1. Prior to the lesson, ask students to bring in several flat, round objects to measure.
2. Divide students into groups of two (or three, depending on class size). Before class, cut out enough circles for each student in the class. Write two of each number and have them find their partner by matching up numbers. For example, if you have 20 students, write 2 of each number 1 through 10 on each circle. Mix them up and hand each student one circle as they walk in the room. Distribute one tape measure to each group and make sure that each group has at least 5 round objects to measure (including a cookie and napkin). If not, use some that you brought from home. Distribute 1 copy of the Discovering Pi worksheet to each group.
3. For each object, have the students fill in the table by measuring with the tape provided. They may have a hard time finding the distance around. Let them troubleshoot to discover an efficient method. If hints are needed, have one person hold the object and the end of the tape while the other wraps the tape around.
4. Once the table is complete, have each group compute an average for the last column ("Distance Around ÷ Distance Across"). I allow my students to eat the cookie when they finish filling out their table. They LOVE this part!
5. While students are working, create a table on a piece of chart paper with a line for each group to record their results. See Sample Table worksheet attached. Have students come and write down their average for the class to see.
7. Ask students if they see a relationship in the results and if the numbers look familiar. The "Distance Around" (circumference, C) divided by the "Distance Across" (diameter, d) is approximately equal to Pi!
8. To derive the circumference formula, write out C/d = ∏. See if a student can solve this formula for C. (Multiply both sides by d and you get C = ∏×d, which is the circumference formula.