A Square of Your Own

January 21, 2018

Squares, scaled

Squares, scaled

Making a plain old square exactly the size that you want can be such a chore. Too much can go wrong.

Squares can become so many different things (think ALL origami) that it’s worth knowing how to make a square just the size you want without getting stressed out.

Here’s how to do it, via the photo essay, followed by the video tutorial.

plain piece of copy paper

plain piece of copy paper

Here’s a regular piece of copy paper. The first steps look like I’m heading towards folding a square whose side is already predetermined by the short edge of the paper, but no. Be patient. This is going to be a surprise. Trust me.

First Step

First Step

Fold that short edge to meet the long edge, making sure that your fold ends (or starts) exactly at that corner. What you are doing here is bisecting that corner angle. If you cut away that rectangular flap on the edge, and unfold the triangle you’d have a square, but this isn’t what we are doing now. (Doing that was a different post, )

Marking the size of the new square

Marking the size of the new square

Unfold the fold then make a mark to indicate size of the square you want to make.

continuing...

continuing…

What I’m going to write next sounds horribly complicated but it’s easy to see and do.

Curl over that corner that has the fold going through it, lining up that corner point with the fold line it is leaning towards, and also lining up the upper edge of the paper with that mark you made. Press the fold.

Here’s a closer to look:

Closer Look

Closer Look

Now draw a line that traces around that folded down corner.

Time to cut out the square

Time to cut out the square

There’s your square!

Confused? Here’s a video to watch:

Got it?

Now make cool stuff.

Addendum: here’s a post that shows what I showed, plus another great way of making a square. https://mikesmathpage.wordpress.com/2018/01/23/a-fun-folding-exercise-for-kids-from-paula-beardell-krieg/

I don’t understand  why certain of my projects with kids get more attention than others. My original post about Sight Word Pockets Book for Kindergarteners  from 2011 still gets viewed every day. My teaching season doesn’t go by without requests for this project. By now I have taught literally thousands of young students how to make origami pockets, but it’s never easy. I’m always looking for a better way to explain this folding method.

A titled square is still a square

A tilted square is still a square

I’ve come into this teaching season thinking differently about folding paper.

For so many years I have been telling students what to do. This year I have prioritized trying to draw their attention towards what to see.

They all recognize a square, but when I tilt it, students say its a diamond, a rhombus, or a kite. Last week I suggested to students that this shape was still a square, then I was relieved when a  classroom teacher chimed in and emphasized that tilt or no tilt, the shape was still a square. The main thing, though, is that this simple rotation and the conversation riveted students’ attention to the shape.

Folding a square point to point, from the top down

Folding a square point to point, from the top down

I’ve been asking students what happens to the square if I fold it corner to corner. They all seem to be able to predict that folding a square point-to-point can make a triangle. This makes them happy. They seem to like triangles. Then I tell them that with just one fold more I can make many more triangles. What magic can this be? I have their full attention. They are watching to see if this can possibly be true.

Folding just one layer of paper, I fold the tip of the triangle down to the base. The children are delighted. We count the triangles. Are there four triangles? Are there five?

The next step is the tricky step but now students are attached to the shapes that the folds make and have a heightened awareness of triangles. When I talk about tucking the edge of one of the triangles under the flap, they see what I mean. Here, look at this video. It absolutely blows me aware that this five-year-old just learned this folding sequence about a half-hour before I filmed her doing it. Notice how sure her hands are as they move through the steps.

This change in my teaching, prioritizing seeing & predicting over telling & doing feels really good.  It’s happening because I’ve begun to be able to answer a question I’ve been carrying around in my mind for years: I’ve really looked hard at origami , trying to figure out what about it compels some people say that origami is somehow like math.

Now I’m coming to understand that it isn’t origami that I needed to see differently, it’s been my understanding of math that I needed to adjust before I could make the connection. Now that I am seeing math less as addition and subtraction, and more as relationships and transformations, the boundary between origami and math vaporizes.

More and more I am trying  to be  attuned to childrens’ seemingly intuitive connection to ideas that are aligned to a broader understanding math, and I am able to tap into this with great results. I help them see what is already familiar to them, and what happens next is that they better understanding what’s going on, and can figure out what to do next. Yes, even five-year-olds can do this.

 

Paper folding in the morning

Paper folding in the morning

Yesterday I watched a video that showed the Lawler family looking at shapes.

One of Mike’s sons said he liked the top shape in the image above. You can’t see from the photo, but it’s a full sphere. The image above is only half of the sphere, the other half looks no different than the half that is showing. I’ve played around with constructing foldable versions of shapes that look something like the one above, and I thought I’d be able to make a foldable version of what was on Mike’s screen.

Template for folding and cutting

Template for folding and cutting

I’m not showing all the steps that led to this map of folding and cutting because what I’m most interested in showing here are the wonderful visuals I got to experience along the way of creating the final structure.

Folding and Cuttin

Folding and Cutting

Silly as it may seem, one of my first realizations was that the indoor, nighttime lighting in my workspace was just all wrong for photographing what I was about to fold. Morning light would be best. So I went to bed.

Assembling in the morning light

Assembling in the morning light

Of course I forgot to recharge the battery of my phone camera before I went to bed, so I didn’t get the earliest light.

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Hmm, I don’t really want to say much more about this process. I’m just going to post pictures now. (Haven’t had my coffee yet.)

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zzzz

Ok. Time for coffee. Am heading to Rochester today to bring my daughter back to college. Will be thinking about all shapes that this structure made. (Which reminds me of a question someone once asked me, “What, do you just sit around thinking about folding paper?” Well, yeah.)

Twist Box tutorial Zhen Xian Bao

Twist Box tutorial Zhen Xian Bao Here’s a link the  PDF

Zhen Xian Bao, Chinese Thread Book, Post #1 intro

Zhen Xian Bao, Chines Thread Book, Post #2, starting with the finished size

Of all the posts that I plan to write about the Zhen Xian Bao, this will likely be my favorite post. Figuring out both how to make this twist box and explain it have kept me happiliy distracted. I’ve looked closely at photos of people making them, watched clips of the twist box being opened and closed, examined templates, and studied videos (all available for you to see on my Zhen Xian Bao Pinterest board). Then I just kept making these boxes until I was happy with the results.

Twist Box, opened and closed

Twist Box, opened and closed

These boxes are the top layer of the Chinese Thread Book, a structure that is made up of layers of collapsible boxes. Not all of the Zhen Xian Bao have twist boxes on the top, but it’s the style of box that I like the best, as it’s so very different from any of the other boxes in the rest of the structure.

There are numerous versions of the twist box.

The version of the twist box that I originally fell in love with was designed and demonstrated by Chrissy Paperkawaii. While I still like much about her no-cut, no-glue version of the twist box, it’s just a bit too bulky for my liking; also, it was really difficult to twist, and if I could barely make it her way I knew I wouldn’t be able to teach it.

A twist box that I thought I liked the least, but which I now appreciate, appears to be made from a template created by Lori Sauer, which Rachel Marsden wrote about. Rachel’s post is one of the most beautiful pieces I’ve seen on the Zhen Xian Bao. You really must take a look at it. Here’ s the photo of the not-yet-folded twist box that Rachel Marsden made from the template.

You might notice that this shape is almost exactly like the nineteenth drawing on my tutorial page, meaning Rachel probably got her twist box done in few less steps than me. The only reason that it’s not my favorite is that it’s made from a template. So what do I have against templates?

The first answer that comes to mind is that it can be tricky to scale a template. As part of a collection of different styles of origami boxes, I want a reasonable way to scale all the different elements so that I can make whatever size thread book that I want.

The other reason that I prefer not to rely on a template is that being able to figure out the system of folds from a rectangle gives me the chance to fully understand and appreciate the foundational symmetry of the structure that I am folding.

Not long ago I wrote about a fairly tricky folding structure. I included in my post the hard-to-read-and-decipher tutorial page that I had followed as well as a video. I then aimed to entice my highly accomplish weblog friend Candy Wooding to make the piece (she did!) and then asked her if she preferred the video or the written directions. She said that the video was good to start with, but then the written directions provided her with reminders. With this feedback in mind, here’s a video of making the twist box.

Disclaimer? I know I’m not that good at making these videos. Sometimes things fall off the edge of the frame, and my hands get in the way, but I’m hoping that the more I make these the better I will get at it. Still, I think this imperfect video is plenty helpful.

One last note:

Twist Box for Zhen Xian Bao Black and White tutorial

Twist Box for Zhen Xian Bao
Black and White tutorial Small PDF File for Twist Box

Here’s the black and white version of the Zhen Xian Bao tutorial page. You can color in this one in yourself. It’s a small PDF file, unlike the huge color file at the top of the page. I haven’t figured out how to make a small, colored downloadable file to post on my blog.If someone wants to offer me some pointers, I’m interested!

My next Zhen Xian Bao post will either be about the box that is the next level down, or about ways to decorate this box. Haven’t decided yet. Though I know I won’t be able to get to it right away, still, I’m looking forward to post #4! Make boxes! Thank you.

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