Look at the equation below.
x - 17.32 = 28.7

Step A

Solve the equation for x.

Step B

Explain why your value for x is correct. Use what you know about solving equations in your explanation. Use words, numbers, and/or symbols.

Step A is scored 0 (Incorrect) or 1 (Correct) and assesses 1.B.2.b.
Step B is scored with a 3 point (0, 1, 2) rubric and assesses Processes of Mathematics.

Note: Sixteen "Sample Student Responses" follow below. Each response appears on its own separate page and includes scoring information. The "Sample Student Responses" represent a range of score points.

Score for Sample Student Response #1:

Annotation for Step B, Using the Rubric: This response is completely incorrect.

Score for Sample Student Response #2:

Annotation for Step B, Using the Rubric: This response is completely incorrect. The justification given does not support the answer for Step A.

Score for Sample Student Response #3:

Annotation for Step B, Using the Rubric: This response demonstrates a minimal understanding and analysis of the problem. A partial application of a strategy to justify the incorrect solution of x=11.42 is indicated; however, the justification is logically flawed as the sum of 11.42 and 17.32 is 28.74, not 28.7 as indicated in the response.

Score for Sample Student Response #4:

Annotation for Step B, Using the Rubric: This response demonstrates a minimal understanding and analysis of the problem. A partial application of a strategy to justify the incorrect solution of x=11.38 is indicated. The justification reveals a logical flaw in that 17.32 should have been added to 28.7, not subtracted from it.

Score for Sample Student Response #5:

Annotation for Step B, Using the Rubric: This response demonstrates a minimal understanding and analysis of the problem. An application of a reasonable strategy to solve for x is indicated. The explanation, "28.70+17.32=46.02'" is a partially developed justification for the mathematical process used to solve the problem.

Score for Sample Student Response #6:

Annotation for Step B, Using the Rubric: This response demonstrates a complete understanding and analysis of the problem. An application of a reasonable strategy for solving and justifying the equation is indicated. The justification for the solution is clear: "45-17=28 and .39-.32=.7." The error in computing with the decimals 0.32 and 0.7 is consistent throughout the problem. This error does not detract from the complete understanding of the mathematical process used to solve the problem.

Score for Sample Student Response #7:

Annotation for Step B, Using the Rubric: This response demonstrates a complete understanding and analysis of the problem. An application of a reasonable strategy for solving and justifying the problem is indicated. The justification for the solution is clear, developed, and logical. Appropriate supportive numbers are provided as all work is shown.

Score for Sample Student Response #8:

Annotation for Step B, Using the Rubric: This response demonstrates a complete understanding and analysis of the problem. An application of a reasonable strategy for solving and justifying the problem is indicated. The justification for the problem is clear, developed, and logical: "I subtracted 17.32 from [46.02] the difference was 28.7." Appropriate numeric support is provided.

Score for Sample Student Response #9:

Annotation for Step B, Using the Rubric: This response demonstrates a minimal understanding and analysis of the problem. An application of a reasonable strategy to solve for x is indicated. The explanation, "I... was adding 28.7+17.32, and I got 46.02," is a partially developed justification for the mathematical process used to solve the problem. Compare to Sample Student Response #5.

Score for Sample Student Response #10:

Annotation for Step B, Using the Rubric: This response demonstrates a complete understanding and analysis of the problem. An application of a reasonable strategy for solving and justifying the problem is indicated. The justification for the solution is clear, developed, and logical. Appropriate supportive numbers are provided as all work is shown. Compare to Sample Student Response #7.

Score for Sample Student Response #11:

Annotation for Step B, Using the Rubric: This response demonstrates a minimal understanding and analysis of the problem. A partial application of a strategy to justify the incorrect solution of x=20.19 is indicated. However, the justification is logically flawed as no decimals are used in the process of solving the problem. Compare to Sample Student Response #3.

Score for Sample Student Response #12:

Annotation for Step B, Using the Rubric: This response is completely incorrect. Compare to Sample Student Response #1.

Score for Sample Student Response #13:

Annotation for Step B, Using the Rubric: This response demonstrates a complete understanding and analysis of the problem. An application of a reasonable strategy for solving and justifying the equation is indicated. The justification for the solution is clear: "If you do 45.39 - 17.32 you will get 28.7." The error in subtracting, "0.39-0.32=.7" is consistent throughout the problem. This error does not detract from the complete understanding of the mathematical process used to solve the problem. Compare to Sample Student Response #6.

Score for Sample Student Response #14:

Annotation for Step B, Using the Rubric: This response is completely irrelevant to the answer given in Step A. Compare to Sample Student Response #2.

Score for Sample Student Response #15:

Annotation for Step B, Using the Rubric: This response demonstrates a complete understanding and analysis of the problem. An application of a reasonable strategy for solving and justifying the problem is indicated. The justification for the problem is clear, developed, and logical: "To check you answer put 46.02 for x... and if it equals 28.7 your answer is correct." Appropriate numeric support is provided. Compare to Sample Student Response #8.

Score for Sample Student Response #16:

Annotation for Step B, Using the Rubric: This response demonstrates a minimal understanding and analysis of the problem. A strategy for solving the equation for x is indicated. The explanation for the process used to solve the problem is overly general: "I added the decimals together." This provides a partial justification for the process used to solve the problem. Supportive information and/or numbers are not provided to justify the solution in Step A. Compare to Sample Student Response #4.

Score 2

The response demonstrates a complete understanding and analysis of a problem.

• Application of a reasonable strategy in the context of the problem is indicated.
• Explanation¹ of and/or justification² for the mathematical process(es) used to solve a problem is clear, developed, and logical.
• Connections and/or extensions made within mathematics or outside of mathematics are clear.
• Supportive information and/or numbers are provided as appropriate. ³

Score 1

The response demonstrates a minimal understanding and analysis of a problem.

• Partial application of a strategy in the context of the problem is indicated.
• Explanation¹ of and/or justification² for the mathematical process(es) used to solve a problem is partially developed, logically flawed, or missing.
• Connections and/or extensions made within mathematics or outside of mathematics are partial or overly general, or flawed.
• Supportive information and/or numbers may or may not be provided as appropriate.³

Score 0

The response is completely incorrect, irrelevant to the problem, or missing.⁴

Note 1:

Explanation refers to students' ability to communicate how they arrived at the solution for an item using the language of mathematics.

Note 2:

Justification refers to students' ability to support the reasoning used to solve a problem, or to demonstrate why the solution is correct using mathematical concepts and principles.

Note 3:

Students need to complete rubric criteria for explanation, justification, connections and/or extensions as cued for in a given problem.

Note 4:

Merely an exact copy or paraphrase of the problem will receive a score of "0".

Rubric Document Date: August 2003