School Improvement in Maryland
Sample Item Scoring Information Return

Standard 5.0 Knowledge of Probability

Topic A. Sample Space

Indicator 1. Identify a sample space

Objective a. Determine the number of outcomes

Assessment limit: Use no more than 3 independent events with a sample space of no more than 6 outcomes in each event.

Brief Constructed Response (BCR) Item

The list below shows the different taco shells, fillings, and toppings sold at Rico's Taco Bar.

Taco Shells Fillings Toppings
Soft Chicken Cheese
Hard Beef Lettuce
  Bean Salsa
    Onions
    Sour Cream

Step A

How many different types of tacos can Rico make using one taco shell, one filling, and one topping?

Step B

Use what you know about probability to justify why the number of different types of tacos you determined is correct. Use words, numbers, and/or symbols in your justification.

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.

Answer Annotation

Step A Answer: 30

Step B Sample correct response: Since there are 2 different types of tacos, 3 different types of filling, and 5 different types of toppings, then using the Fundamental Counting Principle, the total number of combinations is 2 · 3 · 5, or 30, different ways.

Step B Sample correct response

diagram

If I count the end branches on my tree diagram, there are 30.

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_7_024.xml