Professional Development
SCMP March 2009
Rolling a Cylinder to Discover Pi
1. Your team will need to construct a graph on a piece of chart
paper. Place the horizontal axis at the bottom of the chart paper
and label it “Diameter”. Place the vertical axis on the left edge
of the paper and label it “Circumference”.
2. For each cylinder the team must find the point on the horizontal
axis that corresponds with the cylinder’s diameter. This can be
done by placing the diameter of the cylinder on the horizontal
axis with one end on the origin. Mark the other endpoint along
the axis to show the distance of the diameter from the origin.
3. Place the cylinder on its side on the paper so that it may be
rolled at a right angle to the horizontal axis, positioning it so it
touches the horizontal axis at the endpoint of the diameter.
Place a mark on the container where it touches the horizontal
axis. Now roll the cylinder ONE complete revolution until the
mark is back on the paper. This is the length of the
circumference.
4. Record the length of the diameter and circumference of each
cylinder in the table below.
C
i
r
c
u
m
f
e
r
e
n
c
e
Diameter
Description
of Cylinder
Ratio
Diameter
Circumference

Average
C
d
 What type of graph does the
relationship of circumference to
diameter represent? What evidence
do you have to support your
conclusion?
 Write an equation that relates the
circumference of a cylinder to its
diameter.
 What is the significance of the slope of the line in the graph?
 How can the graph be used to predict the circumference given its diameter?
 How can the graph be used to find the diameter given its circumference?
Adapted from “Looking at Lines Grades 6-9” by AIMS Activities Integrating Math and Science
Activity: “Functions in Circles” pp 51-58
Professional Development
SCMP March 2009
Rolling a Cylinder to Discover Pi
Goal of the lesson: Students will deepen their understanding of diameters and circumferences of
cylinders by using manipulatives, find the relationship between the diameter of a cylinder and its
circumference, construct a graph, create an input/output table, write a rule and recognize that the slope
of the line is π.
Materials needed: For each group of students you will need 3 to 5 cylinders of different sizes, large
chart graph paper, and marking pens. Each student will need a copy of the directions.
Engage
Review or introduce the students to the vocabulary needed for the lesson. (Cylinder, Circle, Diameter
and Circumference) Tell the students they will be finding the length of the diameter and circumference
of several cylinders, graphing these two lengths and then looking for any relationships between them.
Explore
Divide students into teams of 4 or 5.
1. Each team will need to construct a graph on a piece of chart paper. Place the horizontal axis at
the bottom of the chart paper and label it “Diameter”. Place the vertical axis on the left edge of
the paper and label it “Circumference”.
2. For each cylinder the team must find the point on the horizontal axis that corresponds with the
cylinder’s diameter. This can be done by placing the diameter of the cylinder on the horizontal
axis with one end on the origin. Mark the other endpoint along the axis to show the distance of
the diameter from the origin.
3. Place the cylinder on its side on the paper so that it may be rolled at a right angle to the
horizontal axis, positioning it so it touches the horizontal axis at the endpoint of the diameter.
Place a mark on the container where it touches the horizontal axis. Now roll the cylinder ONE
complete revolution until the mark is back on the paper. This is the length of the
circumference.
4. Record the length of the diameter and circumference of each cylinder in the table provided.
Explain
Ask students the following questions:
1. What type of graph does the relationship of circumference to diameter represent?
evidence do you have to support your conclusion?
2. Write an equation that relates the circumference of a cylinder to its diameter.
3. What is the significance of the slope of the line in the graph?
4. How can the graph be used to predict the circumference given its diameter?
5. How can the graph be used to find the diameter given its circumference?
What
Extend
Read “Sir Cumference Dragon of Pi” by Cindy Neuschwander and compare methods others have used
for finding pi.
Evaluate
Students should be able to:
 describe pi as the ratio of the circumference of a circle to it’s diameter.
 use their graph to predict the circumference of a circle given its diameter or diameter given its
circumference.
Adapted from “Looking at Lines Grades 6-9” by AIMS Activities Integrating Math and Science
Activity: “Functions in Circles” pp 51-58