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.

Understanding the problem

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

Scoring

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

  1. Identification of problem-solving strategy used matches the evidence.
  2. Evidence is appropriate for solving the problem.
  3. Written explanation is clear and organized.
    (step-by-step format works well, nothing is confusing)
  4. Written explanation includes all key aspects of the solution.
    (nothing is missing)
  5. Final answer is consistent and correct

Problem solving strategies

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

Strategy Evidence Written explanations
Diagram Diagram with key and/or key features explained. Explain how the diagram solves the problem.
Systematic list Systematic list with clear headings and/or key.

Explain system for creating list.

Explain how the list helps to solve the given problem.

Eliminate possibilities List possibilities. Optionally use systematic list. Explain why each possibility is eliminated. Steps work well here.
Matrix logic

Matrix convention: X's for not possible, O's for match.

Subscripts useful to denote clues.

Explain adjunct list or other notes.

Explain at least 3 key steps for constructing the matrix.

Look for pattern Identify pattern in words or formula.

Explain how to use pattern to solve problem.

Guess & check

Lucky guessing not allowed, so minimum of 3 guesses is required.

Typically organize guessing in a table.

Explain how the incorrect guesses lead to a correct guess.
Subproblems

Explicitly state each subproblem (or question).

Answer each subproblem (or question).
Analyze units Identify goal, which may focus on units Clear labels with canceling. Other details to understand solution, like assumptions (e.g., 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. Explain solution to problem (visual representations may help).
Work backwards Shows steps (either forward or backward) Explains how steps are organized. Clearly indicate final answer.
Venn diagrams Provide Venn diagram. Explain at least two key steps for creating the Venn diagram or using the diagram. Use of ∪ and ∩ are allowed.
Algebra

Key for variables.

Formulas.

Explain formulas and keep algebraic work clear and organized.
Finite differences Create finite differences tables. Show how to solve the formula's coefficients and how to get the answer.