Math
Spring Operational 2015
Algebra 1
PBA Item #18
Quality Control Technician
M41195
Prompt
Rubric
Task is worth a total of 3 points.
M41195 Rubric
Score Description
3
Student response includes the following 3 elements.
• Modeling component = 2 points
o correct equation, w ≈ 16 − 0.19h
o accurate use of notation and vocabulary to support
correct calculations and mathematical reasoning,
identifying variables as needed
•
Computation component = 1 point
o correct application of the model to make an accurate
prediction
Sample Student Response:
If the burn rate is believed to be constant, determine the
average burn rate for the eight candles as the ratio of weight
loss per hour.
ounces lost over three-hours
0.5 + 0.6 + 0.5 + 0.7 + 0.7 + 0.5 + 0.5 + 0.6 ≈ 0.575
8
ounces lost per hour on average
0.575 ≈ 0.19
3
2
For 0 hours, the weight of each candle is 16 ounces. Therefore,
w ≈ 16 − 0.19h.
This model can be used to predict the weight of the candle
when h, the number of hours of burning, is 5.
w ≈ 16 − 0.19(5)
≈ 16 − 0.95
≈ 15.05
According to the model, the weight of the candle after 5 hours
of burning would be about 15.05 ounces.
Student response includes 2 of the 3 elements.
1
Student response includes 1 of the 3 elements.
0
Student response is incorrect or irrelevant.
Anchor Set
A1 – A8
A1
Score Point 3
Annotations
Anchor Paper 1
Score Point 3
This response receives full credit. The student includes each of the three required elements:
•
The response includes the correct equation for net candle weight (w=16-.2h). A burn
rate of .19h rounded to .2h is acceptable.
•
The response includes the correct application of the model to make an accurate
prediction (w=16-.2(5), w=16-1, w=15).
•
The response includes accurate use of notation and vocabulary to support correct
calculations and mathematical reasoning, identifying variables as needed (I found the
average rate at which the candle burns an hour by finding the average of the numbers
given then dividing that by three. The average rate at which the candle burns per hour
is .2 ounces).
A2
Score Point 3
Annotations
Anchor Paper 2
Score Point 3
This response receives full credit. The student includes each of the three required elements:
•
The response includes the correct equation for net candle weight (w=16-(.192h)). The
decimal .192 is correct to the thousandths place.
•
The response includes a correct application of the model to make an accurate
prediction (w=16 -(.192 x 5), 15.04=16-.96).
•
The response includes accurate use of notation and vocabulary to support correct
calculations and mathematical reasoning, identifying variables as needed (.575 is the
average rate of weight loss; .192 is the average weight loss per hour . . . after 5 hours
the candle will weigh 15.04 ounces).
A3
Score Point 2
Annotations
Anchor Paper 3
Score Point 2
This response receives partial credit. The student includes two of the three required
elements:
•
The response includes a correct application of the model to make an accurate
prediction (w=.192 5=.96 is the loss of weight. therefore the weight loss is
subtracted from the original 18. so the weight after five hours is 17.04). This is a
correct methodology deriving from the original transcription error.
•
The response includes accurate use of notation and vocabulary to support correct
calculations and mathematical reasoning, identifying variables as needed (the starting
weight is 16oz. and the average loss is 0.575 after 3 hours. so for 1 hour the average
is .192 . . . so the weight after five hours is 17.04).
There is no correct equation. The student makes a transcription error in which the starting
weight of 16 oz. is represented by 18 in the equation. This results in an incorrect equation,
which is the only error. No credit for element 1 but follow through points are awarded.
A4
Score Point 2
Annotations
Anchor Paper 4
Score Point 2
This response receives partial credit. The student includes two of the three required
elements:
•
The response includes the correct equation for net candle weight (w=16 - h(.2)).
•
The response includes a correct application of the model to make an accurate
prediction (w=16-5(.2), w=16-1, w=15).
This response does not receive the credit for the second modeling component. There is no
attempt to explain any portion of the work.
A5
Score Point 1
Annotations
Anchor Paper 5
Score Point 1
This response receives partial credit. The student includes one of the three required
elements:
•
The response includes accurate use of notation and vocabulary to support correct
calculations and mathematical reasoning, identifying variables as needed (0.2 is
average amount of weight loss for a candle that has been burning for 1 hour. Sub in 5
for h to find out how much weight a candle will lose after burning for 5 hours).
There is an incorrect equation (w=0.2h); this equation computes the candle’s lost weight,
not net weight. There is no correct application of the model to make an accurate prediction.
5 is substituted correctly for h, but because this is an equation for candle lost weight and not
net weight, no credit is earned.
A6
Score Point 1
Annotations
Anchor Paper 6
Score Point 1
This response receives partial credit. The student includes one of the three required
elements:
•
The response includes a correct application of the model to make an accurate
prediction (13.5=16-.5(5)).
The response includes an incorrect equation (w=16-.5(h)); the burn rate corresponds to the
3-hour burn rate for candle #1, not the average hourly rate of all candles. The candle weight
prediction is correct, given the equation used. This response does not receive credit for the
second modeling component. There is no attempt to explain any portion of the work.
A7
Score Point 0
Annotations
Anchor Paper 7
Score Point 0
This response receives no credit. The student includes zero of the three required elements.
The predicted weight loss for the candle is incorrect and the reasoning on which it is based is
also incorrect. Incorrect prediction and no other bullets are addressed. No credit is earned.
A8
Score Point 0
Annotations
Anchor Paper 8
Score Point 0
This response receives no credit. The student includes zero of the three required elements.
The equation given uses the test candle number as a factor for the candle’s weight, which is
incorrect. The reasoning is too seriously flawed to warrant any credit.
Practice Set
P101 - P105
P101
P102
P103
P104
P105
Practice Set
Paper
Score
P101
2
P102
0
P103
2
P104
1
P105
3