Juan has 5 pairs of socks in his drawer. The pairs of socks are: 3 white and 2 blue. He also has 4 T-shirts in the drawer: 2 white and 2 gray. He randomly picks one pair of socks and one T-shirt from the drawer.

Step A

What is the probability Juan picks a pair of white socks and a gray T-shirt?

Step B

Use what you know about probability to explain how you determined the probability of Juan picking a white pair of socks and a gray T-shirt. Use words, numbers, and/or symbols in your explanation.

Step A is scored 0 (Incorrect) or 1 (Correct) and assesses 5.B.1.a.
Step B is scored with a 3 point (0, 1, 2) rubric and assesses Processes of Mathematics.

Answer Annotation

Step A Answer: or equivalent

Step B Sample correct response: Since there are 5 pairs of socks and 3 pairs are white, the probability of selecting a pair of white socks is 3 favorable outcomes (white pair of socks) out of 5 total number of outcomes (total pairs of socks) or . The probability of selecting a gray T-shirt is 2 out of 4 or . The probability of selecting a pair of white socks and a gray T-shirt is

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