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

♦ 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

**MATHEMATICS SCORING RUBRIC**

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

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

**2 ♦ **uses some correct mathematical terminology and notations

- may contain major algorithmic or computational errors
- 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

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

♦ | shows complete evidence of an appropriate strategy that would correctly solve the problem | ♦ | may include a diagram with a complete explanation of all its elements |

♦ | identifies most of the important elements of the problem and shows a general understanding of the relationships among them | ♦ | gives a nearly complete written explanation of the solution process; clearly explains what was done and begins to address why it was done |

♦ | shows nearly complete evidence of an appropriate strategy for solving the problem | ♦ | may include a diagram with most of its elements explained |

- 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

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 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

♦ no apparent strategy

♦ no written explanation of the solution process is provided

♦ no answer attempted

August 2005