A Fractions Book

I’ve finished up this fractions/number-line project that I’ve been thinking about. I worked with a class of fourth graders who were just starting their fractions unit. My plan from the start was to try to present a project that was dynamic enough to capture their interest. The center piece of the project was to make a “magic wallet,” which is a shortened variation of a Jacob’s Ladder. I’ve been using the name “Li’l Jacob” instead of “magic wallet” because, originally, I couldn’t remember the magic-wallet name, and Li’l Jacob seems properly descriptive.  This structure opens in two different ways, to reveal two different visuals. It’s tricky, and seems magical. I am happy to report that these students were over-the-moon happy to learn how make this.


The students told me that the first step of arrangement of papers reminded them of a person

After showing the students what the finished book project would look like we dove right into making the L’il Jacobs. Making this requires a completely non-intuitive sequence of precise folding and gluing. The students have to keep track of where they are in the sequence in order to get the folding to work. I was nervous about how I could get them to see for themselves what was going on. A great surprise was that they offered me the best description I could hope for: they saw the arrangement of papers and immediately recognized it a human figure, legs and torso. Perfect! Now I was completely convinced that I would continue calling this a Little Jacob.

???????????????????????????????The students decided that this next step was best described by saying that they were covering Jacob’s innards.


As the sequence of folding continues, the Jacob becomes smaller. (Notice the paper that student is using  to protect the desk from getting mucked up with glue.)

Jacob squared

Li”l Jacob squared

The last fold reduces the paper into a square.

Each student made four Li’l Jacobs. Each of these had a set of equivalent fractions written on and in it. But we didn’t even start with the fraction labeling until the third class. Our second class was about making the book that was going to hold our fraction cards.

We folded a 33″ x 4.5″ paper int halves, then quarters, then eighths, to make an eight page accordion. I know that most people don’t have access to paper this size, but with a some thought this can be created by combining smaller sheets of paper.


Origami Pockets on every other page. Student chose their own colors.


Students then made origami pockets out of 5.5″ squares of paper. Starting with the second page, these were glued on to every other page of the book.

zero page

Creating a cover with a fold-in, to extend the number-line to inside

Next came the cover. The book needed an extension  so that the number line could start at zero. To accomplish this we attached an extra long cover piece then folded it over. I know I’ve explained that badly, so I hope the pictures above are adequate explanation.

fractions-Zero-to-OneFinally we were ready to label the Little Jacobs with equivalent fractions. I talked to students about how fractions could be a way of counting to one: one-fourth, two-fourths, three-fourths, four-fourths(one). I showed them my animated zero-to-one gif and some static images of equivalent fractions  but they seems to like the image above the best. We circled the columns of fractions equivalent to eighths. The really seemed to get the concept, and kept referring to it as they did their labeling.


The picture above is my sample that shows the labeling, with different ways to write equivalent fractions, as well as a simple addition problem, using the fractions.


Here are some images of the students finished books.


The even pages hold the fractions in the pockets.

odd pages

On the odd pages, students wrote out the fractions. These fractions had no equivalents on our chart. Forth graders don’t do fractions beyond the twelfths, so 1/8, 3/8. 5/8, and 7/8 stand alone.

K's book Some students were more inclined than other to do decorations on the books.


One thing that was wonderful about this class was that the students were incredibly helpful to each other. I could have never gotten this far with this project if I had to problem shoot with each child individually. The students who grasped each step were enthusiastic about working with a classmate that didn’t quite get a step.

big line


We lined up the fractions so the eighths showed, thus showing the 1, 2, 3, 4, 5, 6, 7 and 8 in the numerator. By the end of my third meeting with these students, just about everyone had finished with their books. This is one class that I can say is excited about equivalent fractions.





Giving You the World

March 24, 2015

Paula Beardell Krieg:

I’m working on getting ready for six different projects tomorrow. One of them will include a wonderfully folded world map. This is one of my favorite activities, so I thought I would repost this tonight. Please to click on this link in the PDF of the World Map rather than the PDF in the post…the one below has an extra line in it and it turns out I can’t change links in posts that I am reblogging! It took a whole evening of tweaking to get it to work just right, to go with the folding instructions. I would be very happy for it to get lots of use.

Originally posted on Playful Bookbinding and Paper Works:

To print out the directions above, here’s the PDF of Origami Base for World Map And here’s the PDF for the World Map That Can Be Folded Into An Origami Base.

I have a slew of agendas when I work with students. One item at the top of my top-heavy list is to incorporate a world map into projects whenever possible and appropriate. If I can provide students with a clever and fun way of using a map, all the better.

This is a 6″ x 6″ square (folded down from a 12″ x’ 6″ paper). Open the cover and you’ll find a map of the world, with Sweden highlighted.

Just in case it’s not clear, the map is a separate piece of paper glued into the cover.

Note the  compass rose, that has been colored in by the student and notice how well the world map sits on…

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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.



Making decisions about text that results in a perfect rectangle

Once you start looking for it, you’ll notice that many titles seem to have an invisible rectangle around them. There is much to said for fitting a title into a symmetrical geometric shape.

One my classroom projects this month is to work with fifth grade students to create books about the Fourteenth  and Fifteenth Amendments to the US Constitution. One of the details that I hope to focus on is how to design a layout for their title. I won’t have a semester to teach them concepts about design and typography, but I will have about 10 minutes. I’ll try to make the most of it.


Yes, I like Star Trek and am sad the Leonard Nimoy is no longer with us

To fit titles into shapes, designers will make some lines of letters larger than others, and they will put more or less space in between letters. The students I will be working with will be writing their titles by hand, so the letter-spacing will be within their control. Otherwise, they would need to use a computer program that allows kerning.

This practice of working with type to make a rectangle creates a strong, stable and pleasing visual.  Having only a couple of words in a title creates an opportunity for a powerful graphic. The Cooper Hewitt, formerly known as the Cooper-Hewitt, Smithsonian National Design Museum, has streamlined its name. Its now two-word name is easier on the eye and fits nicely into a rectangle. A take-away for my fifth graders is that they could consider using a shorter title than The Foourteenth Amendment of the United States Constitution. If they want to make a long title, though, rectangles can still be used, but there are more decisions to make.

The hobbit

Here, the seven words on the Hobbit title work because of how the words fit together like puzzle pieces. The alternating lines of different sizes of type create a pleasing rhythm.


This In the Heart of the Sea title seems particularly elegant to me. The smaller words are delicately positioned, The larger words, Heart and Sea are all in capital letters and twice the size of the rest of the text, but everything fits together so that these big words, rather than shouting out, feel profound and mysterious.


Here’s another rectangular design, this time with, count ‘em, ten words. So many words could look too crowded and too busy, but the top three words nearly fade into the background, which simplifies the look of the writing, and lets the focus be more on the words that are unique to this particular Narnia movie.


This Snow White title shows another way to create the rectangular look: take just one of the letters and stretch it so that it goes from top to bottom, thus unifying the composition.


Something else that I will want to talk to the students about is that there is no one right way to make a title.  The best way to drive this point home is to show them the same title over and over again, each designed in a different way. The Red Riding Hood title above is a tall rectangle, with the word Red emphasized. BTW, I love the little sign on the right.


Here, Red is again emphasized, but, instead of a rectangle, the lines are offset, and which is echoed, thus re-enforced, by the introduction of the sharp, unstable, and scary triangles. This is a more dynamic composition. This point here, also, is that designers don’t always have to choose the rectangle.


Nor is there always a right word to emphasize. Here, Hood gets the spotlight.


Riding Hood gets most of the attention in the title above, but in the title below,


Red Riding are the words in the limelight here. Note, too, that there’s no attention paid to making the title mimic any particular shape.

It is always important to make some of the words in a title bigger than the rest? These designers of the following images didn’t seem to think so.


The focus is on the picture, though the text stands out nicely without calling too much attention to itself. If you think this treatment of the text being all the same size is somewhat old-fashioned, and reserved for text that accompanies pictures, think again, or at least keep looking.

red riding hood title

Here, the text is the same size, and, again here’s an example of a composition that feels unstable. This time the danger that this instability implies is enhanced by the spatters of red.


Front and Back Cover

Here, again, in this last image of a Red Riding Hood title, no particular word stands out.  Because of all the white space, paired with the text that looks handwritten, there’s a quieter, more innocent tone than what’s in the previous image.

So, here’s the presentation I will be making to the fifth graders. I hope it’s obvious that I am not going to tell them what decisions they should be making . There’s  not a generous amount of time that we will have to work on the titles, so it will be interesting for me to see if they are able to make small adjustments to what they might have otherwise done. I am hoping that they will enlarge a word or two, maybe use more than one color on the page, and be mindful of the overall look. What I am mostly hoping for, though, is give them a bit of awareness of design, and to get them realize that they too can make deliberate and considered visual decisions which will enhance their work.





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