Playing With Math: Stories From Math Circles, Homeschoolers, and Passionate Teachers

Sue VanHattum's blog Math Mama Writes was one of the earliest math blogs I frequented. Sue and Shireen, Dan, Kate, and Sam were among the first people who showed me — through their passionate writing — that there was an online community where we may share the teaching and learning of mathematics in the classroom.

When I started this blog, Sue dropped in to leave a comment or two. Or five. We even talked on the phone, and she shared with me how her son got his name. I remember reading someone's post and wanting to leave a comment because I connected with the piece and its author in some small way, and inevitably I would find that Sue had already left a comment. This happened over and over again. I felt we were reading the same stuff; and the same stuff touched us in similar ways.

Then, within a year Sue asked if I would like one of my posts to appear in a book she was putting together.

So, it's with much love and honor that I get to help launch Sue's new book:

Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers brings together the stories of over thirty authors who share their math enthusiasm with their communities, families, or students. After every chapter is a puzzle, game, or activity to get you and your kids playing with math too.

To know Sue is to know that she loves teaching and learning mathematics, and she loves writing, therefore this book — this work of consummate love - has to happen.

Playing With Math is really a collection of love stories because the authors, including yours truly, want to share something we're pretty crazy about. It's the stuff we do beyond the regular school day — we play with math after hours, at the dinner table, on a napkin at the coffee shop, with our own child or with a neighbor's child, at a family picnic, with our in-laws whom we don't even like.

So, today is the first day of our crowd-funding campaign to cover production costs. We're hoping to find support in our community of teachers and parents and math connoisseurs — a community of people whom I adore and respect. You can contribute anything from $1 to $1 billion. But for a contribution of $25, this wonderful book will be sent to you as soon as it's printed. Please see more details here.

Thank you so very much.

Area of a Circle

After finding the formula for the circumference of a circle, my 6th graders were ready to work on finding the area of a circle.

I asked them to draw a circle on notebook paper, any size, but not too small. Then I gave each a centimeter cube to trace one face onto their paper to remind them how much the area of one square centimeter covered. (You can see it drawn on top right pic below.)

Question 1: Give me a guess — only by looking — what is the area of your circle, in square centimeters? Please write that number on your paper, label it "guess."

Question 2: Now use whatever tools you need, give me a better answer. I know some of you already know the formula for the area of a circle, but you may not use it unless you can tell me where it came from. (No one even tried.)

I can't tell you how happy I was to see all the different ways the the kids had tried to approximate area. Their perseverance humbled me. A few students drew triangles, knew to use "base times height divided by two," but erroneously used radius as height.

Last week I was reading Mimi's post about estimating area of circles, and Sue VanHattum reminded me of the rectangle model in her comment.

I had the kids fold their circles like this.

They cut out the pieces — turning every other piece 180 degrees — and glued them together. Cristian said, "First we had a circle, then triangles, then a rectangle. That's crazy!"

Never once did I answer any of the questions. I just asked them. I began with, "What is the area of this rectangle or parallelogram?" Step by step, as a class, the kids walked this equation all the way to Area = pi x radius^2.

This morning, two days after the activity, I did a My Favorite No to see if they remembered: 31 out of 33 students got the correct circumference formula; 24 of 33 got the correct area formula. Bonus if they showed me how the rectangle model helped explain the area of a circle.