Math
Spring Operational 2015
Grade 8
PBA Item #12
Explain Solutions Conclusion
VF525935
Prompt
Task is worth a total of 3 points.
VF525935 Rubric
Score
3
Description
Student response includes the following 3 elements.

Computation component = 1 point
o

Correct conclusion about the equation with an appropriate
explanation of why the conclusion is valid
Reasoning component = 2 points
o
Correctly uses the distributive property to simplify both sides
of the equation
o
Correctly combines like terms, resulting in a false equation in
which the variable has been eliminated and two non-equal
numbers appear on opposite sides of the equal sign
Sample Student Response:
-2(11-12x) = -4(1-6x)
-22+24x = -4 +24x
Subtracting 24x from each side
-22+24x -24x = -4 +24x -24x
-22 = -4
This is impossible, since -22 is not equal to -4. Therefore, there is
no
solution to the equation.
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 conclusion about the equation (This is No Solution) with
an appropriate explanation (because -22 cannot or will never be able to equal to -4).

The distributive property is used correctly to simplify both sides of the equation (-22 +
24x = -4 + 24x).

The response correctly combines like terms, which results in two non-equal terms on
 22  24x  4  24x 


 24x
 24x  .


 22  4


opposite sides of the equal sign 
There are various ways to combine like terms that are acceptable.
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 conclusion about the equation (there is no solution) with
an appropriate explanation (-18 does not equal 0).

The distributive property is used correctly to simplify both sides of the equation (-22 +
24x = -4 + 24x).

The response correctly combines like terms, which results in two non-equal terms on
opposite sides of the equal sign (-22+24x=-4+24x, -18+24x=24x, -18 = 0).
There are various ways to combine like terms that are acceptable.
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 distributive property is used correctly to simplify both sides of the equation (-22 +
24x = -4 + 24x).

The response correctly combines like terms, which results in two non-equal terms on
opposite sides of the equal sign (subtract 24x – 24x = 0, -22 = -4) [indicating subtraction
of 24x from both sides].
The response provides an incorrect conclusion about the equation (the equation has infinitely
many solutions).
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 distributive property is used correctly to simplify both sides of the equation (-22 +
24x = -4 + 24x).

The response correctly combines like terms, which results in two non-equal terms on
 22  24x  4  24x 


 24x
 24x  .


 22  4


opposite sides of the equal sign 
Although the response provides a correct conclusion about the equation (No Solution), it
lacks an explanation to support the conclusion. Both a correct conclusion and an appropriate
explanation are required to receive credit for this element.
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 distributive property is used correctly to simplify both sides of the equation (-22 +
24x = -4 + 24x).
Although the response provides a correct conclusion about the equation (no solution) it lacks
an explanation to support the conclusion. Both a correct conclusion and an appropriate
explanation are required to receive credit for this element.
The response does not combine like terms.
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 distributive property is used correctly to simplify both sides of the equation (-22 +
24x = -4 + 24x).
The conclusion about the equation is missing.
The response combines like terms incorrectly (x = 18). It should be [0 = 18].
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 conclusion about the equation is incorrect (Infinite solutions there is only one equation).
The work showing the distributive property used to simplify both sides of the equation is
incorrect ((-22 -24x) = -4(1-6x), (-22-2x) = (-4 -24)).
The response does not combine like terms.
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.
Although the response provides a correct conclusion about the equation (no solution), the
explanation (you can’t plug any number in that will give the same answer for both) is too
vague to receive credit.
The work using the distributive property is missing.
The work combining like terms is missing.
Practice Set
P101 - P105
P101
P102
P103
P104
P105
Practice Set
Paper
Score
P101
1
P102
0
P103
3
P104
1
P105
2