Piling Kaleidocycles

Piling Kaleidocycles

They did it! This group of fifth grades did this hand-lettering kaleidocycle class project! I described the details of this project a few posts back so check out that post for more details. Here’s the general gist: After introducing the project, which is a 3D paper construction with rotating faces that will be graced with references to the Bill of Rights, students were given pages of letter fonts to choose from.


Using the windows of the library as light boxes, students traced out letters to created one phrase each that described one of the first ten constitutional amendments, aka The Bill of Rights.

At the window

Every single student was highly engaged. Really.

Within two class sessions the students produced something that I could take home and scan into my computer . I won’t lie..scanning and cleaning up their work took time. Above you can compare what they gave me, on the left, to what I ended up with on the right. Some pages required much more work than others. The middle example above was so easy to work with that next time I will encourage students to just give me outlines. The most time-consuming letters to work with were those that were colored in and touching other letters. I moved things around a bit, like in the top example you can see I centered the word “OF.”

I brought home their work, scanned them into my graphics program, cleaned them up and laid them into a kaleidocylce template. Brought them back for students to cut around the perimeter and score.

Scoring the paper

Scoring the paper

Students made score lines so that the paper would fold easily and accurately. Scoring is generally done with bone folders but we used glitter pens to score the lines. They worked great, and kids were excited to be using the gel pens.

Assembling the Kaleidocylce

Then came the folding and gluing. I didn’t take many pictures of this process as I was, like, really really occupied helping move this process along.

One of four faces of the Kaleidocycle

One of four faces of the Kaleidocycle

This project turned out so well. Not everyone had a chance to finish up and decorate, but the wonderful school librarian will be able to help with the few than still need finishing.

Kaleidocycle yellow borders

Kaleidocycle yellow borders

Students enjoyed individualizing their own kaleidocycles.

Another side

Another side

I tried to get them to use completely different color schemes on each face, so that the differences between the four rotation of faces were dramatic. Students didn’t much listen to my suggestions.

Here’s one of their kaleidocycles in action:

I consider this project a great success. I got to talk to the students about design, about hand lettering, and they got to work with some cool geometry. I’d even go so far as to say that they are also much more familiar with the Bill of Rights , as they were constantly asking each other, which one do you have, which one is yours, and talking about their own.  I have to say that at first the students were confused about what I was asking them to do, after which the librarian told me that doing a group project was pretty much out of their experience, so the concept was hard to grasp at first.

One thing that made this possible was that this was a small class, just 12 students. I often work with 60 to 70 students in a grade level: I wouldn’t do this project with a big group. OH, but it was so delightful doing this with a small group.

Tower of Kaleidocycles

Tower of Kaleidocycles

Do I get to pick a favorite project of my teaching season? Yes? This is it.


Here’s something that can only be described as playful.


It’s four squares, which have been folded into eights, like an 8-cut pizza. I made this as a sample book when I was teaching the Book Arts at Bancroft series of classes at the Bancroft Library here in Salem.  I would teach eight classes in the fall and eight more classes in the spring, to groups of 3rd and 4th graders. I did this for ten years. It was a really great program, funded by New York State Council on the Art Decentralization Program.  No one was in charge of me so I did whatever projects I felt like doing with these kids. This was when my own children were as young as they come, so this book arts program kept me thinking about the arts at time when I would have otherwise been thinking only about laundry, meals and bedtime.
img_20161205_161718.jpgThis way of folding squares and then just connecting them together is an idea I came across during a day that I passed at the Patents Office in NYC long ago, before the internet. I’d go up there now and then,  into this great cavernous room on the west side of Manhattan and just looked through cool stuff. I’m pretty sure that this way of folding was in a folding toy section, patented by a woman from Israel. There were some great drawings with the patent (which I copied and probably still have).


When I did this with kids during my book arts workshop I was aware of one big obstacle: There are 64 distinct areas to decorate. Since the charm of this structure is finding all sorts of different configurations to display it in, it seemed to me that the patterns should be varied on each facet. But, 64? That’s a lot of designs. I had the kids for 90 minutes. Could they fill the papers? How could I facilitate this?


We spent the first 25 minutes making the structure. 65 minutes left. 64 areas to fill.

img_20161205_161655.jpgWhat I did was prepare 64 notecoards, each with a different design. The children sat in a big circle, each with a  marking tool. Each note card had a different design suggestion on it. Kids were not bound by my suggestions, but they would have only about a minute to decorate one of the triangular areas, then they would pass their marker and note card to the person to their left and receive a new suggestion and marker.img_20161205_161641.jpg

I’m usually not so regimented with my classes, timing things in short intervals and making commands, but this time it was great fun.


So, got that? Four squares folded pizza-style and linked together and decorated. Then filled with designs.



How to Make an Origami Toy Boat

How to Make an Origami Toy Boat

Full disclosure: I did not try out teaching 4-year olds how to make origami boats. It’s not that I didn’t want to, or that I chose not to, it was just that there were other things I wanted to do more, and my time with these little ones was limited. Much to my delight, though, after we used the boats in  our activity, the children asked me about how they were made. I did a demonstration, with hope that this may encourage an interest in  paper-folding.

Toy Boats

origami Boats, stacked

I chose to use these paper boats because they stack. Just for the record, I was curious to see if they floated. Turns out ;Yes! Until the paper absorbs too much water, these vessels are sea worthy. What was more useful for me, though, was that they can stand on their own, so that we could use them as playing pieces for a board game.

During my workshops with these children I noticed that even the most accomplished child in the group could not coordinate counting items with the movement of his hands. In other words, if there was a  pile of 8 stones, these children would end up counting inaccurately because their fingers would move out of sync with the numbers that they were reciting. I was really interested to see this, partially because  I’ve read that there is something about learning to play the piano that  helps children be better at math: this now makes sense to me, as playing notes would help train a person to coordinate fingers with intention.

Toy Boats and Board

Toy Boats and Board, drawn on large paper

Wanting to try out a simple, and, yes, frugal, made-from-paper activity to encourage accurate counting skills, I worked out a sweet game that the kids seemed to like . What we did mimics  classic board games where a die is thrown, and the player advances a certain number of spaces along a line. It was, however,  important to me that I didn’t want to create winners or losers.  This is how it went: the playing pieces were these paper boats, and when two boats land on the same space, they become a team, and stacked together. The point of the game is to get all the boats stacked together as a team before any boat reaches the end of the meandering number line, which, just, for no particular reason other than I ran out of space on my paper, was 42 units long.

Beginning at 0

Beginning at zero

Unfortunately, I didn’t get a photo of the kids playing this game, but, they played in groups of three and four, and they seemed to enjoy watching others play as well as playing the game themselves. Counting spaces, counting the dots on the dice, and (especially!) anticipating what throw of the die would yield the desired outcome were all challenging but doable for these kids.

Each of the five sessions that I worked with these students, one-third of my lesson plan was to focused my interpretation of relationship thinking, such as creating patterns from shaped paper,  developing finger sense, estimating, discussing what was the same and different about shapes and flowers, and this unit counting game.

Other parts of my time of my time with these kids was artful numbers, which I what my next and last post about my time with these students will be about.

I had to learn how to make these origami boats for this project. I looked many different models, but this one that I’ve shown  I found most enchanting. I put together a video of it, that is worth watching because there’s some pointers included that I just can’t fit onto a tutorial page.


Happy boating.



Although I intend the title of this post to refer to what I’ve been messing around with this weekend, I’m not really sure it means anything. What’s been happening in my studio is that I’ve wanted to mix up some interesting lines with some interesting folds.

After a person with the handle of GHS Maths posted a group of images made by rotating the graph of a trig equation I got it into my head to see what one of them would look like on a hexagon-flexagon.

If you don’t know what a hexagon-flexagon is, you haven’t watched enough Vy Hart videos. In 2012 Vy offered her own utterly delightful interpretations of what she thought people should know about this piece of paper wizardry in Hexaflexagon, (6 MILLION views!), Hexaflexagon 2, and the sequel Hexaflexagon Safety Guide .

 A Hexagon-Flexagon has three distinct sides, which results in six distinct designs: I’ve written about these here, here, and showcased student work here. I haven’t thought about these in a while, but it seemed to me that the image at the top of this post, and others that I had been working with lately, might be interesting to put on a hexaflexagon. 


I had  ideas for all sorts of images but I became so enchanted by what the variations of the image above that in the end this is what I went with.


My computer did not like this idea at all. I spent half my weekend redoing what I lost when my program crashed, half my weekend watching that blue swirly thing going around, and half my weekend coddling my computer so it wouldn’t crash. I know that I’ve listed three halves, so if that bothers you, here’s what I did with  fourth half: I was able to actually make an image that became a hexaflexagon.

This is what a hexagon-flexagon looks like on two sides of copy paper. I always want things to fit onto standard copy paper, so I had made this template: hexagonflexagontemplatecolor


It’s a bit tricky to follow, but it actually works really well. I love being able to print these up on my little printer.

This is a dynamic structure, that is not easily appreciated in still photos. I am going to either get my son to make a video of me working the structure or will post the more appropriate stills that I can come up with. Tomorrow. Edited into this post. See you then.

Update: I made a quick video! My first one! Based on the image in this PDF which is printed on both sides of the paper.

UPdate #2

For a hexaflexagon template that has a snowflake, a Christmas wreath and a Star of David, visit Chalkdust magazine at http://chalkdustmagazine.com/blog/how-to-make-christmas-special/. You’ll find a link there, and now here too, for Martin Gardner’s famous article on Hexaflexagons.

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