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Diameter
Description of Cylinder
Diameter
CircumferenceRatio
EMBED Equation.DSMT4 Average
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?
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 g r a p h , c r e a t e a n i n p u t / o u t p u t t a b l e , w r i t e a r u l e a n d r e c o g n i z e t h a t t h e s l o p e o f t h e l i n e i s .
M a t e r i a l s n e e d e d : F o r e a c h g r o u p o f s t u d e n t s y o u w i l l n e e d 3 t o 5 c y l i n d e r s o f d i f f e r e n t s i z e s , l a r g e c h a r t g r a p h p a p e r , a n d m a r k i n g p e n s . E a c h s t u d e n t w i ll 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.
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.
For each cylinder the team must find the point on the horizontal axis that corresponds with the cylinders 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.
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.
Record the length of the diameter and circumference of each cylinder in the table provided.
Explain
Ask students the following questions:
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?
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 its diameter.
use their graph to predict the circumference of a circle given its diameter or diameter given its circumference.
Professional Development SCMP March 2009
Adapted from Looking at Lines Grades 6-9 by AIMS Activities Integrating Math and Science
Activity: Functions in Circles pp 51-58
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.
For each cylinder the team must find the point on the horizontal axis that corresponds with the cylinders 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.
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.
Record the length of the diameter and circumference of each cylinder in the table below.
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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.
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