Art and Math · Arts in Education

Paper, Books and Math Workshop

There’s this overlap of paperfolding, bookmaking and math that’s been in my sights for sometime now. Next month The Center For Book Arts has me on the schedule to share my interest with educators.

It’s a natural fit: Fold a piece of paper in half a couple of times and you’ve got a book. There you have it, all this things I’ve been thinking about in one sentence.

Bookmaking by Paula Beardell Krieg


Why math and book arts, you might ask? CBA asked me to propose a course for educators. Over the years I’ve taught classroom bookmaking dozens of times, though my focus during those years was literacy. In recent years it has occured to me, as I visit many schools and work with hundreds of different students each year, that teachers have loads of support for teaching literacy.

Teaching math, on the other hand, can be more challenging. In my desire to stay relevant, the hands-on projects I’ve been designing for classrooms had evolved towards supporting math curriculum and math thinking. And, oh yeah, I love this work.

Everyone folds paper, many people teach math, less people make books. Not too many people have a strong relationship with all three, Basically, I want to be teaching this workshop because otherwise I doubt it will exist.

Here’s what I know about offering a workshop for teachers:

  • They want content that they can use on Monday.
  • They do not have time to do special prep which requires more than the school copy machine.
  • They don’t have easy access to special materials.
  • They like having a handy resource folder.
  • They want their students to be learn and be happy.
Equivalent Fractions
Equivalent Fractions

Here’s how I know about math:

  • I play with math kind of obsessively….never got the memo about math being scary
  • I went through K -12 math three times, once as a student, twice as a parent.
  • I’ve been working in schools, discussing math projects with teachers and math coaches. We discuss standards and curriculum goals, and I talk to students about the math they are learning.
  • I’ve been rather passionately working on deepening my math knowledge in workshops, conferences, and connecting with math educators through their writing and through the #MTbos and #iteachmath communities on twitter as @PaulaKreig

In this one-day PD workshop I plan on focusing on deepening connections, doing hands-on, classroom friendly projects that address areas of math that will help students create strong foundation for future learning.

For instance, we’ll be working with number lines in a way that is both interactive and which illuminates patterns. I’ve been working out ways of presenting number lines in ways which delight kids. The sounds of discovery that come from students when they start seeing what I show them has been one of the most beautiful sounds of my career with kids. I will also have hands-on ways of showing the number line that moves from natural numbers to negative numbers and beyond.

Since the number line stays with children, evolving from finger counting through the coordinate plane (and beyond) my focus here in not only to use the number line, but also to elevate it as an important tool that they have reason to embrace. One of my favorite responses, which informs my work with number lines, was from a first graders who told me that they looked at number lines earlier in the year and now they were done with that.

How to make an origami Pocket by Paula Krieg
Click to enlarge for reading or printing

We’ll also be doing some work with perimeter and area. What frustrates me about students’ learning here is that they often mix up perimeter and area, not remembering which is which. One of the projects we’ll be making is a perimeter-pocket. We’ll make an origami pocket, which in itself is a wonderful lesson as is goes from being a square to a triangle to a trapezoid to a pentagon. But this perimeter pocket will have a ruler embedded in the structure and a string in the pocket to use to measure around things. Then there will be an area-rug book, with lift the flap peek-a-boo images hiding under the area rugs. Fun, easy, memorable!

I love that shapes are part of school curriculum at an early age. There are numerous projects I have in my toolbox that compose and decompose shapes.

I have some nice peek-a-boo projects that address the same composing and decomposing concept with numbers.

Symmetry will also get the attention that it’s due. Sure, we’ll talk about lines of symmetry by way of making pop-ups, but we’ll also look at the idea of symmetry as a it relates to equations, which can be seen as numerical symmetry. One of my exciting discoveries has been how naturally young kids grasp the idea of symmetry, and how well they they can connect it to equations.


A one hundred cents flower
A one hundred cents flower

We’ll even do some hands-on play with play money. I do these one-hundred cents designs with kids which gives then lots of practice with money, as well as practice counting by fives and tens and twenty-fives.

I could go on and on here, but I think you get the idea. And, actually, that’s part of my aim for the day, not just to present projects that can be immediately used by teachers in the classroom, but also that the idea of making the curriculum more hands on will inspire teachers to create their own simply made projects.

This is a rich, wide open inquiry into what we can do together to make math real.

The Center for Book Arts, NYC, Saturday, October 26



Sewn books

Playing with my Paper

Some of my papers, some vintage papers designed by Axel Salto
Some of my papers, some vintage papers designed by Axel Salto

I tend to accumulate beautiful papers. Some of the papers I have hanging around are papers I’ve bought, but, increasingly, I am designing papers of my own. Coming up with these designs are a direct result of how I’ve been processing math ideas. Lots of times it’s a journey to get things right: some designs aren’t what I’m after, but they’re still lovely.

My Papers
My Papers

May of these papers are too beautiful for me to want to get rid of. These papers have been piling up.

Since it’s Labor Day weekend, I decided to put everything else aside for a couple of days and do something I’ve been wanting to do for a long time, which is to make some books using these papers with my designs on them.

After all, I love making books, and I love these papers, so it seemed like the right thing to do.

I made six books, three different styles of binding.

I used some vintage papers in my collection for the books’ covers.

I started with making just one four-signature exposed-spine notebook. It’s nearly 100 pages (that’s 24 pieces of folded paper).  I like this style of sewing where I get to use one needle per sewing station.

Pamphlet bound, Asahi bookcloth, Axel Salto papers
Pamphlet bound, Asahi bookcloth, Axel Salto papers


Then I made three nifty single-signature pamphlet bound books. 32 pages each. They look the same on the outside, but each one has its own set of unique papers.

I had a particularly good time choosing the endpapers  for these, as I couldn’t use papers in my stash, as they were the wrong weight for endpapers. Instead, I searched out some old files and printed up some papers that I’ve actually never printed out for myself.

Bimply bound books
Books bound in Wallpaper with Beads

Next were these simple little beauties. No glue, simple sewing, elegant folding. These are made from wallpaper samples, a paper that I’ve worked with many times, like here  (If you’re not convinced look here too: What I like about using wallpaper samples is that the books can take quite a bit of abuse and still look good. There’s a sturdiness about wallpaper books.

Since these books are so slender I added beads to the sewing, as this makes it easy to find them on the bookshelf.

The insides of the wallpaper-covered books have a pockets in the front and back covers. I have a few of these that I use all the time. The pockets are really handy. Also, I slip a piece of stiff paper in the pockets so that the covers feel more solid.


Every spread in every book looks different.

Some pages have less color than others. This was one of my favorite spreads.

Here are the three styles hanging out together. They are all just a bit bigger than 4.25″ x 5.5″.

Here they are willy-nilly, looking for a good way to be photographed.

Don’t really know what I will do with these. My bookshelf is already filled with handmade books. I’ve put them on etsy, but am also thinking that they would make good Christmas presents for my sisters’ families. We’ll see.

But am happy to have finally used these papers. Now I feel freer to make more.

Felt good to be messing around with papers.



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, and . 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 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 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.


Zhen Xian Bao

Chinese Thread Book To Go

This past winter I submitted a proposal to the National Museum of Mathematics to present a family workshop at their paper folding MOVES conference this summer. Much to my surprise (and non conveyable delight) they accepted my proposal for hands-on workshop in which people would make a Zhen Xian Bao -Chinese Thread Book- made of three expandable origami boxes, housed in a cover with a ribbon closure.

Much more to my surprise I realized that my workshop time was strictly only 25 minutes.

Finally even much much more to my surprise, the workshop worked out great. Here’s why:

  • I created a highly simplified variation of the thread book
  • I made packets so no time was lost handing out materials
  • I included written instructions so people could work independently
  • I made designs on the paper that would help guide the folding
  • I made a video of how to finish at home
  • I relaxed and had fun

Now here’s the shocking part. Everyone finished their project.

Full disclosure, since this was the very last workshop of the day, we were able to run a little over time. But just a little.

Making a video of how to make this structure was key for me to create an good event. When I realized that I could give people a link that they could reference at home everything seemed doable, and we had a great time with no pressure!

This was a family workshop, though most people were solo. I did have three kids in the room, and they were all very good about helping their parents.

So, yes a good time was had by all. As usual, I completely overprepared (something I do when I am nervous) (which, actually, is always) and the good new is I actually HAVE LEFTOVER PACKETS! that already has a video that goes along with them. I AM SELLING THESE ON ETSY.

The packets includes the paper for the boxes, directions, a cover piece that is prepared with slits for the ribbon and double-sided adhesive tape already applies, ribbon, and a link to the video (which will also appear on my Etsy site). Also I’ll be giving you a few paper strips which you can use to decorate the cover.

The finished, closed thread book is about the size of a large cell phone: 6″x 3″.

Here’s the video that shows you how to make this structure:

Here’s the link to buy the kit on Etsy:

It’s $15, which includes shipping in USA.

Addendum: The kits sold like hot cakes…they are now no longer available. Grateful to all who bought them!