A Math Forum Web Unit
Jon Basden

Jon Basden's Lessons ||  Teacher Exchange || TE: Grades 6-8

Grade Level

7th Grade

Illinois Learning Standards

• 6.B.3a  Solve practical computational problems involving whole numbers...
• 6.B.3c  Identify and apply properties of real numbers, including pi...
• 7.B.3  Select and apply instruments including rulers... and units of measure to the degree of accuracy required.
• 7.C.3b  Use concrete and graphic models and appropriate formulas to find perimeters... of two-dimensional... figures.

Approximate Time

Two forty minute class periods

Materials Required

• six or so circular objects of various sizes
• string
• meter sticks
• paper
• pencils
• student worksheets
• overhead transparency of student worksheet
• computer with spreadsheet program

Optional Materials

• Pre-made spreadsheet in Microsoft Excel 97
• Math Madness cassette tape -- the Pi Song
  (Can order from Bob Garvey for $8.50 at bgarvey@aol.com)
• First 1001 digits of Pi on overhead transparency

Sources

• "Discovering Pi" lesson from Math in the Middle Handbook, Prentice Hall, 1993
• Circles - Diameter, Circumference, Radius and the Discovery of Pi

Description

1. Divide students into small groups.
2. Have each group measure diameter and circumference of each of the circular objects in the room.  They should record their results on their student worksheets.
3. Students should complete the requirements on the worksheet.  Hopefully, they will see the pattern that circumference divided by diameter is about 3.14159265358... ().
4. Depending on time, space, and resources, the groups can begin taking turns entering their data into the spreadsheet, so that we can begin to see that the class averages for the C/d ratio is very close to pi each time.
5. From the generalizations that C/D = pi, the teacher can lead the students to see how we get the formulas C = D and C = 2r.
6. To to help the students avoid the common misunderstanding that the digits of Pi do not stop after 3.14, one may show them the first 1001 digits of Pi.  This can aid them in visualizing the complexity of the number.
7. To reinforce the formulas that the students have generated, the teacher can assign an assignment that requires the students to apply the relationships between diameter, radius, and circumference.

Software

Microsoft Excel or other spreadsheet

Web sites

Pi Mathematics

Pi Pages

Pi through the ages

Assessment

The instructor will be able to informally assess the comprehension of the students as the lesson progresses.  This will enable the instructor to  determine if any additional lecture is needed concerning the relationship between circumference and diameter before additional examples are shown.

Also, before he or she assigns independent practice, he or she will check for understanding by asking questions of individual students, and he or she will have students work examples for the class.

More formal evaluation will come as a result of the students completing an independent assignment that allows them to practice using the formula for the circumference of a circle and to work backwards with the formula to find the radius and/or diameter if given the circumference.

Send comments to: Jon Basden - jbasden@mac.com