University of Seattle When Was Hosni Moving Away from Motion Detector Questions

Name: ___________________________________Date: ____________
Mid-Topic 7 Test
1) How far away from the motion detector was Hosni when he started his
walk?
2) A. When was Hosni standing still?
B. When was Hosni moving away from the motion detector?
C. When was Hosni moving toward the motion detector?
3) How long did Hosni’s walk last?
In questions, 4-7,
4.
5.
6.
7.
8.
You start at the motion detector and walk 5 feet away from it at a steady rate for 3
seconds, stand still for 2 seconds, then walk back to the motion detector at a steady rate
for 5 seconds. Sketch a graph that matches this description.
Topic 7: Exploring rate of change in motion problems
1
Lesson 5: What’s my rate?
7.5 CORE ACTIVITY
1.
Fill in the table with the information from Terrence’s skateboarding.
2.
Notice that the graph is horizontal from 4 seconds to 10 seconds. What was Terrence’s rate then?
3.
What is the rate for the skate modeled by this graph? Show your
work.
Copyright © 2017 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc.
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Topic 7: Exploring rate of change in motion problems
4.
Here is another graph that shows Terrence’s movement while skateboarding. Fill in the blanks to complete the
following statements about the different rates of change you see on the graph.
a.
Segment _
shows a rate of change of 0 ft/sec.
b.
Segment _
shows a negative rate of change.
c.
Segment
d.
Looking at segment A, Terrence’s rate of change for
_ shows a positive rate of change.
the first 2 seconds was ___ ft/sec.
e
Looking at segment C, Terrence’s rate of change for
the last 5 seconds was
5.
_ ft/sec.
The table shows the information for one of Terrence’s skates.
Time (sec)
0
1
2
3
Distance (ft)
2
4
6
8
a.
Use the table to create a graph
for this skate.
b.
How fast was Terrence skating?
Copyright © 2017 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc.
3
Topic 7: Exploring rate of change in motion problems
6.
According to the graph, how fast were the elevators
moving?
Elevator A: ____________ Elevator B: ____________
8.
Describe how you found the rates from the graphs.
Part I: Find the rate for each graph or table.
1.
Rate = ______
3.
7.
According to the graph, how fast were the elevators
moving?
Elevator A: ____________ Elevator B: ____________
2. Rate = ______
Time (sec)
Dist (ft)
Time (sec)
Dist (ft)
0
1
0
1
1
6
3
7
2
11
6
13
Rate = ______
4.
Rate = ______
Copyright © 2017 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc.
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Topic 7: Exploring rate of change in motion problems
Part II: Match each rate with a table and graph.
TABLE (A-D)
GRAPH (W-Z)
5. Rate of 2 feet per second
6. Rate of -2 feet per second
7. Rate of 1 foot per second
8. Rate of -1 foot per second
A.
Time (sec)
0
4
8
12
Dist (ft)
2
6
10
14
B.
Time (sec)
0
2
4
6
Dist (ft)
2
6
10
14
C.
Time (sec)
0
2
4
6
Dist (ft)
12
8
4
0
D.
Time (sec)
0
4
8
12
Dist (ft)
12
8
4
0
Copyright © 2017 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc.
1
Topic 7: Exploring rate of change in motion problems
Lesson 6: More about rates of change
LESSON 5: REVIEW/PREVIEW – CALCULATE THE RATE FOR EACH
LESSON 6: OPENER
Distance in feet
Sketch two different graphs on the same grid of
2. Sketch two different graphs on the same grid of distance
distance versus elapsed time for an elevator rising at a
versus elapsed time for an elevator descending at a rate of
rate of 1 foot per second.
2 feet per second.
Distance in feet
1.
Elapsed time in seconds
3.
Elapsed time in seconds
Suppose everyone in the class added their lines to the same grid on which you sketched your graphs. What patterns, if
any, would you see?
Copyright © 2017 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc.
2
Topic 7: Exploring rate of change in motion problems
LESSON 6: CORE ACTIVITY
1. A graph of Terrence’s skateboarding is shown.
Use the graph to answer the following questions.
a.
Build a table from this graph.
Time (sec)
Distance (ft)
b.
Find Terrence’s average rate from 0 to 1 second. You
can use either the table or the graph to do this!
c.
Find Terrence’s average rate from 1 to 3 seconds.
d.
Find Terrence’s average rate for each of the remaining intervals.
From 3 to 5 seconds, Terrence’s rate was
From 5 to 8 seconds:
From 8 to 10 seconds:
e.
How do the rates from 3 to 5 seconds, 5 to 8 seconds, and 8 to 10 seconds compare to the rates you found in parts
b and c? Explain these differences in the context of the situation.
Copyright © 2017 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc.
Topic 7: Exploring rate of change in motion problems
3
LESSON 6: CONSOLIDATION ACTIVITY
A student recorded three different skates, each with a constant rate. The student recorded some of the information for
each skate in tables. For each skate, fill in the table, create a graph of the data, and find the rate.
1.
Time (sec)
0
Distance (ft)
5
1
2
7
3
2.
Time (sec)
0
Distance (ft)
3
1
2
3
9
Time (sec)
0
Distance (ft)
8
2
6
3.
4
6
Copyright © 2017 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc.
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Topic 7: Exploring rate of change in motion problems
LESSON 6: HOMEWORK
Notes or additional instructions based on whole-class discussion of homework assignment:
1.
Fill in the missing information about these skates recorded by a student. (Fill in the table, create the graph and/or find
the rate.) Assume that these graphs are linear.
a.
How fast was he skating? ______
Time
(sec)
0
1
2
3
b.
How fast was he skating? ______
Time
(sec)
c.
Distance
(ft)
How fast was he skating? ______
Time
(sec)
1
2
3
4
2.
Distance
(ft)
6
5
Distance
(ft)
1
5
What are the differences between a positive rate and a negative rate? Use a graph and a table to support your answer.
3. What does it mean for an elevator to have a rate of
1
2
floors per second? Use a graph and table to support your answer.
Copyright © 2017 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc.
End of Topic 7 Study Guide
Name:_________________________
Calculate the rate of change.
1.
2.
Work:
Work:
3.
4.
Time (sec)
0
1
2
3
Work:
Distance (ft)
2
4
6
8
5. The elevator started on floor 5, three
seconds later it was on floor -2. Find the
rate of change.
Work:
6. The elevator started on bottom floor,
seven seconds later it was on floor 8. Find
the rate of change.
End of Topic 7 Study Guide
Name:_________________________
7. Describe the skate modeled by this graph. Include the rates, direction, and times for each
portion of the skate.
Description:
8. An elevator started at the ground floor and traveled to floor 9 at a constant rate of 3 floors
per second. The elevator then paused on floor 9 for 2 seconds, then traveled to floor 1 at a
constant rate of -1 floors per second.
Create a graph to show the distance from the ground floor and time for this situation.