# Math/ Geometry with Origami

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A friend PM-ed to ask how we teach geometry using origami and I responded with the below. I've found origami to be a great tool to bring some excitement to learning. If you are an enthusiast, please share origami resources you have enjoyed too!

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Would you mind elaborating a bit on how you teach geometry with origami?

I taught very little, he's a very intuitive learner. Apart from executive functioning issues and some math when he was younger, and just frequent discussions, there's very little that I "teach" my son. Even when we started, we just folded together especially to give as gifts or he folds for fun and collects them all in wicker baskets under his bed. It is mostly a fidget activity while he focuses on a video lecture or watches TV. We started with a bunch of origami books (cheap ones from Amazon, used book stores etc -- doesn't really matter what title you choose as long as it is easy to follow along) and we didn't actually set out to teach geometry with this. But when he was younger while folding, I would mention the shapes, I would mention how a fold he just made bisects an equilateral triangle etc, I would point out acute angles, vertices and so on, not in an obvious, pre-planned way but just whenever it occurred to me to do so. When he started using Patty Paper Geometry, he started seeing more connections (we never finished PPG...ended up unschooling it). Now after starting Geometry proper, he can name some of the things he does with the paper by the theorem or he'll come up with some idea and see if he can fold it. It isn't necessarily always beautiful...that's not the end objective. Our objective is just fold, focus, have fun in the process, observe what happens.

I think the biggest lesson was that learning can be fun. It can be cool. That math is everywhere. Once you can establish this attitude, there's actually very little teaching you need to do because a very interested kid can self-learn. You have to trust in that process.

Origami is very fun for geometry reinforcement. And the sense of having made/ produced something with your hands is very satisfying. And I love how calm and focused he gets when he is folding. We always include origami somehow in our Christmas celebrations...to attach to gifts, to create ornaments for the tree, to give to friends who visit and so on.

I have some links bookmarked if you want to look into it some more:

http://www.greenfuse...rigametria.html (also available on youtube -- search for origametria)

Between the Folds documentary streams instantly on Netflix

http://www.utc.edu/F...a04origami.html

http://www.origami.org.uk/

http://www.origami.as/home.html

http://origami.wonderhowto.com/

• 10
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Funny that you mention this as I was just thinking yesterday about origami and math. :001_smile: Is your friend using Singapore math? We do, and yesterday our first grade math lesson demonstrated halves and quarters by folding square papers.

We've used an origami daily calendar, and we could tear off an origami square with instructions for a design each day. My kids loved it! http://www.amazon.com/gp/offer-listing/B008M1AD2O/ref=sr_1_1_olp?ie=UTF8&qid=1361904078&sr=8-1&keywords=daily+calendar+origami&condition=new

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Thank you for the resource. It looks cool

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I've just been googling the middle-highschool Waldorf Geometry. It's soo.. pretty..

off to google Patty Paper Geometry. All we have is the magnetic mighty mind.

We did get a paper airplane orgami set from the dllr. store once.

There was only one he could do.

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Oh! Subscribing to this thread . . . I have a DD who loves origami and can do very complex shapes and then tells me she's not very good at math.

:)

I'm on it.

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I recommend Vi Hart's videos to any gifted child interested in creative math. She has great videos on many topics, including paper-folding. My 7 yr old spent 3 hours one afternoon watching this video frame-by-frame so she could fold hexaflexagons.

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My ds just constructed an all white "5 interlocking tetrahedral frames" shape. It took him 4 hours! He got the instructions off the internet. It is origami -- no tape, no glue.

I've inserted an image for your enjoyment!

Ruth in NZ

• 23
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That is just gorgeous, Ruth! Wow! Amazing stuff. Tell him I love it!

I thought of this thread earlier this evening, as ds and I were listening to AstronomyCast. They mentioned that JAXA (Japanese Aerospace Exploration Agency) was using origami techniques to pack and deploy solar sails. This link is for science and origami. Scroll to the bottom for the solar sails info.

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I loved that between the folds documentary. DD loves to play with making origami but is a little young still and struggles somewhat and often needs my help to get the folds right, I think that the book we have is a little confusing in it's written directions at times!

Love the origami calendar idea, I'll have to remember that for next year.

What age/skill level would you recommend the Patty Paper Geometry for?

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• 3 weeks later...

Quark,

This is a great thread which I saw once but then couldn't find! The search feature seems a bit lacking now. So I started a new thread in the Logic Stage forum. Oh well. :rolleyes:

Ruth, your photo totally inspired me! :thumbup: You see my son *loves* origami. So I shared an instructional with him on the interlocking tetrahedral. A few hours later here is his rendition:

Please share more photos of your kiddos' work guy/gals. There are so many cool shapes, creatures, etc... out there to make. I found an awesome eagle which is very complex. The instructions are only available from a hard to find book called 'License to Fold.' I tracked down an eBook version of it which I may purchase, though its in Euros. I guess Paypal could still work regardless: http://www.origami-s...6_208-2026.html

BTW, has anyone looked at the book by Robert Lang entitled 'Origami Design Secrets: Mathematical Methods for an Ancient Art?' I am considering this as our next purchase.

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This is too cool. I think I want to make it...

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Oooo Very cool thread. I love Vi Hart's videos. We have a Dover origami book (http://www.amazon.com/Dover-Publications-The-Complete-Book-Origami/dp/B0055DBXWQ/ref=sr_1_13?ie=UTF8&qid=1364430306&sr=8-13&keywords=dover+origami) that has nice directions. If you don't know your origami terminology, you have to start at the beginning because the author teaches the terminology and folds in successively more difficult projects. Not very mathy, but we've had lots of fun with it. Youtube should be great for origami. I wish we'd had it when I was little. I can remember begging my mother to help me make things out of this gorgeous big origami book our public library had. She usually put me off, knowing that it was going to take time for her to figure it out. I really needed youtube lol, for lots of things.

Nan

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• 2 months later...

I spent my pregnancy with DD (on bedrest for several months) building and needlepointing 3D platonic solids and polyhedra(perhaps it isn't a surprise that DD ended up being a math geek ;) ). Plastic canvas can also do curves, which makes it a nice medium to work in for geometric constructions.

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• 2 weeks later...

My 7 yr old spent 3 hours one afternoon watching this video frame-by-frame so she could fold hexaflexagons.

My 7 year old is absorbed in the book Hexaflexagons and other mathematical diversions by Martin Gardner. MAA posted the chapter here http://maa.org/pubs/focus/Gardner_Hexaflexagons12_1956.pdf

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Here's another ds11 just folded for a Father's Day gift. I wanted a two toned blue version which I plan to take it to work. ;)

I ordered him Origami Design Secrets: Mathematical Methods for an Ancient Art for his birthday. It looks like a great book.

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What a beautiful thread - thank you for posting.

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I want to thank you for starting this thread, also. My kids have had a lot of fun with origami and hexaflexagons and more. Great entertainment value in the extreme heat!

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Squishy origami anyone? :D

See thumbnail for DS's version.

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I loved that between the folds documentary. DD loves to play with making origami but is a little young still and struggles somewhat and often needs my help to get the folds right, I think that the book we have is a little confusing in it's written directions at times!

Love the origami calendar idea, I'll have to remember that for next year.

What age/skill level would you recommend the Patty Paper Geometry for?

DS is 10 and still struggles with some folds too. He is a little delayed in the fine motor area but I can tell you that perseverance helps and so does a can-do attitude and a willingness on my part to not expect perfection (it's hard for me!). It's wonderful that your DD has interest. Interest trumps everything else in my book!

Not sure if you already have your answer for PPG. We used PPG off and on starting from age 8-ish. I feel that a 9-12yo will appreciate it better.

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I ordered him Origami Design Secrets: Mathematical Methods for an Ancient Art for his birthday. It looks like a great book.

Derek, that's such a cooool gift! And thanks so much for sharing the link...the book looks wonderful!

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• 4 weeks later...

The kiddo has been making his own simple origami designs for a couple of years but lately, he is graduating to creating even more intricate origami creations. He made a fun-looking folded contraption yesterday and wrote out all the instructions for others to follow but it feels way too complicated to me without pictures. One way we think he could offer the instructions is through a youtube video but I'm also curious about origami diagramming software so that he can include sketches with just a few clicks. He could also draw them out manually on paint or something but it might take more time than he wants to spend. If anyone is interested, here are some bookmarks I've found on producing origami instructions with diagrams using some kind of online tool:

Diagramming Origami

Inkscape.org - haven't used it yet but I think it's free and it looks like the best one out there for now. Youtube instructions here.

Foldinator - bummed that this doesn't seem to have made it to the launch stage. Looks like it could the simplest one to use...fingers crossed that the creator gets the financing he needs.

Some of the ideas above seem a little dated but I'm not able to find newer, easier-to-use resources, e.g. like an Origami Diagramming for Dummies software. :) Or maybe I'm just not looking in the right places?

Please update if you have ideas or know better origami diagramming resources!

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Does anyone have a recommendation for a source for origami paper? My kids are young enough that I'm going for quantity over quality for this round, but I'm interested in recommendations for both, as well as for sizes.

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Not sure what your budget is.

Do check ebay. Rainbow Resource has them too. I have always bought from Amazon...I can't remember the specific pack I bought. This 500-sheet pack for e.g. is about \$11 and should last awhile: http://www.amazon.com/School-Specialty-Folia-Origami-Pack/dp/B000I0QCOK/

This is the standard-ish 6x6 size. Smaller sizes will usually be more uncomfortable for smaller hands.

Since you have young-ish ones you might want to go for something like 10x10 (or sometimes it's an odd size like 9.75x9.75) paper but you might not need to buy it in a huge quantity because by 3rd grade my son was doing okay with the 6x6 size. Depends a lot on fine motor control. Mine had issues that resolved only when he was 9.

We've also used newsprint, gift wrapping paper, flyers we get in the mailbox, printer paper cut into squares, patty paper...

You may also want to try scrapbook paper...the thinner ones do look good when folded. Not the card stock types.

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Daiso and Kinokuniya have nice ones in all kinds of sizes. However for quantity, cutting up cheap rolls of gift wrapping paper makes more economical sense. We buy off season wrapping paper very cheaply and the thickness and glossiness is similar to origami paper.

Great, thanks!

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• 1 year later...

I know this is an old thread, but I am wondering if anyone can help me with a book title or two.

This morning I showed my origami- and math-obsessed 7th-grader the Vi Hart videos and the photos of interlocking tetrahedral frames some people posted here.  Her eyes lit up and if she hadn't had a lot of other obligations today I think she would have spent all day on them.  At one point she said, "I wish I could find books with this kind of thing."  She far prefers paper books over internet sites.

She already has several Lang books, several Tomoko Fuse books, and several other origami books, and has made all of the hardest shapes out of all of them (except she keeps hanging up in one place on Lang's bass player!).  She has made an amazing spring, some gorgeous unit origami shapes, and some beautiful animals, among many other things.

Her birthday is coming up, and I'd love to get her a book that helps her move forward with this passion.  Can anyone recommend a book that has things like the hexaflexagon and the interlocking tetraheral frames?  Even if they don't have those specific shapes, I'm sure there are lots of cool things out there for her to discover.

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These are my ds's favorites:

Origami Design Secrets version 2 by Lang (mathematics behind designing origami)

The Works of Satoshi Kamiya volume 1 and 2. (contains some super complex designs)

We also bought some origami super large paper from France.

Ruth in NZ

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Thank you, Lewelma and Endofordinary! I am going to look up all of these. They look really promising!

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This thread has rekindled my childhood interest in origami! I've just ordered paper and have requested a book (origami dinosaurs!) for Christmas. Once I get proficient at folding I hope to tackle some of those beautiful geometric shapes.

Thanks for the inspiration!

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• 6 months later...

Just giving this a bump for some summer fun.  :)

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Thank you 8! I can't wait for DS's finals to finish next week. We have much fun planned including origami sessions at home and possibly, with friends.

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Thank you, quark!  You are the one who started the thread.  :)  My kids had a lot of fun with this when the thread was first posted. Our life has been pretty stressful b/c my 16 yod has been quite ill.  I was looking for a distraction for the 13 and 9 yr olds to do with big brother.  This link is it.

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8, I hope your 16yo recovers quickly. I just said a prayer for your family.

Thank you for bumping this thread!

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This thread has rekindled my childhood interest in origami! I've just ordered paper and have requested a book (origami dinosaurs!) for Christmas. Once I get proficient at folding I hope to tackle some of those beautiful geometric shapes.

Thanks for the inspiration!

Quoting myself to give an update. Thanks to this thread I did get that origami book for Christmas and have been making adorable little paper dinosaurs! I also got ds a beginner origami kit and he has been having fun too. He made a paper ball and I knew it looked familiar. I dug out my memento box from my trip to Japan many years ago, and there inside was the exact same origami ball I had crafted while on the trip. We went through the whole box and I got to share my memories of Japan with him.

Hugs to your family, 8. I hope the origami gives your kids some peaceful moments in this time of stress.

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I recommend Vi Hart's videos to any gifted child interested in creative math. She has great videos on many topics, including paper-folding. My 7 yr old spent 3 hours one afternoon watching this video frame-by-frame so she could fold hexaflexagons.

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