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……


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.


To Your Station Mister, We’re Evaluating Expressions

This is my room set up for stations

Have you ever had one of those teaching days when you’re like, “Wow! This is really working!”? Well, I did today. For years, I have always wanted to set up stations in my classroom to allow students to move around the room, work in groups, and do different things throughout the hour. I was lucky enough to find a book on that is built around “stations” for math. Because of my class sizes, I set up two sets of four stations, a set of “A” stations and a set of “B” stations. The stations were four groups of desks, a manilla file folder with the station number, and whatever materials were needed for that station. The following is a list of the stations and their required materials:

Station 1: Worksheet, one dice, a set of 5 index cards with the following expressions written on them:
3n + 4,  2m^2,  15 – x,  60 / p,  2x – 2

Station 2: Worksheet

Station 3: Worksheet

Station 4: Worksheet, set of 5 index cards with the following expressions written on them:
2x + 2, 5 + x, 36 / x,  16 – x,  2x^2

set of 5 index cards with the following values of x written on them:
x = 2, x = 3, x = 4, x = 5, x = 7

Give the students ten minutes at each station. The worksheets explain how to conduct each station, but I still had to help a few of the groups. The following pictures are of the worksheets for each station. 

Worksheet for Station 1- Expressions
Worksheet for Station 2 - Expressions
Worksheet for Station 3 - Expressions
Worksheet for Station 4 - Expressions

Cut, Tape, and Repeat

What an excellent activity for a Friday! They were given five different nets. Nets are the two dimensional shapes that make up a three dimensional figure. They first had to answer two questions for each net. 1. Describe the shapes in the net. 2. What three dimensional figure do you think these shapes will make? They then cut the shapes out and taped them together. I used tape because I knew the glue sticks wouldn’t dry fast enough to hold the shapes together (good call and thanks Shane for going and getting me the tape at 10:00 last night after your wrestling dual). Every kid seemed to absolutely love doing this activity. Our bell work for the beginning of the class was, “1. What are two differences between a prism and a pyramid. 2. What shapes make up a rectangular prism? 3. What shapes make up a triangular pyramid? 4. What shapes make up a cylinder?” I was extremely pleased with the number of students who could answer these questions and explain them, when the only lesson we had on them was some notes we took yesterday. I have so many students this year who are thinkers. I believe giving them all of these hands-on activities and games have molded them into becoming thinkers. It’s not a teacher standing up and telling them what they need to know, it’s “Here, here is a little bit of information, now you examine and discover different things about that information. You play a game and argue with your partners on the correct answers and stand up for your positions.” I have never felt as confident in my teaching and my students as I do this year. Not passing out textbooks opened up a whole new world for me. The only problem is, is that we are getting in trouble for making too many copies on the copy machine. While I don’t give out “worksheets” per se, most of these activities and games I give them have handouts or game pieces that I have to make copies of. In order to do the “net activity” today, I had to make two hundred copies for all of my classes. Oh well, they can just find the funding somewhere. Cut the budget from something that doesn’t go straight to the students. Educational funding is a whole other topic for me. Anyway, super great day! No homework, we will be finishing up our nets on Monday.

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