One class period
The number pi is a mystery to
students. Most students are unaware of how the value of pi was
determined. In this lesson, students explore the ratio of circumference
to diameter in order to estimate a value for pi.
Plane Geometry
Students will be able to:
• Use the ratio of the circumference of a circular object
to its diameter to find an approximation for pi.
National:
Principles and Standards for School Mathematics
http://Standards.nctm.org/document
• Analyze characteristics and properties of two- and three-dimensional
geometric shapes and develop mathematical arguments about geometric
relationships.
State:
Louisiana Mathematics Framework Bulletin
http://www.lcet.doe.state.la.us/doe/assessment/standards/MATH.pdf
In problem-solving investigations, students demonstrate an understanding
of geometric concepts and applications involving one-, two-,
and three-dimensional geometry, and justify their findings.
G-1-H: Identifying, describing, comparing, constructing,
and classifying geometric figures in two and three dimensions
using technology where appropriate to explore and make conjectures
about geometric concepts and figures;
G-2-H: Representing and solving problems using geometric
models and the properties of those models (e.g., Pythagorean
Theorem or formulas involving radius, diameter, and circumference)
Geometry Journey (World of Geometry) Video
1, Plane Geometry
The Story of Pi
http://www.projectmathematics.com/storypi.htm
This Project Mathematics Web site is a collection of video segments
on the discovery, history and use of pi.
The Story of Pi
www.geocities.com/CapeCanaveral/Lab/3550/pi.htm
The Web site provides a brief historical look at efforts in
different cultures to determine the value of pi.
Geometer’s Sketchpad (optional)
– Key Curriculum Press
Per Group
• 10 circular objects,
• measuring tool,
• yarn or string,
• paper
The day before you plan this lesson, ask students to bring in
3-4 circular objects from home, e.g. cans, bowl lids, buttons,
etc. Ask students to make sure objects vary in size. It may
be wise to randomly group students prior to class as well.
• CUE the video for classroom viewing.
• Students may even be assigned a written report on the
history of pi prior to class.
1. Provide a brief research opportunity
or assign as an introduction to the activity an Internet search
to find the value and history of pi. Solicit responses from
each group. Discuss that pi is an irrational number and give
a brief history of its first use. One or more of the web sites
listed in the media components or sites discovered by the students
during their search may be projected as appropriate to the class
discussion.
2. FOCUS for Media Interaction.
Think of many circles of different sizes.
What objects first come to mind when you think of a circle?
Do you think there is a relationship between the circumference
and the diameter?
If there is one, what kind of relationship might that be?
Instruct the students to record three striking points as they
view the video segment. PLAY the video clip from World
of Geometry
3. At the conclusion ask the various students to provide
one of their three facts from the program. As a student finishes
giving a fact ask the class who else had that point of information
and then ask for someone else to share what they noted.
1. Have students arranged in small groups (3-4 students
in each group).
2. Each group should have about 10 circular objects to
measure. The objects should be different sizes. Have students
trace the objects on paper.
3. Pass out measuring tools (ruler, tape measure, etc.).
Suggest using metric measurements.
4. Define circumference. Measure the circumference
of each circular object using the yarn or string.
5. Define diameter. Measure the diameter of each
circular object using the yarn or string. (Note: It is easier
to find the diameter of the objects once traced on paper. Have
the students fold the paper circle in half and measure along
the crease.)
6. Complete the table below using the measurements found
in steps 3 and 4. Find the ratio of the circumference to the
diameter. Have students round their answers to 2 decimal places.
7. Ask students to find the average of the ratios
found. This will represent their approximation of pi.
8. Have students answer the following questions regarding
their results.
a. What value did your group get as an approximation
of the ratio of the circumference to the diameter?
b. What does your group think this value represents?
c. Write a conjecture regarding the relationship between
the circumference of a circle and its diameter. Can you write
a formula relating the two? Can you write a similar formula
relating the circumference to the radius?
d. Share your findings with the class. Did each group
come to the same conclusion?
Social Studies: Identify buildings around the world with
round or rounded sections. When were they built?
Human Ecology: Celebrate pi day by baking a pie and comparing
the volumes of slices from a round and a rectangular cakes.
Art: Research high profile architectural projects currently
underdevelopment today that incorporate round structures. Are
they from one firm?
• Have the students survey the community for facilities
(swimming pools, water fountains) that are round or have circular
bases.
• Students can compare manufacturers packaging styles.
What is packaged in round cans versus square or rectangular
boxes or plastic containers? What does the packaging reflect
about the product?
