The first thing I heard in my geometry class this year from a student was, "What really is pi?" I thought that was taught in middle school. However, I soon learned that they knew pi was approximately 3.14, but that did not understand it. The students did not know where the number came from. They just memorized pi's value. I started wondering if my students from the previous four years merely memorized values as well, so I asked them. They said they did. This was the 1st year a student was bold enough to ask so I told him when we got to circles I would make sure he understood.
The Pi Activity
The circumference of a circle is the distance around a circle. A diameter of a circle is a line segment that has its endpoints on a circle and goes through the center of the circle. In order to make sure the students understood that, I had them take a tape measure and measure a circle that we made with a 360 protractor in inches and tell me the circumference. Then, they measured the diameter of that circle. The circle could be made with compasses, I just chose not to. After I was sure everyone knew and understood what the diameter and circumference of a circle was, I divided the class into groups of four and told them their homework assignment. Each person in the group was to bring to school a circular object the next day. One person should bring a small circular object such as a button, the other medium, the other large and the other extra large. My circular object is either cookies or a pie. The kids are surprised when I bring my circular object! The next day, the students are to fill out the chart below:
|
Object |
Diameter | Circumference | C/D |
| Small (mm) | |||
| Medium (cm) | |||
| Large (in) | |||
| Extra Large (in or ft) | |||
| Mrs. James special object |
Tell the students we are measuring the objects in different units in order to see if the ratio C/D will stay the same. Make sure students know to measure the diameter and circumference in the same units. Each student is to do their own measurements with all the different size circles. They are only in groups in order to have different size circles, not to do group work. After students finish recording their data, ask them what seems to be true about the results of the third column. Tell them to compare their data to the other members in the group. Is everybody's data the same? Instruct students to make a conjecture about the relationship between the circumference and diameter of a circle.
The Pi Activity with Technology
After doing the activity above, I realized that the data within the groups were a little different sometimes. The kids did not all the time get 3.14. It was close, but it was not 3.14. I figured it was human error and technology would be a huge help here. Next year I still plan to do the activity above, then I plan to discuss with students why some may have been a little off with their data. Then, in order to show precise measure, I plan to redo the activity with GSP.
Click here in order to see the activity in GSP
Students should realize that pi =C/D. Multiplying by D on both sides gives us the equation C = pi * D. Since D = 2r. We can replace D in the equation and get C = 2 pi r.
History of Pi
Students understood where the constant came from and how we derived the circumference formula. Now they were asking me how did it get to be called pi. Who recognized the relationship and how or why did they stumble upon it. Then, I assigned them a history paper. It did not have to be any particular length. I just wanted them to have their questions answered. They had to report what they found orally in class. A couple of sample student papers are listed below.