Ratio and Proportion
Lab: Circles
Name
Date
Directions: Do complete solutions on a separate sheet of folder paper. Show all of your work.
1.
List the items you brought in a table like the one below.
2.
a.
Find the diameter of each item without measuring. Describe your method for
finding the diameters.
b.
Use the diameter of each item as one unit to measure the circumference of that
item. Describe your method for measuring the circumference.
3.
Enter your data in your table.
4.
List some interesting mathematical observations you made.
Circle
Diameter
Circumference
1.
2.
3.
4.
5.
SMS Math-Talk Learning Community
CRDG – November 2008
Teacher’s Notes
Intent:
This task is intended to give students an investigative experience that is part of
developing an understanding of a ratio. Students will explore properties of a circle
and establish a relationship between the circumference of a circle and its diameter.
The discussion should lead to an observation about the consistency of that
relationship and its identification as π (pi).
Teacher’s Insight:
After students have noticed the circumference to diameter ratio being close to 3,
introduce the term pi (π) and the calculator button.
Questions:
Focus:
How did you find the diameter?
How did you measure the circumference?
Discussion:
What was the measurement of the circumference when the diameter was
one (1) unit?
What can you say about the diameters and circumferences of all circles?
Reflection:
Why do you think we all got close to the same answer for the circumference?
SMS Math-Talk Learning Community
CRDG – November 2008
Ratio and Proportion
Lab: Circles + Navigator
Name
Date
Directions: Do complete solutions on a separate sheet of folder paper. Show all of your work.
1.
List the items you brought in a table like the one below.
2.
a.
Identify the diameter of each circle and find its length in centimeters. Record
this information in the table.
b.
Identify the circumference of each circle and find its length in centimeters.
Record this information in the table.
a.
When prompted, enter the information from you found as ordered pairs in
List 1 [length of diameter] and List 2 [circumference].
b.
When all your data is entered into the two lists, send the data.
3.
4.
Group data: Group data: When all the points are placed on a graph, what do you
predict the graph will look like? Explain your reasoning.
Individual work: Create the line of best fit and find the regression line
5.
If the length of a diameter of a circle is 16 cm, what is your prediction for the
circumference of that circle? Explain your reasoning. [Can you do this with the
TRACE function? – might need to adjust window]
6.
If the length of the circumference of a circle is 16 cm, what is your prediction for
the length of the diameter of that circle?
Circle
Diameter
Circumference
1.
2.
3.
4.
5.
7.
Create list L3. L3 = L2/L1. What does the data in L3 mean? Find Average of entries
on L3. [new entry in L3; - 3 >> to 1, select 3 mean( , - 3 and select L3, b b---the
entry should reflect the average of entries in L3.]
SMS Math-Talk Learning Community
CRDG – November 2008
Teacher’s Notes
Intent:
This task is intended to give students an investigative experience that is part of
developing an understanding of a ratio. Students will explore properties of a circle
and establish a relationship between the circumference of a circle and its diameter.
The discussion should lead to an observation about the consistency of that
relationship and its identification as π (pi).
Teacher’s Insight:

After students have noticed ‘a linear relationship’ when ordered pairs relating the
length of the diameter of a circle and the length of the circumference of circle have
been graphed, focus on 1) a manual line of best fit, and 2) computer calculated line of
best fit.
The line should go through the origin and the equation y = mx also expresses the ratio m
y
= . m is the slope; m is a ratio; m is a constant all are important ideas related to the
x
linear relationship between the length of a diagonal of a square and the length of the
perimeter of the square.
After students have noticed the slope/ratio being close to 3, introduce the term pi (π)
and use the π button to see an approximation. Compare this to the slope calculated
above.
Questions:
Focus:
How did you find the diameter?
How did you measure the circumference?
What is the equation of the line telling about the relationship between the length of a
diameter of a circle and the length of the circumference of the circle?
Discussion:
What was the measurement of the circumference when the diameter was
one (1) unit?
What can you say about the diameters and circumferences of all circles?
Reflection:
Why do you think we all got close to the same answer for the circumference?
How did the average of the values in L3 compare to the value of π?
SMS Math-Talk Learning Community
CRDG – November 2008