Art and Math · Math and Book Arts

Kindergarten Folder for Making Math

Making Symmetry
Making Symmetry

There are some kindergarten teachers I’ve been working with for years. This year I’ve worked with them to create a math-centered book project for their young students. I launched this with a small class earlier this season then repeated it with about 4 groups, total of about 70 kindergarteners, this past week. It went well.

Actually I’m so delighted with how it went that it’s almost embarrassing.

Making the folder
Making the folder

We made a folder out of a long strip of paper, 35″ x  7.5.”

Folder with four compartments
Folder with four compartments


I put some score lines in to help these 6 years olds get started but they made most of the folds themselves. I make a big deal about how to fold paper.

The folder is basically a four page accordion, with pockets for a different math activity in each of the pockets.

The first pocket has a paper with peek-a-boo flaps to help kids visualize the composition of groups of numbers. This was an  unusual folded structure, but they caught on really quickly, as you can see in the video clip below.

After the folding comes the cutting


Cutting the peek-a-boo flaps
Cutting the peek-a-boo flaps

Then the coloring…

Compositions of the number 4
Compositions of the number 4

…finally they used these images to become more familiar with number compositions. We made these cards for the numbers 2, 3, 4 and 5.

Here’s how it looked watch kids use these to learn their number facts:

Okay, so that was for one pocket.

In another pocket there were squares that the students cut out. I used these to talk about symmetry.

Symmetry with cards
Symmetry with cards

Where one student placed a card on their side of the midline (pencil)  another student mirrored the placement. Seeing symmetry is important in math as students as it is a non-numerical way for them to experience the balance that an equation like 2 +3 = 5 expresses.


I extended this symmetry activity beyond the cards in their pockets. We used items around the classroom to create symmetrical designs, something my twitter community liked and retweeted generously.

We also did a project using beads, reminiscent of an abacus, to make groups of 10.

Separating10 beads into groups
Separating 10 beads into groups

The idea here is to give kids another way to interact with ways to make groupings of 10, contributing to their fluency and grasp of combinations of numbers.

Bead counting book
Bead counting cards


Finally, we did a fortune-teller, aka chatterbox, which many of us made when we were children.

Fortune Teller, Chatterbox
Fortune Teller, Chatterbox


Of course the insides were math themed, using their sight words, too.

Fortune Teller template
Fortune Teller template

Here’s a little clip of the kids playing with these. They absolutely loved this toy.

At first I had a hard time trying to teach this structure to kindergarteners. Once I realized that if I taught it after I worked with them on the symmetry part of this project, the folding would then make more sense to them. It turned out to not be nearly as hard to show them as it originally seemed to be.

The final touch was putting hands on the covers. Literally.

Front and back covers
Front and back covers

Since the kindergarten math curriculum emphasizes using fingers for counting, it seemed highly appropriate to decorate the covers this way.

Whew! What a week!

I was able to meet with each class for a little over an hour three times each.

Looking forward to repeating this project with other groups.

Also, now I want to create something like this for first graders! That’s what I will be working on this week.



Art and Math · design · Geometric Drawings

Copy, Rotate, Reflect and add eggs

In the middle of my arts-in-ed season I’ve kept trying to find time to mess around, trying to make beautiful images.

Today I started a wonderful, week-long math activity folder project with four classes of kindergarten students, am barely able to stay awake right now, but I’ve been wanting to at least throw these  images into my blog here.

I started doing this some time before Easter. Just wanted to make something. Started with a graph that I was able to reduce to just these few lines:

Then I copied, rotated and reflected these lines and came up with a nice tiled surface.

I honestly just loved this image. Parts of it I expected, other parts came as a surprise.

Spent lots of time coloring it in. Mostly used watercolor brushes, SAI Japanese Traditional Colors, but also used some colored pencils.

When it was done, I didn’t much care for the finished result.

It was okay, but didn’t make me as happy as I would have liked.

But then I started playing with it. Put it into Photoshop, isolated squares….


…then did some copying, rotating and reflecting…

I kept coming up with all sorts of stuff that surprised me.


I kept trying out different combinations…

… and then because Easter was on my mind I started wondering if I could map these on to eggs in Illustrator.

Turns out the answer was yes.


These were so fun to do.

I liked how the watercolor translated so well in to the digital environment.

Was very surprised that I ended up with these eggs. But very happy.

OK, that’s it for now. Gotta get ready for tomorrow with kindergarten!


Art and Math · Geometric Drawings · group project

Rotational Symmetry project with 5-9 year olds and Moms

I got to spend some time with a group of kids and moms this past Sunday. They had asked me to plan a math/art project for them. Last time we did this we played with shapes scaled according to the golden ratio. This time I wanted to help them make images that are made by rotating a graphic around a circle. We used a circle that was divided into twelve equal sections, and we got to talk about how rich the number 12 is, in that it comes up often in measurement of time (hours, months), quantities (dozen), distance (Inches) and so much more.

Images were made in two ways. One was to connect the dots around the circle according to a rule, such as connect the first dot to the fifth, connect the fifth dot to the tenth, connect the tenth dot to the dot that is plus+5 further around the circle, then continue until you are back where you started from. A star emerges!

Connecting the points around a circle

We started the afternoon by sitting in a circle of eight people, and doing the skip-counting activities that I described above. This was actually a thrill to me, as it’s something I’ve wanted to try out for a long time. As the star shape grew within the circle of people, who were the “points”, everyone was thrilled. They had no idea a star would emerged. I knew, but I was thrilled too.

I had PDF printout of circles and shapes.People cut out shapes that they wanted to rotate around the center, then colored them in if they wanted to.

I think the young man who did this image is about 8 or 9 years old.
I think the young man who did this image is about 8 or 9 years old.

The moms seemed to like this activity at least as much as the kids.

I never know how these projects will go. A couple of the boys didn’t want to be coloring any more after a while. One boy in particular really liked cutting paper, so I got him started with another kind of rotational symmetry: making snowflakes!

Snowflakes have rotational symmetry
Snowflakes have rotational symmetry

I hadn’t thought about snowflakes beforehand, but liked the way I was able to link to something that was already familiar to this group.

After awhile one of the girls was finished with coloring, I showed her how to make an origami pockets that were sized for the drawings to slip into.

Lot of pockets
Lot of pockets

She really liked making the pockets, and made them for everyone. This also let me segue into showing her how to make a square from a sheet of paper.

In the end, we had made lots of images, pockets, snowflakes and our work area was delightfully messy. Everyone helped with the cleanup, especially with the tiny pieces of paper on the floor.

At the end we put our tiles out on display.

Our tiles
Our tiles

A couple of hours later one of the mom’s texted me saying that, on the way home, her kids were asking to do more of these. YAY!


Art and Math · Arts in Education

Designing Outside My Envelope

I’m continuing to work on coming up with designs to use with some of my paper folding projects. This time around curvy lines are what I’m interested in. Valentine’s day is around the corner so of course I’m thinking about curvy lines.

After seeing some images I posted on twitter ,my friend Kathy H @kathyhen_asked me to blog about how I make these so her students might have some fun with curves. My initial reaction to her inquiry was negative, as I rely heavily on Adobe Illustrator, which isn’t very accessible. It took me a day or two to realize there are other options available for a student/person-with-computer, so here goes.

I start out in a free on-line graphing program called Desmos. To plot curvy lines we need to direct the graphing calculator to plot something that is cyclical. Think of a pulsing wave that goes up and down. The easiest way to tell the graphing calculator to make a wave is to reference a sine function. This is as easy as typing in a few letters. Here, take a look! Be sure to play around with changing the numbers on this graph, so you can see how simply changing the numbers changes the curve.

Decorated Boxes
Decorated Origami Boxes

The next thing I do is try to make the curves more interesting. One the ways I do this is to direct the graphing calculator to multiply two cyclical functions together. To see what this looks like, go here BTW one of the advantages of going to these graphing links is that you can use and modify these if that is more comfortable for you. The only thing to keep in mind is that if you want to save your own changes you have to make your own account, Which I recommend.

Origami Masu box
Origami Masu box

Last thing I play around with is making curves which relate to the curves that I have, but are different. These secondary curves are derived from the first curves, but follow different rules, Look at this link Be sure to read the notes.

Here’s the graph that I made, after much playing around, to use on the box in the photo above:

Design to apply to origami box
Design to apply to origami box

What I need to do next is to make the graph into a an image that I can color. For me, that means taking it into Adobe Illustrator and trace it using the pen tool, then color it in with the Live Paint Bucket tool. There are other options.

The simplest option would be to hit the print button in Desmos, then simply trace the pattern you’ve made and color it in. Make copies of this if you have access to a printer. Doing these by hand has a charm that no computer can match.

Another option is to use a different graphing tool called Geogebra that can output a file that can be opened in a free online vector program called Inkscape. What you have to do is, from the dropdown menu on the upper left hand corner of Geogebra, is choose Download As, then choose SVG. Then, open this file in Inkscape.

Personally, I can’t do everything I want in Geogebra simply because I am not familiar enough with Geogebra. Today I wanted to use the workflow I’m describing here, but I couldn’t figure out how to tell the graphing program what I wanted to do. What I did next was ask for help. Jen Silverman @jensilvermath came to my rescue and inputted my curves. Asking for help is a completely reasonable workflow. These programs are so user friendly that, after not-too-long, we won’t need to ask for help. But ask for help for as long as it takes to learn how to do this on your own.

Used Inkscape for the first time today. I didn’t know how to do anything. Googling questions about Inkscape was easy. Again, this is a program that is designed to be user friendly.

Heart, with help from Jen
Heart, with help from Jen

This is a post that makes sense to me, but am not sure if I’ve been clear enough.

Having access to this technology that creates these magnificent curves can be so enjoyable. Be patient, though as it takes a good bit of playing around to get a really satisfying image. Then don’t forget to hit the save button! Happy almost-Valentines day.

Addendum, later today.  Read all about it!

This may make for an easier workflow.

My friend John Golden got me to try out coloring a Desmos file in Paint, which, I think, is standard program on most computers? Well, as least my computers always seemed to come with Paint, so it must be easy to get. It’s a raster program, so images won’t be super smooth, but, for classroom work, it’s looks great.

The workflow would be to save the Desmos file as a PNG by clicking the Share icon that’s in the upper right corner, then choose export. But before you do this, go into the settings by clicking the wrench icon on the near the top right and make sure everything is UNCHECKED! Your png will look like this:

Polar Rose, Desmos
Polar Rose, Desmos

Next open the image in Paint then use the paint bucket to fill in the blanks.

polar rose raster
polar rose raster

It’s true that the edges won’t be perfect. Raster images don’t do curves well.

polar rose raster detail
polar rose raster detail

Even though, close up, the edges are rough, still, this prints up quite nicely.  This is definitely a way of getting the job done!

Here’s what John just did, using this workflow