Homework assignments

Homework usually consists of five problems, two of these problems will be randomly graded for a total of 10 MP. Remaining problems will be discussed in class.

Please check the class schedule for problem assignments.

Understanding the problem

Eligibility for credit will be based on one of the following criteria:

FULL credit - Correctly understands the problem.
HALF credit - Problem is misunderstood in a significant way, but is not trivialized.
ZERO credit - Completely misunderstands the problem and/or trivializes the problem.

Scoring

Each graded problem will be scored use an ordered triple (2, 2, 1) based on the following:

Strategy name and evidence are consistent and appropriate for solving the problem. In the absence of a strategy name, the instructor will do their best to match the evidence to strategies from class.
Written explanation is clear and complete. A "step-by-step format" often works well.
Final answer is consistent and correct

Problem solving strategies

The table below highlights desired evidence for each problem solving strategy.

Strategy name	Evidence	Written explanations
Diagram	Includes pictures	Explains important features of how the diagram was created and/or how the diagram solves the problem.
Systematic list	Provides a list with clear headings and/or key.	Explains system for creating list. Explains how the list helps to solve the given problem.
Eliminate possibilities	Often done as part of the explanation where options are listed (possibly using a systematic list), then some are removed.	Explains why options are eliminated. Steps work well here. If there are many eliminations, provide at least 3 key steps.
Matrix logic	Matrix convention: X's for not possible, O's for match. Subscripts useful to denote clues.	Explains adjunct list or other notes. Explains at least 3 key steps for constructing the matrix.
Look for pattern	Identify pattern in words or formula.	Explains how the pattern was found.
Guess & check	Lucky guessing not allowed, so minimum of 3 guesses is required. Typically organize guessing in a table.	Explain how incorrect guesses lead to a correct guess. For example, "result is too high so guess needs to be lower".
Subproblems	Explicitly state each subproblem (or question).	Answer each subproblem (or question).
Analyze units	Multiplication that shows "canceling" of units.	Clear labels with canceling. It is also recommended to identify the units you are trying to find or assumptions like 365.25 days per year.
Easier related problem	Explicitly state the easier problem, including how it is easier or assumptions made.	After solving easier problem, explain what information was gained for actual problem.
Physical representations	Document what manipulatives were used.	Explains solution to problem (visual representations may help).
Work backwards	Shows steps (either forward or backward)	Description of setup. Final answer clearly indicated.
Venn diagrams	Provide Venn diagram.	Explains at least two key steps for creating the Venn diagram or using the diagram. Use of \(\cup\) (union) and \(\cap\) (intersection) are allowed.
Algebra	Define variables. Formulas.	Explains formulas and keep algebraic work clear and organized.
Finite differences	Create finite differences tables.	Create equation and use equation to solve problem.
Organize more ways	Give organization (tree diagram or 2D array) with key.	Explains how organization constructed. Explains how organization was used to find answer.
Change focus	Discuss how problem is interpreted with different focus. (e.g., POV, complementary/opposite problem, different representation)	Explains how to solve problem with new focus.