folding · How-to

The Paper Spring in the Classroom

Teaching kids how to make a paper spring is always thrilling. Children ooh and ahh, and practically jump out of their seats when I show them what we’ll be making.

The only problem has been is that it takes up a big chunk of my teaching time, as only about 55% of the students (who are usually 6-8 years old) in the classes I teach are able to make paper springs without extra help.

I’ve been teaching kids how to make paper springs for probably 20 years. Have shown it to thousands of students. We usually glue something to the top of it it, like a cut-out of their hand, to give the books we are making another dimensional element.

About a year ago, driving to another of my itinerant teaching-artist jobs, I was stressing over the fact that, due to time constraints I needed to cut something from my agenda . Realized the paper spring was going to have to be eliminated…unless…unless I could figure out how to get all of the kids to do make it without any extra help.

A caterpillar of paper springs
A caterpillar of paper springs

The way I’ve been teaching it is to glue two paper strips together to form a right angle, then alternate folding the strips on top on each until the papers fold down into a square. It’s easy to teach this method to adults, but kids keep folding in front then wrapping behind, which sabotages their springs.

 

 

Notice the corner is like a square, Draw a happy face on the square.

What if I ask students to fold the other way, to fold it below the glued corner, rather than above it? And to keep them from folding forward, draw a happy face which they are told should not be covered up?

Really, no one wants to cover up a happy face.

So I tried it out. Asked the students to alternate colors folding behind the happy face, said what we wanted to end up with is a little square.

Almost done

Couldn’t believe how well this went when I first tried it out. There is still a bit a confusion that happens when they see these flaps at the end.  I probably should say to cut off these pieces, but…

Last step

…these flaps can be  folded back too, then secured with a bit of glue.

This method of teaching has worked out for me unbelievably well. Unbelievable, even to me. Students have been nearly 100% successful in class after class.  So exciting to have discovered this way of teaching the paper spring.

Here’s a video:

 

folding · Paper Toy

Six-fold, flat-fold, Paper-fold

Paper Folding the Ferozkah Jaali
Paper Folding the Ferozkah Jaali

I found a fold.

If paperfolding graps your attention, prepare to be overwhelmed.  There’s three things to unpack here: the fold, the pattern on the fold, and how they interact.

I had been wondering if I could fold a tetrahedron out of a rectangle.

Tetrahedrons and other shapes
tetrahedrons and other shapes

Turns out, yes. I can make a tetrahedron with a square base or a triangular base out of the same piece of paper using the same folds in different ways.

Looks like a fish
Looks like a fish

Then I started seeing that I could make other shapes out of the same pieces of paper using the same folds differently.

Some shapes are flat, others are dimensional.

I’ve been playing with these all week, and I am still finding different shapes that these folds create.

 

I’ve also been drawing this six-fold pattern from Islamic Geometry called the Ferozkoh Jaali. It occurred to me that it would go perfectly with the folds I was making.

detail of Ferozkah Jaali
detail of Ferozkah Jaali

 

This is just a small portion of the pattern. I’ve been coloring copies of these in all week, trying to get to know the shapes.

Here’s the fold that I’m using:

 

Mountain and Valley folds
Mountain and Valley folds

It’s four mountain folds (diagonals) and two valley folds (horizontal and vertical) that are created around equilateral triangles. Oh, and there’s a slice in the middle. One horizontal slice.

Now here’s the first wonderful thing about using this image with my folds:

No matter how you use the creases (which are around the equilateral triangles) , the pattern lines up. In the photo above, a corner is peeking through that slice in the paper, and, look, the pattern lines up.

Equilateral triangle(s)
Equilateral triangle(s)

I printed the design on the fronts and backs of my papers, and look, when the paper wraps around itself, the pattern lines up.

Now there is one more thing to mention. Hold on to your seats. This is wonderful. But, first, here’s the foundation of the image I created, first by hand, then on the computer, because I needed the precision of the computer image.

Six-fold-geometry
Six-fold-geometry

Okay, so as I’ve been folding and refolding and refolding again, and finding different shapes all the time, the last final amazing thing that I noticed (and this makes so much sense) ….

Some heart shapes?
Some heart shapes?

…is that every shape I make with these folds is echoed somewhere in the lines of the  geometric drawing that is printed on the paper.

This makes me so happy, well, I can’t even describe it.

Another heart shape
Another heart shape

Well, there you have it. Hope you love it as much as I do.

covered with NOT geometry
covered with NOT geometry

Oh, and just in case you’re wondering, I think this fold looks good with just about anything on it.

 

 

 

 

folding · geometry and paper · geometry and paperfolding

A Square of Your Own

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?

Origami Pockets
Origami Pockets

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/

Arts in Education · folding · Uncategorized

Seeing Differently, Teaching Differently

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.