View
Tubes: Teacher Notes
MA.8.S.3.1
MA.912.A.3.11
Conceptual Understanding
Data Collection
Graphing
Line of Best Fit
Interpret Data
Procedural Knowledge
Organize Data
Graph Data
Make Predictions
Problem Solving
Reasoning
Connections
Representation
Does the length of a viewing
tube, its diameter, or the distance from an object affect the type
of data collected and the resulting graph?
Work in groups of four
or five.
Each group needs:
 Measuring Tape placed
vertically on the wall from the floor upward.
 Assorted tubes with
varying lengths and diameters to correspond to the investigation
assigned to each group
 Tape to mark standing
positions on the floor in front of the measuring tape
 Grid paper for each
group
 Students will work in
groups at designated "viewing stations."
 Each viewing station has a measuring tape on the wall and standing
positions marked on the floor in front of the wall.
 Each student standing at indicated distances from the wall will
use a tube to view the measuring tape and then describe to other
group members what portion of the poster is visible.
 Other group members will measure the height of the described viewable
portion to the nearest inch.
 Data is recorded as collected for each member of the group.
 Graphs of bestfit lines or curves are drawn and interpretations
made.
 Investigating the relationship between the dimensions of the tubes,
slopes, and intercepts should reveal:
 When tube length and diameter are constant, the viewable
height is a linear function of the distance from the wall. The
intercept is the diameter of the tube.
 When distance from the wall and tube length are constant,
the viewable height is a linear function of the diameter of
the tube.
 When the distance from the wall and tube diameter are constant,
the viewable height is a nonlinear function of the length of
the tube.
Investigation A
 Collect the Data: Each
member of the group will view the poster with the given tubes at
varying distances from the wall. Others will mark the top and bottom
of the described portion to determine the measurement in inches
of the viewing height. Calculate the average visible height for
each of the distances.
 Graph the Data: Choose
appropriate labels and scales for the horizontal and vertical axes.
Plot the data as ordered pairs, (x, y).
 Read the Results: Looking
at your points, do they seem to lie along a line or a curve? Draw
the line that best fits your data.
 Describe in words how
to determine the height of the visible portion if you know the distance
from the wall.
 Describe by equation
how to determine the height of the visible portion (y) if you know
the distance from the wall (x).
y =
 Predict the height
of the visible portion, if you were standing 10 feet
from the wall.
 Predict the distance
from the wall you would have to stand in order to see a 25inch
portion of the poster.
Viewing
Height:
Same Tube Length & Tube Diameter
Varying Distances from Wall
Student
name

Distance
from Poster

1
foot

2
feet

3
feet

4
feet

5
feet

6
feet

7
feet

8
feet
































































Total 








Investigation B
 Collect the Data: Each
member of the group will view the poster with the given tubes at
varying distances from the wall. Others will mark the top and bottom
of the described portion to determine the measurement in inches
of the viewing height. Calculate the average visible height for
each of the distances.
 Graph the Data: Choose
appropriate labels and scales for the horizontal and vertical axes.
Plot the data as ordered pairs, (x, y).
 Read the Results: Looking
at your points, do they seem to lie along a line or a curve? Draw
the line that best fits your data.
 Describe in words how
to determine the height of the visible portion if you know the diameter
of the tube.
 Describe by equation
how to determine the height of the visible portion (y) if you know
the diameter of the tube (x).
y =
 Predict the height of
the visible portion for a tube with a diameter of five inches.
 Predict the diameter
of a tube that would allow you to see a 10inch portion of the poster.
Viewing
Height:
Same Distance from Wall & Tube Length
Varying Diameters
Student
Name

Diameter
of Tube

1"

2"

3"

4"

5"

6"











































Average 






Investigation C
 Collect the Data: Each
member of the group will view the poster with the given tubes varying
in length, a designated distance from the wall. Others will mark
the top and bottom of the described portion to determine the measurement
in inches of the viewing height. Calculate the average visible height
for each of the lengths.
 Graph the Data: Choose
appropriate labels and scales for the horizontal and vertical axes.
Plot the data as ordered pairs, (x, y).
 Read the Results: Looking
at your points, as the length of the tube increases, what is happening
to the height of the visible portion of the picture?
 Would the height of
the portion ever decrease to zero? Why?
 What height does the
line seem to be approaching as a minimum?
Viewing
Height
Same Tube Diameter & Distance from Wall
Varying Length
Student
Name

Length
of Tube

4
inches

7
inches

22
inches

33
inches































Average 




As a result of this activity,
students learn to analyze data that they have collected, look for
relationships, and make predictions.
Have students answer the following
questions:
 Explain how you knew the graphs were or were not linear.
 Predict the height of the visible portion of the measuring tape
if you were standing 15 feet from the wall.
 Predict the distance you would have to stand from the wall in
order to see a 30inch portion of the measuring tape.
 Predict the height of the visible portion for the tube with a
diameter of 7.5 inches.
 Predict the diameter of a tube that would allow you to see a 20inch
portion of the measuring tape.
