Look at the expression below.

90 - 48 ÷ 6 + 2

Step A

What is the value of this expression?

Step B

Explain why the value you determined is correct. Use what you know about order of operations in your explanation. Use words, numbers, and/or symbols in your explanation.

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

Answer Annotation

Step A Answer: 84

Step B Sample Correct Response:

To evaluate this expression, I first had to divide 48 by 6 to get 8 because in order of operations, division must happen before addition and subtraction. I then subtracted 8 from 90 to get 82 because the subtraction symbol came before the addition symbol. Finally, I added 82 and 2 to get 84.

Step B Sample Correct Response:

90 - 48 ÷ 6 + 2
    = 90 - 8 + 2
    = 82 + 2
    = 84

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