Accordion Books · Art and Math · Arts in Education · Math and Book Arts · Number Line

Endless Accordion

pocketed-accordion-fives

I’m once again revisiting accordions and number lines, because they are both  infinity fun. What I’ve attempted to do here is to create a classroom friendly accordion book whose pages are pockets which can contain changing content, in this case a variety of number lines.

What makes this project classroom friendly is that it is designed to be used with a ubiquitous material: standard sized, standard weight copy paper. It requires a few simple folds, and very few materials. I’ve made templates that can be printed out, but lacking the resource of a copy machine, this can all be easily constructed without my templates.

Endless accordion with pockets.
Endless accordion with pockets.

The accordion is made from units of full-size sheets of paper, folded, then attached together. For the basic number line I recommend using 6 papers, which will result in 12 pockets. Since zero through 10 needs 11 pockets, the extra pocket at the end conveniently implies “dot dot dot …. on and on …to be continued. ”

The shows where the fold lines occur.
The shows where the fold lines occur.

A full sheet of 8.5″ x 11″ (or A4) is folded so it ends up looking like the picture below:

Two pockets from one sheet of paper
Two pockets from one sheet of paper

The tabs at the side are there to create an attachment surface for other the next pockets.

pocketed-accordion-paper-clips
Attaching pockets together

The tabs of adjoining papers can be attached with glue, tape, sewing, paper fasteners, staples or paper clips. I ch0ose paper clips.

One piece of paper, folded, has room for four numbers
One piece of paper, folded, has room for four numbers

The cards with the numbers are also made from sheets of uncut, folded paper. They are folded so that they are just a bit narrower than the pockets.  Once they’ve been folded they can be glued (or taped etc) shut but I don’t bother doing this, as they seem to stay together just fine without gluing.

Counting by 10's
Counting by 10’s

One set of numbers can make four different number lines.

Counting by ones
Counting by ones

I’m providing links to PDF’s. There’s a PDF for the pocket, which I recommend that you make 6 copies of. This template is in black and white only. I hand colored in the dividing lines.

As for the numbers, I have one full color PDF here, and one that has the black and white outlines of the numbers if you prefer to let have your students color in the numbers themselves. At the moment I only have files for paper measured in inches, but in the next day or two I will update with A4 versions as well.

template for pocket
template for pocket

PDF 8.5 x 11 for accordion pockets lines

numbers color accordion pocket screen shot
Numbers in color

PDF 8.5 x 11 accordion number line, colored numbers

Number to color in yourselves
Number to color in yourselves

PDF  8.5 x 1 blank numbers number line for accordion pockets

If you’re interested I’ve posted something about my interest in the number line on my Google+ page https://goo.gl/ScI0nZ

I would love to hear from anyone who constructs this project with a class!

8 1/2" x 11" Book Making · Accordion Books · Art and Math · geometry and paperfolding · Making Books with children · Making books with elementary students

Five Days of Summer Workshops with 3rd and 4th Graders

Pop Ups with more Pop ups
Pop Ups with more Pop ups

In the summertime, when school is not in session, I’m on my own in terms of deciding on what kinds of projects that I want to teach in workshops. Last week I taught for five days  at the local community center.  My sessions with the kids were 40 minutes long, and although I prepared for 30 rising third and fourth graders, there was no telling how many students would attend each day. I had originally thought I would make a plan for the week, but quickly realized that it was more satisfying to create projects each day based on what I found interesting in the children’s work from the day before.

Making Pop-ups in an Accordion Structure
Making Pop-ups in an Accordion Structure

My own goal for the week was to do explorations with shapes and symmetry.  On Day 1 we made a four-page accordion book and did some cut-&-fold to make pop-ups. The students were amazing paper engineers;  With impressive ease, they created inventive structures.

Pop-up Worksop
Pop-up Worksop

There were plenty of counselors in the room, and from this very first project, these counselors joined right in with creating their own projects.

Overlapping Rotated Squares
Overlapping Rotated Squares

I was so impressed with the students’ folding skills that the next day I helped them create an origami pamphlet that contained more pop-ups, as well as some interesting other cut-outs. What turned out to be the most interesting work on Day 2 was how much the kids liked the little bit of rotational symmetry that I encouraged them to do: I gave them each a square of paper, asked them to trace it on to the cover of their book, then rotate it and trace again.

summer squares 3

These students like the shapes created by shapes, so the next day I brought in a collections of shapes and asked them to arrange tracings of these shapes on a piece of heavy weight paper, which was folded in half.

Tracing Shapes to Create  More Shapes
Tracing Shapes to Create
More Shapes

Students seemed to enjoy creating these images.

summer shapes 2

After they created the outlines they added color.

Colored Shapes
Coloured Shapes

When the coloring was done we folded the paper, and attached some pagesto the fold so that the students had a nice book to take home. The kids seemed to like this project and made some lovely books, but I ended up  feeling like there wasn’t anything particularly interesting going on with this project in terms of explorations of building with shapes. So …

Building Stars and Hexagons with Regular Rhombuses
Building Stars and Hexagons with Regular Rhombuses

…the next day I brought in colored papers that were printed with rhombuses, as well as some white paper printed with a hexagon shape. Each student filled in their own hexagon with 12 rhombuses.

Making a Hexagon with a Star in the Middle
Making a Hexagon with a Star in the Middle

My plan for this project was to have each student make their own individual hexagon then put them all together on a wall so that it would be reminiscent of a quilt.

Paper Hexagon Quilt
Paper Hexagon Quilt

Here’s our paper quilt made from 22 hexagons!

The next day, Day 5, was my last day at this program. I liked the engagement with and results of how the students worked with shapes when they were given structure. There’s a balance that I try to honor of providing structure while allowing individual choices. For my last day, then, I decided to give the students a page that I created that is based on the geometry that uses intersecting circles and lines to create patterns.

A work in progress by one of the couselors
A work in progress by one of the counselors

If you look closely at the photo above you’ll see many different lines and curves overlapping and crisscrossing.

summer geometryI asked students to look for shapes that they liked, to use the lines that they wanted to use, and to ignore the lines that they did not want. It was interesting to watch how the students worked; I was particularly interested in seeing how some children chose to start looking at designs starting in the center, while other children gravitated to the outside edges first.

summer geometry 8

Some students filled areas with color, while others were happy to make colorful outlines of shapes.

summer geometry 2Some drawings were big and bold.

summer geometry 5

Some drawings were delicate and detailed.

summer geometry 4I think that every one of the teenage counselors sat and made their own designs, right alongside of the students. Actually, I think that my favorite unexpected outcome of the week was how involved the teenagers got with the projects.

summer geometry3

This last project of the week was my own personal favorite (though the quilt project runs a really close second). I had never done anything quite like this before with students, and was really surprised to see how much they enjoyed this work, and how differently they each interacted with the lines and curves. This kind of surprise is what’s so great about summertime projects.

Accordion Books

Referencing Recent History: A Folded Record Medium

US-patent-4856818-1
Folded Record Medium and a Blank for a Record Medium, Inventors: Horst Rabenecker and Jurgen Kruger US Patent # 4,856,818

Anne in Australia left me a comment that she and her group we able to construct the Envelope Number Line that I described in my two previous posts, but, in her words, ” our group of 4 found it difficult to fold it into a book which was predominantly our aim.” I responded to her comment by emphasizing that if they were careful about making sure that the title page stayed visible during the back and forth folding process, that things should go well.

But that’s not the whole story.  A tricky part of this structure is how it opens back up after having been folded into a square.

I first came across the bones of this structure decades ago in the NYC Patent Library. The drawings here come from this patent, # 4,856,818, It’s title is Folded Record Medium and a Blank for a Record Medium, Inventors: Horst Rabenecker and Jurgen Kruger. While my variation of this form deviates from the original in both intent and construction, one of the most interesting characteristics of this book remain, which is that it opens from the left, from the right, from the top and from the bottom, each time revealing a different sequence of pages. Using my directions for a Number Line book doesn’t rely on this novel way of manipulating the pages, so I didn’t pause to emphasize this atypical page turning: I’m thinking  that this is what may have stymied Anne’s group.

Patent-US4856818-2
Folded Record Medium and a Blank for a Record Medium, Inventors: Horst Rabenecker and Jurgen Kruger US Patent # 4,856,818 A perspective view of the record medium in the folded state.

Once this structure is folded up into a square it can easily be unfolded into its completely long, wavy state, but unfolding it page by page can seem like a challenge. Think about the simple accordion fold: although we generally open an accordion from one side, like a typical book, an accordion book can be opened with equal ease from both sides. Content can exist on the front and the back of the accordion and be equally accessed from a left side opening or a right side opening. The image below, a book by Lilli Carre, is a good example of an accordion that opens uses both sides of the accordion.

Hoo Dunnit by Lilli Carre
An accordion book that makes use of both sides of the paper; Hoo Dunnit by Lilli Carre
http://lillicarre.blogspot.com/2013/09/helsinki-comics-fest-and-hoo-dunnit.html

By the way, I found this image of Lilli Carre’s during a search for 2-sided accordion books. I was surprised by how few examples I could find of  a book that showed images on both sides of the paper.  Thank you, Lilli, for such a great example of an accordion that uses both the front and back.

The Folded Envelope Book that I describe in my two previous posts goes a whole step further than the accordion that opens from both the left and right, In addition opening form the left and right sides,  it also opens from the top and bottom.  The rub is that  we’re just not used to a book that opens in  four directions.

US4856818  patent-figure-3
A US4856818 patent-figure-3

 

The way this structure opens is difficult to show in picture, and it’s not so easy to describe either. The Abstract of Rubenecker and Kruger’s patent begins like this: ” A folded record medium for two to four different, segmentally arranged information portions is configured so that the interrelated segments of the information portions are easily accessible in a meaningful arrangement.”

So there you have it. If you attempt this structure, which Anne noted was easy to make, be prepared for some conceptual challenges.

ADDENDUM!

Anne sent me photos of her group working on this envelope-pockets structure!

Workshop Table
Workshop Table

What I noticed about this right off was that they utilized used/recycled envelopes as well as blank ones. I loved the character that this gave to their books: really personalized.

Envelope Number LIne Book used for Pictures
Envelope Number Line Book used for Pictures

It looks like they discovered various ways of setting this book up to display content.   I like how the pictures are at different heights here. It seems to invite me to pluck one picture to take home.

Pictures in a Line
Pictures in a Line

Fun and lovely! Thank you to Anne and her friends for sending these photos to me, half-way around the world.

Accordion Books · Book Art · Book Artists · Drawings

Drawing On Health

Italian Parsley

Every few days I wander into the North Main Gallery in Salem, where my hanging books are displayed until September 3.  Each time the exhibit looks different to me.  As Ed Hutchins and I were working together to hang the show it was hard to have any idea of what I was looking at since the pieces we were hanging were so freshly finished.  I imagine that this is true of anyone who creates something: that it isn’t until there’s some distance from the finished piece that it can be really seen by the person who made it.

Rosemary

I am relieved to say that I love the look of the show. The majority of the pieces are works that I think of as Drawing On Health, which refers a preoccupation pf mine, which is to stay healthy.  This is a joyful interest, one that celebrates living.  The attention that I lavish on to the herbs, fruits, greens, and veggies is meant to help me hold them more closely in my being. I hope this comes through and resonates, too, with the viewer.

I love Kale

Drawing these plants somehow makes me like them more.

After seeing the drawing above my friend Sarah told me that she thought that kale, which is quite nutritious, could save the planet because you can pick it and pick it and it keeps producing more and more: an interesting theory!

My favorite piece is nine panels long, dedicated entirely to blueberry season. Blueberries have a special nook in my heart, and I look forward to going to the local U-Pick places to load up for the winter.

Blueberry Season

Summertimes I would visit relatives near Scranton, Pennsylvania.  During blueberry season Uncle Lou would drop off me and Aunt Jane on a mountain top, where we would pick for hours. If the crop was plentiful my aunt would be overjoyed…I can still hear her repeating, over and over “Look at these berries! Look at these berries!” Then we would take those berries back to her lake house where she would make the most wonderful blueberry buckle on the planet.

Here’s a look at my wall of the gallery. The hinges between the panels are designed so that the they can spin. I used some different materials for the hinging, but most of them are cords which I dyed and knotted like this:

Knot In Color

Another wonderful facet to this show is an exquisite gem of a catalogue, designed by Ed Hutchins and Joe Freedman. Here’s a peek at the catalogue:

I have a number of copies of these that I am happy to share for the asking: leave me a comment here asking me for one and I will  get in touch with you, off-blog, you to ask for your address.