# Two Beautiful

The four-year-old children in my summer workshops made numbers so lovely that I had to make an accordion book out of photographs of the numbers.  These images are so exquisite that I don’t expect anyone to believe that they were assembled by such young children, so at the end of this post I’ve embedded video links that show, in fast motion, a couple of the numbers being made. You’ll notice that the children created the assemblages without adult interference.

The materials that students used were mostly from my husband’s garden. One particular harvest of beans had been buried in the back of our pantry for too long and dearest was going to throw it into the compost. These, therefore, are rescued beans. I also picked a selection of flowers (marigolds are the  best) Some of the students went outside and brought in leaves from the community garden. There was also pasta in the activity boxes in the room, so we used pasta too.

We worked as a group to make the first number. I pondered over whether to start with zero or one, and took to twitter, asking the math community that shows up there what they thought. There was no definitive consensus but seemed to me that there was more said in favor of starting with zero.

I’ve come to a way of thinking about what number to start with. In the course of my five sessions with these students we made or used three different number lines. Each one was different. Our Great Big Number Line  went from one to ten. The meandering number line went from zero to 42. This sequence went from zero to 10. Did the children notice the differences? Turns out, yes, they did!… which gave them the opportunity to see that the number line is not a fixed item.

Students worked mostly in pairs of two. It took about 8 to 10 minutes for each number to be made. We did not glue anything down. These assemblages were created to be photographed.

I was a bit worried that these kids would be unhappy about the fact that, as soon as a the picture was taken, the number was undone.

As usual, these kiddos totally surprised me. Dumping the contents of the numbers back into the big bowl was one of their favorite moments!

.My daughter Angela did a great job of photographing this process.

The first thing I did with the photos was, with Photoshop, isolate the numbers from the background, vectorize, then print them up. The next day that I saw these children I showed them the prints and we did a number line clothes line.

I’ve been inspired by Joe Schwartz and Tracy Zager, who have written about facilitating the building of number lines with clothes lines and Post-its, So the first thing we did with our numbers was to hand them out in random order, and have the student estimate where the numbers should be located….

Next stop was Kinko’s to make copies of the numbers on standard sized copy paper, that could be folded into accordion books. I had one problem. I didn’t want to just have a line of numbers. I wanted there to be some corresponding items that could be counted, you know, like five things associated with the number five. After agonizing over what these things should be I realized that we had already created designs on the backs of the Great Big Number Line, so I recreated, with acceptable accuracy, the students’ designs and made them part of the book.

Now, here’s the little accordion number line book:

What’s great about accordion books is that they have fronts and backs. Flipping the book upside down reveals the designs that correspond to the numbers.

Completely opening up the book reveals numbers and images!

I’ll be making a few copies of this book to give to the kindergarten teachers who will have these students in their classes.

Now if you haven’t seen enough images on this project, here are two clips of the children working, in fast-action mode.

Yup, love this project.

# The Number Five in Beans

I still have some in-school arts-in-ed projects to show up for before my season ends, but it’s not too early to think about the summer. I’ll be working with pre-K children this summer, in the local Lunch, Learn & Play camp. I’ll be there three hours once a week for five weeks. It’s just the sort of situation that I’m best at: completely unpredictable.  This is a free, show up when you want program so I won’t ever know the number of children who will be in attendance and I won’t be able to predict continuity of the participants.

The goal of the program is to support preparing children for kindergarten. Two teachers from the local school will be on premises. Mostly the mandate for these kids is to work on literacy, and that’s what most of the involved adults will be doing. I will be the only one of the group that will be focusing on numbers and relationship thinking. The teachers have said the goal for these 4- and 5-year olds is simply number recognition: assigning value or even writing the numbers is not part of what I will be doing. Given all these conditions,  I’ve worked out a curriculum that I’m very excited about.

I’ll likely start out with some form of this finger counting drawing activity that I’ve previously done with kindergartens. I like planting this happy connection between fingers and counting into the minds of these young children. I am happy to see current research  supporting this kind of thinking. Addendum:  There’s a wondeful 12-minute talk by Jo Boaler, in which she speaks about finger counting between 7:22 and 8:57.

I won’t be asking children to draw numbers but I will be asking them to interact with them. The number 5 at the top of the page is the filled in outline of the number five.. Here’s a video, in 8x, showing how I built up the form:

There’s no gluing done here. I will be taking photos and hopefully even videos of the children making these numbers to help instill lasting impressions.

We’ll also be working cooperatively to fill in big numbers. I will have these number drawn on heavy weight paper…

— and ask children to paint, draw and collage items on the number. Staying in the lines won’t be an issue because…

…the numbers will be cut out and mounted on these accordion supported structures. This number two is 25 inches tall.

I’m considering adding in some sort of door so that children can actually get into the space behind the numbers. My thought is to scatter these numbers around the hallway  outside our meeting room each week, and asking children to gather them into our room and line them up in order.

In addition to the numbers I will be packing other kinds of activities that will, hopefully, support relationship thinking.  Included in these other activities, I will be bringing along a variation of a project that  Christopher Danielson has developed around the concept of “which one doesn’t belong?”  What I will be creating are  cards to accompany the questions: How are these the same? How are they different?

My thought is that I will be trying to coax out or introduce words that have to do with scale, position, shape and color and whatever else those active minds come up with.

We’ll so come coloring, too.

Likely I will make coloring pages like this one but I will wait until after I start to create these as I want to get a feel for the things first.

Also, I will bring books to read.

In the Night Kitchen Farm donated this gem One Was Johnny by Maurice Sendak to LL&P, so this is the beginning of my travelling library. I would be thrilled to hear recommendations for other books, so please help me out here!

For the grand finale, I want the kids to make really humongous numbers, which, hopefully, will be filmed and/or photographed as the numbers are made. I was flailing about, trying to figure out what to use to make the numbers….

… and finally it seemed to me that having the children become the number, in other words, choreographing them into the shape of the numbers, like the number four in the drawing above, might be a fun thing to try out. Hmm. Wish me luck and look for updates on how this goes during July and August!

Addendum: When Malke Rosenfeld saw this post, she tweeted me a link to this post of hers, which referenced her math work as a five-year old. It knocked my socks off, so I’m sharing it here 1970’s Kindergarten Worksheets

# An Out of Pocket Experience

My thoughts do not naturally go towards developing projects for students who are very very young. But, when I wrote about using an unending accordion for number lines John Golden left a comment saying ” Ooh! It’d be fun for young learners to put pictures of things in that pocket that come in a number on that page. Could make a guessing game out of it, or just a way to record number observations.” I liked the suggestion and I thought that I could develop a response in just one day, but nothing happens fast with me. TEN days later I finally got it worked out in a way that I like.

You may notice that I used dots, not pictures. I like dots. Everyone likes dots. Granted, dots can get kind of, well, repetitive after a while, so it’s a good thing that there’s a one side and another side and that dots are malleable.

Here’s the thought behind this project. First, it’s a pockets project. Students seem to like pockets even more than they like dots. Anything at all that would benefit from a peek-a-boo kind of experience would be fine subject matter for the pages.  I just happen to be on a numbers kick at the moment. I have gleaned from the #MTBoS math people who I follow on Twitter that associating numbers with groupings can be a good foundation skill: creating groupings of, say, three things could help support the understand that the symbol for three is an abstraction representing three somethings.

As usual, the challenge I set out for myself was to make this out of standard copy paper. This structure is similar in many ways to the structure in my previous post, the one difference being that I’m not linking the papers together as I don’t see an advantage to this being a continuous number line, though it certainly could be.

I made some PDF templates for this project. (The good news is that I finally figured out how to make PDF’s in a small file size!!! I will eventually be going back and make all my pdf files smaller). I did not however, provide colorful dots and pictures. I see this as a class project, where students can either color in the dots or turn them into balloons and ladybugs. (Let them color it and they will own it.)

Here’s what you can print out if you like:

8.5 X 11 open dot groups

8.5 x 11 Filled dot groups

8.5 x 11 simple pockets

I haven’t included directions on how these pieces fold, but if you fold on the dotted lines and look at the pictures, I think it’s decipherable (?).

Maybe the next step after this is, well, dice….which, in a few years could lead you to fedricomath’s Weird Dice.  (which I link to here so that I can keep track of it).

Just for the record, this is what’s been keeping me distracted lately.

It’s a magnificent autumn in Upstate New York.

# Counting to Ten

Today I did a numbers project with students who haven’t quite reached the number 10 yet in their studies. They have gotten as far as number 8. These are Pre-k students, all around the age of four years old.

My thinking here is that I want these students to create a visual that connects the numbers that they are learning to the fingers that they count on.

This is standard size copy paper, folded in half, so that students might be nudged into tracing each hand  in each half of the page.

Here’s something I found interesting: I’ve worked on this project with three pre-school teachers so far, and each of them were surprised that the students did so well with the tracing.

These children sometimes mentioned that they might need help tracing their other hand, but no one actually received or needed help.

After tracing, students labeled their finger tracing with numbers, then crayons were distributed.

I asked students to trace over their pencil lines.

It was quite wonderful to see how carefully they considered their color choices for their numbers and hands.

What started happening next in this class was a complete surprise to me.

Some students started to embellish their handiwork with ornament and drawings.

When these happy faces started showing up on the hands, I was delighted. What a great image for this student to carry around in her head, happy hands counting her numbers.

These four year-old students were completely engaged in this project, and I was enamored by their work. If you are interested in knowing more about why I would do this project, look at an article I’ve written, called Starting at the Beginning which was published in an on-line teaching artists journal ALT/Space.  This journal is full of a diverse cross-section of artists who are doing all sorts of dynamic, educational work. I highly recommend that you take a look.

In the meantime, smile when you count.

Addendum: April 12, 2015   Just came across this article that discusses why students should use their fingers for counting. http://www.theatlantic.com/education/archive/2016/04/why-kids-should-use-their-fingers-in-math-class/478053/