This is a long post I know, but there is so much information I wanted to share about how I teach finding the circumference of a circle. I see FAR too many teachers just teaching students the formula and not teaching for that depth of knowledge that common core expects. The formula for circumference and area is one of the last things I explain to them before I give a formal assessment over it. If you asked my students how you find the circumference of a circle, they would most definitely say that the distance around the circle is the same as going across the diameter “three plus a little more” times. Then they would tell you that “three plus a little more times” is what we call pi and is actually 3.14.
Using these hands-on activities takes a little while to do in class. It takes a little preparation. It takes a lot of patience as the teacher. The payoff for all of this time, preparation, and patience is HUGE!!! I can totally remember in my earlier years of teaching, wanting so badly to do activities and games in my classes. At that time, all I could think of was the amount of skills we had to master by the time our state tests came around. I PROMISE you when I say that the amount of time it takes to do some of these activities is made up by the lack of having to reteach the skill a million times. Try it with this lesson, and you will learn very quick what I am talking about!
I have a whole freebie packet that I made for you. Believe me when I tell you that this freebie is AMAZING!!! You MUST download it!!!! Hey…it’s free….what’s it going to hurt to try? Below is exactly what I did for teaching the circumference of a circle to my sweet little sixth graders a couple of weeks ago (and yes I called them sweet because I absolutely believe that this group is the sweetest group of students I have ever had). I want to add that I only teach math. I am a secondary math teacher that somehow landed the role of teaching in sixth grade. I love it, and so I’ve stayed down there. I am in a middle school, so I teach the same lesson four times a day. By the end of the day, I have mastered the art of teaching whatever I am doing that day (ok. maybe not mastered, but definitely ironed out all of the kinks.) The very first thing I do is read them the book Sir Cumference and the First Round Table. I love to read this book because it helps them remember the vocabulary needed for this lesson. It helps them remember which one circumference is (they get confused between circumference and area), and they also remember which one is diameter and which is the radius. Trust me, I’ve taught this long enough to know that MANY students get these confused. After reading the story, we move on to the activity. Read on for more……
Supplies for this lesson on circumference of a circle:
template of circles located in the freebie download in this post
a piece of string at least long enough to go around the circle
I place students in groups of four, but each student has their own set of supplies. I want them each to experience the activity, but I also want them to be able to ask questions amongst each other and compare their measurements. This helps students to realize that they can figure things out amongst each other and not rely solely on me.
Direct students to as-close-as-they-can place one end of the string on the edge of the circle and outline the circle with the rest of the string. Make sure students only go around the circle once. Trust me….you will have to monitor this and make sure they are doing it correctly. I always have to correct several students in each hour. Here is a picture of what it should look like.
Tell them 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. THEIR ANSWERS WILL VARY!! Your hope is that the majority of them will say, “three plus a little bit more.” Of course you’ve got students who will say, “three and a half” or “three and a third” or something like that. Ask them if they are completely certain it’s exactly a half or a third.
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. After they measure those, have them divide the length of the string “the circumference” by the diameter. Their answers should be close to a little over three. I always run through the first circle with them. I have them share their answers throughout and we talk a little bit about it, and then they each do the other two while discussing their answers within their group.
Once they have finished their activity and we’ve discussed the answers, we do several examples and I emphasize that one time around the circle is the same as going across the circle “three plus a little more times.” On my white board, I give them examples of circles with certain diameters and have them estimate the circumference. If the diameter is 4, then the circumference is 4, three plus a little more times, so the circumference would be a little more than 12. After doing a few examples with diameters, they will feel extremely confident (some of my students will start to ask for hard ones, even some of my low performing students). I then tell them that I am going to trick them and give them a hard one. I then draw a circle with a radius instead of a diameter. Inevitably, most of them will start calling out that they know it and will be extremely excited, wanting to give you the answer. I always tell them not to give the secret away until everybody has had a chance to work the problem. I will do a few more of those examples.
In Oklahoma, our sixth grade PASS skills say that they only need to write their answers using pi. I tell them that in seventh grade, they will have to multiply their diameter by 3.14, but this year we just show our answer as the diameter times pi (sorry, I don’t know how to put the pi symbol on here). For practice, I give them the practice worksheet I made and have included in the freebie download.
I have included an I Have/Who Has game for circumference in the freebie. I didn’t play it with this group of students. I have an additional math class for students who didn’t pass the state math test the year before. In that class, we played it. Here is my warning for the bubble activity that is in the freebie. I got that idea a long time ago from somewhere. I never actually did the activity, but thought it was a wonderful idea. This year in that remedial math class, I was going to do it. I went to the store and bought each of them their own little bottle of bubbles. My mistake was that I didn’t try this out ahead of time. Needless to say, the activity did not work. The bubbles didn’t make any kind of splash on the construction paper. I am leaving it in the freebie pack, just in case you find bubbles that will leave a wet splat.
I am including a link to a product I made. I used it after I taught circumference and area of a circle. It is an “I Have/Who Has” that incorporates both circumference and area. I didn’t have time in my regular classes to do those games separately, so we did this particular game as a review before the test. The students were comfortable enough with it that they really enjoyed it. Needless to say, my students worked thirty-two circumference/area problems without one complaint. I know this post is long, but I hope you got a lot out of it!
What did I do with the bubbles that I purchased for my remedial class for the activity that didn’t work? I told them they were to celebrate the fact that they were circumference and area of a circle superstars! Hey…it worked.
The following is the circumference lessons freebie download.
The following is an “I Have/ Who Has for Circumference and Area” game that I have for sale here or in my Teachers Pay Teachers store. Click on the picture to go to my TPT store and buy it. There are a total of thirty-two cards. It is only $2! Your purchases from my Teachers Pay Teachers store and this blog store help support my ability to blog about all of the things I know about teaching math. Thank you so much for your support!
Click the “Add to Cart” button below to buy it straight from my blog, or click on the picture above to go to my Teachers Pay Teachers store. It’s only $2.00.