Step A
How many gallons of lemonade did Michael make?
__________gallons

Step B
Explain how you found the number of gallons. Use what you know about equivalent units of measurement in your explanation. Use words, numbers, and/or symbols in your explanation.

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

Note: 5 "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 is completely incorrect. The student's conversion factors, ("4 pints in in a ounce…two ounces in a gallon") are incorrect, and the conclusion reached, ("9 gallons in 72 pints") is irrelevant, given the supportive numbers used in the response.

Score for Sample Student Response #2:

Annotation for Step B, Using the Rubric: The mathematical process used to solve the problem is partially developed. The student uses an incorrect conversion factor ("16 Pint's = 1 gal"), as there are only eight pints in a gallon. However, given the conversion factor error, the process for converting units ( ÷ ) is carried out correctly (" 72 ÷16 = 4.5 ").

Score for Sample Student Response #3:

Annotation for Step B, Using the Rubric: The response states a relevant conversion factor, ("8 pint in 1 gallon") correctly. However, this response shows only a partial development of the mathematical process used to solve the problem, as the student does not explain how equivalent units were used to find the number of gallons shown in Step A.

Score for Sample Student Response #4:

Annotation for Step B, Using the Rubric: This response demonstrates a complete understanding and analysis of the problem. The explanation of the mathematical process used to solve the problem is clear and logical, despite one computation error (34). The student lists the relevant equivalent units, ("2 pints in a quart; 4 quarts in a gallon") and explains how they were used ("divided 72 by 2; divided that by 4"), explaining the strategy and providing the numbers used to solve the problem from start to finish.

Score for Sample Student Response #5:

Annotation for Step B, Using the Rubric: This response demonstrates a complete understanding and analysis of the problem, as the student lists the relevant equivalent units ("2 pints = 1 quart; 4 quarts = 1 gallon") and explains how they are used ("72 ÷ 2; 36 ÷ 4") to solve the problem. The explanation of the mathematical process used to solve the problem is fully developed, clear, and logical, as the student provides numerical support (36) where appropriate.

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