Tonya's dad is making a concrete patio in their backyard. Concrete is made from cement, sand, gravel and water. It takes twice as much sand as cement to make the concrete mix.

Tonya's dad used 3 gallons of sand in the mix.

Step A

How many quarts of cement did he use?

Step B

Explain how you found your answer. Use what you know about 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.

Sample correct response: He used half as much cement as sand. One half of 3 gallons is 1 gallons. Each gallon is 4 quarts. A gallon would be of 4 quarts or 2 quarts. So 1 gallons is 4 quarts plus 2 quarts which is 6 quarts.

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