Books are Fractions

March 3, 2016

Equivalent Books

Equivalent Books

I’ve begun my winter/spring season of working with schools, doing curriculum related projects with students. I’m once again revisiting the idea of using books along with fractions. This past summer I had some conversations with  Dr. Maria Droujkova about how she uses paper to illustrate fractions. It was such a simple and brilliant idea that it stayed with me. Bookmaking is, after all, folding down large papers to make smaller papers. It’s such an obvious connection that I’ve been too close to see it!  Now I’ve built a project around this idea, and tomorrow I will be introducing it to the students. Consider this the before post…the after post will be seeing what the 4th graders do with this!

Equivalent papers

Equivalent papers. all 8 1/2″ x 11″

The idea is to start with the same size papers and fold them into books of different sizes: fourths, eighths, and twelfths. They will be in a folder that will be 3/4 of the original size.

All four structures start off the same.

Fold in half, short edge to short edge

Fold in half, short edge to short edge

Each paper gets folded in half.

Folded in Fourths

Folded in Fourths

The papers are opened up, then three are folded in half the other  (long edge to long edge) way, then opened up again. The folder (far right, above) is folded up 1/4 of the way.

Zine-of-eighths

Zine-of-eighths

From this point on the books are folded according to the fractions that they are illustrating.  Here’s the PDF for the book of eighths. The illustrations on PDF are unadorned, on each page there is simply a square divided into eighths, accompanied by a number line labeled with a zero an a one (as suggested by Kristin Gray). I will leave it to the students to do the labeling and partition the parts.  Here are its directions for folding. 

Book of Halves

Book of Halves

Here’s the book to show quarters. I’ve made a halves PDF for this too but I will be giving the students the option to make and partition their own images. Here’s the directions for folding this structure, which I call a Book Base.

Book of Twelfths

Book of Twelfths

The Twelfths book, again, is a pretty minimal PDF in terms of images. Each page has a twelve-sided structure, a dodecagon, which is divided into twelve parts. I added shading, which students can color in or keep plain, to show the parts of twelve on each page. I included these shaded areas because I don’t want these books to be about the coloring, and this would take too much time to color, though students who want to color certainly can. I don’t have printed directions for how to fold this structure, but I did include a scissors icon to show where to star cutting, and dots to show where to end the cut in the middle. After the cutting is done it’s just a matter of making an accordion fold  with the pages, exactly like an Origami Pamphlet.

Folder

Folder

The number line for folder  sports a  dotted line to indicate where to fold up a flap for a pocket, so that all of the equivalent books have a place to get tucked into.

tucked-in

All tucked in: fourths, eighths, and twelfths

It will take a number of visits to this class over the next few weeks to get started and finished with this project. This is a great group of students that I will be working with, and I am grateful to the teacher to let me tackle fractions with his class (thanks Mr. A!) I look forward to posting the students work and their comments on this projects. Now it’s time for me to get tucked in…

Last look

Last look

The PDF’s for this projects are above, but here they are again, all together:

number line for folder

halves,  book of eighths and Twelfths

Addendum: First  day of this project went well. We talked about the fractions the students had been studying, and looked at the graphic of fractions on the folder. We also made the Book of Eighths. The students seem to make a great connection to this project. The math specialist at the school saw what we did and hunted me down express her enthusiasm about what she was seeing. Her main comment was about how glad she was to see the number line so present in this collection of fraction books.

in progress book of eighths

One Response to “Books are Fractions”


  1. Colorful. I always enjoy surfing through your creative paper works. Well done

    Liked by 1 person


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