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



Arts in Education · Math and Book Arts · Math and Paper Folding · Math with Art Supplies

Peek-a-Boo Skip Counting for First-Graders

Peek-a-boo skip counting
What number is under the heart?

For weeks I’ve been burning through piles of papers and ideas trying to work out an engaging skip-counting project to make as part of a math-activities folder for first graders. Having just done a math activities folder with kindergarteners, which went really well, I’ve been wanting to do something similar for first graders. As I’ve also been doing math-with-art-supplies bookmaking projects with second graders, I’ve been keen to design something for the next grade up.

What I’ve  needed to get me going on this is a school to want me to create a project for them. A couple of weeks ago, late in the season, a school called me, asked if I had any time for them, and we struck a deal. We’re doing the project that I’ve been wanting to create.

There will be four hands-on projects in a folder that the students will be making. This post is about just one of the projects, one that supports skip counting, reasoning, and attention to numerical patterns.

Show me what under the butterfly, Oh, it's a 14.
Show me what’s under the butterfly, Oh, it’s a 14. Still not sure what’s under the heart.

Skip counting is a big deal in first grade. Not only does it set the stage to understand multiplication, it also is helps with learning to count money.

My work with second graders has piqued my intereste in skip counting. The projects we’ve been doing, which is making designs with “coins” that add up to $1.00, has been interesting in that I’ve noticed that even though a student can count by fives, you know, 5, 10, 15, 20, 25, 30, 35, 40….,, they have a really hard time doing this same counting by 5’s when you ask them to start at any number other than zero. So, if they have 25 cents plus two nickels they are at a loss as to how to proceed.

Show me what's under the flower. Oh, it a 6, Now can you tell me what's under the heart?
Show me what’s under the flower. Oh, it a 6, Now can you tell me what’s under the heart?


Maybe by now you’ve guess what is under the heart in the photo above. Maybe not. If you need more hints, I can reveal that there is an 8 under the star. This will likely finally be enough for you know know that there’s a 10 under the heart.

We’re not just counting by twos here. I’ve made a paper that slides under the windows that helps with counting by 2’s, 5’s, and 10’s.

I consider this to be an elegant design. One piece of folded paper for the holder, with a one piece of paper for four different number series. The little designs on the peek-a-boo doors are cut with paper punches, which I’ve collected over the years. The rhombus shaped window are made by folding the paper and cutting triangles on the fold.

One of my thoughts with this project is that  it can support students in practicing with going both forward and backwards with their skip counting. For instance, if they see two numbers, say 80 and 85, can they tell me the number that is before the 80 and after the 85? This takes some practice, some thinking, and reasoning, but if they can figure out what number is behind the hidden door, I anticipate the pleasure at solving this puzzle will delight them when the peek-a-boo door reveals the answer.

I do plan to share the template for this after I try it out with some real live first graders. To be continued.

Addendum 6/11/2019

Two classes of first graders made this with me. It went really well! To teach them to use it, I do the demonstration on the board, drawing doors that they could “look” behind for clues.

Here’s a video of what playing with this looked like:

Here’s a template so you can make these yourselves: skip counting first grade

Arts in Education · folding

Swing Card for Fifth Graders

elebration Swing Card, condensed
Celebration Swing Card, condensed

I recently spent a short amount of time with a fifth grade class. I wanted to create something dynamic and memorable with them. I knew I’d be meeting with these students during their social studies time, so it made sense to do something that would reference what they’ve been studying in class, which has been the United State Constitution. My thought was to created a moveable card, not exactly a pop-up, that would, hopefully, delight these kids, but that would be pretty straightforward to assemble.

I decided that it would be fitting that the theme of the card would be a Fourth of July Celebration card, celebrating an amendment to the Constitution that the students themselves chose to highlight.

Celebration Swing Card, expanded
Celebration Swing Card, expanded

When you pull the sides of the card out the paper expands and the middle section flips.

It looks like WordPress is going to let me embed a little video of the movement of the card. This is a new feature here in WordPress? If this video doesn’t play for you, let me know. This is the first time I’ve tried to embed a video that isn’t linked to YouTube.

This project may seem, tricky to decipher at first, but it’s actually super simple to construct. It’s something I’ve been meaning to try out for quite a while. I got the template from this book by Trish Witkowski , who is one of my paper-folding heroes. She is one of those people who makes the whole world feel better to me because she’s in it.

I needed to modify Trish’s template to use with my fifth graders, to make it fit on standard copy paper.

Swinging Card Teimplate,
Swinging Card Template, Click here for the PDF

The students just needed to score the dotted lines, cut the solid lines, then fold the scored lines like a zig-zag. The cut-out in the middle swings freely.

If none of that made sense to you, just try it out. You’ll see.

Scoring on the dotted lines
Scoring on the dotted lines

First step is to score the dotted lines. Scoring means to press the lines, not cut them or draw on them, but, instead, to press into the paper. An empty ink pen works well for this. I showed the students that they needed to put a soft surface under the card, so that there’s something soft to press into.

Cutting on the solid line
Cutting on the solid line

Cutting on the solid line was a bit tricky, since there’s no way to start the cut from the edge of the paper. At home I use a craft knife (razor blade) but, obviously, can’t hand out razor blades in schools. Instead, the students curled the paper, made a snip on the curve….

Continuing the cut
Continuing the cut

…then uncurled the paper and continued cutting. Watching these students, who were doing a great job, it was obvious to me that these kids don’t cut with scissors much, so I was doubly happy to be doing this project with them.

In progress
In progress

I think you can make out the zig-zag folding in the photo above.

The students seemed to really like this project. It was fun for me to see that they were super surprised and delighted at how the scoring helped to make the folds fold so easily.

Since we had so little time, I showed them a quick cut paper design method. I call it an exploding paper strip. I give them a paper strip, ask them to a bunch of glue on the back, then they make snips and lay the pieces down in the order they were cut, leaving a little space between the pieces that were cut apart.

Swinger Card Celebrating the Constitution

One last detail: I asked the students to write something personal, something about their own thinking as to why they chose a specific amendment to celebrate.

His Favorite Amendment
His Favorite Amendment

The lines and dotted lines were printed on cover weight (67lb) paper. The writing here is printed on a contrasting color, regular copy weight paper (22lb).

Fun project!




Arts in Education

Constructing Names in Pre-K


After making beautiful letters with a pre-K class we used popsicle sticks to create symmetry. In our last short session each student built their name from materials.


This is not an activity I had originally planned. It grew out of watching the what they had been doing with the some of the materials we had used in previous sessions.


I might have missed thinking about encouraging them to construct their names, but I heard their regular classroom teacher remark on how hard it is to write their names, but they seemed engaged in trying to create their names with sticks. So the next time I saw them I showed up with colorful foam sticks and harvested some other materials from the classroom.


Okay, some of them had trouble making their names with materials too. But what a great effort!


It was really interesting for me to see their sense of spatial relationships on display.

Jack, with his brother's name too (Liam)
Jack, with his brother’s name too (Liam)

An advantage to this activity was that they were so easily able to self-correct when things wouldn’t fit.


Kids with “i’s” in their names invariably dotted them.


I have a copy of the handwritten version of their names. There’s a remarkable similarity between the handwriting and the constructions, such as Michael makes the H in his name oversized when he writes it, just like he’s done here.

I love that I get to do these projects with kids, This summer I will work with Pre-K students once a week for six weeks. I hope to do projects like this repeatedly and see how or if kids sense of construction develops.

For now, this is the last of my pre-K photos. I think I will next be writing about what the fifth grade project.