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Standard 6.0 Knowledge of Number Relationships and Computation/Arithmetic

Topic C. Number Computation

Indicator 1. Analyze number relations and compute

Objective f. Represent multiplication and division basic facts using number sentences, pictures, and drawings

Assessment limit: Use basic facts of no more than 9 x 9 = 81
Note: Highlighted assessment limits will be tested in the no calculator section of MSA.

Brief Constructed Response (BCR) Item

Brittany has 15 heart stickers. She put them in 3 equal groups.

Step A
Make a drawing to show how many heart stickers are in each group.

 

 

 

Step B
Brittany wants to put her stickers in 5 equal groups instead of 3 equal groups.
Explain how this would change your drawing.
Use what you know about division in your explanation.
Use words, numbers, and/or symbols in your explanation.

Step A is scored 0 (Incorrect) or 1 (Correct) and assesses 6.C.1.f.
Step B is scored with a 3 point (0, 1, 2) rubric and assesses Processes of Mathematics.

Note: Five "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.

Sample Student Response #1

image of student response

Score for Sample Student Response #1:

Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1
Step B - Processes of Mathematics: 0

Annotation for Step B, Using the Rubric: The response is completely incorrect.


Sample Student Response #2

image of student response

Score for Sample Student Response #2:

Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 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. Some knowledge of division ("15 ÷ 5 = 3") is shown.


Sample Student Response #3

image of student response

Score for Sample Student Response #3:

Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 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 of the strategy used to show how the drawing would change ("I would have to circle three hearts in each group") is provided.


Sample Student Response #4

image of student response

Score for Sample Student Response #4:

Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 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. The strategy used to solve how the drawing would change ("end up being 3 groups of 5; 15 ÷ 3 that will = 5") is provided. Supportive information about division ("is when you put things into groups … is the opiset of multiplucation") is also provided.


Sample Student Response #5

image of student response

Score for Sample Student Response #5:

Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 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 correct strategy to determine how the drawing would change ("I would put 5 groups with 3 dots inside … reverse the intervols in my equation") is provided. Supportive information for this strategy ("3 × 5 = 15") is also shown in step A.


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_3_043.xml