“Classifying Solutions”
Name
SCUSD Math Common Core
Date
Question 1
Fill in the boxes to complete the equation so it has no solutions.
8x  3x  2  x 
x
Explain why you chose the numbers in your equation above.
Question 2
Fill in the boxes to complete the equation so it has one solution.
8x  3x  2  x 
x
Explain why you chose the numbers in your equation above.
Question 3
Fill in the boxes to complete the equation so it has infinitely many solutions.
8x  3x  2  x 
x
Explain why you chose the numbers in your equation above.
Period
Scoring Rubric
“Classifying Solutions”
SCUSD Math Common Core:
Question 1 Sample Top-Score Response:
8x  3x  2  x  4 x  5
4x  2  4 x  5 gives this equation no solutions. I knew that if I made 4x the same on both sides of the equation, then I
could make the constants on each side different numbers, and that would make an equation that is never true. I chose 5 as
my constant because I needed it to be a number other than 2. There is no solution for x that makes this equation true
because when solving the equation (i.e. subtract 4x from both sides), you end up with 2 = 5, which is never true. This
means that there are no values for x that will work in this equation.
Question 1 Scoring Rubric:
Responses to this item should receive 0 – 2 points, based on the following:
2 points: The student shows a thorough understanding of a linear equation with no solutions. The student gives
acceptable values for the missing coefficients and provides correct and complete explanations for why those values
result in creating an equation with no solutions.
1 point: The student shows a partial understanding of a linear equation with no solutions. The student may have
correctly filled in the boxes of the equation, but did not give a thorough explanation of the numbers he or she chose. Or
the student may have given clear and logical explanations for choosing the numbers to complete the equation, but
made some minor computational errors.
0 points: The student shows inconsistent or no understanding of a linear equation with no solutions.
Question 2 Sample Top Score Response:
8x  3x  2  x  2 x  1
4x  2  2 x  3 gives one solution of x 
1
. I knew that I needed a coefficient for x other than 4, because otherwise the
2
x’s would cancel out and the equation would result in either no solutions or infinite solutions. So I made the first term 2x
and the constant 1. I chose 1 as the constant because 1 is an easy number to work with. I solved the equation, to make
sure that it had only one solution, and I got x = ½. This is the only value for x that will make this equation true, so this
equation only has one solution.
Question 2 Scoring Rubric:
Responses to this item should receive 0 – 2 points, based on the following:
2 points: The student shows a thorough understanding of a linear equation with one solution. The student gives
acceptable values for the missing coefficients and provides correct and complete explanations for why those values
result in creating an equation with one solution.
1 point: The student shows a partial understanding of a linear equation with one solution. The student may have
correctly filled in the boxes of the equation, but did not give a thorough explanation of the numbers he or she chose. Or
the student may have given clear and logical explanations for choosing the numbers to complete the equation, but
made some minor computational errors.
0 points: The student shows inconsistent or no understanding of a linear equation with one solution.
Question 3 Sample Top Score Response:
8x  3x  2  x  4 x  2
4x  2  4x  2 gives this equation infinitely many solutions. I knew that if I made 4x the same on both sides of the
equation, then I could make the constants on each side the same numbers, so I would be left with an equation that is
always true. When solving the equation (i.e. subtract 4x from both sides), you end up with 2 = 2, which is always true, and
will result in infinite solutions. This means that any value of x could be substituted in this equation and it will always
produce a true statement.
Question 3 Scoring Rubric:
Responses to this item should receive 0 – 2 points, based on the following:
2 points: The student shows a thorough understanding of a linear equation with infinitely many solutions. The student
gives acceptable values for the missing coefficients and provides correct and complete explanations for why those
values result in creating an equation with infinitely many solutions.
1 point: The student shows a partial understanding of a linear equation with infinitely many solutions. The student may
have correctly filled in the boxes of the equation, but did not give a thorough explanation of the numbers he or she
chose. Or the student may have given clear and logical explanations for choosing the numbers to complete the
equation, but made some minor computational errors.
0 points: The student shows inconsistent or no understanding of a linear equation with infinitely many solutions.