# Simple Folds that are Hard

Folding a square diagonally is not in most people’s skill set.

There are so many applications of diagonals, not just in paper folding but also in math, that it’s a worthwhile concept to chase down and cozy up to, but it needs to be done carefully.

Having this extra time home these days, I find myself wanting to write about these big/small details that teaching has taught me, that feel important to share.

If I ask a student to fold a piece of paper in half, they fold the paper in half. Generally I ask students to refine their intentionality with the paper so that their paper is folded evenly. The older they are the more they love this lesson. The whole experience of folding paper is half is a pretty happy place. Until it isn’t.

What shape is the paper in when you fold a square in half? Think about it before you raise your hand, and don’t change your answer because of what someone else says, and I’m going to call on everybody who has their hand up.

I see every hand go up. Rapid fire around the room, rectangle, rectangle, rectangle. Then someone say triangle. Just one person. That person is so brave. I ask that student and another student to come to the front and prove their response to me and to the class. They are both correct. We celebrate.

The fact that making a diagonal fold fries brain circuits was driven home to me one day when I asked a class of third graders to make three folds with a square piece of paper. I didn’t anticipate any problem as I already had already done quite a few folds with this group.

The lesson for this day was to do one diagonal fold, unfold it, flip it over, fold vertically, open it, and then fold horizontally.

I could not have been clearer in my instructions. I had drawn out the directions, which were projected on to the classroom smartboard. The papers I handed out were printed so that they could compare their progress easily with my sample.

I have rarely so quickly and completely experienced the chaos that followed. The students were totally confused; there were renegade folds on nearly every paper. Students struggled with paper orientation. They fearfully charged ahead in complete darkness. My perfect simple lesson was simply a disaster.

This was a class of 25 students. I would be facing four more classes who needed to learn this folding sequence.

The problem wasn’t the diagonal fold. The problem was the sequence of folding. Did I lose you for a moment when you read this:

“The lesson for this day was to do one diagonal fold, unfold it, fold vertically, open it, and then fold horizontally.”

Turns out that making the diagonal fold in the first step of this lesson disoriented the class in a way from which they could not recover. Immediately, students were felt unsafe, afraid of doing something wrong, and I could not gather them back to me.

The fix turned out to made perfect sense. I showed the diagonal fold last instead of first.

Students folded papers in half (the “regular” way), opened the paper, folded it in half in the other direction, opened it, flipped it over and made one diagonal fold. Before any confusion took hold of their brains, their folding was done.

I want to write more about the diagonal, how to make it safe, and why it’s important, but that’s another story.

Today’s story is simply about how something that is simple can go haywire.

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# Giving You the World

I’m working on getting ready for six different projects tomorrow. One of them will include a wonderfully folded world map. This is one of my favorite activities, so I thought I would repost this tonight. Please to click on this link in the PDF of the World Map rather than the PDF in the post…the one below has an extra line in it and it turns out I can’t change links in posts that I am reblogging! It took a whole evening of tweaking to get it to work just right, to go with the folding instructions. I would be very happy for it to get lots of use.

To print out the directions above, here’s the PDF of Origami Base for World Map And here’s the PDF for the World Map That Can Be Folded Into An Origami Base.

I have a slew of agendas when I work with students. One item at the top of my top-heavy list is to incorporate a world map into projects whenever possible and appropriate. If I can provide students with a clever and fun way of using a map, all the better.

This is a 6″ x 6″ square (folded down from a 12″ x’ 6″ paper). Open the cover and you’ll find a map of the world, with Sweden highlighted.

Just in case it’s not clear, the map is a separate piece of paper glued into the cover.

Note the  compass rose, that has been colored in by the student and notice how well the world map sits on…

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# Giving You the World

To print out the directions above, here’s the PDF of Origami Base for World Map And here’s the PDF for the World Map That Can Be Folded Into An Origami Base.

I have a slew of agendas when I work with students. One item at the top of my top-heavy list is to incorporate a world map into projects whenever possible and appropriate. If I can provide students with a clever and fun way of using a map, all the better.

This is a 6″ x 6″ square (folded down from a 12″ x’ 6″ paper). Open the cover and you’ll find a map of the world, with Sweden highlighted.

Just in case it’s not clear, the map is a separate piece of paper glued into the cover.

Note the  compass rose, that has been colored in by the student and notice how well the world map sits on the paper.   Allow me to tell you that it took me hours of searching for the images, then resizing and positioning the map and the compass rose so that it would work well for this project.  I want you to think of this as a gift to you from me, for taking the time to read my posts.

Here, again, is the PDF of the World Map That Can Be Folded Into An Origami Base. You will have to cut off the bottom 2 1/2″ of the page so that it will become a square. I don’t quite know how people in A4 land can use this….let me know how it works out if you try it, OK?

I generally print out the map on lightweight blue paper so that students only have to color in the land masses. Students have a hard time identifying places on the map, so I am happy to do my part in giving them a reason to look at continents and oceans.

A fun map exercise is to ask students to look at the map and come up with fanciful ways of traveling from their home to another destination in the world.  Helicopters, dog sleds, walking, and sailing are all acceptable,  as long as it’s possible (ie no driving from India to Australia).

There’s a trick to glueing the map into the cover: make sure that the point of the origami base is just touching the middle of the fold of the cover. Use the minimum amount of glue on the paper (it’s pretty obvious where the glue goes, especially if you do it wrong a few times), then CLOSE THE COVER over the map, rather than raising the map up to the cover. Try this out a few times before you (blush) embarrass yourself in front of a roomful of students. Good Luck to the brave hearted who try this out.