## Little Black Book

### May 17, 2015

Sometimes I make a book for no other reason than it’s something I like to do. I like folding papers and sewing them together. I like working out the details: the color and weight thread to use, which folds to make, what papers to use, what sewing pattern to follow.

I have quite a number of heavy weight black paper strips left over from last week’s school residency. This paper has a linen-like finish, it feels good in my hand, and it is rich and beautiful. I wondered what kind of small book I could make. The strips are 4 inches tall and 26 inches wide (about 11 cm x 68 cm). I folded a number of accordion pleats from the center out, left enough unfolded to so I could fold in a cover.

I have stacks of interesting papers which I like to mix up when I’m making a book. I used white, beige flecked, gray, graphing, and soft white papers, cut to 4″ x 6″.

At each stage of construction this book looked good to me. This is a reliable sign that the finished product will have some charm.

After this book was sewn together it wanted to pop open all the time. Here’s something I’ve never seen anyone write about: often books don’t seem to want to stay shut when they’ve first been made. A book like this should be placed on bookshelf, fully closed and between other books, and a week later that same book that was popping open now remains shut. It’s like the papers have to get used to the idea of having been transformed into a book.

The cover of this book is two thickness of paper, created by folding over the ends. I wanted the fold to stay shut, but didn’t feel like gluing it down, so I sewed it down, and the folded over paper became a pocket. .

There’s a pocket on the other end of book, too. I sewed one of the accordion flaps on to the cover to make a narrowe pocket.

Over the last few days I’ve made 5 or 6 of these books, trying to work out what looks best to me. The book on the left is where I started. First thing to change was the sewing. It just didn’t look good to me. I had seen as description of this linked binding and wanted to try it out, so that’s what I did. I like this change in sewing (though it used far more thread: 45″ of 4 ply waxed linen) , but it seemed to me that the signatures were too thick, so the next book the signatures were made from 5 papers rather than eight (5 papers = 10 leaves = 20 pages, and since there are three signatures, that makes this book 60 pages long). All good. But then I wanted to see if liked a more colorful spine, so I tried out purple. I’m not sure whether I like the black or the purple better, so now I’m stuck, and will stop here for now. Which is good thing because I need to get ready for teaching tomorrow.

I’ve been reading on-line conversations lately about scaling and dilation (which are two terms for the same thing, I think). Repeatedly I’ve seeing questions from various people on scaling activities. This confused me at first, not the concept itself, but why did there seem to be such an interest in methods of teaching dilation? Turns out that this idea of proportional change is a key concept to grasp in math, and the nuances of it are tricky to teach. After thinking about it I thought about how artists and designers use scaling all the time, and I mean *all the time. *So, this week, when I was working with first grade students, I decided that I would present the decorative part of their project as an a math lesson, as an exercise in scaling.

Each student picked six strips of paper, which were 1.5″ x 3″ each. I told them that these strips are the shape of two squares on top of each other, and I knew that because they are twice as high as they are wide. I don’t think they understood that part, but that was fine. I just wanted them to hear the language, as I think that it conveys a sense of importance. I then showed them how if they lined up the papers so that they made an “L” they could see a square, which they could then cut, as in the photo above. From there we talked about how they could use the square for decoration. Since a plain square is,well, not too exciting I tilted the square for a more interesting look. Next I showed them what happened when the square was cut in half, corner to corner -one cut, two triangles! We then looked at what happened when the triangle was cut in half again, and then again.

I also showed the students that to make a scaled down square that they had to cut the original square twice, once in both directions. There is something about making “baby squares” that particularly captured their interest.

Baby triangles were a big hit too.

This is an activity that I’ve taught many times bu it seems to me that, judging from the results, this was the most successful day I’ve had of teaching this kind of embellishment.

Their project, by the way, was making a book for their animal reports.

Students have done their research, now they’ve made their books, next they will be adding writing to the books. This elephant will eventually be flanked by facts about his habitat and other interesting facts.

These students will be able to continue with these embellishments as they complete the rest of the books, I won’t be there for that part, but I think they’ve got the idea and these books well become even more wonderful.

## The Animated Equation Book

### May 3, 2015

My Do-It-Yourself Equation of the Line Flip Books are ready to share.

I’ve been writing about these, on and off for months, but my work on them has been steady. My goal has been to create PDF pages that I can distribute on-line which a class of students can assemble in about 10 to 15 minutes, and which show how the changing variables in the equation of the line, y = mx + b, changes the look of the graph. I am doing this because it seems to me that the understanding of this particular equation is either a gateway or an obstacle into the continuing study of mathematics. This is my way of contributing to the conversation of how to nurture a more math literate culture.

My thought is that if students can hold the equation in their hands, that it will give them the opportunity make sense of it for themselves.

I’ve made four sets of PDF’s. I find that heavier weight papers makes the best flip book. I use Hammermill Color Copy Digital Cover paper, 60lb, but that said, if all you have is standard weight copy paper, use it.

Here they are the PDF’s!

The PDF for flip book of changes of b in y= mx +b

The PDF for flip book of changes of m between negative one and positive one in y = mx + b

The PDF for Flip Book to show the changes in m greater than positive one, less than negative on in y = mx + b

The PDF for Flip Book to show changes in x on the graph of y = mx + b

There, now that you’ve downloaded all the PDF’s you’ll notice that, oddly, they look like this:

What may or may not be obvious is that there are six pages on each panel, and half of these pages are upside-down. So now it’s time to give you some hints on how to make these pages into flip books, and tell you what’s up with the upside-down.

Each piece of 8 1/2″ x 11″ copy paper will contain six pages of the flip book. (To my **A4** friends, I will be making an A4 version of these, but they are just not ready yet.) The pages need be cut out on the solid gray line. Let students do this with scissors! The pages are numbered, so it should be easy enough to get them in the right order. The important part, when assembling these books, is that the FLIPPING EDGES are even!!! That’s why half the pages are upside-down on the page, so that the flipping edge always falls on the edge of the paper so it doesn’t have to be cut.

Now, how to bind these small books…

Bookbinders will figure out their own ways to bind these books. These simple binding solutions are meant for the classroom or home school venue.

Before you start, note that the front and back covers aren’t numbered. You can figure out which is which. Just be sure to *flip over the back page so the graphic shows *otherwise your back cover will look boringly blank.

The easiest way to put these paper together is to make sure that the flipping edge is even, then wrap a rubber band tightly around the spine. This simple solution works surprising well, though every so often you might have to remove the rubber band and realign the edges. The thinner the paper, then thinner your rubber band should be. Experiment. You’ll know what works and what doesn’t.

My favorite simple solution is to use strong clips, like on the upper right in the photo above. I just found out that these are called binders’ clips. Excellent name. Use the smallest size that works. The small ones, 3/4″ wide, work just fine.

If you have access to a drill, then doing a simple sewing is swell. Drill three holes evenly spaced, about 1/4″ from the spine and follow this sequence: go through the middle hole, leaving a tail of thread behind, sew through the top hole, travel down to and go through the bottom hole, then go back up through the middle hole and tie your ends together.

That’s it. Make lots of books. Let me know how it goes.

## Flip Books, nearly done

### April 22, 2015

I didn’t think these would take so long to design and create.

I thought I was starting with something easy. My endgame plan is to make flip books that show hypotrochoids, aka spirograph shapes. I thought that starting with something as straight forward as a straight line wouldn’t take long. These books show variations of the equation of a line (y=mx+b). Four books, one to show changes in b, one to show changes in x, and two to show changes in m. This process has been anything but fast and easy.

I didn’t count on there being so many decisions to make. I didn’t count on having to make so many revisions. I had to learn a whole lot more about the graphics program that I’m using.

I am ready to finish up this project.

I have loved every second of working on these books.

This is a short post because I hope to finish up these books in two days, and to post PDF’s for Do-It-Yourself flip books, so that anyone can make them.