9th Grade Performance Task
Developed by: RAND Corporation (RAND)
Stanford University and the Far West Laboratory, 1994
Rate of Cooling Analysis
Scoring Rubric
#1 (pg.2)
1a Graph - Axes
1.1 Labeled (1 point for "time",
1 point for "temperature")
1.2 Appropriate units specified
- "seconds or "minutes" for time
- "degrees Celsius", "degrees", or "Celsius"
for temperature.
1.3 Equal Intervals (if origin is 0,0 and there is a gap
in numbering for an axis, no credit for that axis unless a break
in the graph is correctly indicated)
1.4 Time on x-axis (indicated by "time", "seconds"
or numbering of axis with "60, 120, 180"
1b Graph - Trials
1.5 Plotted and identified
- any points plotted
- key, labels, or colors must be used to permit identification
of trial by letter, number of fabric
1.6 Line graph drawn rather than bar graph (points must
be connected in conventional manner).
1.7 Single set of axes used for all 3 trails (give credit
for single set of axes labeled but slightly staggered plots drawn.)
1.8 All 6 data points plotted (or 6 bars) per trial
1c Graph - Results
1.9 Proper slope (all plots indicate cooling)
1.10 0 sec. = 37 deg. Celsius for all three trials. (If
equal intervals are used, can infer the 0 on the x axis, don't need
"0" or "start" to give credit for 0 = 37 deg.)
1.11 End points in order: 3>1>2 (if separate graphs
are used but not identified, can assume that trial 1 is on the left.)
#2a (pg. 3)
Trials
2a.1 Pattern (1,1,1,1,1)
- Numbers must be used
- Entire pattern must be described
- Rate must be indicated ("degrees Celsius/min." is
best; "degrees for each time interval" is acceptable.)
- Rates of cooling for minutes 1-5 of trial 1, in deg. Celsius/min.
are 1,1,1,1,1 (rate is constant). (note: for this trial only,
"it decreased 1 degree per minute" or "it was 1
degree perminute" is given credit for both summary and pattern
information.)
2a.2 Summary - mean rate, total change or comparison of rate,
speed or amount of temperature change
makes an accurate (but can be approximate) statement about one
of these features of trial 1:
- average change (e.g. "it decreased 1 degree per minute")
- total change (e.g. "it changed 5 degrees", endpoints
alone are not sufficient)
- comparison (e.g. "the temperature decreased more slowly
than trial 2" (Note: if comparison is made to a specific
other trial, give summary credit for both trials)
#2b (pg. 3)
2b.1 Pattern (2,1,2,1,1)
- Numbers must be used
- Entire pattern must be described
- Rate must be indicated ("degrees Celsius/min." is
best; "degrees for each time interval" is acceptable)
- Rates of cooling for minutes 1-5 of trial 2, in degrees Celsius/min.
are 2,1,2,1,1
2b.2 Summary - mean rate, total change or comparison of rate,
speed or amount of temperature change
makes an accurate (but can be approximate) statment about one of
these features of trial 1:
- average change (e.g. "it descreased 1 1/2 degrees per minute")
- total change (e.g. "it changed 7 degrees", endpoints
alone are not sufficient)
- comparison (e.g. "the temperature decreased more slowly
than trial 1" (Note: if comparison is made to a specific
other trial, give summary credit for both trials)
#2c (pg. 3)
2c.1 Pattern (2,1,2,1,1)
- Numbers must be used
- Entire pattern must be described
- Rate must be indicated ("degrees Celsius/min." is
best; "degrees for each time interval" is acceptable)
- Rates of cooling for minutes 1-5 of trial 3, in degrees Celsius/min.
are 1,1,1,0,1
2c.2 Summary - mean rate, total change or comparison of rate,
speed or amount of temperature change
makes an accurate (but can be approximate) statement about one
of these features of trial 1:
- average change (e.g. "it decreased 1 degrees per minute")
- total change (e.g. "it changed 4 degrees", endpoints
alone are not sufficient)
- comparison (e.g. "the temperature decreased more slowly
than trial 2" (Note: if comparison is made to a specific
other trial, give summary credit for both trials.)
#3 (p.4)
3.1 Equation: Q = V x T (can also multiple by 1 (specific
heat of water))
3.2 V column (all 6 correct values)
3.3 T column (all 6 correct values)
3.6 Q column (5 of 6 correct values)
column Q has at least five of the six calorie calculations correct
#4a (pg. 5)
4a.1 Trial 5 identified as trial with the greatest change
in temperature.
#4b (pg. 5)
4b.1 "20" written (with or without degrees Celsius
or degrees)
4b.2 degrees Celsius or degrees used as unit
#5a (pg. 5)
5a.1 Trial 4 identified as trial with greatest heat loss
#5b (pg. 5)
5b.1 "3200" written (with or without "calories")
5b.2 Calories used as units
#6 (pg. 5)
6.1 Reason given for rate difference
- Examples: random error, difference in ice water temperature,
different air temperatures
- reason must not be volume or fabric
#7a (pg. 5)
7a.1 Trials 4 & 5 or Trials 5 & 6 used to observe
the effect of volume
#7b (pg. 5)
7b.1 Volume varies - student states that cans have different
volumes
7b.2 Same color
- asserts that the two trials have identical fabric conditions
(no fabric) or
- states that the conditions are the same except for volume
#8 (pg. 6)
8.1 Volume effect - directly or indirectly indicates that
the rate of cooling is greater for smaller volumes or less for larger
volumes.
#9a (pg. 6)
9a.1 Fabric C is best.
#9b (pg. 6)
9b.1 Evidence from experiment to support choice
Notes:
1. general reference okay, for example: "fabric C kept the
water the warmest" or "fabric C lost less heat"
2. Indirect reference okay, for example, "because the temperature
decreased the least"
3. Do not give credit if experimental evidence not mentioned (no
credit for only "fabric C was proven to be the best" or
"fabric C is made of wool").
9b.2 Specific data - Answer cites numbers from Tables 1
or 2 (or numbers that can be derived from the tables, such as calorie
calculations or graph points.)
Rater Answer Form - Cooling Analysis
Rater Name: ___________________________
Rater ID Number ___________________
1a. Graph - Axes (1 for each axis |
|
|
|
|
Labeled (time and temp) |
0
|
1 |
2 |
|
Appropriate units specified (seconds, minutes,
degrees) |
0 |
1 |
2 |
|
Equal intervals |
0 |
1 |
2 |
|
Time on X-axis |
0 |
1 |
|
|
1b. Graph - Trials |
|
|
|
|
Plotted and identified (1 per fabric) |
0 |
1 |
2 |
3 |
Line graph |
0 |
1 |
|
|
Single set of axes |
0 |
1 |
|
|
All 6 data points plotted for each trial |
0 |
1 |
|
|
1c. Graph - Results |
|
|
|
|
Proper slope |
0 |
1 |
|
|
0 seconds = 37 degrees |
0 |
1 |
|
|
End points in order: 3>1>2 |
0 |
1 |
|
|
2. Trials (Summary = mean; total D;
compare speed, rate, amount) |
|
|
|
|
Trial #1 - Pattern (1,1,1,1,1) |
0 |
1 |
|
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Summary |
0 |
1 |
|
|
Trial #2 Pattern (2,1,2,1,1) |
0 |
1 |
|
|
Summary |
0 |
1 |
|
|
Trial #3 Pattern (1,1,1,0,1) |
0 |
1 |
|
|
Summary |
0 |
1 |
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3. Formula and Table |
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Equation Q = V x DT |
0 |
1 |
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V column (6 correct values) |
0 |
1 |
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DT column (6 correct values) |
0 |
1 |
|
|
Q column (5 of 6 correct values) |
0 |
1 |
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|
Table (at right) |
V
200
200
200
200
50
200 |
DT
5
7
4
16
20
15 |
Q
1000
1400
800
3200
1000
3000 |
|
4. Greatest change: 1 = Tr.5, 1 =
20, 1 = degrees |
0 |
1 |
2 |
3 |
5. Greatest heat: 1 = Tr.4, 1 = 3200,
1 = calories |
0 |
1 |
2 |
3 |
6. Reason: 1 = e.g., chance, variation
in air or ice water temp, other... |
0 |
1 |
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7. Compare volume: |
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1 = Tr.4/5 or 5/6 |
0 |
1 |
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1 = Volume varies |
0 |
1 |
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1 = Other variables remain the same (e.g. fabric) |
0 |
1 |
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8. Volume effect: 1 = faster cooling
with smaller volumes |
0 |
1 |
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9. Which fabric: |
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|
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Fabric C |
0 |
1 |
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Evidence from experiment |
0 |
1 |
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Specific data - quantities from table, curves
on graph |
0 |
1 |
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