## This lesson plan, brought to us by “fortheloveofteachingmath.com,” outlines a great way to teach not just the ‘how’ but the ‘why’ of the circumference of a circle, aligned to the Common Core Standards.

By Cameron Pipkin

The Common Core doesn’t exactly force math teachers to start from the drawing board, but it compels them to do about the nearest thing to it. Every subject, at every grade level, now demands a different approach to teaching math. Gone are the days of rote formulas and read-and-recite lesson planning. The Common Core calls for students to acquire a depth of mathematical knowledge that will help them understand the ‘why,’ not just the ‘how.’

I came across a blog post the other day on For the Love of Teaching Math that outlines a nice little object lesson in the difference between math before the Common Core, and math after it, and provides teachers with a nifty lesson plan in the process. The post covers how to teach the circumference of a circle.

Like many of you, when I learned how to find the circumference of a circle, I was given a formula and taught to simply plug and solve. This could be done easily enough. However, by the time I got to calculus, I had been suckled for so long on plug-and-solve math that I had a heck of a time tackling conceptual stuff. This may explain my noteworthy-for-all-the-wrong-reasons AP test score (1).

So, in the spirit of starting our kids on the right path early, here’s a deeper approach to finding circumference, from Andrea, the author of For the Love of Teaching Math.

- Break you students into groups of four, and supply each group with the following:

- Template of a circle
- A piece of string at least long enough to go around the circle
- Ruler
- Calculator

- Get your hands on a copy of the book
*Sir Cumference and the First Round Table*and read it to your class to help students remember the vocabulary needed for this lesson. - Ask students to place one end of the string on the edge of the circle and outline the circle with the rest of the string. This may end up being more difficult that it sounds.
- Tell students to pinch the part of the string that touches the loose end on the circle. Make sure they understand that they are putting the string around the circle in order to “measure” the distance around the circle. You can’t measure it with a ruler because it is straight and the circle is round.
- Once they pinch and pick up the string, have them see how many times that part of the string goes across the diameter of the circle.
- After they figure out how many times it goes across the diameter, have them measure the length of the string that went around the circle and then measure the diameter. Then, have them divide the length of the string, “the circumference,” by the diameter. Their answers should be close to a little over three.

Talk to your students about their answers, and complete more examples if necessary. It’s important to make it clear that once around the circle is equal to winding the string across it “three plus a little.”

Once the class has the hang of this, you can draw circles on the board and have them estimate the circumferences. When you sense that they are comfortable with this, tell them you are going to trick them and give them a hard one. Draw a circle with a radius rather than a diameter. Help your students through this exercise as well.

For more on this lesson, click here and visit For the Love of Teaching Math.