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.

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

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

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

- Identification of problem-solving strategy used matches the evidence.
- Evidence is appropriate for solving the problem.
- Written explanation is clear and organized.

(step-by-step format works well, nothing is confusing) - Written explanation includes all key aspects of the solution.

(nothing is missing) - Final answer is consistent and correct

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 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. |

Organize more ways | Give organization (tree diagram or 2D array) with key. |
Explain how organization constructed. Explain how organization was used to find answer. |

Change focus | Discuss how problem is interpreted with different focus. (e.g., POV, complementary/opposite problem, diff representation) |
Explain how to solve problem with new focus. |