math · simple book binding

Graduated Page Book with Radian Circle

Radian Circle distributed through a graduated-page book
Radian Circle distributed through a graduated-page book

My collegiate son will soon be entering the Trig section of his Physics class. While that may sound like lots of fun, I know that he feel less than delighted when he encounters problems that require him to, say,  find the cosine of 135 degrees. Of course he can look at a handy chart like this one below:

Radian Circle
Radian Circle/ Unit Circle….memorize this….

I have actually been wanting to play around with the info on the radian circle, to see if I could simplify the look of it, to make it seem less scary.  Separating into four pages makes the patterns of the coordinates more obvious. Putting these separated sections into a graduated-page book  translates this idea  into an easily referenced tool.

The 30-120-210-300 degree page
The 30-120-210-300 degree page

This book structure has the novelty factor of having its pages staggered, which invites labeling the edges with the information that is located on the page. I’ve often used this structure with classes, especially when I am going for creating a book within a book, like in the weather book below.

A graduated-page book within a book about weather
A graduated-page book within a book about weather

Here, using the different layers of the book to generally reflect the different altitudes of different clouds helps to make these nebulous concepts more tangible.

Using  graduated Page book to show off clouds
Using graduated Page book to show off clouds

On each page of this sample book drawings and information accompanied the label on the edge of the book.

A first grade teacher that I know, Mrs. Kavney, used this structure to create a book about ocean fish that live at different depths in the ocean. Since the drawing area on the pages gets larger one goes further into the book, and since ocean creatures tend to get larger in deeper ocean depths, I thought it was a fitting use of this structure.

Mrs. Pipino's Rainforest info sample book
Mrs. Pipino’s Rainforest info sample book

A third class that I worked with made a book about Brazil that included a graduated page book about the rainforest. I had envisioned using the layers to describe layers of the rainforest, but the teacher wanted to use the page heading more like chapters. The students seemed to be comfortable with the size and the format, and made really lovely little books.

A third grader's book about the rainforest
A third grader’s book about the rainforest

There’s many ways to do variations of this structure. Over the next few days I hope to be able to put together a tutorial about how to make this structure…which is something I have been wanting to do for quite some time.   (Addendum: Graduated-Pages Tutorial is now posted!)

How to Make a Graduated Pages Book
How to Make a Graduated Pages Book

At the moment, though, I am basking in the glory of having given my son something that he called “AWESOME!”

6 thoughts on “Graduated Page Book with Radian Circle

  1. I’m so happy to have run across this post. I can’t wait to make some of these for my students/children. This will definitely help with the trigonometry and I’m going to do one for geometry too I think.

    –Isn’t it nice when our children say things your son did? You are helping him on his way to achieving academic success, and I think that is AWESOME!!!


    1. I would love to see images of what your students come up with. The cool thing about doing the radian circle this way is that the patterns emerge so clearly, and then memorizing it actually seems possible. I am curious as to what age students you are teaching…


  2. I am currently homeschooling 3 at the ages of 6, 14, and 16. They are all artistic in their own way. While I have made books for them I am hoping to get them more involved in the book making part of the process this time around.


    1. You might like to take a look at the fractions book that I’ve done with students…it’s challenging but worth it. shows the finishing of the book and
      shows the starting of the book.
      The book image you posted on your post is amazing.
      Good luck with your homesschooling. Your kids are so lucky.


      1. I will definitely check out the fractions book. The 6 year-old loves fractions! On the plus, plus side he loves the entire process of book making. For me, I love any chance I get to mix different types of art with learning.

        By the way, I’ve enjoyed some of your previous posts as well. Even though I’m on WP I found you through a Google search on book making a few weeks ago. Today is just the first chance I’ve had to reply. 🙂


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