Been taking some classes…

Made this along with Dr. Lizzie Burns at https://www.youtube.com/watch?v=bTE2Y-jdI8c&feature=youtu.be starting at 8L40 mark.

I’ve been unusally distracted lately in wonderful ways, mostly having to do with taking classes and planning classes.

The lovely origami image above was made watching Dr. Lizzie Burn. I try to watch her in real time. Sure, I could catch up on her recorded video, but I like when I can tune in for real on Wednesday mornings at 9 am EST. She’s folding in England, after lunch, I think, but, for me, it’s a sweet early day romp.

Lizzie has not been the main culprit behind my distraction. Becky Warren claims that dubious distinction.

Made in Geogebra

The class with Becky Warren, which teaches artful skills to apply in Geogebra, has taken up a huge amount of headspace. It’s been a real challenge, not just with the learning of skills, but also trying to understand what I’m doing, and then I try to remember what I’ve learned. I’ve taken lots of notes and have revisited things constantly.

Not only am I learning about what’s been taught in the class, but I’m also trying to wrap my mind around this new landscape of on-line instruction.

Ever since I’ve had access to the internet I’ve looked at tutorials of all sorts, and made a bunch of my own, so I have a feel for on-line learning. There is something different though about this way of learning right now. The pandemic has changed everything.

Here are a few things I’ve been thinking about.

The experience of 10 weekly meetings with Becky seemed onerous at first, which might have seemed even harder because I had trouble with every little detail of what I was trying to learn. If I hadn’t practiced a lot between classes (which was possible because Becky provided recordings of the class) I would have learned nothing. I often showed up early to class to ask my clueless questions.

After awhile it was like I was building up some muscle memory. Things started getting easier. It’s still really hard, but basic skills have become easier.

I am over the moon about what I’ve learned in these classes. They’ve given me a foundation to build on.

Folded Stars with Dr. Lizzie Burns https://www.youtube.com/watch?v=Mbj4C7aQl2I&t=1276s

I’ve also been sometimes sitting in with Dr Lizzie Burns on Wednesdays, 9am EST. The videos are posted for reference afterwards too, but it is such a pleasure to join her in real time.

Since I am so comfortable with paperfolding in general, the origami demonstrations are a more relaxed kind of class for me. I can tell that Lizzie wants people who are unfamiliar with folding to be comfortable in her class. For her, the message is about the comfort of creation. She works slowly, slow enough for me to watch her, then do the fold myself without missing her next step. As soon as the session is over it is available to watch on youtube, so if I forget a step, there it is, right away.

As I am learning from others, I am planning some new classes. Being part of Lizzie’s classes and Becky’s classes have influenced my thinking tremendously.

I’ve done a couple of free Saturday morning Zoom classes, but have not provided a video afterwards. Now I think that this was cruel of me!

Here’s what I’m thinking about for my next open class:

Paper folds

I’d like to show people what I’ve discovered about how to fold this lovely thing. It’s something I saw in one of Paul Jackson’s books. He shows a template, but what I want to highlight are tips about how to fold efficiently.

I am thinking of doing three different short classes (30 minutes or less), once a week for three weeks, just because I like the continuity. Then I will try to post a video right away, either of the class itself, or of a tutorial that I’ve made in advance.

I’m also planning on doing a class 2 hours a week for 12 weeks, something that is more like a college level class, that I will be teaching through The Center for Book Arts. Susan Share and I will be co-teaching this. Soon after we’ve completed our proposal, hopefully today or tomorrow, I will announce the class. It will be based on teaching the Zhen Xian Bao structure, but it will be about so much more than just making one book. Like Becky’s class, I hope that this will be a deep dive into accumulating skills over a period of time.

Here’s a teaser photo:

To be continued!


Summer Projects with Teens

It’s not really possible to express how excited I was to be working with teenagers this summer. I saw a group of 6 thirteen-year olds and along with two 18 year- old assistants, who did most of the projects right along with the younger teens.  We met once a week for six weeks, three hours at a time. I’ve written two posts already about my time with these kids, https://bookzoompa.wordpress.com/2019/07/04/cards-compasses-and-lights-with-teenagers-summer-2019/ and https://bookzoompa.wordpress.com/2019/07/21/hexaflexagons-in-the-summertime/ . It would have been best if I had written something after each session, but since that didn’t happen I’m going write a post that is both way too long and way too brief,  as I want a reminder here about the great projects that I haven’t written about yet.

Just for context, I met students at Salem Art Works, which is an internationally known local  visual arts venue. These classes were organized by a magnificent summer program in our small community. These kids met 5 days a week for six weeks. I was their Wednesday.

This post shows peeks at some of the projects that I haven’t written about yet. We spent a good bit of time on different kinds of patterns. This is about the age where these kids are learning about the equation of the line in algebra. We did a number of projects that referenced this equation. Different equations create different patterns. I wrote about this technique of pattern making a couple of years ago https://bookzoompa.wordpress.com/2015/06/30/line-designs/ I use Dan Anderson;s Linear Mod Open Processing sketch to help students decide which equation they will use to create their designs.

Part math, part art!

We also did some little and big origami. I was really surprised how much this group liked doing origami. Here we’re making doing a group project. Each person made two units, of what is called an Origami Firework.

This bit of modular origami is quite a stunning piece. What’s wild, though, is that it rotates outwards, making kaleidoscopic patterns. Here’s the video of this one:

Another paper folding activity was to show them how to make an accordion folded fan, which was quite handy on this particular day as it was quite hot.


We did other paper folding projects, too. I was excited to show them how to make some pop-ups, but also wanted to show them some more unusual paper folds.

One week we made these tabletop models…

…then the last week we broke out the really big paper….

…did some big folding…

…and made some large models…

…which looked great at the end-of-the-season art show.

But that’s not all we did.

Following instructions from Clarissa Grandi’s Mathematical Art Lesson Page Curves of Pursuit, we created Archimedean Tessellations.

Starting with a regular geometric shape of their own choosing, students would add lines, about a centimeter apart, which would guide them to make slightly rotated scaled down versions of their original shape.

Making these patterns is an iterative process, which is to say that the students repeated a process using a previous result to make the next result.

I think they were surprised by the designs they were able to make.

This was actually the second project we did that was done with an iterative process.

This spiral was done on, I think, our second meeting. They did a measurement between the spokes of this circle using a rectangle, then they’d start from the new mark to make the next mark.

As I said, this was a quick project. Each session that I saw these kids I would plan one short project to start out with. These were always great fun.

Another one of our short projects was to put together a small pamphlet-stitch sewn book.

We did some paper folding, used needle and thread, and used some of the geometric patterned paper that I had made this past winter.

One thing that was so fun about these kids is that they were all in on everything. Nothing was too precious to play with. One of the girls in the group had her whole book filled with quotes and lists and who knows what else before the end of that session.

Actually the most fun I think I’ve ever had with a group of students was doing one of these quick projects,  the one that introduced them to the wonders of a Mobius strip. Please watch this video then do this with kids. It will blow their minds.

As I’ve already written about the hexaflexagons we made I’m not going to write any more about them here, but here’s some photos that I didn’t include last time. This…

..becomes this:

So fun.

I made a PDF of our activities, with links. Here it is, if you’re interested. 8th grader projects for Intersection of Art and Math

Towards the end of the summer I saw a post by Farica Erwin, who did a week long session with teens, also three hours per sessions, also doing math and art.  I’m including a link to her post here https://www.nerdqed.com/post/camp-time-2019 because I was so enchanted by the work she did with her students. Also, it was fun to see that we both leaned on Clarissa Grandi’s work, we both did some Islamic Geometry with the kids, and we both included some bookmaking.

I’m already looking forward to doing this again next summer.


Math with Art Supplies · Uncategorized

Summer 2019 Projects with Kids Begins!

House with awesome roof and a patio
House with awesome roof and a patio

I’ll be working with kids twice a week for six weeks this summer. Today’s group was five year olds. I came totally prepared to do numerous projects. I’ve made a list of my priorities. We’re going to do paper folding with a focus on squares, explore symmetry, play games, make patterns, look at books and think about numbers.

My suitcase of supplies was totally full. And mostly went untouched. But what we did get to today felt fun and worthwhile. Actually I know if was worthwhile because I heard one of the 5 years-olds explain to an adult that we made a house out of a square! Was so happy to hear that remark, as what I’m emphasising with the paperfolding that we are doing is that we are transforming shapes. I get to use the names of shapes, as well as words like rotate, middle, bottom, and I get to teach folding skills.

The back of the house, showing the pocket to store pictures of yourself and friends
The back of the house, showing the pocket to store pictures of yourself and friends

This house project is adorable. House on the front, pocket on the back, and only a few folds. Start with a square, make a triangle, then create a couple more triangles (see photo above) and you’ve got a house. The pocket in the back is to hold pictures of yourself and your friends. which, of course, you draw.

Drawing the house
Drawing the house

This was a great project for me to start with. Touches so many of the ideas I want to talk about.

The time flew by. I worked with two groups of great kids.

Then my time was up. Time to pack up.

I packed up, but was a bit disappointed.

I had wanted to do something with numbers. But it was time for the kids to have time to free play.

So I did what something I sometimes do when I want to do a bit more with kids.

I sat by myself and started working all by myself, in this case I was coloring in numbers for a project that I will write about next week.

I really  wanted the kids to help color in 40 different numbers. That’s a lot. But I just started all by myself.

Then someone came along who wanted to color in numbers too. Then someone else. Then someone else. You get the idea.

Got nearly all the numbers colored in. We’re going to make a special deck of cards to play a game that Kent Haines wrote about. 

Which will be a story for next week. 🙂


Art with Math Supplies · Fractions · Math with Art Supplies · Uncategorized

About Halfway There

Equivalent Fractions
Equivalent Fractions

I’ve been interested in creating fractions projects for kids exactly as long as I’ve been working with children in schools (decades). This year, after enjoying,messing around with a hexagon/golden ratio project I wondered if I could modify the idea of using scaled hexagons to help fourth graders make better sense of fractions. My first attempt at this didn’t work out so well.

Making 1, or 100%
Making 1, or 100% out of two halves

I gave students hexagons that were scaled to 1, one-half, a third, a fourth, a fifth, a sixth, an eighth, a tenth, and twelfths. The task was to pair and arrange them so they would span the length of a whole, aka 100% across.

1/3 + 1/6 + 1/6 + 1/3 = 1
1/3 + 1/6 + 1/6 + 1/3 = 1

The project went okay, but it just didn’t snap for me.

I’ve been thinking about how to improve this project. Today I had a chance to work with a small group of kids. I tried a new approach that worked so much better. What was especially great was that it included making a simple book. Yay!

Fractions for a Book
Fractions for a Book

I started kids off with a hexagon that was labeled 1/2. I explained about how the lengths we would be looking at would be the horizontal or vertical length of the hexagon (I didn’t use these words, rather gestured what I meant). Then we layered the hexagon with equivalencies. Here you can see two 1/12ths equals 1/6, three 1/6ths equals 1/2, and 1/6th and two 1/12ths equals 1/3.

Equivalent Fractions
Equivalent Fractions

Nice, right? Snap!

The books we made were just two sheets of paper folded in half, bound with yarn using a modified pamphlet stitch. 

Equivalent Fractions Book
Equivalent Fractions Book

What’s great about using hexagons for this project is that you can still see the labels of the lower layers as the equivalencies are built up. The adults in the room had a bit of trouble with accepting that the hexagons were scaled (similar) versions of each other, but the kids had no problem with it. This reinforces my notion that children have a better intuitive understanding of scale than do adults.

This is the way I explain the scaling to adults: We all know what half a candy bar looks like. That’s one way of thinking of one-half. But when we say a child is half the size of the parent, we don’t envision the child to be half a parent, like they were half a candy bar. Instead, we envision them smaller than the parent in their height as well as width.  This explanation seems to work.

The bullseye view of fractions
The bullseye view of fractions

After doing a bunch of equivalencies, this child decided to nest her fractions.

Okay then. Here, what’s obvious is the hierarchy of the hexagons that are scaled by fractions. Nice!

This project can use a bit more refinement, but this is as far as I’m going with it right now.

I’m including PDF of the hexagons. The labeling includes the colors of the paper I use for printing.  Yeah, it’s lots of files. Welcome to my life.


hexagon halves blue

hexagon sixths halve grape

hexagon 3rds 12ths chartreusegreen

hexagon 4ths orange

hexagon 5ths 8ths pink

hexagon 6ths halves grape

zhexagon 12ths full page chartreuse

2 pieces to make 12 inch hexagon

12 inch hexagon

Notes about hexagons