Math
Spring Operational 2015
Algebra 2
PBA Item #15
Constraints on Calories and Fat
VF641201
Prompt
Rubric
Task is worth a total of 3 points.
VF641201 Rubric Part A
Score
1
Description
Student response includes the following element.
•
Computation component = 1 point
o
Machine scored
Sample Student Response:
0
Student response is incorrect or irrelevant.
VF641201 Rubric Part B
Score
2
Description
Student response includes the following 2 elements.
•
Modeling component = 2 points
o
o
Identifying the two points
Interpreting and explaining the meaning of the two points
Sample Student Response:
The point (2, 2) satisfies the constraints, and (3, 3) does not satisfy
the constraints. The point (2, 2) represents eating 2 hot dogs and 2
hamburgers. This satisfies both constraints, so it is a possibility for
Enrique. The point (3, 3) represents eating 3 hot dogs and 3
hamburgers. This satisfies neither constraint, so it is not a possibility
for Enrique. He could eat 2 hamburgers and 2 hotdogs and still be
under 1200 calories and 60 grams of fat, but if he ate 3 of each he
would exceed his weekly calorie and fat intake.
Note: The information in Part B can be scored independently of Part A
if the response does not specifically reference the graph in Part A.
However, any response in Part B that does specifically use the graph
in Part A for support or justification must be correct based on the
graph to receive credit. If the student graphs the line incorrectly but
interprets the meaning in a way that is consistent with the incorrect
graph, this point can still be earned.
1
Note: There are a variety of points that would work as long as they are
justified. Non-integer coordinates are acceptable.
Student response includes 1 of the 2 elements.
0
Student response is incorrect or irrelevant.
Anchor Set
A1 – A6
A1
Part B: Score Point 2
Annotations
Anchor Paper 1
Part B: Score Point 2
This response receives full credit. The student includes each of the two required elements.
•
Two points are correctly identified (point that satisfys the constraints (2,1)) and (point
that does not satisfy the constraints (6,3)).
•
The two points are correctly interpreted (The x coordinate is the amount of hotdogs
Enrique can eat, and the y coordinate is the amount of hamburgers Enrique can eat; 2
hotdogs and 1 hambuger; 6 hotdogs and 3 hamburgers) and the meaning is correctly
explained (he meets his requirents of eating less than 1200 calories and 60 grams of
fat; he does not meet his requirements).
Notice that just defining the x-coordinate as the number of hot dogs and the y-coordinate as
the number of hamburgers is sufficient by itself for interpretation, as it applies to each
ordered pair.
A2
Part B: Score Point 2
Annotations
Anchor Paper 2
Part B: Score Point 2
This response receives full credit. The student includes each of the two required elements.
•
Two points are correctly identified ((1,1) satisfies the constraints) and ((4,4) does
not).
•
The two points are correctly interpreted (Enrique could eat one hamburger and one
hot dog; if he ate 4 of each) and the meaning is correctly explained (still be under
1200 calories and 60grams of fat; he would exceed his weekly calorie and fat intake).
Notice that the response does not need to specify 4 hot dogs and 4 hamburgers; it is
sufficient to state that Enrique may eat 4 of each, provided it agrees with the point
given.
A3
Part B: Score Point 1
Annotations
Anchor Paper 3
Part B: Score Point 1
This response receives partial credit. The student includes one of the two required elements.
•
Two points are correctly identified ((2.5,2) He can eat at most) and ((3,3) He cannot
eat . . . as that would put him over his limits).
The two points are correctly interpreted (two and a half hot dogs and two hamburgers; three
of both) but the meaning is incomplete (He can eat at most; that would put him over his
limits). Neither explanation adequately explains why these points meet or do not meet the
constraints and are considered vague.
A4
Part B: Score Point 1
Annotations
Anchor Paper 4
Part B: Score Point 1
This response receives partial credit. The student includes one of the two required elements.
•
Two points are correctly identified ((2,2) satisfies the constraints) and ((4,2) does not
satisfy the constraints).
Only one point is correctly interpreted (two hot dogs and two hamburgers) but the meaning
for both points is correctly explained (still be under his limit; he would over his limit of
calories and fat intake). The second point is incorrectly interpreted (4 hot dogs and 3
hamburgers); two hamburgers would be correct.
A5
Part B: Score Point 0
Annotations
Anchor Paper 5
Part B: Score Point 0
This response receives no credit. The student includes neither of the two required elements.
Neither of the two points has been identified. The numbers of hot dogs and hamburgers given
are not in ordered pairs and so are considered to be interpretation and not identification of
two points.
Two points are interpreted (4 hamburgers . . . and 5 hot dogs; 6 hamburgers . . . 3.75
hotdogs) but the explanation of the meaning is incorrect (without going over 1200 calories . .
. without going over the fat limit). The numbers of hot dogs and hamburgers indicate two
points that each satisfy only one, not both, of the constraints.
A6
Part B: Score Point 0
Annotations
Anchor Paper 6
Part B: Score Point 0
This response receives no credit. The student includes neither of the two required elements.
Only one point has been correctly identified ((0.5,0.5) satisfies the constraints). Both points
are required to receive credit.
The interpretation of the two points is missing and only the meaning of one point is correctly
explained (it is under the limit of his calorie and fat intake). Both points must be interpreted
and the meaning explained to receive credit.
Practice Set
P101 - P105
P101
P102
P103
P104
P105
Practice Set
Paper
Score
P101
2
P102
1
P103
0
P104
2
P105
1