Math
Spring Operational 2015
Grade 5
PBA Item #11
Use Common Denominator
M01285
Prompt
Rubric
Task is worth a total of 3 points.
M01285 Rubric
Score Description
3
Student response includes each of the following 3 elements.
• Reasoning component = 2 points
o Identification of Leah’s mistake
o Correct work shown for adding 2 + 1 + 5
3
•
2
12
Computation component = 1 point
o Correct value of 2 + 1 + 5 , 19 or equivalent
3
2
12
12
Sample Student Response:
Leah used the wrong numerators. To add fractions with different
denominators, you have to find the common denominator. Then you
convert each fraction to an equivalent fraction using the common
denominator. Then you add the numerators together and put the
result as the numerator.
2
1
0
2 + 1 + 5
3
2
12
8
6
=
+
+ 5
12
12
12
8
+
6
+
5
=
12
19
=
12
Student response includes 2 of the 3 elements.
Student response includes 1 of the 3 elements.
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 provides an identification of Leah’s mistake by explaining the
methodology to be used (Leah needed to multiply the numerator by the same number
as the denominator).
•
The student finds the correct value of
( 19
12
•
=1
7
12
2 1 5
+ +
3 2 12
).
The correct work is shown by converting the given fractions to the equivalent
fractions, with the common denominator 12, and adding them.
8
6
5
).
( 12
+
+
12 12
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 student provides an identification of Leah’s mistake explaining that Leah did not
multiply the numerator (she did not multiply the numerator). The explanation by itself
would be inadequate as it does not clarify that the numerators should multiplied by
the same number the denominator is multiplied with in order to get to the common
denominator. However, it is deemed complete because the supporting work shows the
equivalent fractions.
•
The student finds the correct value of
7
( 19
).
=1
12
12
•
2 1 5
+ +
3 2 12
The student shows the correct work by converting the given fractions to the
equivalent fractions with the common denominator 12 and adding them.
8
6
5
)
( 12
+
+
12 12
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 student correctly identifies Leah’s mistake (she didn’t multiply the same number
that she multiplied to the bottom number. She kept the numerator the same).
•
The student finds the correct value of
7
( 1 12
)
The work to find the answer is not shown.
2 1 5
+ +
3 2 12
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 student finds the correct value of
7
( 19 . . . 19 ÷ 12 = 1 12
).
2 1 5
+ +
3 2 12
12
The student shows the correct work by converting the given fractions to the equivalent
fractions, with the common denominator 12, and adding them
8
6
5
+
+
)
( 12
12 12
Leah’s mistake is not identified correctly. The explanation is incorrect (he didnt change the
denominator). The item shows that Leah did change all the denominators to the common
denominator 12, but made an error by not multiplying the numerators by the same number.
The student explanation would need to correctly identify the error made to receive credit.
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 student finds the correct value of
2 1 5
+ +
3 2 12
7
( 1 12
).
Leah’s mistake is not identified correctly. The explanation (she forgot to multiply the
numerator too) is inadequate as it does not clarify that the each numerator should be
multiplied by the same number as each denominator in order to get equivalent fractions with
a common denominator. The work is not shown or explained. The response shows the given
fractions but does not find the equivalent fractions.
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 student finds the correct value of
2 1 5
+ +
3 2 12
7
( 1 12
).
The student does not correctly identify Leah’s mistake. The explanation (she did not change
the numerators but just the denominators) is inadequate as it does not clarify that the
numerators should be multiplied by the same number the denominator is multiplied with in
order to get the common denominator. The work is not shown or explained.
A7
Score Point 0
Annotations
Anchor Paper 7
Score Point 0
This response receives no credit. The student includes none of the three required elements:
Leah’s mistake is not identified correctly. The explanation (she added wrong) is vague and
does not identify the error made. The value of
2 1 5
+ +
3 2 12
8
is incorrect ( 17
). Even though the
explanation (you add the noumerator and denamenator) is appropriate for the answer, it is
incorrect methodology for the given task.
A8
Score Point 0
Annotations
Anchor Paper 8
Score Point 0
This response receives no credit. The student includes none of the three required elements:
The student does not correctly identify Leah’s mistake. The explanation (she added the
numerators wrong) is vague and is not supported by any work shown. The value of
2 1 5
+ +
3 2 12
is not found. The student does not show work or explanation to find the answer.
Practice Set
P101 - P105
P101
P102
P103
P104
P105
Practice Set
Paper
Score
P101
2
P102
0
P103
3
P104
1
P105
2