Cooperative Group
Problem Solving
Chris Meyer
christopher.meyer@tdsb.on.ca
York Mills C. I.
Brought to You by...
• Pat and Ken Heller of the University of
Minnesota
• Outstanding, free, online resource
•
http://groups.physics.umn.edu/physed/Research/CGPS/CGPSintro.htm
Context-Rich Problems
• Situations presented in colloquial
language, almost as a story
• Challenge: identify the physics ideas at
work
• Challenge: identify the important
information
• Challenge: no “plug'n'chug” solutions
Group Format
• Problems are more difficult than a
single person could handle
• Group roles assigned
• Planning, explanation and discussion
are critical
Roles - Manager
• Direct the sequence of steps.
• Keep your group “on-track”.
• Make sure everyone in your
group participates.
• Watch the time spent on each
step.
"Let's come back to this later if we have time.“
"We need to move on to the next step.“
"Chris, what do you think about this?”
Recorder / Checker
• Act as a scribe for your group.
• Check for understanding of all
members.
• Make sure all members of your
group agree on plans and
actions.
• Make sure names are on group
products.
"Do we all understand this diagram?“
"Explain why you think that.“
"Are we in agreement on this?"
Speaker / Skeptic
• Speak on behalf of your group
in class discussions
• Help your group avoid coming
to agreement too quickly.
• Make sure all possibilities are
explored.
• Suggest alternative ideas.
"What other possibilities are there?“
"Let's try to look at this another way.“
"I'm not sure we're on the right track."
The Process
Problem Statement
A: The Picture
B: The Question
C: The Plan
D: The Work
E: The Results
The Physics Challenge
•
•
•
Add in the physical world!
Physical objects need to be explored /
measured
The final result is physically verified
Your Challenge!
The Washer Drop
Your group will be given a length of string, five
washers and some tape. Your challenge is to attach
the five washers such that when you release the
string and the washers hit the ground, there is a
steady succession of sounds.
clink-clink-clink-clink-clink.
Not clink .… clink ……... clink, clink..clink.
A: The Picture
• Draw a clear diagram
showing what’s
happening
• Attach important
information using simple
phrases
• Make measurements
• Attach unknowns if
possible
• Indicate coordinate
system and sign
convention
• Complete? Problem
statement is discarded
Problem Statement
A: The Picture
B: The Question
C: The Plan
D: The Work
E: The Results
A. The Picture
all washers released from rest,
v1=0
t4
length of string,
Δd4 = 4.15 m
gravity,
ag = 9.80 m/s2
+
t3
Δd3 = ?
t2
Δd2 = ?
Starts just above ground
t1
Δd1 = ?
B: The Question
• Create a specific
physics question that
will give the answer to
the problem.
• Indicate which
quantities will allow you
to answer the question.
Problem Statement
A: The Picture
B: The Question
C: The Plan
D: The Work
E: The Results
B. The Question
What are the displacements from the three middle
washers to the bottom of the string such that the time
intervals between each washer hitting the ground are
equal?
Δd1, Δd2, Δd3 = ?
C: The Plan
Problem Statement
A: The Picture
• List the important
physics concepts or
ideas involved in the
solution.
B: The Question
• Outline the key steps
involved in solving the
problem
C: The Plan
• List any useful
“textbook” equations
and relationships
D: The Work
E: The Results
C. The Plan
Key concepts and
ideas
Key steps
Key equations and
relationships
• Washers accelerate
uniformly due to
gravity.
• Washers start from
rest
• Big 5 equations valid
ΔΔd = vit + ½at2
• Find time for whole
string to drop, divide
n
tn  t4
into 4 equal intervals.
4
• Use intervals to find
position of each
washer above the
ground.
D: The Work
• Create the specific
equations you will use –
write them down with a
simple statement
explaining what you are
doing.
Problem Statement
A: The Picture
B: The Question
• Perform the algebraic
work first, whenever
practical.
C: The Plan
• Verify the units of derived
expressions
D: The Work
• No number crunching yet!
E: The Results
D. The Work
Find the time for the top washer to drop:
d 4  vi t 4  1 a g t 4 ,
2
2d 4
 t4 
ag
2
vi  0
s  
m
m / s 
2
 [s 2 ]
 [s]
Find the other time intervals:
t1  (1 / 4)t4 ,
t2  (2 / 4)t4 ,
t3  (3 / 4)t4
Determine the displacements of the middle washers:
2
 d 3  1 a g t3
2
2
 d 2  1 a g t 2
2
2
 d1  1 a g t1
2
E: The Results
• Substitute numbers into
your manipulated
equations and calculate
a result.
• State the final answer in
response to the
question you created.
• Write brief statements
explaining why the
answer seems
reasonable in size,
direction and units.
Problem Statement
A: The Picture
B: The Question
C: The Plan
D: The Work
E: The Results
E. The Results
2(4.15 m)
 t4 
 0.920 s
2
9.80 m / s
 t1  (1 / 4)(0.920 s)  0.230 s
 t 2  (2 / 4)(0.920 s)  0.460 s
 t3  (3 / 4)(0.920 s)  0.690 s
 d 3  1 (9.80 m / s 2 )(0.690 s) 2  2.33 m
2
 d 2  1 (9.80 m / s 2 )(0.460 s) 2  1.04 m
2
 d1  1 (9.80 m / s 2 )(0.230 s) 2  0.26 m
2
The washers should be positioned 0.26 m, 1.04 m and 2.33 m from the
bottom of the string.
Reasonable size, units, direction?
Size: The values are smaller than the full length and
create successively larger displacements from the
bottom. This makes sense for a series of accelerating
objects.
Units: The unit is metres, which is appropriate for
displacements.
Direction: All displacements were positive - meaning
downwards, which makes sense for falling washers.