Discovering Pi

This lesson introduces students to Pi through the discovery method of instruction. Students practice simple measuring skills to discover the relationship between the circumference and diameter of circular objects (Pi).They will be able to use this concept to find the circumference of any circle when the diameter is given.

A lesson plan for grades 6 and 8 Mathematics

By Betty Shell

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Related topics

• Learn more about circles, circumference, diameter, discovery learning, mathematics, measurement, and pi.

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Learning outcomes

Students will:

• discover the relationship between the circumference and diameter of a circle (Pi).
• use that discovery to determine the circumference of any circle with a given diameter or radius.

Teacher planning

Time required for lesson

60 Minutes

Materials/resources

• Rulers
• String for measuring
• Collection of circular objects of various sizes (such as plastic lids)
• Chart for data collection
• Assessment worksheet
• Calculators

Pre-activities

• A few days prior to this lesson ask students to help begin a collection of various circular objects. Show a few appropriate examples of the kinds of things needed. Strive for variety of diameters. You will need enough for each group of 3 or 4 students to have a variety with which to work.
• Number each of the circular objects you will be using.
• Review the terms diameter and circumference.

Activities

1. Divide the class into small groups of 3 or 4.
2. Give each group a collection of the circular objects collected by the class.
3. Each group should also have rulers, string for measuring, and a chart for collecting their data.
4. Explain that in this lesson students will be measuring the circumferences and diameters of circles of different sizes and recording those measurements on the chart they have been given.
5. Discuss the need for the string each group has been given.
6. Students collect and record their data on the chart provided.
7. They are to discuss the relationships they observe and answer the questions on the page with the chart.
8. Small groups share their findings with the entire class.
9. Students will have discovered that the circumference is a little more than 3 times the diameter.
10. Introduce the concept of Pi, the symbol, and the number itself.
11. Using the Math Explorer calculator Pi key, discuss the decimal and how most often it is rounded off as in 3.14. (This may be a good place for a quick review of rounding decimals.)
12. Discuss how they have the necessary information to arrive at the circumference of any circle if the diameter or radius is given.
13. Return to small groups, exchange circular objects, and measure diameters.
14. Estimate and then calculate circumferences using a calculator or pencil.
15. Discuss findings in large group.
16. Complete the assessment worksheet.

Assessment

• Observation of small group activities
• Data Collection Charts
• Large group discussion
• Assessment worksheet

Supplemental information

Comments

Students who often have difficulty with math will almost always remember this concept after doing this activity.