Math
Released Item 2015
Grade 8
PBA Item #13
Gas Prices
1419-M21875
Task is worth a total of 4 points.
1419-M21875 Rubric Part A
Score
2
Description
Student response includes the following 2 elements.
•
Computation component = 1 point
o
•
Determines both percentage increases
Reasoning component = 1 point
o
Correctly reasons that the student’s claim is justified
Sample Student Response:
Percent increase from 1998 to 2000 is (1.354 - 1.291)/1.291 ≈ 0.0488.
Percent increase from 2011 to 2013 is (4.069 - 3.874)/3.874 ≈ 0.0503.
The percent increase for both periods is about 5%, so the student’s
claim can be justified.
1
Student response includes 1 of the 2 elements.
0
Student response is incorrect or irrelevant.
1419-M21875 Rubric Part B
Score
2
Description
Student response includes the following 2 elements.
•
Computation component = 1 point
o Determines the percent error of the prediction, 0.8%
•
Reasoning component = 1 point
o Correctly reasons that the newspaper’s claim is correct
Sample Student Response:
The percent error of the prediction was 0.8%.
( 4.10 − 4.069 )
= 0.008
4.069
Since 0.8% is less than 2%, the newspaper’s claim was correct.
1
Student response includes 1 of the 2 elements.
0
Student response is incorrect or irrelevant.
Anchor Set
A1 – A11
A1
Part A: Score Point 2
Part B: Score Point 2
Annotations
Anchor Paper 1
Part A: Score Point 2
This response receives full credit. The response includes each of the two required elements:
•
•
The response provides valid work or explanation to determine the percent increases
(1.354−1.291)
(4.069−3.874)
≈ 4.88%: [2011 to 2013]
≈5.03%).
([1998 to 2000]
1.291
3.874
A correct explanation to justify the claim based on a valid strategy to calculate the
percent increases is provided (The prices in both time ranges increased by about 5%
when rounding to the nearest percent, so the student’s claim was correct because the
increase was about the same in both situations).
Part B: Score Point 2
This response receives full credit. The response includes each of the two required elements:
•
•
The response provides valid work or explanation to determine the percent error of the
(4.1−4.069)
≈ 0.76%).
prediction (
4.069
A correct explanation to justify the claim based on a valid strategy to calculate the
percent error of the prediction is provided (The newspaper promised that they would
be within 2% of the actual price. There error was about 1%, meaning that their claim
was correct).
A2
Part A: Score Point 2
Part B: Score Point 2
Annotations
Anchor Paper 2
Part A: Score Point 2
This response receives full credit. The response includes each of the two required elements:
•
The response provides valid work or explanation to determine the percent increases
.063
([1998 to 2000] 1.354 – 1.291 = .063;
≈ 4.88%: [2011 to 2013] 4.069 – 3.874 =
.195;
•
.195
3.874
1.291
≈5.03%).
A correct explanation to justify the claim based on a valid strategy to calculate the
percent increases is provided (Yes, it was about the same. It was only 2 tenths of a
percent off).
Part B: Score Point 2
This response receives full credit. The response includes each of the two required elements:
•
•
The response provides valid work or explanation to determine the percent error of the
0.31
prediction (4.1 – 4.069 = .031;
≈ 0.76%).
4.069
A correct explanation to justify the claim based on a valid strategy to calculate the
percent error of the prediction is provided (The newspapers claim was correct they
were within 2 percent of the actual gas price. The percent error was about .76%).
A3
Part A: Score Point 2
Part B: Score Point 1
Annotations
Anchor Paper 3
Part A: Score Point 2
This response receives full credit. The response includes each of the two required elements:
•
The response provides valid work or explanation to determine the percent increases
0.063
≈ 4.8%; [2011for the two time periods ([1998-2000] 1.354 – 1.291 = 0.063,
2013] 4.069 – 3.874 = 0.195,
•
0.195
3.874
1.291
≈ 5%).
A correct explanation to justify the claim based on a valid strategy to calculate the
percent increases is provided (The student’s claim is accurate). The results (4.8%,
5%) support the claim that the percent increase for both periods is about 5%.
Part B: Score Point 1
This response receives partial credit. The response includes one of the two required
elements:
•
The response provides work or explanation justifying that the newspaper’s claim is
4.10
≈ 101%, The newspaper’s claim is correct because it is within 2% of
correct ( 4.069
100). The percentage calculated when dividing the prediction price (4.10) by the
actual March 2013 price (4.069) is less than 102% or within 2% of the newspaper’s
claim.
The percent error of the prediction is missing.
To determine the percent error of the prediction, the difference between the predicted price
[4.10] and the actual price [4.069] in March 2013 is calculated. The difference [0.031] is
divided by the actual price in March 2013. The result [0.00761…] is converted to a
percentage [0.08%].
A4
Part A: Score Point 2
Part B: Score Point 1
Annotations
Anchor Paper 4
Part A: Score Point 2
This response receives full credit. The response includes each of the two required elements:
•
The response provides valid work or explanation to determine the percent increases
0.063
0.195
, 4.8% increase from 1998 – 2000; 4.069 – 3.874 =
, 5%
(1.354 – 1.291 =
1.291
increase from 2011 - 2013)
3.874
The work is provided for finding the percent increase, but the work is in the form of a run-on
equation; e.g., 6 x 7 is not equal to 42 + 9 x 6. A scoring decision exists that if a run-on
equation occurs in a given response and the response would have received the top score
[Part A: 2, Part B: 2] without the run-on equation, a score point will be deducted. A response
that is not a top score point will receive no further deduction.
•
A correct explanation to justify the claim based on a valid strategy to calculate the
percent increases is provided (He’s right since it states nearly the same and they’re
only about 0.2% away). The results (4.8%, 5%) support the claim that the percent
increase for both periods is about 5%.
Part B: Score Point 1
This response receives partial credit. The response includes one of the required elements:
•
The response provides work or explanation justifying that the newspaper’s claim is
correct (Yes since 1% of a gallon of gas is 0.04 cents. The price was about 4.07,
which meant it stayed within 2% percent) [of the actual cost, 4.069]. Although written
incorrectly (0.04 cents), the student has calculated the cost of half (1%) the
prediction [4 cents]. The incorrect form does not detract from the understanding of
the task.
Using price is an acceptable way to justify the claim. The price for March 2013 (4.069 dollars)
multiplied by 2% (0.02) would define the range of price for the prediction. The value would
be ±0.08 making the price range for a gallon of gasoline, which the prediction would have to
be within, 4.07 [4.069 rounded to the nearest penny] ±0.08 or 3.99 to 4.15. The prediction
of 4.10 would be within this range, justifying the newspaper’s claim.
The percent error of the prediction is missing.
A5
Part A: Score Point 2
Part B: Score Point 0
Annotations
Anchor Paper 5
Part A: Score Point 2
This response receives full credit. The response includes each of the two required elements:
•
The response provides valid work or explanation to determine the percent increases
(January 1998 – 2000: 1.354 ÷ 1.291 = 1.048; March 2011 – 2013: 4.069 ÷ 3.874 =
1.050).
Dividing the final price by the initial price for a given time period is an acceptable alternative
method to determine percent increase.
•
A correct explanation to justify the claim based on a valid strategy to calculate the
percent increases is provided (yes they are about the same percentage). The
percentage calculated when dividing the final value of the time period by the initial
value of the time period is about 1.05 (105%) or about 5% for the percent increase.
The results (1.048, 1.050) support the claim that the percent increase for both periods
is about 5%.
Part B: Score Point 0
This response receives no credit. The response includes none of the two required elements.
The explanation justifying the newspaper’s claim is incorrect (no i dont think that the
newspaper was correct . . . would be about $7 not $4.10).
The percent error of the prediction is missing.
A6
Part A: Score Point 2
Part B: Score Point 0
Annotations
Anchor Paper 6
Part A: Score Point 2
This response receives full credit. The response includes each of the two required elements:
• The response provides valid work or explanation to determine the percent increases
4.069
( 1.354
=
1.048,
=
1.050 ).
1.291
3.874
•
A correct explanation to justify the claim based on a valid strategy to calculate the
percent increases is provided (1.048 can be rounded up to 1.05, so the student’s claim
is correct). The percentage calculated when dividing the final value of the time period
by the initial value of the time period is about 1.05 (105%) or about 5% for the
percent increase. The results (1.048, 1.050) support the claim that the percent
increase for both periods is about 5%.
Part B: Score Point 0
This response receives no credit. The response includes none of the two required elements.
The explanation provided justifying the newspaper’s claim is incorrect (The newspaper’s claim
is correct because the price of gasoline jumped 1.05 percent from 2011 to 2013, and the
price rose 0.195 and their prediction was only 0.031 off).
The percent error of the prediction is missing.
A7
Part A: Score Point 1
Part B: Score Point 1
Annotations
Anchor Paper 7
Part A: Score Point 1
This response receives partial credit. The response includes one of the two required
elements:
•
The response provides valid work or explanation to determine the percent increases
(1.354 – 1.291 = .063, 1.291 ÷ .063 ≈.048; 4.069 – 3.874 = .195, .195 ÷ 3.874 ≈
.05). Although the dividend and divisor have been incorrectly switched in the work for
the 1998 – 2000 time period, the correct result (≈ .048) and the correct work for the
other time period indicates a transcription error. A transcription error does not detract
from the understanding of the task.
The explanation to justify the claim is incorrect (About a .048% increase between ’98 and
’00, From ’11 to ’13 there was about a .05% increase. .048% is close to .05%, so the
student was correct). All percentages provided are less than 1%.
Part B: Score Point 1
This response receives partial credit. The response includes one of the required elements.
•
The response provides work or explanation justifying that the newspaper’s claim is
correct (4.069 x .02 ≈ .08, 4.069 - .08 = 3.989, 4.069 + .08 = 4.149, The paper’s
prediction was within 2% of the actual price). The student has defined the range of
price for the prediction and the prediction falls within the range.
The percent error of the prediction is incorrect (.007%) with no work provided.
A8
Part A: Score Point 1
Part B: Score Point 0
Annotations
Anchor Paper 8
Part A: Score Point 1
This response receives partial credit. The response includes one of the two required
elements:
•
The response provides a correct explanation to justify the claim (percent of increase
between 1998 and 2000 = 4.9%; percent of increase between 2011 and 2013 = 5%;
The student is right because the percentages are about the same).
The work or explanation to determine the percent increases is missing.
Part B: Score Point 0
This response receives no credit. The response includes none of the two required elements.
The explanation justifying the newspaper’s claim is incorrect (the newspapers claim was
incorrect because the graph shows that the price would be 4.069 dollars).
The percent error of the prediction is missing.
A9
Part A: Score Point 0
Part B: Score Point 1
Annotations
Anchor Paper 9
Part A: Score Point 0
This response receives no credit. The response includes none of the two required elements.
The work to determine the percent increases is incomplete (1.354 – 1.291 = 0.063, 4.069 –
3.874 = 0.195).
Complete work would also show dividing the differences by the initial value for the time
period.
The explanation to justify the claim is incorrect (the students claim is wrong the difference is
different. from january 1998 . . . to March2013).
Part B: Score Point 1
This response receives partial credit. The response includes one of the two required
elements:
•
The response provides work justifying that the newspaper’s claim is correct
− 4.069
0.031
= 4.104.069
= 4.069
× 100 ).
( Difference
Original
The work provided is clear and should have produced the correct percent error of the
prediction (0.8%), which would justify the newspapers claim.
The percent error of the prediction is incorrect (3.1%).
The response does not provide a determination about the newspapers claim.
A10
Part A: Score Point 0
Part B: Score Point 0
Annotations
Anchor Paper 10
Part A: Score Point 0
This response receives no credit. The response includes none of the two required elements.
The work to determine the percent increases is incorrect (1.291 ÷ 1998 =.000646 = .0007. .
. 4.069 ÷ 2013 =.002021 = .002). Dividing the average price per gallon by the year is an
incorrect process to determine the percent increases.
The explanation to justify the claim is incorrect (The average is the same if you round it to
the nearest tenths).
Part B: Score Point 0
This response receives no credit. The response includes none of the two required elements.
The explanation justifying the newspaper’s claim is incorrect (4.10 ÷ 2% = 205, There wrong
because when you divide 4.10 ÷ 2% it equals 205).
The percent error of the prediction is missing.
A11
Part A: Score Point 0
Part B: Score Point 0
Annotations
Anchor Paper 11
Part A: Score Point 0
This response receives no credit. The response includes none of the two required elements.
The work to determine the percent increases is missing.
The explanation to justify the claim is incorrect (these percents are similar because 2011 to
2013 is .0487 percent and 1998 to 2000 it is .0503 percent). Although the numerical values
are correct, the student converts the decimals incorrectly to percentages. The percentages
provided are less than 1%.
Part B: Score Point 0
This response receives no credit. The response includes none of the two required elements.
The explanation justifying the newspaper’s claim is incorrect (it was of by about 3 percent).
The percent error of the prediction is incorrect (about 3 percent).
Practice Set
P101 - P105
P101
P102
P103
P104
P105
Practice Set
Paper
Score
P101
0,0
P102
2,1
P103
2,0
P104
1,1
P105
2,0