School Improvement in Maryland

Sample Item
Brief Constructed Response Item for Grade 8

Standard 5.0 Knowledge of Probability

Topic B. Theoretical Probability

Indicator 1. Determine the probability of an event comprised of no more than 2 independent events

Objective a. Express the probability of an event as a fraction, a decimal, or a percent

Assessment limit: Use a sample space of 36 to 60 outcomes

Marty has a bag with 5 yellow candies, 4 blue candies, 7 green candies, and 3 red candies. His friend, Susan, picks a candy without looking.

Step A

What color candy is Susan most likely to pick?

Step B

Explain why your answer is correct.
Use what you know about probability in your explanation.
Use words and/or numbers 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.

Correct Answer
Step A
a green candy
Answer Annotation

Sample correct response: 7 green is more than 5 yellow, 4 blue, or 3 red candies. So Susan is more likely to pick green than any other candy.

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

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