Math
Released Item 2016
Grade 5
Cheese for Tacos
VH049385
Prompt
Rubric
Task is worth a total of 4 points.
Cheese for Tacos – Part A
Score Description
Student response includes the following 2 elements.
•
•
2
Reasoning component = 1 point
o The student writes a multiplication equation that can be
used to solve the problem.
Reasoning component = 1 point
o The student writes a division equation that can be used
to solve the problem.
Sample Student Response:
c×4 =
1
8
1
÷4 = c
8
Notes:
•
•
A variety of equations are possible. As long as the student uses
a correct multiplication equation, credit should be given.
A variety of equations are possible. As long as the student uses
a correct division equation, credit should be given.
1
Student response includes 1 of the above elements.
0
Student response is incorrect or irrelevant.
Cheese for Tacos – Part B
Score
Description
Student response includes the following 2 elements.
•
•
2
Reasoning component = 1 point
o The student uses the relationship between
multiplication and division to explain why both
equations work to solve the problem.
Computation component = 1 point
1
o The student provides the response of
32
Sample Student Response:
“Both equations work because multiplication and division are
opposites. The dividend of a division problem is the same as the
1
1
product of its related multiplication problem. So, if ÷ 4 =
, then
8
32
1
1
×4 = . “
8
32
Notes:
•
•
•
A variety of explanations are valid. As long as the student uses
the relationship between multiplication and division to explain
why both equations work, credit should be given.
If a computation mistake is made, credit cannot be given for
computation, but credit should be given for a valid explanation
of the relationship between multiplication and division.
It is not necessary to use terms such as inverse relationship,
dividend, product, quotient, factor, etc. as long as it is clear the
student understands the concept.
1
Student response includes 1 of the above elements.
0
Student response is incorrect or irrelevant.
Anchor Set
A1 – A10
With Annotations
A1
Part A: Score Point 2
Part B: Score Point 2
Annotation
Anchor Paper 1
Part A: Score Point 2
This response receives full credit. It includes each of the two required
elements:
•
•
A multiplication equation that can be used to solve the problem is
1
provided (4 × c = 8).
A division equation that can be used to solve the problem is provided
1
(8 ÷ 4 = c).
Part B: Score Point 2
This response receives full credit. It includes each of the two required
elements:
•
The relationship between multiplication and division is used to explain
why both equations work to solve the problem (The reason that both
equations result in the same value for c is that multiplication and
division are inverse operations).
•
Correct computation is provided (32).
1
A2
Part A: Score Point 2
Part B: Score Point 2
Annotation
Anchor Paper 2
Part A: Score Point 2
This response receives full credit. It includes each of the two required
elements:
•
•
A multiplication equation that can be used to solve the problem is
1
provided (c × 4 = 8).
A division equation that can be used to solve the problem is provided
1
(8 ÷ 4 = c).
Part B: Score Point 2
This response receives full credit. It includes each of the two required
elements:
•
The relationship between multiplication and division is used to explain
why both equations work to solve the problem (multiplication and
division are opposite operations).
•
Correct computation is provided (32).
1
A3
Part A: Score Point 2
Part B: Score Point 1
Annotation
Anchor Paper 3
Part A: Score Point 2
This response receives full credit. It includes each of the two required
elements:
•
•
A multiplication equation that can be used to solve the problem is
1
provided (4 × c = 8).
A division equation that can be used to solve the problem is provided
1
(8 ÷ 4 = c).
Part B: Score Point 1
This response receives partial credit. It includes one of the two required
elements:
•
The relationship between multiplication and division is used to explain
why both equations work to solve the problem (Both equations result in
the same value for c because you are using use inverse operations,
which undo each other).
The computation is not provided.
A4
Part A: Score Point 2
Part B: Score Point 1
Annotation
Anchor Paper 4
Part A: Score Point 2
This response receives full credit. It includes each of the two required
elements:
•
•
A multiplication equation that can be used to solve the problem is
1
1
provided (8 × 4 = c).
A division equation that can be used to solve the problem is provided
1
(8 ÷ 4 = c).
Part B: Score Point 1
This response receives partial credit. It includes one of the two required
elements:
•
1
Correct computation is provided (32).
The explanation for why both equations work to solve the problem is
1
1
1
incorrect (8 ÷ 4 and 8 × 4 are the same because when you divide fractions
you have to switch the numerator and denominator). This does not explain
the relationship between multiplication and division and how the relationship
is used to explain why both equations result in the same answer.
A5
Part A: Score Point 2
Part B: Score Point 0
Annotation
Anchor Paper 5
Part A: Score Point 2
This response receives full credit. It includes each of the two required
elements:
•
•
A multiplication equation that can be used to solve the problem is
1
provided (c × 4 = 8).
A division equation that can be used to solve the problem is provided
1
(8 ÷ 4 = c).
Part B: Score Point 0
This response receives no credit. It includes none of the two required
elements:
The explanation for why both equations work to solve the problem is
1
incorrect (Both equations result the same for c which is 36 because c is equal
to how much cheese is on a taco and there is 4 tacos so c multiplyed by 4
1
1
1
would get you 8 also if there is 8 pound of cheese for all four tacos than 8
divided by 4 equals c). The explanation describes how c is used in the
equations but does not explain the relationship between multiplication and
division and how the relationship is used to explain why both equations result
in the same answer.
1
The computation is incorrect (36).
A6
Part A: Score Point 1
Part B: Score Point 1
Annotation
Anchor Paper 6
Part A: Score Point 1
This response receives partial credit. It includes one of the two required
elements:
•
A division equation that can be used to solve the problem is provided
1
(8 ÷ 4 = c).
The multiplication equation that can be used to solve the problem is incorrect
1
(8 × c = 4).
Part B: Score Point 1
This response receives partial credit. It includes one of the two required
elements:
•
1
Correct computation is provided (32).
The explanation for why both equations work to solve the problem is
incorrect (Both equations result in the same value of c because they both
represent the problem that involes c).
A7
Part A: Score Point 0
Part B: Score Point 1
Annotation
Anchor Paper 7
Part A: Score Point 0
This response receives no credit. It includes none of the two required
elements:
The multiplication equation that can be used to solve the problem is incorrect
1
(8 × 4 = c).
The division equation that can be used to solve the problem is incorrect
1
(c ÷ 4 = 8).
Part B: Score Point 1
This response receives partial credit. It includes one of the two required
elements:
•
The relationship between multiplication and division is used to explain
why both equations work to solve the problem (Both equations result in
the same value because multiplication and division are reversible
meaning they undo each other).
4
The computation is incorrect (32).
A8
Part A: Score Point 0
Part B: Score Point 1
Annotation
Anchor Paper 8
Part A: Score Point 0
This response receives no credit. It includes none of the two required
elements:
The multiplication equation that can be used to solve the problem is incorrect
1
4
(8 × 4 =8 ).
The division equation that can be used to solve the problem is incorrect
4
1
(8 ÷ 4 = 8).
Part B: Score Point 1
This response receives partial credit. It includes one of the two required
elements:
•
The relationship between multiplication and division is used to explain
why both equations work to solve the problem (Both equations have
the same value for c because multiplication and division are opposites).
The computation is not provided.
A9
Part A: Score Point 0
Part B: Score Point 0
Annotation
Anchor Paper 9
Part A: Score Point 0
This response receives no credit. It includes none of the two required
elements:
The multiplication equation that can be used to solve the problem is incorrect
1
4
4
(8 times 4 equals 32).
The division equation that can be used to solve the problem is incorrect
4
4
1
(32 divided by 4 equals 8).
Part B: Score Point 0
This response receives no credit. It includes none of the two required
elements:
The explanation for why both equations work to solve the problem is
incorrect (Both equations worked because it had a number in the number
model that ended up being the answer).
4
The computation is incorrect (32).
A10
Part A: Score Point 0
Part B: Score Point 0
Annotation
Anchor Paper 10
Part A: Score Point 0
This response receives no credit. It includes none of the two required
elements:
The multiplication equation that can be used to solve the problem is incorrect
1
(8 × 4 = c).
The division equation that can be used to solve the problem is incorrect
(4 ÷ 8 = c).
Part B: Score Point 0
This response receives no credit. It includes none of the two required
elements:
The explanation for why both equations work to solve the problem is
incorrect (The c replaces the pounds of cheese Mason uses for each of his
tacos).
The computation is not provided.
Practice Set
P101 - P105
No Annotations Included
P101
P102
P103
P104
P105
Practice Set
Paper
Score
P101
2,2
P102
1,1
P103
2,1
P104
1,0
P105
2,2