Math
Released Item 2015
Grade 7
PBA Item #16
Incorrect Square
VH030360
Task is worth a total of 4 points.
VH030360 Rubric Part A
Score
2
Description
Student response includes the following 2 elements.
•
Computation component = 1 point
o
•
Correct computation, numerical support, or graphical support
that is consistent with the student’s reasoning
Reasoning component = 1 point
o
Correctly reasons that the lengths of the sides of the
quadrilateral JKLM are not all the same, so it cannot be a
square
Sample Student Response:
In a square, the lengths of all four sides are the same. If
quadrilateral JKLM is a square, all four of its side lengths would be the
same. Since the y-coordinates are the same in points J and K, the side
length of JK is the positive difference between the x-coordinates of each
point. So, JK = |-4.5 – (-1.2)| = |-4.5 + 1.2| = |-3.3| = 3.3 units.
Similarly, the side length of KL is the positive difference between the ycoordinates of each point. So, KL = |3 – 8.7| = |-5.7| = 5.7 units. The
lengths of two sides of the quadrilateral are not equal, so
quadrilateral JKLM is not a square.
1
Notes:
o The student may still receive credit for this part if the student
chooses to compute or compare side lengths without using absolute
values.
o The student may receive a total of 1 point for Part A if the reasoning
processes are correct but the student makes one or more
computational errors resulting in incorrect answers or an incorrect
conclusion.
o Student may receive the 1 computation point if the correct answer is
computed but shows no work or insufficient work to indicate a
correct reasoning process.
Student response includes 1 of the 2 elements.
0
Student response is incorrect or irrelevant.
VH030360 Rubric Part B
Score
2
Description
Student response includes the following 2 elements.
o
Computation component = 1 point
o
o
Correct new coordinates for points L and M
Reasoning component = 1 point
o
Correctly reasons why the two new coordinates of points L
and M must would make quadrilateral JKLM a square
Note: Numerical or graphical support that is consistent with the
student’s reasoning is acceptable for full credit.
Sample Student Response:
The given coordinates form a rectangle with sides JK and LM both 3.3
units and sides KL and JM both 5.7 units. If the coordinates of
points L and M change so that quadrilateral JKLM is a square, they
should be lowered on the coordinate plane 5.7 – 3.3, or 2.4 units. This
will change sides KL and JM from 5.7 units to 3.3 units, making the
resulting quadrilateral a square. Lowering points on a coordinate plane
changes their y-coordinates. So, the new coordinates of point L would
be (-1.2, 6.3) since 8.7 – 2.4, or 6.3. The new coordinates of point M
would be (-4.5, 6.3) since 8.7 – 2.4, or 6.3 units.
Notes:
o
1
The student should receive credit for this part if the student
chooses new coordinates for points L and M that are below
points J and K, as long as the student shows or explains that the
side lengths of all four sides are the same length.
o The student may receive a total of 1 point for Part B if the
reasoning processes are correct but the student makes one or more
computational errors resulting in incorrect answers or an incorrect
conclusion.
o The student may receive the 1 computation point if the correct
answer is computed but shows no work or insufficient work to
indicate a correct reasoning process.
Student response includes 1 of the 2 elements.
0
Student response is incorrect or irrelevant.
Anchor Set
A1 – A10
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 student includes each of the two required elements:
•
The response provides correct reasoning that quadrilateral JKLM cannot be a square
(because a square must have sides of equal length . . . these sides are not of equal
length).
•
The response provides numeric support that is consistent with the reasoning (The
quadrilateral JKLM is 5.7 units by 3.3 units).
Part B: Score Point 2
This response receives full credit. The student includes each of the two required elements:
•
The response provides two new coordinates for points L and M (…point L will be
(-1.2,6.3) . . .point M will be (-4.5,6.3)).
•
The response provides correct reasoning for why the new coordinates of points L and
M would make quadrilateral JKLM a square (each side of the square must be 3.3 units
long . . . This made point M exactly 3.3 units away from point J…).
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 student includes each of the two required elements:
•
The response provides correct reasoning that quadrilateral JKLM cannot be a square
(the figure is a rectangle, not a square).
•
The response provides a graphical support that is consistent with the reasoning.
Part B: Score Point 2
This response receives full credit. The student includes each of the two required elements:
•
The response provides two new coordinates for points L and M (New points: L:
(-1.2,6.3) M: (-4.5,6.3)).
•
The response provides correct reasoning why the new coordinates of points L and M
would make quadrilateral JKLM a square (Step #1 find distance between J and K 4.5 –
1.2 = 3.3 Step #2 find distance between L and K 8.7 – 3.0; 4.5 step #3 subtract the
two numbers 5.7 – 3.3; 2.4 step #4 subtract from 8.7, 8.7 – 2.4; 6.3).
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 student includes each of the two required elements:
•
The response provides correct reasoning that quadrilateral JKLM cannot be a square
(The points are not evenly spased out to make a square).
•
The response provides graphical support that is consistent with the reasoning.
Part B: Score Point 1
This response receives partial credit. The student includes one of the two required elements:
•
The response provides correct reasoning why the new coordinates of points L and M
would make quadrilateral JKLM a square.
The response does not provide two new coordinates for points L and M (L to (1.2,7) and
coordinate M to (4.5,7)).
A4
Part A: Score Point 1
Part B: Score Point 2
Annotations
Anchor Paper 4
Part A: Score Point 1
This response receives partial credit. The student includes one of the two required elements:
•
The student provides correct reasoning that quadrilateral JKLM cannot be a square (a
square has to be even on all sides).
The response does not provide support that is consistent with the reasoning.
Part B: Score Point 2
This response receives full credit. The student includes each of the two required elements:
•
The response provides two new coordinates for points L and M (L (-1.2,6.3) M
(-4.5,6.3)).
•
The response provides correct reasoning why the new coordinates of points L and M
would make quadrilateral JKLM a square (it makes the distance between all sides
equal. Because -1.2 and -4.5 are |3.3| away, the y values should also be |3.3| away
from the other y values of 3).
A5
Part A: Score Point 1
Part B: Score Point 1
Annotations
Anchor Paper 5
Part A: Score Point 1
This response receives partial credit. The student includes one of the two required elements:
•
The response provides correct reasoning why quadrilateral JKLM cannot be a square
(because the quadrilaterl is a rectangle, because 2 sides are longer than the others).
The response does not provide support that is consistent with the reasoning.
Part B: Score Point 1
This response receives partial credit. The student includes one of the two required elements:
•
The response provides correct reasoning why the new coordinates of points L and M
would make quadrilateral JKLM a square. (you would have to move L am M down).
The response does not provide two new coordinates for points L and M.
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 student includes each of the two required elements:
•
The response provides correct reasoning that quadrilateral JKLM cannot be a square
(the sides are uneven and made a rectangle).
•
The response provides support that is consistent with the reasoning (i drew a graph
and put the points on it and K to L made a longer side than J to K).
Part B: Score Point 0
This response receives no credit. The student includes none of the required elements:
The response does not provide two new coordinates for points L and M (L on point (-1.5,6)
And M on point (-4.5,6)).
The response does not provide correct reasoning why the new coordinates of points L and M
would make quadrilateral JKLM a square.
A7
Part A: Score Point 1
Part B: Score Point 0
Annotations
Anchor Paper 7
Part A: Score Point 1
This response receives partial credit. The student includes one of the two required elements:
•
The response provides correct reasoning that quadrilateral JKLM cannot be a square
(the coordinates that she made make a rectangle).
The response does not provide support that is consistent with the reasoning.
Part B: Score Point 0
This response receives no credit. The student includes none of the required elements:
The response does not provide two new coordinates for points L and M.
The response does not provide correct reasoning for why the new coordinates of points L and
M would make quadrilateral JKLM a square (draw a graph with positive and negative axis.
then plot the points . . . Lastly connect the lines).
A8
Part A: Score Point 0
Part B: Score Point 1
Annotations
Anchor Paper 8
Part A: Score Point 0
This response receives no credit. The student includes none of the required elements:
The response does not provide a correct reasoning that quadrilateral JKLM cannot be a
square (has to have all 4 right angels to make a square but she dosent have all of them).
The response does not provide support that is consistent with the reasoning.
Part B: Score Point 1
This response receives partial credit. The student includes one of the two required elements:
•
The response provides the new coordinates for points L and M ((-1.2,6.3) (-4.5,6.3)).
The response does not provide a correct reasoning for why the new coordinates of points L
and M would make quadrilateral JKLM a square.
A9
Part A: Score Point 0
Part B: Score Point 0
Annotations
Anchor Paper 9
Part A: Score Point 0
This response receives no credit. The student includes none of the required elements:
The response does not provide correct reasoning that quadrilateral JKLM cannot be a square
(if it was a square all the cooudinates would be the same).
The response does not provide support that is consistent with the reasoning.
Part B: Score Point 0
This response receives no credit. The student includes none of the required elements:
The response does not provide two new coordinates for points L and M (Point L would be 4.5, 3 and point M will be -1.2,3).
The response does not provide correct reasoning for why the new coordinates of points L and
M would make quadrilateral JKLM a square.
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 student includes none of the required elements:
The response does not provide correct reasoning that quadrilateral JKLM cannot be a square
(because negative numbers can’t make up a square).
The response does not provide support that is consistent with the reasoning.
Part B: Score Point 0
This response receives no credit. The student includes none of the required elements:
The response does not provide two new coordinates for points L and M.
The response does not provide correct reasoning for why the new coordinates of points L and
M would make quadrilateral JKLM a square (You could change L from -1.2 to a positive 1.2.
And you cando the same as well for M -4.5 to a positive 4.5).
Practice Set
P101 - P105
P101
P102
P103
P104
P105
Practice Set
Paper
Score
P101
1,0
P102
2,2
P103
2,1
P104
1,1
P105
0,2