Characteristics | Descriptions |

Precision | -Be explicit about precise definitions (e.g., use definitions as a basis for logical reasoning); -Pay attention to precise statements (e.g., present mathematical ideas clearly). |

Coherence | -Demonstrate interconnectedness of mathematical ideas (e.g., show the algebraic and geometric representations of a mathematical concept and idea, where appropriate); -Show logical/sequential progression of mathematical ideas (e.g., show a deliberate effort at scaffolding mathematical ideas from simple to complex, specific to general). |

Purposefulness | -Emphasize key or big mathematical ideas; -Provide rationale for why key mathematical ideas are relevant to the teaching of a particular mathematical topic at hand. |