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

Date: 1994

Grade Level(s): 5, 6, 7

Subject(s):

• Mathematics/Geometry

OVERVIEW: Many students tend to memorize, without understanding, formulas that we use in geometry or other mathematic areas. This particular 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

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.

May, 1994. These lesson plans are the result of the work of the teachers who have attended the Columbia Education Center's Summer Workshop. CEC is a consortium of teacher from 14 western states dedicated to improving the quality of education in the rural, western, United States, and particularly the quality of math and science Education. CEC uses Big Sky Telegraph as the hub of their telecommunications network that allows the participating teachers to stay in contact with their trainers and peers that they have met at the Workshops.