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!

Counting to Ten

March 16, 2015

Table of Papers

Setting the Tables

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.

Two hands on a page

Perfect Fit

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.

Five Fingers

Five Fingers

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.

Boy's Hand


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.

Girls Hand


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

IMG_0338After tracing, students labeled their finger tracing with numbers, then crayons were distributed.


I asked students to trace over their pencil lines.

Numbered Fingers

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

More colors on traced hands

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

IMG_0341Some students started to embellish their handiwork with ornament and drawings.

Happy Hands

Happy Hands

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.

More Happy Hands

More Happy Hands

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/


Jacob’s Ladder Details

November 24, 2014

Mixed-up number line, Paula Beardell Krieg

Jacob’s Ladder in transition

Time to finish up this Jacob’s Ladder. I had it in mind to develop this way of working with the Jacob’s Ladder so that it could be replicated by others, but it’s just way too specific and involved for me to actually encourage someone it do what I’ve done here. Rather than being a project to share, this has been more like designing a product to produce. But, still, there’s a few things here that I want to write about.

(If you’re not sure what a Jacob’s Ladder is take a look at  http://toymakingdad.blogspot.com/2010/09/making-jacobs-ladder.html or https://bookzoompa.wordpress.com/2014/11/16/a-jacobs-ladder-number-line-in-progress/.)

 Jacob's ladder

Jacob’s Ladder, in the early stages

I’ve been working with the Jacob’s Ladder in the same way that I would work with a flexagon: in other words, I’ve been interested in making complete transformations happen when the Ladder is flexed. This resulted is having four completely separate sides to discover. Here they are:

Side # 1

Side # 1

Side #2, (Flip side of Side #1)

Side #2, (Flip side of Side #1)

Side #3

Side #3

Side #4 (flip side of Side #3)

Side #4 (flip side of Side #3)

I had such a good time watching this come together!

The first thing I want to point out is the first and last panels of Side#1 and Side #4: they are both zero’s and both title pages. These two pages are the only two sides that don’t really change. I had to work these panels into the sequence, and I had to keep in mind that, in fact, they do change, but that change is only that they flip upside down. So not only did I have to make them work as part of sharing a sequence, but I had to figure out a way to have them make sense upside-down and right-side up in each of the sequences. And if that sentence just made your head hurt you can empathize with me. (Thank you.)

At first I thought I would begin with a one, since that can go upside-down, but finally decided that a zero was better. It took me awhile to realize that I couldn’t make the other end a number, I just couldn’t make it work. Making a cover page, though, seemed like a good solution.

Cover/ Title Page

Cover/ Title Page

I think that this turned out to be equally legible from any vantage point.

If you decide to try to make one of these I do have one major tip for you to consider. I think that most of the sets of directions that are out there have this one fatal flaw in common: they direct you to assemble the different sections in a line, growing it so that it resembles the completely unfolded Ladder. I have followed different renditions of this same theme, and, although the directions have been flawless in terms of accuracy they are confusing to follow. Following directions for sewing book sections together have can also have this same maddeningly confusing accuracy about them, too, so I’ve learned to look for patterns in the sequences, so I can just discard the directions. It’s a great way of working.

For the Jacob’s Ladder, assembling it is much easier if you stack the sections, weaving the ribbon around the blocks in the only logical way to wrap them. The trick is to start out right. Here’s how to start out right:

Step 1

Step 1

Make sure your three long strips of ribbon are a bit longer than  your finished Jacob’s Ladder will be (some set of directions have you cut lots of small pieces and attach them in certain patterns, but I find this, at best, cumbersome).  In the photo above I’ve been overly generous in the overhanging piece, but you should get the idea that the upper and lower long ends extend to the left and the middle long end extends to the right.


Step 2,

For the second step, lay the second board on top of the first, and wrap the ribbons around the board in the only way that makes sense.( If this makes no sense to you now, you’ll see what I mean if you try it.)

Step 3

Step 3

Next, lay down the third board, and, again wrap it. Continue doing this until you’ve run out of ribbon or boards. You’ll have a neat little stack that you should hold together well until you are able to attach (with nails or staples) the ribbons to the edges of the board.

Jacob's Ladder, stacked

Jacob’s Ladder, stacked

The ribbons make this checkerboard-like pattern. Quite distinctive.

I had meant to take some time in this post to write more about why I keep doing these number lines, but I think I will save that for a different day. It’s time for me to sign off for the night. I’ll be counting sheep soon…

How to Make a Number Line with a Parade of Envelopes , Paula B. Krieg

How to Make a Number Line with a Parade of Envelopes

This page has been many days in the making: It has been some time since I’ve felt so challenged by a tutorial page that I wanted to make.

I see this structure as a way to make a number line, but it can be many different things. My last post showed pictures of how the pockets facilitate exchangeable content. I can imagine it with all sorts of variations. Milestones of a journey would lend itself well to this structure. A timeline comes to mind, too, showing hours, or days, or weeks, or months, or years, or centuries, with the cards giving information about changes over various time intervals.

One of my favorite time-line projects that I’ve done with 10-year-old children is one that showed major world events on the top side of the line, and personal life events, such as the birth of a cousin, on the bottom side. Hmm…I should dig up those photos, that was a great project, but I digress.

number line evens

One version of this number line, set up to show even numbers

Here’s my black and white version of the directions:

How to Make a Number LIne out of a parade of Envelopes, B & W

How to Make a Number Line out of a parade of Envelopes, B & W

If anyone makes this PLEASE send photos! You can find my email under the About tab.


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