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Standard 6.0 Knowledge of Number Relationships and Computation/Arithmetic

Topic A. Knowledge of Number and Place Value

Indicator 1. Apply knowledge of whole numbers and place value

Objective a. Read, write, and represent whole numbers using symbols, words, and models

Assessment limit: Use whole numbers (0 - 1,000,000)

Brief Constructed Response (BCR) Item

Olivia made the number 506,890 with cards.

Step A
Write Olivia's number in word form.

Step B
Olivia removed the card with the five on it. Explain how this would change the word form of the number.
Use what you know about numbers and place value in your explanation.
Use words and/or numbers in your explanation.

Step A is scored 0 (Incorrect) or 1 (Correct) and assesses 6.A.1.a.
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.

Correct Answer
BCR
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 irrelevant to the problem.


Sample Student Response #2

image of student response

Score for Sample Student Response #2:

Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 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. Some knowledge of how the word form of the number would change ("no hunred thousand's place so the number would change to the ten thousands place") is provided.


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. An initial strategy for showing how the word form would change ("it would take out the 500,000 in the number 5006, 890") is given.


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. A thorough explanation of how the word form would change ("now that there is no 5, there is a 0 before the six and the number would only be sixthous, eight hundred and ninety because there is no ten thousand") is 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 thorough explanation of how the word form would change ("ther isn't a hundred thousand and their are 0 ten thousands so it would change…to six thousand eight hundred ninty") is provided.


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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