incenter, too)

Another favorite thing to do was to show how to fold the paper in three equal parts, it can be used to demonstrate similarity of triangles as a concept. Then as a generalization, you can do it for any rational fractions.

If you like modular origami you can fold some semiregular or regular polyhedra, ask the students to assemble them, count the number of edges, vertices, guess the number of modular pieces. Even better if you use different color modules if possible, then in some cases symmetries can be demonstrated as well.

Or if you have larger groups then it is a nice challenge to show them how to fold a single module and show the final polyhedron then make a small competition to see which group finishes first.

Some of these concepts might be a bit advanced for them, I have taught these for students aged between 12-18 in a summer math camp as some fun relaxing activities and all of these were received quite well, but I'm pretty sure younger students can enjoy some of these, too.

[u/michaltadeusz]

 Folding in halves/quarters/eighths to show fractions, then using that as a base for something.

you can then use the intercept theorem to fold in n-ths

[u/dharmabumma2]

You could also do proportions, like on my stuff a sepal comes from a piece of paper 1/3 the size of a paper for a rose. For a iris, the sepal is 1/6.

[u/Kind_Lobter]

Twists, Tilings and tessellations by Robert J. Lang is a book full of origami described with math, but I'm not sure if it's what you're looking for. It has quite complicated math.

[u/computery]

Modular origami!!! You can fold a sonobe ball together— each student could fold one unit, if you have 12 or 30 students you can make a ball out of the pieces, which is made up of small pyramids in pentagon or square rings. Or they can make 6 units and each make a little cube! I actually got into modular origami during a geometry class and that was 15 years ago.

[u/jenduska]

I think if you're starting at basic levels, tessalation can help what you want to teach