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Understanding Pi

Procedures for Teachers is divided into three sections:
Prep -- Preparing for the Lesson.
Steps -- Conducting the Lesson.
Tips -- Managing Resources and Student Activities.

Prep

Computer Resources:
You will need at least one computer with Internet access to complete this lesson. While many configurations will work, we recommend:

-- Modem: 28.8 Kbps or faster.
-- Browser: Netscape Navigator 3.0 or above or Internet Explorer 3.0 or above.
-- Macintosh computer: System 7.0 or above and at least 16 MB of RAM.
-- IBM-compatible computer: 386 or higher processor with at least 16 MB of RAM, running Windows 3.1. Or, a 486/66 or Pentium with at least 16 MB of RAM, running Windows 95 or higher.

For more information, visit What You Need to Get Connected in wNetSchool's Internet Primer.

Materials:
• Circular or cylindrical objects. Students should collect these themselves and bring them into class. (Note: Objects with larger circumference will reduce measurement error and therefore improve the accuracy of the approximation of pi found through calculation.)
• String.
• Rulers.
• Paper.
• Pencils.
• Calculator.
Bookmarks:
The following sites should be bookmarked:

• Exploratorium -- Pi in Color
http://www.exploratorium.edu/pi/pi98/selectframe3.html

This site shows a visual representation for pi, using resistor beads to represent digits. Two is red, five is green, zero is black. . . . It's a great way to conceptualize the infinite number.

• Exploratorium -- Pi in Words
http://www.exploratorium.edu/pi/pi98/selectframe9.html

This Web page provides an interesting verbal description of pi. You will find out amazing things you never knew about pi.

• RJN's More Digits of Irrational Numbers
http://antwrp.gsfc.nasa.gov/htmltest/rjn_dig.html

What are the first 2 million digits of the square root of 2? The first 5 million? These questions and others are answered. It also offers approximations of several interesting irrational numbers.

• A Common Book of Pi
http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Pi_through_the_ages.html

This Web site contains interesting information about pi, including a short history of pi, Archimedes' method, and pi links.

• The Pi Search Page
http://www.aros.net/~angio//pi_stuff/piquery.html

This site allows you to search for a sequence of digits in pi. You can enter as many as 120 digits into the search.

• Math Forum
http://forum.swarthmore.edu/dr.math/faq/faq.integers.html

This page provides definitions and information concerning integers, rational numbers, and irrational numbers.

• Paul's Page of Pi: Music of Pi
http://www.escape.com/~paulg53/math/pi/music/index.html

Paul's site offers a piece of music based on pi and an explanation of the mathematical approach he used to compose it.

• Math Forum's Ask Dr. Math FAQ
http://forum.swarthmore.edu/dr.math/faq/faq.pi.html

Dr. Math answers frequently asked questions about pi. The answers include a brief history of pi, how it's used, what it is, and how many digits it has.

• Pi Links
http://www.jgk.org/links/pi.html

This site contains links to many interesting pi sites.

 Steps Time Allotment: This lesson requires approximately one class period. Review definitions of irrational numbers and rational numbers. Review the topic of ratios. Divide class into pairs and distribute Pi Chart, in Organizers for Students. They will use this organizer to record information throughout the lesson. Have students measure and record each item's circumference and diameter. Then they should divide the circumference by the diameter and record the results in the "circumference/diameter" column. Have students find the average for the "circumference/diameter" column. Then explain that this is an approximation for pi. Ask students to write out a formula for finding the circumference of a circular object using its diameter and the number pi. (The formula should be 2(pi)r.) Have students check their formula by performing calculations based on the objects they used in Step 5. Distribute Can You See or Hear Pi? and Where? How? What Else?, in Organizers for Students. These need to be completed by students using the computer only. Depending on the number of computers available, you may need to rotate computer access.

Tips

One Computer in the Classroom
If you have access to one computer in your classroom, you can organize your class in several ways. Divide your class into two groups. Instruct one of the groups to do paper research while the second group is working on the computer. Bring in books, encyclopedias, etc., from the library for the group doing paper research. When the groups have finished working, have them switch places.

If you have a big monitor or projection facilities, you can do Internet research together as a class. Make sure that every student in your class can see the screen, go to the relevant Web site(s), and review the information presented there. You can also select a search engine page and allow your students to suggest the search criteria. Again, bookmark and/or print the pages that you think are helpful for reference later.

Several Computers in the Classroom
Divide your class into small groups. Groups can do Internet research using pages you have bookmarked. Group members should take turns navigating the bookmarked site.

You can also set up the class so that each computer is dedicated to certain sites. Students will then move around the classroom, getting different information from each station.

Using a Computer Lab
A computer center or lab space, with a computer-to-student ratio of one to three, is ideal for doing Web-based projects. Generally, when doing Web-based research, it is helpful to put students in groups of three. This way, students can help each other if problems or questions arise. It is often beneficial to bookmark sites for students ahead of time.

Submit a Comment: We invite your comments and suggestions based on how you used the lesson in your classroom.

Overview | Procedures for Teachers | Organizers for Students