Includes clear diagrams or sketches. Major math errors or serious flaws in reasoning. May be some serious math errors or flaws in reasoning. No major math errors or serious flaws in reasoning. No significant math errors.
Response shows some understanding of the problem.
Shows substantial understanding of the problem, ideas, and processes. Shows complete understanding of the questions, mathematical ideas, and processes. Does not go beyond the requirements of the problem. Goes beyond the requirements of the problem. Includes counter examples.