Math
Spring Operational 2015
Geometry
PBA Item #11
King-Sized Mattress
VF800122
Prompt
Rubric
VF800122 Rubric Part A
Score Description
1
Student response includes the following element.
• Modeling component = 1 point
o Defining the variable and setting up the equation
Sample Student Response:
queen-sized mattress
, where w is the width of the
OR
, where w is the width of the queen-sized mattress
Notes:
The variable must be defined or the point cannot be
awarded.
o Student should receive credit for any valid model written
in terms of length.
o The student can use one equation for the area of the
king-sized mattress, such as
, as long
as the variable is defined.
0
Student response is incorrect or irrelevant.
VF800122 Rubric Part B
Score Description
2
Student response includes the following 2 elements.
• Computation component = 1 point
o
o Correctly solves the equation and provides valid work
•
Note: The student can earn points for Part B if the
student correctly solves an incorrect equation from Part
A.
Modeling component = 1 point
o Reporting the results
Sample Student Response:
The width of the queen-sized mattress is 60 inches. The length is
found by adding 20 inches, which gives 80 inches. Queen-sized: 60
in. x 80 in.
1
0
The length of the king-sized mattress is the same as the queen-sized
mattress (80 inches). The width is found by adding 16 inches, which
gives 76 inches. King-sized: 76 in. x 80 in.
Student response includes 1 of the 2 elements.
Student response is incorrect or irrelevant.
Anchor Set
A1 – A8
A1
Part A: Score Point 1
Part B: Score Point 2
Annotations
Anchor Paper 1
Part A: Score Point 1
This response receives full credit. The student includes the required element:
•
Modeling component 1: The student sets up a correct equation and defines each
variable (w(w+20)+1280=(w+16)(w+20) Where w is the width of the queen sized
mattress).
Part B: Score Point 2
This response receives full credit. The student includes both of the required elements:
•
Computation component: The student correctly solves for the width of the queen-sized
mattress (w(w+20)+1280=(w+16)(w+20), w²+20w+1280=w²+36w+320, 960=16w,
w=60).
•
Modeling component 2: The student provides the dimensions of the king-sized and
queen-sized mattresses, including the units (the queen sized mattress would be 60
inches by 80 inches and the king sized mattress would be 76 inches by 80 inches).
A2
Part A: Score Point 1
Part B: Score Point 2
Annotations
Anchor Paper 2
Part A: Score Point 1
This response receives full credit. The student includes the required element:
•
Modeling component 1: The student sets up a correct equation (1,280÷16=80). This
equation is equivalent to the alternate equation presented in the rubric
(16(w+20) = 1,280), but it is written in terms of length: 80 [the length] is shown as
the quotient rather than [w+20] [the width of the queen-sized mattress + 20 is the
length]. Per the rubric’s second Note, the student will receive credit for a valid model
that is written in terms of length.
Part B: Score Point 2
This response receives full credit. The student includes both of the required elements:
•
Computation component: The student correctly solves for the width of the queen-sized
mattress in the answer space for Part A (1,280÷16=80 . . . 80–20=60). The student
first calculates the length of the mattresses, then subtracts 20 to find the width of the
queen-sized mattress. Note that a scoring decision exists that any part of previous
work shown in a response can be used to score subsequent parts of the item; e.g., if
the response shows a correct answer for Part B in Part A, credit can be given.
•
Modeling component 2: The student provides the dimensions of the king-sized and
queen-sized mattresses, including the units (L=Length, W=Width [in the answer space
for Part A], L of queen=80in, W of queen=60in, L of king=80in, Width of king=76in).
A3
Part A: Score Point 1
Part B: Score Point 1
Annotations
Anchor Paper 3
Part A: Score Point 1
This response receives full credit. The student includes the required element:
•
Modeling component 1: The student sets up a correct equation and defines each
variable (A=x²+36x+320, A is area, x is width of queen sized mattress). While all of
the variables must be defined [including A], the equation is equivalent to the one
presented in the rubric’s third Note [A = (w+16)(w+20)].
Part B: Score Point 1
This response receives partial credit because it loses a precision point.
•
Computation component: The student correctly solves for the width of the queen-sized
mattress (x²+36x+320–(x²+20x)=1280, 16x+320=1280, 16x=960, x=60). The
student subtracts the expression for the area of a queen-sized mattress (x²+20x)
from the expression for the area of a king-sized mattress (x²+36x+320) to equal the
difference in area presented in the item (1,280).
Modeling component 2 does not receive credit because it loses a precision point. Although the
student includes the correct dimensions (Queen mattress is . . . 60 and 80 . . . king mattress
is . . . 76 and 80), the units are not provided. A scoring decision exists that if units are not
labeled in a given response and the response would have received the top score with correct
labeling, a score point will be deducted.
A4
Part A: Score Point 0
Part B: Score Point 2
Annotations
Anchor Paper 4
Part A: Score Point 0
This response receives no credit. The student does not include the required element.
Modeling component 1 does not receive credit. Although the equation provided is correct, the
variable x is not defined. To receive credit, all the variables must be defined.
Part B: Score Point 2
This response receives full credit. The student includes both of the required elements:
•
Computation component: The student correctly solves for the width of the queen-sized
mattress in the answer space for Part A (1280+(x+20)(x)=(x+16)(x+20),
1280+x²+20x=x²+20x+16x+320, 1280+x²+20x=x²+36x+320, 960=16x, x=60).
•
Modeling component 2: The student provides the dimensions of the king-sized and
queen-sized mattresses, including the units (Queen . . . 80in,60in, King . . .
80in,76in).
A5
Part A: Score Point: 1
Part B: Score Point 0
Annotations
Anchor Paper 5
Part A: Score Point 1
This response receives full credit. The student includes the required element:
Modeling component 1: The student sets up a correct equation and defines each variable
(x=width of queen matress, a=area of queen matress (a=x(x+20)),
(x+20)×(x+16)=a+1280).
Part B: Score Point 0
This response receives no credit. The student includes none of the required elements.
The Computation component does not receive credit because no work is shown to solve for
the width of the queen-sized mattress.
Modeling component 2 does not receive credit because the dimensions of the king-sized and
queen-sized mattresses are not provided. The response includes the areas rather than the
dimensions (queen matress=4800in², king matress=6080in²).
A6
Part A: Score Point 0
Part B: Score Point 1
Annotations
Anchor Paper 6
Part A: Score Point 0
This response receives no credit. The student does not include the required element.
Modeling component 1 does not receive credit. Although an equation is presented (80 ×
76=6080), it is not equivalent to any of the acceptable equations presented in the rubric.
Part B: Score Point 1
This response receives partial credit. The student includes one of the two required elements:
•
Modeling component 2: The student provides the dimensions of the king-sized and
queen-sized mattresses, including the units (Queen: 80” by 60”, King: 80” by 76”).
Note: that the marks after the numbers (”) indicate inches. Work is not required for
Modeling component 2.
The Computation component does not receive credit because no work is shown to solve for
the width of the queen-sized mattress.
A7
Part A: Score Point 0
Part B: Score Point 0
Annotations
Anchor Paper 7
Part A: Score Point 0
This response receives no credit. The student does not include the required element.
Modeling component 1 does not receive credit because the equation is incorrect
(1280=(16+w)(20+w)). Also, the variable used in the equation is inadequately defined
(w=width). It does not specify which size mattress’s width it represents. The definition for
the width variable must specify the mattress size because the mattresses are different
widths. Either one of these errors [an incorrect equation or an inadequately defined variable]
will prevent Modeling component 1 from receiving credit.
Part B: Score Point 0
This response receives no credit. The student includes none of the required elements.
The Computation component does not receive credit because there is an error in the work
(1280=36+w should be 1280=320+36w+w²).
Modeling component 2 does not receive credit because, although the dimensions provided
(w=1254 inches, l=1274 inches) would be appropriate for a queen-sized mattress based on
the width shown (w=1254 inches), they are not identified as the dimensions of a queensized mattress. Also, the appropriate dimensions of a king-sized mattress are not provided.
Either one of these errors [not specifying the mattress size to which the dimensions belong
or not including the dimensions for both mattress sizes] will prevent Modeling component 2
from receiving credit.
A8
Part A:Score Point 0
Part B:Score Point 0
Annotations
Anchor Paper 8
Part A: Score Point 0
This response receives no credit. The student does not include the required element.
Modeling component 1 does not receive credit. The response shows an expression, not an
equation (x²+36x+320). The expression is not set equal to anything, so it is not an
equation. Also, the variable is inadequately defined (x stands for the width). It does not
specify which size mattress’s width it represents. The definition for the width variable must
specify the mattress size because the mattresses are different widths.
Part B: Score Point 0
This response receives no credit. The student includes none of the required elements.
The Computation component does not receive credit because no work is shown to solve for
the width of the queen-sized mattress.
Modeling component 2 does not receive credit because the actual dimensions of the kingsized and queen-sized mattresses are not provided. The response includes expressions and
variables rather than final dimensions in inches (queen sized length is x+20, the width is x.
king sized length is x+20 and the width is x+16).
Practice Set
P101 - P105
P101
P102
P103
P104
P105
Practice Set
Paper
Score
P101
0,2
P102
1,0
P103
0,0
P104
1,1
P105
0,1