School Improvement in Maryland
Sample Item Scoring Information Return

Standard 5.0 Knowledge of Probability

Topic A. Sample Space

Indicator 1. Identify possible outcomes

Objective a. Determine possible outcomes of independent events

Assessment limit: Use two independent events with no more than 4 outcomes each and an organized list or tree diagram

Brief Constructed Response (BCR) Item

Brendan is playing a game with these two spinners. The spinners are each divided into 4 equal sections. He spins the arrows on both spinners and records the color and number he got each time. For example, on his first spin, Brendan got blue, 2.

two spinners

Step A

How many possible outcomes are there?

Step B

Explain how you found your answer. Use what you know about probability in your explanation. Use words, numbers, and/or symbols in your explanation.

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

Correct Answer
Step A
16

Answer Annotation

Sample correct response: I used a tree diagram.

tree diagram

Brief Constructed Response (BCR) Rubric
Print: Scoring Rubric

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

/share/rubrics/msa/mathematics/xml/bcr.xml
/toolkit/vsc/assessment_items/msa_math_5_020.xml