Regarding mathematics problems: "... its educational value cannot be overestimated. It is the ladder by which the mind ascends into higher fields of original research and investigation. Many dormant minds have been aroused into activity through the mastery of a single problem."
----- B. F. Finkel, founding editor of the M.A.A. journal, American Mathematics Monthly -----
Homework:
Students are encouraged to work on them with other students, and must only use colored pens (no pencils). Properly paced, students should be able to complete their homework at school, and not have to bring any of it home (unless that's the only way they will be able to work with others). Choosing to reflect on, or to pursue deeper, any of the ideas discovered during math class, would be a more meaningful way of working on math outside of school hours.
Intent:
Not knowing how to solve a problem, is not an acceptable excuse for giving up on a problem (part of the reason for problem sets, is for students to practice what to do, when they don't know what to do).
Credit for problems will be based on how well solutions are defended (just because a solution is given, does not ensure credit will be earned). Homework sets will be one of the best opportunities for students to demonstrate readiness and mathematical proficiency.
Although it may not be obvious at first, problems can be solved, and should be solved, without using calculators (the exception being geometry problems containing trig and/or involved calculations).
Students who are eventually able to successfully solve at least 95% of the problems, will be well prepared for the high school algebra final and and the high school geometry final (passing both is a prerequisite for getting into honors algebra 2).