Math
Released Item 2016
Algebra 1
System of Inequalities
VF648815
Prompt
Rubric
Task is worth a total of 3 points.
VF648815 Rubric Part A
Score Description
1
Student response includes the following element.
•
Computation component = 1 point
o Correct System of Equations
Sample Student Response:
0
Student response is incorrect or irrelevant.
VF648815 Rubric Part B
Score Description
2
Student response includes the following 2 elements.
•
Reasoning component = 2 points
o Valid reasoning about why all points in the first quadrant
have coordinates that satisfy
o Valid reasoning about why all points in the first quadrant
have coordinates that satisfy
Sample Student Response:
All points (x,y) in quadrant I have a positive x-coordinate and a
is satisfied. Because all
positive y-coordinate. Therefore
points (x,y) in quadrant I have a positive x-coordinate and a
positive y-coordinate, the sum of x and y must also be positive. If
is greater than 0, then
must be greater than -2, and
is satisfied.
Note: The response does not have to include the identification
(x,y); referring to the x- and y-coordinates in general is
enough. To earn the second point, the student must make the
connection that anything greater than 0 is also greater than -2.
It is ok if the student uses a specific example; such as showing
the point (2,3) meets both conditions. However, if only a
specific point is used and the student never refers to all points
in general, award at most 1 point for reasoning.
1
Student response includes 1 of the 2 elements.
0
Student response is incorrect or irrelevant.
Anchor Set
A1 – A8
With Annotations
A1
Part A: Score Point 1
Part B: Score Point 2
Annotation
Anchor Paper 1
Part A: Score Point 1
This response receives full credit. The student includes the required element.
•
The response includes the correct system of inequalities (y > 0, x + y >
-2)
Part B: Score Point 2
This response receives full credit. The student includes both of the two
required elements.
•
•
The response satisfies condition one that the y coordinate is positive
(the first quadrant is when both the y and the x values are positive.
Every Y value in the in the first quadrant is greater than 0).
The response satisfies condition two that the sum of the coordinates is
greater than -2 (the first quadrant is when both the y and the x values
are positive. . . and every x + y will be greater than 0. 0 is greater
than -2).
The description identifies both coordinate points, the y coordinate and x
coordinate, as positive numbers and states that adding them is greater than
the negative number. This is the minimal amount of specificity to earn credit
for condition two in Part B.
A2
Part A: Score Point 1
Part B: Score Point 2
Annotation
Anchor Paper 2
Part A: Score Point 1
This response receives full credit. The student includes the required element.
•
The response includes the correct system of inequalities (y > 0, x + y >
-2)
Part B: Score Point 2
This response receives full credit. The student includes both of the two
required elements.
•
•
The response satisfies condition one that the y coordinate is positive
(The only numbers that are greater than 0 are positive numbers, which
means the y coordinate is above the x axis).
The response satisfies condition two that the sum of the coordinates is
greater than -2 (A positive number + a positive number is greater than
the negative number, which means the x coordinate can be a positive
number too. A point with both coordinate points positive is in Quadrant
1.)
The description identifies both coordinate points, the y coordinate and x
coordinate, as positive numbers and states that adding them is greater than
the negative number. This is the minimal amount of specificity to earn credit
for condition two in Part B.
A3
Part A: Score Point 1
Part B: Score Point 1
Annotation
Anchor Paper 3
Part A: Score Point 1
This response receives full credit. The student includes the required element.
•
The response includes the correct system of inequalities (y > -x-2, y >
0).
y > -x-2 is an equivalent inequality to x+y > -2.
Part B: Score Point 1
This response receives partial credit. The student includes one of the two
required elements.
•
The response satisfies condition one that the y coordinate is positive
(points in the first quadrant are all positives … any positive number is
… greater than 0).
The response does not satisfy condition two, that the sum of the coordinates
is greater than –2. While the description says positive values are greater
than -2, which is true, there is no mention of adding the coordinates
together; therefore, no credit is earned for condition two. There is also no
specific mention that the coordinates are positive – only that the points are
all positives.
A4
Part A: Score Point 1
Part B: Score Point 1
Annotation
Anchor Paper 4
Part A: Score Point 1
This response receives full credit. The student includes the required element.
•
The response includes the correct system of inequalities (x+y>-2,
y>0).
Part B: Score Point 1
This response receives partial credit. The student includes one of the two
required elements.
•
The response satisfies condition one that the y coordinate is positive (y
is anything greater than 0).
The response does not satisfy condition two, that the sum of the coordinates
is greater than -2. The description fails to note that the x-coordinate is
positive in quadrant I. Therefore, no credit is earned for condition two.
A5
Part A: Score Point 1
Part B: Score Point 0
Annotation
Anchor Paper 5
Part A: Score Point 1
This response receives full credit. The student includes the required element.
•
The response includes the correct system of inequalities (y>0, y+x>2).
Part B: Score Point 0
This response receives no credit. The student includes neither of the
required elements.
The response does not satisfy condition one, that the y coordinate is positive,
or condition two, that the sum of the coordinates is greater than -2. The
description the student provides is a repeat of information given in the
prompt. It addresses neither the quadrant I condition nor the greater than –2
condition.
A6
Part A: Score Point 0
Part B: Score Point 1
Annotation
Anchor Paper 6
Part A: Score Point 0
The response receives no credit. The student does not include the required
element.
The response does not provide the correct inequalities.
Part B: Score Point 1
This response receives partial credit. The student includes one of the two
required elements.
•
The response satisfies condition one that the y coordinate is positive
(Quadrant 1 contains positive, positive coordinates).
The response does not satisfy condition two, that the sum of the coordinates
is greater than –2. The description fails to make the connection that x+y>0;
therefore, no credit is earned for condition two.
A7
Part A: Score Point 0
Part B: Score Point 0
Annotation
Anchor Paper 7
Part A: Score Point 0
The response receives no credit. The student does not include the required
element.
The response does not provide the correct inequalities.
Part B: Score Point 0
This response receives no credit. The student includes neither of the
required elements.
•
The response does not satisfy condition one that the y coordinate is
positive (none of the numbers in quadrant 1 are negative). The answer
does not account for 0, which is not a negative number, but is also not
in Quadrant I.
The response makes no attempt to respond to the elements associated with
condition two.
A8
Part A: Score Point 0
Part B: Score Point 0
Annotation
Anchor Paper 8
Part A: Score Point 0
The response receives no credit. The student does not include the required
element.
The response does not provide the correct inequalities.
Part B: Score Point 0
This response receives no credit. The student includes neither of the
required elements.
The response does not satisfy condition one, that the y coordinate is positive
or condition two, that the sum of the coordinates is greater than -2. The
description is a repeat of information in the prompt.
Practice Set
P101 - P105
No Annotations Included
P101
P102
P103
P104
P105
Practice Set
Paper
Score
P101
0,1
P102
0,0
P103
1,1
P104
1,1
P105
0,1