Circumference of a Circle

This is the second year that I have taught finding the circumference of a circle using the lessons out of the “Hands On Math!” book. Refer to my “Resources” section to find this book. Here is a picture of the book though……

Circumference:

The “Hands On Math!” book is set up by objectives. Each objective contains three different activities. The first activity is very concrete, the second lesson is pictorial (they are usually drawing or coloring something), and the third activity is a cooperative learning game. The lesson I used for teaching circumference of a circle starts on page 355. Before I started these activities, I gave them a colored sheet of paper and we drew a circle and labeled the diameter, radius, center, and we wrote along the margin that the circumference is the distance around the circle.

For these activities, I had the students grouped in pairs. The first activity is called “All Wrapped Up.” The actual activity calls for assorted plastic lids, but I didn’t think about saving up lids (maybe I’ll start saving now for next year’s group. I’ll make a note). Instead of actual lids, I drew three different sized circles on a piece of paper and made copies for each student. While they are in pairs, I still wanted each student to actually do this exercise themselves but still look at their partner for “security” making sure they are doing the activity correctly. This helps because as there are twenty-something students in the class, there is only one teacher.

Hand drawn circles for "All Wrapped UP"

I also gave them cotton twine (not stretchy) long enough to at least go around the largest circle.

 

The cotton string I use

The students were asked to, as accurately as they could, put the string around the medium sized circle and then mark with their fingers where the end of the string meets the rest of the string after it wraps around once. Basically they are measuring the circumference of the circle with the string.

Then ask them to see how many times that marked off string will go across the center of the circle (the diameter).

Go around the room asking the students how many diameters they were able to get out of the marked off string. Hopefully they will get “three plus a little more.” After several of the students saying three plus a little more, then you can explain that this “three plus a little more” actually has a name in math. That name is pi. I draw the symbol on the board and tell them that the actual number is 3.14………

Second Activity: Around and Across

With this activity, I give each pair a copy of the worksheet in the book, adding machine tape, centimeter rulers, and a calculator.

The students are to wrap the adding machine tape around the circle (a little easier since it already wraps).

They should mark the adding machine tape with a pencil at the place where the end meets the rest of the tape. They then need to measure the marked off piece of the tape to see the measurement of the circumference of the circle to the nearest cm. You may have to explain how to measure with a ruler. They then place that measurement in the appropriate place in the table on the back of the worksheet. Then they need to measure the diameter with the ruler and record that in the table. Using the calculator, they need to type in the circumference divided by the diameter. They need to do that will all of the circles. After everyone has completed, go around the room asking for what there circum/diam was. Hopefully most of them will say three point something. I always emphasize the “three plus a little bit more”. I then ask them if that sounds familiar, and they always yell out pi! This is where I go into the discussion and I question them until they start realizing that the distance around the circle (the circumference) is the same as three plus a little bit more diameters. Drawing pictures on the white board is always beneficial in my classes. I then tell them that the actual formula for the circumference of a circle is C=pi * d (sorry, I don’t know how to type the pi symbol on here). We also talk about how it takes two radius to make a diameter, so we also may need C= 2 * pi * r.

Activity Three: Circlespin

This is a pretty cool “game”. Still in pairs, I give each group a copy of the spinners, a large paper clip, and they need a pencil.

This is not the original spinner that came out of the book. I used white out and changed it to fit our sixth grade PASS. First of all, we don’t use decimals with circumference and area, and they won’t have to find the diameter or radius given the circumference. Because of this, I changed the “circumference” on the spinner to “both” and changed the numbers to all be whole, even numbers. The students then flick the paper clip once for each spinner. Both students must find the circumference based on the information they are given by the spinner. For instance, if the paper clip landed on “radius” on the top spinner and “6″ on the bottom spinner, both students would find the circumference of a circle with a radius of six. They are to then check each others answers to see if they are the same. In sixth grade, PASS only asks them to find the circumference to pi and not multiply it out. Because of that, this game should not take very long at all. I usually ask them to do ten problems all together. Each pair’s paper should look identical when they turn them in.

I have different worksheets that I give them if I feel they need a little practice. I usually give them at least one homework assignment for finding the circumference.

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