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

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.

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

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

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