Endless Accordion

October 4, 2015


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.


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!

A Pre-K Project

A Pre-K Project

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.

An Accordion Book with Pockets for Kindergarten Sight Words

An Accordion Book with Pockets for Kindergarten Sight Words

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.

How to Bind Loose Leaf Papers by Paula Beardell Krieg

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

Accordion Fractions Book designed by Paula Krieg

Accordion Fractions Book

Here’s the rest of what I started in my last post about this book with the narrow accordion spine.  What I like about combining this structure with fractions is that it makes a concrete (ok, paper) connection  between the relationship of different “families” of fractions to each other.  For instance, just by looking at the pages when the book is expanded, as it is in the photo above, it’s clear that two-fifths is bigger than one-fourth, and 2/2 is the same as 3/3.

After making the accordion spine in the last post, there’s actually one more step, because I needed not four, but  five accordion folds.

To make the fifth accordion, start by folding  just one edge over to meet the closest crease.

To make the fifth accordion, start by folding just one edge over to meet the closest crease.

To make the fifth accordion pleat the students folded one of the edges to the closest crease, pressed down the fold then turned the paper over and brought the crease up to the master fold.  Done.

Accordion spine with covers

Accordion spine with covers

Now the covers go on….

pages of fractions, 8" x 5 1/2"

pages of fractions, 8″ x 5 1/2″

…and the pages go in.  After a conversation with  my wise special ed friend teacher, Melanie, I decided to label the left side of the pages with part of the fraction that each slice of paper singularly represents.

Adding Pages to Fractions Book

Gluing pages into Fractions Book

Students cut the papers  to their appropriate sizes  (on the lines that were printed onto the papers).  This step, to my surprise, didn’t take long and went quite smoothly.  There was the occasional leaking out of glue that made some pages stick a bit to each other, but that was easily fixed.

Fractions pages

The students labeled the right, exposed edge of the fractions book, with the fractions written sequentially.

Now it’s time to decorate the cover, using 2 inch squares to cut into fraction pieces.

And decorated they did.

The only thing left to do, if they choose, is to write on the blank parts of the pages, perhaps adding in math facts.

A big thank you to the teachers who trusted me when I said, hey, we can do a fractions book…I’m sure they had no idea what I was talking about. And it worked out so well! Everyone was happy.

Books in Process, Accordion Spines

Books in Process, Accordion Spines

If you know something bookmaking you know how useful it can be for the spine of a book be  narrow accordion folds, as pages can be tipped (glued) on to or sewn into the accordion.  The big thing that I didn’t know about this structure was if I could do it with 75 3rd graders in one day.  The motivation behind doing this was to make a book  that could expand, as accordions do, to reveal pages of fractions which could help students understand the relationship between different sets of fractions.

Accordion Book With Tipped on Fraction Pages

Accordion Book With Tipped on Fraction Pages

The photo above shows the finished product, but that’s getting ahead of myself. What I want to show is how we made the folds. In the interest of full disclosure, the following photos are taken of a class of 7 fourth graders making the same book. Working with seven students in class allows me the leisure of taking pictures. When I was working with the third graders (3 classes of 25 students) I had to stay on the move.

I started out by sitting down and talking to the classes about what we would be doing. I wanted to emphasize that even though there were no “hard” to understand steps, all of the folding was just different from what they were used to doing, and it was this difference that would make it seem hard to do. So I asked them to be open to doing something different so that they would be able to be successful.

A 16" x 8" paper folded in half

A 16″ x 8″ paper folded in half

Having the middle fold in exactly the right place is so crucial to the success of the structure that I handed out the papers to the students with this fold already in place. Therefore the first thing that each  student needed to do was to unfold their 16″ x 8″ paper.

Folding the edges into the middle

Folding to the Middle

Next, one side at a time, the edges are folded to meet up with the middle fold, which henceforth will be called the master fold.

Folding the edge of the Paper to meet the further away crease

Folding the edge of the Paper to meet the further away creases

This may not be readily seen and understood, but think slowly. Open the paper flat, then fold one edge over to meet the furthest away crease, flatten. Repeat, starting from the other edge.

Foldin half again

Folded in half, like the first step

Next, open the paper flat again,Noticing that there are four “columns, in defined by folds, in the paper.  Refold in half, as in the first step so that the master fold is at the edge of the paper.

Make a new crease by bringing crease to master crease

Still with me? Now, look at the crease that is closest to the master crease, then curl the paper so that this crease meets the master crease. Press to make a crease (which is unseen, as it is between two layers of paper). Repeat with the next crease below the master crease, then flip the paper over and repeat.

Okay, you’ll end up with something like this. Actually, with my classes, we did one more fold, to make just one more accordion pleat, but I will describe that in my next post.

It’s important to have long edges to glue covers on to.

And, for now, we’re done. The  next step will be to add the fractions pages.

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