Math and Book Arts · Math and Paper Folding · Uncategorized

A Fractions Number Line Project for Fourth Graders

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.






Li’l Jacob

How to make a Li'l Jacob
Li’l Jacob

 In a previous post I had written about a structure that I am planning to teach to a group of fourth graders next month.  There’s a fun folding trick to it that feels like magic: its two panels flex in such a way that allows the front and back covers to reverse positions, and it offers two different configurations of the inside spread.  I’ve put together the instruction sheet above for anyone who feels up for something completely different. I think that the instruction page above will print just fine, but, just in case, here’s the Li’l Jacob PDF 

Now for my dire warnings.

If you attempt to make this or teach this you will be unsuccessful unless you release any attachment to thinking for yourself. Follow the directions precisely. Chances are you will not heed this warning until you have botched up the first few tries of making this. Oh well. I tried to warn you.little-3-6

Any students you work with should also be encouraged to work along with you lest their attempts fail. Precocious student will anticipate the next step, thinking that they see a pattern in the steps. These students will likely find themselves with a structure that is glued shut. I have a special name for this kind of mistake. I call it a bad Christmas present: it looks interesting from the outside, but it just won’t open. Can be funny, but ultimately it’s not something you want.


I did not invent this structure. I don’t know the history of it, or what it’s called. I have seen it used a novelty gag, something that will hide or reveal a dollar bill. If someone knows its official name, I would be grateful to hear it. Only recently, when I had been exploring the folk toy known as the Jacob’s Ladder, did I realize that this structure is a shortened version of the Jacob’s Ladder. It seems fitting, therefore, for me to call it Li’l Jacob. I really like this name.


Let me mention too that there is nothing special about the dimensions that I present in my instructions.  The squares can be rectangles. The strips of paper can be all the same width, or all different widths. The dimensions that I illustrated will be the ones that I will be using when teaching, so that’s what I based the tutorial on.

I’m looking forward to seeing how students react to this odd folding activity.  If you try it out please please please let me know how it goes.