| **4** | **3** | **2** | **1** | |

**Explanation** | A complete response with a detailed explanation. | Good solid response with clear explanation. | Explanation is unclear. | Misses key points. | ____ |

**Use Of Visuals** | Clear diagram or sketch with some detail. | Clear diagram or sketch. | Inappropriate or unclear diagram. | No diagram or sketch. | ____ |

**Mechanics ** | No math errors. | No major math errors or serious flaws in reasoning. | May be some serious math errors or flaws in reasoning. | Major math errors or serious flaws in reasoning. | ____ |

**Demonstrated Knowledge** | Shows complete understanding of the questions, mathematical ideas, and processes. | Shows substantial understanding of the problem, ideas, and processes. | Response shows some understanding of the problem. | Response shows a complete lack of understanding for the problem. | ____ |

**Requirements** | Goes beyond the requirements of the problem. | Meets the requirements of the problem. | Hardly meets the requirements of the problem. | Does not meet the requirements of the problem. | ____ |

**Counter Examples** | Includes counter examples. | a | Does not include counter examples. | yy | ____ |

| | | | **Total---->** | ____ |