Mathematical Knowledge:

Knowledge of mathematical principles and concepts which result in a correct solution to a problem.

Score
Level

•	
4

shows complete understanding of the problem’s mathematical concepts and principles

•	uses appropriate mathematical terminology and notations including labeling answer if appropriate

•	executes algorithms and computations completely and correctly

•	
3

shows nearly complete understanding of the problem’s mathematical concepts and principles

•	uses mostly correct mathematical terminology and notations

•	executes algorithms completely; computations are generally correct but may contain minor errors

•	
2

shows some understanding of the problem’s mathematical concepts and principles

•	uses some correct mathematical terminology and notations

•	may contain major algorithmic or computational errors

•	
1

shows limited to no understanding of the problem’s mathematical concepts and principles

•	may misuse or fail to use mathematical terminology and notations

•	attempts an answer

•	
0

no answer attempted

Strategic Knowledge:

Identification and use of important elements of the problem that represent and integrate concepts which yield the solution (e.g., models, diagrams, symbols, algorithms).

•	identifies all important elements of the problem and shows complete understanding of the relationships among elements

•	shows complete evidence of an appropriate strategy that would correctly solve the problem

•	identifies most important elements of the problem and shows a general understanding of the relationships among them

•	shows nearly complete evidence of an appropriate strategy for solving the problem

•	identifies some important elements of the problem but shows only limited understanding of the relationships among them

•	shows some evidence of a strategy for solving the problem

•	fails to identify important elements or places too much emphasis on unrelated elements

•	reflects an inappropriate strategy for solving the problem; strategy may be difficult to identify

•	no apparent strategy

Explanation:

Mathematics Scoring Rubric
The following rubric is used for the extended-response items for grade levels 3 through 8.

Written explanation of the rationales and steps of the solution process. A justification of each step is provided. Though important, the length of the response, grammar, and syntax are not the critical elements of this dimension.

•	gives a complete written explanation of the solution process; clearly explains what was done and why it was done

•	may include a diagram with a complete explanation of all its elements

•	gives a nearly complete written explanation of the solution process; clearly explains what was done and begins to address why it was done

•	may include a diagram with most of its elements explained

•	gives some written explanation of the solution process; either explains what was done or addresses why it was done

•	explanation is vague, difficult to interpret, or does not completely match the solution process

•	may include a diagram with some of its elements explained

•	gives minimal written explanation of the solution process; may fail to explain what was done and why it was done

•	explanation does not match presented solution process

•	may include minimal discussion of the elements in a diagram; explanation of significant elements is unclear

•	
August 2005

no written explanation of the solution process is provided