Lesson Description for Teachers

The students use a Java Applet¹ to discover the fact that the ratio of the circumference to the diameter is a constant that applies to all circles. In other words, it teaches them the concept of pi and how it is derived. The lesson also includes a sheet with interesting facts about pi.

Grade Level:

6^th to 12^th

Objectives:

The students will measure the diameter and circumference of many circles and will estimate their relationship. By doing so, they should discover the approximate value of pi. By discovering it on their own they should feel rewarded and gain a deeper understanding of the fundamental concept of pi.

None other than a computer with internet access. They might not even need pencil and paper as they can fill out the data table on the computer.

This lesson is completely self guided and the students can do it on their own. You could assign it as a homework and have a meaningful discussion the next day or do it during class. Even though everything is explained within the lesson, you may want to describe (or review) what the circumference and diameter of a circle are and show them (with the applet or with a similar method) how can one measure both quantities. Ask them if they think there is a relationship between the two, what that might be, if it holds true for all circles, etc.

Next you may want to divide them in groups of 2 to 3 students (if you do not have enough computers) and tell them to go through the lesson, measure about 10 different size circles, and complete the first two columns in the table. All of this is described in the Measuring Circles page.

Once they complete that, you should tell them that they need to find out a relationship between the circumference and the diameter and to check if it depends on the size of the circle or not. You can give them the go ahead to do the Analyzing the Data page.

At this point you should have an open discussion with the whole group to have each of them describe their findings and discoveries. You can then share some of the Interesting Facts about Pi with all of them.

I hope that you use this lesson with your students and I welcome your feedback.

[Note 1] -- A Java applet is simply a computer program written in the Java computer language. One of the good features of a program written in Java is that it can be downloaded from the web and run on almost any computer.