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.
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.
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.)
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.
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.
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.
Finally 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.
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.
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.
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.