Flip Book · math

Flip Books as a Bodacious Learning Tool

Flip Books and some Flip Book pages
Flip Books and random pages. The Birthrite flip-book by Ruth Hayes, published by The Real Comet Press, 1988, was a gift from Lewanne Jones and Jim Fleming when my son was born.

After all these years of teaching how to make books I have now become smitten with using books as a teaching tool. Yes, I know, using books for instruction is anything but a new idea. This said, flip books have captured my interest because they are fun and dynamic. Among other things, I’m pairing them up with mathematical equations to illustrate how the picture of an equation changes when there are changes in a variable. So far I’ve shown some of these flip books to a couple of my smart but not particularly mathy friends and what happened next is so worth writing about.

y equals mx plus zero by Paula Beardell Krieg
y equals mx plus zero ( this should play through 2 times. Click on it into play again)

The first thing that happens, of course, is that my friends flipped the pages. Everyone loves a show. The gif in the box above is a pretty good representation of what they saw in one of the books. A gif is fun, too, but it’s not as effective as a flip book in that it doesn’t allow the viewer to slow down and examine what’s going on. I saw this happening so clearly: my friends were drawn into the equation by the action of the flipping, then they slowed down, looked at the images more slowly and tried to understand what was going on. They had great questions.


For instance, Sarah thought I had made a mistake in labeling these pages. She hadn’t sorted out how the graph of y=50x could be so similar to y= negative 50, after all 50 is arguably a large number while negative 50 is indisputably a very small number. It was easy enough to explain how this works, and she absolutely understood it. What I understood was that, without the flip book, she would have never been interested in having had this conversation.

Comparing the slopes of a line
Comparing the slopes of a line

John also had some questions. He couldn’t fathom why I showed lines with slopes equaling 1 to 8 in sequence, then started skipping to 12, 20 and 50. When I pointed out how the lines were becoming increasingly indistinguishable from each other as the slope becomes larger, he better understood my choices of which slope values to use.

It’s taken me quite a bit of time to get to the point where I’m ready to show this first equation-of-a-line book to anyone. There will be two or three more books to go with this one: one that shows only “b” changing; one that shows the graph when the changes in “m” are between positive one and negative one; and a book that shows b and m changing at the same time.

I’m hoping to get some feedback on these from classroom teachers. Here’s my plan: after I have this y=mx Flip-Book finished I will make a few extra copies and send some out to teachers who are willing to point out flaws in my presentation. In my next post, when I’m ready (hopefully tomorrow) let me know if you want to be one of my collaborators. Even though I’ve already worked through at least a half-dozen different variations of this one book, there are still things that I am not sure about. More about that when I continue…

6 thoughts on “Flip Books as a Bodacious Learning Tool

    1. These little books are really so fun. The biggest downside are the revisions. This book here has gone through so many changes, and I when I think that I’m just about done, then, no, I see something that needs to be rethought, and it can mean changes to nearly all the panels. I feel like I’ve been on radio-silence for nearly two weeks, as all of my attention had been focused on making this book just right. Thank you for your supportive comment! I really appreciate it.


  1. This is an excellent craft for young calculus. Calculus is about change – about patterns in algebraic functions – and this method shows patterns perfectly. I plan on referring to this in our next Calculus for Kids course.

    Liked by 1 person

    1. I would love to brainstorm with you about this sort of thing, or at least see what you do with this idea. Be sure to look at https://bookzoompa.wordpress.com/2015/05/03/the-animated-equation-book/ which, towards the end of the post, talks about how to assemble flip books.
      Really, I would love know how you are thinking about using flip books! This summer I’ve volunteered to work for a week with young students in the local Lunch, Learn & Play program, and I want to be doing dynamic activities that have math ideas embedded in them, and I will be trying to work this out over the couple of months.


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