Discovering Pi 

Middle School Lessons || Contents
A lesson in which students work with circumference in order to discover Pi.

Author: Jack Eckley, Sunset Elem., Cody, WY

Grade Level/Subject: 5-7, geometry

Overview: Many students tend to memorize, without understanding, formulas that we use in geometry or other mathematic areas. This activity allows students to discover why pi works in solving problems dealing with finding circumference.

Objectives: The students will:

  1. Measure the circumference of an object to the nearest millimeter.

  2. Measure the diameter of an object to the nearest millimeter.

  3. Explain how the number 3.14 for pi was determined.

  4. Demonstrate that by dividing the circumference of an object by its diameter you end up with pi.

  5. Discover the formula for finding circumference using pi, and demonstrate it.

Resources/Materials: Round objects such as jars, lids,etc., measuring tapes, or string and rulers, paper, pencil,calculator

Activities and Procedures:

  1. Divide class into groups of two.

  2. Give materials to student teams.

  3. Have student teams make a table or chart that shows name or number of object, circumference, diameter, and ?.

  4. Have students measure and record each object's circumference and diameter, then divide the circumference by the diameter and record result in the ? column.

  5. Have students find the average for the ? column and compare to other groups in the class to determine a pattern. Students can then find the average number for the class.

  6. Explain to the students that they have just discovered pi, which is very important in finding the circumference of an object. (You may wish to give some historical information about pi at this time or have students research the information.)

  7. Have students come up with a formula to find the circumference of an object knowing only the diameter of that object, and the number that represents pi. Students must prove their formula works by demonstration and measuring to check their results.

Tying it all together:

  1. Have students write their conclusions for the activities they have just done. Students may also share what they have learned with other members of the class.

  2. Give students three problems listing only the diameter of each object and have them find the circumference.

  3. Encourage students to share learned knowledge with parents.
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