Students in a marching band collected money for new uniforms. This table shows the amount of money they collected last week.

COLLECTIONS

Step A
What is the mean amount of money the students collected?

$___________

Step B

The amounts for Saturday and Sunday were recorded incorrectly. Saturday should have been $34.24, and Sunday should have been $75.18. Use what you know about determining the mean to explain how these changes will affect your answer in Step A. Use words, data, and/or symbols in your explanation.

Step A is scored 0 (Incorrect) or 1 (Correct) and assesses 4.B.2.a.
Step B is scored with a 3 point (0, 1, 2) rubric and assesses Processes of Mathematics.

Note: 4 "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: The response demonstrates a minimal understanding and analysis of the problem. A partial explanation of how the changes affect the mean ("The Sat. total bef. Division was off by $10.02. The Sun. total before dividing was off by $18.00") is provided when the student states the changes in the totals for Saturday and Sunday.

Score for Sample Student Response #2:

Annotation for Step B, Using the Rubric: The response demonstrates a minimal understanding and analysis of the problem. A partial explanation of how the changes affect the mean ("it mad the mean go up from the original") is provided by stating that the new mean will increase.

Score for Sample Student Response #3:

Annotation for Step B, Using the Rubric: The response demonstrates a complete understanding and analysis of the problem. A complete explanation of how the changes affect the mean ("the mean would increase $1.14") is provided by stating the exact amount of increase in the new mean.

Score for Sample Student Response #4:

Annotation for Step B, Using the Rubric: The response demonstrates a complete understanding and analysis of the problem. A complete explanation of how the changes affect the mean ("it is now $46.66") is provided by stating the exact amount of the new mean.

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