4 points

Contains complete response with clear, coherent, and unambiguous explanation; includes clear and simple diagram, if appropriate; communicates effectively to identified audience; shows understanding of question's mathematical ideas and processes; identifies all important elements of question; includes examples and counter examples; gives strong supporting arguments

3 points

Contains good solid response with some, but not all, of the characteristics above; explains less completely; may include minor error of execution but not of understanding

2 points

Contains complete response, but explanation is muddled; presents incomplete arguments; includes diagrams that are inappropriate or unclear, or fails to provide a diagram when it would be appropriate; indicates some understanding of mathematical ideas, but in an unclear way; shows clear evidence of understanding some important ideas while also making one or more fundamental, specific errors

1 point

Omits parts of question and response; has major errors; uses inappropriate strategies

0 points

No response; frivolous or irrelevant response