Math
Spring Operational 2015
Grade 7
PBA Item #12
Cost of Lunch
M560696
Prompt
Matt and his friends paid $30 for 4 sandwiches and 4 bottles of water.
• The bottles of water cost $2 each.
• Each sandwich cost the same amount.
The equation 4(x + 2) = 30 can be used to determine x, the cost of each
sandwich.
Matt solved the equation using the following steps:
4(x + 2) = 30
4x + 2 = 30
4x = 28
X=7
Therefore, Matt calculates the cost of each sandwich as $7. Did Matt solve the
equation correctly?
• If he did, justify each step of Matt's solution using mathematical properties.
• If he did not, describe any error Matt made in his calculation and determine
the price of each sandwich. Justify each step you used to come to your
conclusion.
Task is worth a total of 3 points.
VF560696 Rubric
Score
3
Description
Student response includes the following 3 elements.

Computation component = 1 point
o

Correctly determines that each sandwich costs $5.50
Reasoning component = 2 points
o
Correctly describes the error Matt made when he solved the
equation
o
Shows the corrected steps for solving the equation
Sample Student Response
“Matt did not correctly use the distributive property when he
simplified 4(x + 2) and changed it to 4x + 2. Both the x and the 2
should be multiplied by 4, so he should have written 4x + 8.”
4(x +2) = 30
4x + 8 = 30
4x = 22
x = 5.50
Notes:
o The student must describe the error made and fix the error in order
to receive full reasoning credit.
o If the student only describes the error made or fixes the error
without describing it, student will receive at most 1 reasoning point.
2
Student response includes 2 of the 3 elements.
1
Student response includes 1 of the 3 elements.
0
Student response is incorrect or irrelevant.
Anchor Set
A1 – A8
A1
Score Point 3
Annotations
Anchor Paper 1
Score Point 3
This response receives full credit. The student includes each of the three required elements.

The response provides a correct description of the error that Matt made when he
solved the equation (he forgot to distribute his four to the two).

The response provides the corrected steps for solving the equation (4x + 4(2) = 30
Distribute both x and 2 to the 4, 4x + 8 = 30 Subtract 8 from both sides, 44x  22
4
Divide 4 by both sides, x = $5.50).

The response provides the correct cost of each sandwich ($5.50).
A2
Score Point 3
Annotations
Anchor Paper 2
Score Point 3
This response receives full credit. The student includes each of the three required elements.

The response provides a correct description of the error that Matt made when he solved
the equation (Matt only multiplied 4·x and not 4·2 to).

The response provides the corrected steps for solving the equation (4x+8=30, 44x 
x = 5.5).

The response provides the correct cost of each sandwich (5.5).
22
4
,
A3
Score Point 2
Annotations
Anchor Paper 3
Score Point 2
This response receives partial credit. The student includes two of the three required
elements.

The response provides the corrected steps for solving the equation ($2 (bottles of
water) x 4 = $8, $30 ─ $8 = $22, $22 ÷ 4 = $5.50).

The response provides the correct cost of each sandwich ($5.50).
The response does not provide a correct description of the error Matt made when he solved
the equation.
A4
Score Point 2
Annotations
Anchor Paper 4
Score Point 2
This response receives partial credit. The student includes two of the three required
elements.

The response provides a correct description of the error that Matt made when he
solved the equation (He forgot to multiply 4 times 2).

The response provides the correct cost of each sandwich ($5.50).
The response does not provide the corrected steps for solving the equation.
A5
Score Point 1 Annotations
Anchor Paper 5
Score Point 1
This response receives partial credit. The student includes one of the three required
elements.

The response provides a correct cost of each sandwich ($5.50).
The response does not provide the correct description of the error Matt made when he
solved the equation.
The response does not provide the corrected steps for solving the equation.
A6
Score Point 1
Annotations
Anchor Paper 6
Score Point 1
This response receives partial credit. The student includes one of the three required
elements.

The response provides a correct description of the error that Matt made when he
solved the equation (He didn’t do the ditsributive property with the 2).
The response does not provide the corrected steps for solving the equation.
The response does not provide the correct cost of each sandwich.
A7
Score Point 0
Annotations
Anchor Paper 7
Score Point 0
This response receives no credit. The student includes none of the three required elements.
The response does not provide a correct description of the error that Matt made when he
solved the equation (matt should have did x+2 then is would be 2x).
The response does not provide the corrected steps for solving the equation.
The response does not provide the correct cost of each sandwich.
A8
Score Point 0
Annotations
Anchor Paper 8
Score Point 0
This response receives no credit. The student includes none of the three required elements.
The response does not provide a correct description of the error that Matt made when he
solved the equation (Matt did solve the equation correctly).
The response does not provide the corrected steps for solving the equation.
The response does not provide the correct cost of each sandwich.
Practice Set
P101 - P105
P101
P102
P103
P104
P105
Practice Set
Paper
P101
1
P102
1
P103
1
P104
1
P105
1
Score