| | 4 | 3 | 2 | 1 | |
| Explanation | A complete response with a detailed explanation. | Good solid response with clear explanation. | Explanation is unclear. | Misses key points. | ____ |
| Use Of Visuals | Clear diagram or sketch with some detail. | Clear diagram or sketch. | Inappropriate or unclear diagram. | No diagram or sketch. | ____ |
| Mechanics | No math errors. | No major math errors or serious flaws in reasoning. | May be some serious math errors or flaws in reasoning. | Major math errors or serious flaws in reasoning. | ____ |
| Demonstrated Knowledge | Shows complete understanding of the questions, mathematical ideas, and processes. | Shows substantial understanding of the problem, ideas, and processes. | Response shows some understanding of the problem. | Response shows a complete lack of understanding for the problem. | ____ |
| Requirements | Goes beyond the requirements of the problem. | Meets the requirements of the problem. | Hardly meets the requirements of the problem. | Does not meet the requirements of the problem. | ____ |
| Counter Examples | Includes counter examples. | a | Does not include counter examples. | yy | ____ |
| | | | | Total----> | ____ |