## The Humongous Rubber Band Book

### April 17, 2015

The sixth grade English teacher in this school likes the idea of each of her students making a book that they can use as (her words) a memory catcher. Writing, pictures, and ephemera will go into these books. The design challenge is that I can’t count on having more than 40 minutes to work with the students. I want them to end up with something large, sturdy, and I want them to enjoy making it.

On my day with these sixth graders, they walked in the library, saw the colorful papers and were immediately delighted. “Do we get to do *this *today?!” They were all so happy! My papers here are tabloid size, 11″ x 17″ 67lb papers (which, by the way, are getting more expensive and harder to source every time I look).

Each student chooses eight papers. We have plenty of space to work. It’s interesting to notice how each student chooses to arrange their stash.

Some students choose to work alone and spread their papers out all out in front of them

Other students work two, three or four to a table and have to stack their papers.

Next step is to fold the papers then nest them together in groups of two.

I’ve worked with these students many times before, and they are all have expert paper-folding skills.

The trick to accurate paper-folding is to hold the paper with one hand, then slide the other hand towards the curl.

These students have been using my bone folders just about every year they’ve been in school. If I forget to hand them out they will ask for them. In schools I refer to them “folding tools” to avoid vegetarian discussions. If the fact that they are made of bone comes up, I advise vegetarians not to eat them.

The students end up with four groups of two folded papers. This grouping is completely non-intuitive: students want to nest them all together, one inside of the other, and wrap one rubber band around the spine and be done. In fact, the book would work just fine that way, but I’m here to show them something different, and, arguably, better. By asking them to make four groups of paper they will end up with a thicker, and much cooler looking book spine, one which shows off some of the colors in the book.

Once the pages are grouped together, there’s one more step before the assembly starts. The corners of the tops and bottoms of the folds are snipped off. These snips create valleys that the rubber bands will settle into.

Two groupings of papers are set next to each other side-by-side, opened in the middle. The rubber band slides over the four adjacent pages, binding the page groupings together. I use Quill Brand Rubber Bands, 7Lx1/8″W which are humongous in just the right way. Smaller rubber bands will actually work for this, but the tighter the rubber band stretches, the sooner it will rot and break. I want these books to stay together for a good long time.

On goes the rubber band! This is done until all four sections are linked, in sequence, one group right next to each other. This book can be made to be just about any number of pages long.

It’s a good idea to decorate the cover of this book right away, as the flexible nature of the spine can make it tricky to figure out which page is the front once it’s been opened and looked through. Students make pockets to go on the front and back covers, to store items that will be eventually attached into the books. I’ve been making these books with this school’s sixth graders for a number of years, but I don’t get to see them finished. Students, however, will joyfully tell me about them, and they will also tell me, oh I remember when my brother made these! From what I understand, they hold a plethora of memories.

## Piecing Together a Project, Over Land and Sea

### March 31, 2015

This story begins in a teachers’ lunchroom, a couple of years ago, in Upstate NY. I was sitting with some teachers when another member of the staff started talking to a first grade teacher, Mrs. K, about a new math mandate. It was something about using manipulatives to create a variety of shapes. I’m a bit foggy on this part but it seems to me that they were required to use rhombuses (or *rhombi*, both are correct) for their shape building.

Upon being told that she would have to incorporate these manipulatives into her math unit Mrs. K asked if there was any money in the budget for manipulatives. The answer was no.

After school I sought out Mrs. K and showed her some paper-folding and shape transformations that referenced rhombuses. This teacher seemed delighted with what I was showing her. I volunteered to send her something that I thought she might find useful, then went home and created these images for her, which are equilateral triangles that become a rhombus.

I never asked Mrs.K if she used what I sent her. I recognize that what I sent was, unfortunately, not a project. Instead, it was just the bones, the beginning of a project that needed to be developed. Every so often I’ve revisited these images, wondering what I could do with them. Then a few nights ago Malke, from Indiana, asked me about projects for a family night.

It was late, and we decided to resume the conversation the next day. The next morning, before Malke and I reconnected, I saw this post from Simon Gregg, in France:

I had an Aha! moment. It suddenly came together. I sent off this note to Simon:

Malke, who I included in the conversation, responded with a reference to a beautiful manipulative that I wasn’t familiar with, but which also showed that she immediately recognized what I was getting at with my DIY paper version of manipulatives.

Since Malke seemed to know exactly what I was thinking about I got to work creating the pieces for this activity. I’m pretty happy with how this has developed. It requires triangle paper, and matching paper shapes that can be printed on colorful papers. My thought is that simple, bold shapes can be created in sort of a free form way…

…or more challenging shapes can be drawn on to the paper…

…and filled in, while trying to make as few cuts as possible and being mindful about cutting along the lines defined by the triangles.

So, where can you get these papers to do a do-it-yourself shape building set? Right here. I’ve created a couple of PDF’s to get you started:

Make beautiful shapes. Send photos. Thank you.

Addendum: Take a look at Malke’s post on hands-on math: she collected and organized many interesting perspectives. It’s a fabulous piece of writing. http://mathinyourfeet.blogspot.com/2015/04/some-thoughts-on-hands-on-math-learning.html

Addendum #2 (April 2016) Malke liked working with smaller rhombuses so I made her this PDF rhombi with spaces So far she is planning on using them without the triangle grid paper. Here’s a link to some images she’s created as samples for an upcoming project https://www.facebook.com/MathInYourFeet/ rhombusphotos

## Pre-K through Seventh Grade

### March 8, 2015

Tonight I’m finishing up gathering supplies for the first day of what is always my most challenging, and most satisfying, school visit of the my teaching-artist season. I have been visiting schools in the Adirondacks for many years, but I have spent the most time in this one particular school. I get to work with nine grade levels, pre-K through 7th grade. I need to create nine completely different projects, which will go from beginning to completion over six days, spread out through the month of March.

In the interest of finishing up the details, and getting to bed (last night, daylight savings time kicked in, so getting up tomorrow morning will be a challenge) I am going to list the nine projects for the nine grade levels, then I’m going to try to write about them over the course of the month.

Here goes.

PreK: the teachers asked that we do a project with the students’ names. We’ll thread beads and cover weight papers on to shoelace-tipped yarn, write a letter on one side of the card, and a picture which starts with that letter on the back. See photo above,

Kindergarten: Accordion Book with pockets, a variation of structure in the picture below.

First Grade: A folding triptych about Alaska and an animal that lives in Alaska. Will include a pop-up, a pocket to hold research papers, and a poetry page. We’ll color the sky with Northern Lights.

Second Grade: A book that folds up like a valise, that has pockets within for a “passport,” a folding map, postcards, a boarding ticket, and little books with information about a country that the student is studying.

Third Grade: We’ll make a journal for the students to use however they want.

Fourth Grade: This is the class that will be making a Zero to One Fractions book that I’ve been writing about

Fifth Grade: I still have some planning to do on this project, but it will likely be a social studies based project made from units of an Origami Base, which opens and closes in a dynamic way.

Sixth Grade: This group will use tabloid size papers, folded in half, and bound, in four separate sections, with large rubber bands. The students will use these with their English teacher, between now and the end of the year, as a memory catcher.

Seventh Grade: We’ll fold down and trim a large, 35″ x 23 ” paper into an 8.75″ x 5.75″ pamphlet, which students will sew, glue in to a hinge piece, add soft covers, and decorate. The book will go with them to their English class, for content to be added between now and the end of the school year.

I keep everything organized ( I hope) in a notebook that I can make in about five minutes, that looks like this.

Hopefully I will be posting all of these projects. But now it’s time to wrap things up for the night.

## The Flux Capacity of an Artful Number Line

### October 23, 2014

I like the number line.

The number line is all about relationships: I can look at the number line and actually see and measure the chasm between two quantities, even when, as in the case of negatives, those quantities don’t even exist.

As an adult I’ve realized that I had some misconceptions about the number line, and I have discovered subtleties about it that surprise me.

I’ve been toying with number lines for quite a while. In my opinion the number line needs to be toyed with. The images that I see of it are not captivating. I’m wanting to rigorously play with this arrangement of symbols in way that captures some of its nuances. I intend to try to investigate numerous bookish solutions** **which means that I suspect that this topic will keep coming up. I hope this will be an ongoing bookmaking/discovery journey. I’m not sure exactly where I will be going with this.

But I do know that a few nights ago , after a disappointing evening of cutting and folding, a way of proceeding finally presented itself, but I was too tired to grab hold of it. The inspiration teased me all night, and before 7 am the next morning I was tending the coffee pot while working out my construction. I’m very pleased with how this particular structure worked out. It was so unexpected and delightful that I am excited to be sharing it.

It’s built from envelopes, the kind we think of as *regular *envelopes, though, technically, they are called “No. 6 3/4” envelopes.

Here’s are some of the things I like about this piece:

- it’s a zig-zag
- it has pockets
- it scales
- the structure suggests infinity since it can keep going in either direction
- it can fold up into a polite accordion-like book.

The pockets are the most distinguishing feature of this number line. These pockets hold cards, which are printed with different sets, or sequences of numbers. This means that the labeling, or the *scaling, *of the line is always in flux, subject to the whims of whichever algorithm that’s called for.

That’s the crux of it: the flux.

As students proceed through their grasp of numbers, the labeling of the number line constantly changes in scale as needed. Eventually the number gets integrated into the coordinate plane, and becomes the x-axis. I remember seeing the little graphs in math books, and I thought that when I got to grown-up math that the lines would get longer. It never occurred to me that it would be the scale that changed, not the size of the line.

You can see that there’s intermediate markings between the numbers. These can be interpreted differently depending on which scale is being used. For instance, when counting by tens, the small lines can be counted as ones, when the number line is increasing by one’s, the intermediate lines become tenths. In my mind, the point of doing this is to drive home the concept that the very same line can morph into whatever one needs it to be for the visuals of the relationship at hand. The maker becomes the master of the line.

Then the maker gets to fold up the number line into this accordion-like square. Just my style.

Over the next few days I will be working on designing a set of instructions on how to put this line together. It’s likely, however, that if you picked up some envelopes you ‘d figure this out for yourself.

* Addendum *Here’s the link to the tutorial: https://bookzoompa.wordpress.com/2014/11/03/the-envelope-number-line-tutorial/