Math
Fall Block 2015
Algebra 1
PBA Item#11
Rug
VF886999
Prompt
Task is worth a total of 6 points.
VF886999 Rubric Part A
Score Description
2
Student response includes the following 2 elements.
 Modeling component = 2 points
o Valid equation for width of the rug
o Valid explanation for the equation
Sample Student Response:
w(w + 4) = 21, where w is the width of rug
The area of the rug is A = lw, which is 21 square feet. The
length is l = w + 4. Replacing l with w + 4 and A with 21 gives
the equation w(w + 4) = 21.
1
0
Student response includes 1 of the 2 elements.
Student response is incorrect or irrelevant.
VF886999 Rubric Part B
Score Description
4
Student response includes the following 4 elements.
 Modeling component = 3 points
o Determination of the original length and width of the rug
o Implementation of the 1.5 feet border into the calculation
o Work to determine the new area

Computation component = 1 point
o Correct computation based on work
3
2
1
0
Sample Student Response:
w2 + 4w −21 = 0
(w + 7)(w − 3) = 0
w + 7 = 0 OR w − 3 = 0
w = –7 OR w = 3
Since width cannot be negative, the width is 3 feet. So, the
length is 7 feet.
The 1.5 foot border would add 3 feet to each dimension.
A = (3 + 3)(7 + 3)
A = (6)(10)
A = 60
60 square feet
Note: A student can earn full credit for the modeling component in
Part B without explicitly stating the width and length of the rug if the
reasoning is mathematically appropriate.
Student response includes 3 of the 4 elements.
Student response includes 2 of the 4 elements.
Student response includes 1 of the 4 elements.
Student response is incorrect or irrelevant.
Anchor Set
A1 – A14
A1
Part A: Score Point 2
Part B: Score Point 4
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 a valid equation for determining the area of the original rug
( 21  ( x  4)  x ). Since this response does not use variables l for length and w for width,
all variables are defined (width = x).
The response explains or shows how the equation is determined (To get the area of a
rectangle you must multiply the length times the width).
Part B: Score Point 4
This response receives full credit. The student includes each of the four required elements.




The response correctly determines the original length and width of the rug (X must
equal 3 because 32 + 4(3) = 21, so width = 3 and length = 7).
The response correctly implements 1.5 feet into the calculation (Add 1.5 to each side
of the rug which adds 3 ft to both length and width).
The response shows work on determining the new area (The new width is 6 and the
new length is 10, 10 x 6 = 60).
The response computes the new area correctly (60 square feet).
A2
Part A: Score Point 2
Part B: Score Point 4
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 a valid equation for determining the area of the original rug
((w)(w + 4) = 21).
The response explains or shows how the equation is determined (The width (w) times
the length (w+4) equals the total area).
Part B: Score Point 4
This response receives full credit. The student includes each of the four required elements.




The response correctly determines the original length and width of the rug
(w = 3, l = 7).
The response correctly implements 1.5 feet into the calculation by using 1.5 twice in
each dimension ((3 + 3) (7 + 3) = area).
The response shows work on determining the new area (6 x 10 = 60).
The response computes the new area correctly (60 square feet).
A3
Part A: Score Point 1
Part B: Score Point 4
Annotations
Anchor Paper 3
Part A: Score Point 1
This response receives partial credit. The student includes one of the two required elements.

The response provides a valid equation for determining the area of the original rug
( 21  x 2  4x ).
The response shows no attempt to explain or show how the equation for the original rug is
determined and includes an undefined variable.
Part B: Score Point 4
This response receives full credit. The student includes each of the four required elements.




The response correctly determines the original length and width of the rug (7 x 3).
The response correctly implements 1.5 feet into the calculation by using 1.5 twice in
each dimension ((7 + (1.5 x 2))(3 + (1.5 x 2)).
The response shows work on determining the new area ((10)(6)).
The response computes the new area correctly (60 square feet).
A4
Part A: Score Point 1
Part B: Score Point 4
Annotations
Anchor Paper 4
Part A: Score Point 1
This response receives partial credit. The student includes one of the two required elements.

The response provides a valid equation for determining the area of the original rug
(21 = (w + 4) x w).
The response shows an insufficient attempt to explain or show how the equation is
determined (w + 4 represents the length). The response does not explain how to calculate
area; it does not include an equation stating that A = l × w.
Part B: Score Point 4
This response receives full credit. The student includes each of the four required elements.




The response correctly determines the original length and width of the rug (length
which is 7 feet. The width of the rug is 3 feet). A scoring decision was made that any
part of previous work shown in the response could be used to score the subsequent
parts of the item. For example, if the response shows a correct answer for Part B in
Part A, credit can be given. In this response, the length and width values are found in
Part A and are used for credit in Part B.
The response correctly implements 1.5 feet into the calculation
(7 + 1.5 + 1.5 = 10, 3 + 1.5 + 1.5 =6, the new measurements must include 1.5
twice).
The response shows work on determining the new area (when you multiply length
times width). The student also shows previous calculations to determine 10 and 6,
which holistically supports his or her work.
The response computes the new area correctly (60).
A5
Part A: Score Point 2
Part B: Score Point 2
Annotations
Anchor Paper 5
Part A: Score Point 2
This response receives full credit. The student includes each of the two required elements.


The response provides a valid equation for determining the area of the original rug
(21 = (4 + w)(w)).
The response explains or shows how the equation is determined (The equation for
area is A = lw).
Part B: Score Point 2
This response receives partial credit. The student includes two of the four required elements.
The response shows incorrect original length and width of the rug (w = 7, l = 11).
The response incorrectly implements 1.5 feet into the calculation. The 1.5 is only added once
to each side instead of twice. However, these incorrect values are used correctly in the final
two elements based on the scoring decision described in A4:


The response shows work on determining the new area. The response shows correctly
multiplying the length times the width (12.5(8.5)).
The response computes the new area correctly (106.25) using the incorrect values for
length (12.5) and width (8.5). A scoring decision was made that if an incorrect
answer from a previous part of a response lost credit and was used in the next part,
the response in the next part could receive full credit for that part. In this response,
the values for original length and width lose credit in the first element of Part B. In
the second element for Part B, the response incorrectly implements 1.5 feet into the
calculation and does not receive credit. The new incorrect length and width are used
correctly to determine the new area and receive credit for elements 3 and 4.
A6
Part A: Score Point 1
Part B: Score Point 3
Annotations
Anchor Paper 6
Part A: Score Point 1
This response receives partial credit. The student includes one of the two required elements.

The response shows a valid equation for determining the area of the original rug
( 21  x  ( x  4) ).
The response shows an insufficient attempt to explain or show how the equation is
determined (3 × 7 = 21 and 3 is 4 less than 7 which is the length). The response does not
define the variable used (x) in the equations and does not include an equation stating that A
= l × w.
Part B: Score Point 3
This response receives partial credit. The student includes three of the four required
elements.

The response correctly shows the original length and width of the rug (3 is 4 less than
7 which is the length) in Part A and receives credit here, as described in A4.
The response incorrectly implements 1.5 feet into the calculation. The 1.5 is only added once
to each side instead of twice. However, the response shows these incorrect values (8.5, 4.5)
used correctly in the final two elements.


The response shows work on determining the new area correctly multiplying the
incorrect length and width (4.5 × 8.5 = 38.25). The response shows the use of these
incorrect values from a prior part for elements 3 and 4, as described in response A6.
The response correctly computes the new area (38.25) based on incorrect values
from element 2.
A7
Part A: Score Point 1
Part B: Score Point 2
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 shows a valid equation for determining the area of the original rug
( ( x  4)x  21 ).
The response shows no attempt to explain or show how the equation for the original rug is
determined.
Part B: Score Point 2
This response receives partial credit. The student includes two of the four required elements.

The response correctly determines the original length and width of the rug (3, 7).
While these values are not labeled, the response determines the new area using
them, and so it is acceptable.
The response incorrectly implements 1.5 feet into the calculation. The 1.5 is only added once
to each side of the rug instead of twice.
The response shows no work to determine the new area.

The response correctly computes the new area (38.25) based on the incorrect length
(8.5) and width (4.5) from element 2.
A8
Part A: Score Point 1
Part B: Score Point 2
Annotations
Anchor Paper 8
Part A: Score Point 1
This response receives partial credit. The student includes one of the two required elements.

The response shows a valid equation for determining the area of the original rug
( (4  x )( x )  21 ). Although variables l and w are not used, the variable that is used (x) is
defined (‘x’ would equal the width of the rug).
The response shows no attempt to explain or show how the equation for the original rug is
determined.
Part B: Score Point 2
This response receives partial credit. The student includes two of the four required elements.
The response shows no attempt to determine the original length and width of the rug.


The response correctly implements 1.5 feet into the calculation. The response shows
3 added to each side of the rug in the original equation ((3 + 4 + x)(x + 3)).
The response shows work on determining the new area ((3 + 4 + x)(x + 3) = ).
The response does not compute the new area.
A9
Part A: Score Point 0
Part B: Score Point 2
Annotation
Anchor Paper 9
Part A: Score Point 0
This response receives no credit. The student includes none of the two required elements.
The response shows an incorrect equation for determining the area of the original rug
(A = 21 x 25).
The response shows no attempt to explain or show how the equation for the original rug is
determined.
Part B: Score Point 2
This response receives partial credit. The student includes two of the four required elements.
The response shows incorrect original length and width of the rug (21, 25).
The response incorrectly implements 1.5 feet into the calculation. The 1.5 is only added once
to each side of the rug instead of twice (21 + 1.5 = 22.5, 25 + 1.5 = 26.5).


The response shows correct work on determining the new area using the incorrect
length and width shown in element 2 (A = 22.5 x 26.5) similar to A6.
Based on the incorrect values for length and width from element 2, the response
shows a correct computation of the new area (596.25).
A10
Part A: Score Point 1
Part B: Score Point 1
Annotations
Anchor Paper 10
Part A: Score Point 1
This response receives partial credit. The student includes one of the two required elements.

The response shows a valid equation for determining the area of the original rug
( 21  ( x )  ( x  4) ). Although variables l and w are not used, the variable that is used (x)
is defined (x is the width, x
4 is the length).
The response shows an insufficient attempt to explain or show how the equation is
determined (x is the width, x + 4 is the length). The response does not include an equation
stating that A = l × w.
Part B: Score Point 1
This response receives partial credit. The student includes one of the four required elements.
The response shows no attempt to determine the original length and width of the rug.
The response shows an incorrect implementation of 1.5 feet into the calculation. The 1.5 is
only added once to each side of the rug instead of twice ( ( x  1.5 )  ( x  4  1.5 ) ).

The response shows correct work to determine the new area based on the incorrect
values of length and width from element 2 (= ( x  1.5 )  ( x  4  1.5 ) ).
The response shows the new area incorrectly computed.
A11
Part A: Score Point 0
Part B: Score Point 1
Annotations
Anchor Paper 11
Part A: Score Point 0
This response receives no credit. The student includes none of the two required elements.
The response shows an incorrect attempt to explain or show a valid equation for determining
the area of the original rug (7 x 3 = 21). Simply plugging in numbers that make the equality
true is not a valid equation.
The response shows no attempt to explain or show how the equation for the original rug is
determined.
Part B: Score Point 1
This response receives partial credit. The student includes one of the four required elements.

The response shows correctly determining the original length and width of the rug
(3, 7). While these values are not labeled, they are used in Part A to make the
equality true, so they are acceptable.
The response shows incorrectly implementing 1.5 feet into the calculation. Each side of the
equation is shown to be multiplied by 1.5.
The response shows no attempt to show work to determine or calculate the new area.
The response incorrectly computes the new area.
A12
Part A: Score Point 1
Part B: Score Point 0
Annotations
Anchor Paper 12
Part A: Score Point 1
This response receives partial credit. The student includes one of the two required elements.

The response shows a valid equation for determining the area of the original rug
((w + 4)w = 21).
The response incorrectly attempts to explain or show how the equation for the original rug is
determined (figure out the length in the first equation and then you put that answer into the
2nd equation).
Part B: Score Point 0
This response receives no credit. The student includes none of the four required elements.
The response shows no determination of the original length and width of the rug. The
response incorrectly implements 1.5 feet into the calculation. The 1.5 is multiplied by 4 and
added to the original area. Also, the response does not correctly show work to determine or
calculate the new area.
A13
Part A: Score Point 0
Part B: Score Point 0
Annotations
Anchor Paper 13
Part A: Score Point 0
This response receives no credit. The student includes none of the two required elements.
The response shows an incorrect equation for determining the area of the original rug
= 4 + w(w)) because (4 + w) is not in parentheses [(4 + w)(w)].
(21
The response shows an insufficient attempt to explain or show how the equation is
determined (a = 4 + w(w)). The response does not include an equation stating that
A = l × w.
Part B: Score Point 0
This response receives no credit. The student includes none of the four required elements.
The response shows no attempt to determine the original length and width of the rug. The
attempt to implement 1.5 feet into the calculation shown incorrectly replaces w with 1.5
(A = 4 + 1.5 x 1.5). Also, the response does not correctly show work to determine or
calculate the new area.
A14
Part A: Score Point 0
Part B: Score Point 0
Annotations
Anchor Paper 14
Part A: Score Point 0
This response receives no credit. The student includes none of the two required elements.
The response shows no valid equation for determining the area of the original rug
(21 = 7 x 3). Simply plugging in numbers that make the equality true is not a valid
equation.
The response shows an insufficient attempt to explain or show how the equation was
determined (7 is bigger than 3 by 4). The response does not include an equation stating A =
l × w.
Part B: Score Point 0
This response receives no credit. The student includes none of the four required elements.
The response shows an incorrect attempt to determine the original length and width of the
rug. Although the length and width are correct in Part A, incorrect values are used in Part B,
so the response receives no credit. The response shows an incorrect attempt to implement
1.5 feet into the calculation (7 x 1.5 = 10.5, 4 x 1.5 = 6). Also, the response shows an
incorrect attempt to explain or show work to determine or calculate the new area by adding
the four sides instead of multiplying length by width (10.5 + 10.5 + 6 + 6 = 33).
Practice Set
P101 - P105
P101
P102
P103
P104
P105
Practice Set
Paper
Score
P101
0,3
P102
1,0
P103
1,3
P104
0,4
P105
1,0