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Standard 1.0 Knowledge of Algebra, Patterns, and Functions

Topic B. Expressions, Equations, and Inequalities

Indicator 1. Write, simplify, and evaluate expressions

Objective d. Simplify algebraic expressions by combining like terms

Assessment limit: Use no more than 3 variables with integers (-50 to 50), or proper fractions with denominators as factors of 20 (-20 to 20)
Note: Highlighted assessment limits will be tested in the no calculator section of MSA.

Brief Constructed Response (BCR) Item

Look at this expression.

Step A
Simplify the expression.

Step B
Use what you know about simplifying algebraic expressions to explain how you determined your answer. Use words, numbers, and/or symbols in your explanation.

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

Note: Four "Sample Student Responses" follow below. Each response appears on its own separate page and includes scoring information. The "Sample Student Responses" represent a range of score points.

Correct Answer
BCR
Sample Student Response #1

image of student response

Score for Sample Student Response #1:

Step A - Content (Knowledge of Algebra, Patterns, and Functions): 0
Step B - Processes of Mathematics: 1

Annotation for Step B, Using the Rubric: The response demonstrates a minimal understanding and analysis of the problem. A partial strategy for simplifying the expression is provided by the attempt to combine like terms. The strategy is flawed by a misunderstanding of how to combine the coefficients.


Sample Student Response #2

image of student response

Score for Sample Student Response #2:

Step A - Content (Knowledge of Algebra, Patterns, and Functions): 1
Step B - Processes of Mathematics: 1

Annotation for Step B, Using the Rubric: The response demonstrates a minimal understanding and analysis of the problem. A partial explanation for how to simplify the expression ("I put the a's together and the B's together") is provided. Supportive information for finding the common denominators is missing.


Sample Student Response #3

image of student response

Score for Sample Student Response #3:

Step A - Content (Knowledge of Algebra, Patterns, and Functions): 0
Step B - Processes of Mathematics: 2

Annotation for Step B, Using the Rubric: The response demonstrates a complete understanding and analysis of the problem. A complete explanation of the process used to simplify the expression is provided by the work at the bottom of the response. The minor mistake of not simplifying two sixths does not detract from a complete understanding of the process used to solve the problem.


Sample Student Response #4

image of student response

Score for Sample Student Response #4:

Step A - Content (Knowledge of Algebra, Patterns, and Functions): 1
Step B - Processes of Mathematics: 2

Annotation for Step B, Using the Rubric: The response demonstrates a complete understanding and analysis of the problem. A complete explanation of the process used to simplify the expression is provided by the student's work,


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_8_039.xml