MOTION DETECTOR
Enduring Understanding: Develop a better understanding of recognizing and describing a linear
pattern represented in a graph. Develop a better understanding of how to determine the equation for a
linear model.
Essential Questions:
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What is meant by “linear function”?
When reading a graph, where are the x- and y-intercepts? What is the relationship between
the intercepts and the context of any problem?
What is meant by positive slope?
What is meant by negative slope?
When is there a slope of “0”? What does that mean?
How can the information in a graph lead to the development of an equation of that line?
Lesson Overview:
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Before allowing the students the opportunity to start the activity: access their prior
knowledge with regards to using a motion detector, charting movement of objects.
Use a motion detector in class to model a graph.
Have some pre-made graphs to put on the overhead and have students try to match the graph
by their movements.
How can you support a conclusion that you make? What evidence from graphs can be used to
support/justify your conclusion?
A good warm-up would be Speed of the Roller Coaster.
Materials necessary to assist in doing this activity: motion detectors/rangefinders (if you don’t
have any in the math department, check with a science teacher). Calculator/computer
interface for motion detector/rangefinders.
Use resources from your building.
EALRs/GLEs
1.4.4
1.5.1
1.5.2
1.5.4
5.1.1
Item Specifications: PS03; AS01; AS02; MC01
Assessment:
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Use WASL format items that link to what is being covered by the classroom activity
Include multiple choice questions
Motion Detector
Adapted from Charles A. Dana Center at the University of Texas at Austin, ©2002
The graph shows how the distance between a person and a motion detector depends on the time that
has elapsed since the person began walking.
1. Describe, in detail, how the person’s position relative to the motion detector changes over the
time interval from 0 seconds to 7 seconds. Include a description of the person’s speed for each
portion of the graph.
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2. When is the person moving the fastest? When is the person moving the slowest? Support your
answer with information from the graph.
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3. Write an equation for each phase shown on the graph.
a. _______________________________________________________________________________
b. _______________________________________________________________________________
c. _______________________________________________________________________________
d. _______________________________________________________________________________
e. _______________________________________________________________________________
4, How far from the motion detector was the person initially? _______________________________
Support your answer using words, numbers and/or diagrams.
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5. Does the person ever reach the motion detector? ______________
Support your answer using words, numbers and/or diagrams.
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6. Chelsea washed her car at the local car wash using a high pressure sprayer. The number of
minutes that the sprayer operates varies directly with the number of quarters deposited. When six
quarters are deposited, the timer on the sprayer is automatically set to four minutes.
Which equation represents the relationship between the number of quarters deposited, q, and the
number of minutes on the timer, m?
O C.
2
q
3
3
m q
2
m  q2
O D.
m  10  q
O A.
O B.
m
7. Ginger left school at 3:00 P.M. and walked home, but went back to school for a book. She then
walked home, had a snack, and took a bus downtown. Later, she took a bus home, arriving at 5:00
P.M.
Which statement is true?
O
O
O
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A.
B.
C.
D.
Ginger’s maximum distance from home was 2 miles.
Ginger’s minimum distance from home was 0.5 miles.
At 3:30 P.M., Ginger is at her farthest distance from home.
At 4:30 P.M., Ginger is back at her home.
8. Travis went on a long trip. The graph represents the relationship between distance and time.
Which interval was Travis’ average rate of travel the fastest?
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O
O
O
A.
B.
C.
D.
0 to 6 hours
6 to 8 hours
8 to 11 hours
11 to 16 hours