# Math Framework

To learn more about how to use the Math Framework, watch this short video.

**Guiding Principles of Mathematics Instruction:**

- Mathematical proficiency is defined by conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition (National Research Council, 2001).
- Mathematical proficiency drives independent thinking, reasoning, and problem-solving.
- Mathematical proficiency is the foundation for careers in science, technology, engineering and mathematics (STEM), and it is increasingly becoming the foundation for careers outside of STEM (NCTM, 2018)
- Effective mathematics teaching “engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically” (NCTM, 2014).
- Standards-based instruction accelerates student gains.
- Students construct mathematical knowledge through exploration, discussion, and reflection.
- Teachers are facilitators of student learning, as they engage students in rich tasks. Administrators are change agents and have the power to create and to support a culture of mathematical proficiency.

Standard | Grade | Area/Subject | Description |
---|---|---|---|

TR.PC.2 |
High School |
H.S. Precalculus: Trigonometry |
State, prove, and use DeMoivre’s Theorem. |

TR.PC.3 |
High School |
H.S. Precalculus: Trigonometry |
Define polar coordinates and relate polar coordinates to Cartesian coordinates. |

TR.PC.4 |
High School |
H.S. Precalculus: Trigonometry |
Translate equations from rectangular coordinates to polar coordinates and from polar coordinates to rectangular coordinates. Graph equations in the polar coordinate plane. |

TR.PF.1 |
High School |
H.S. Precalculus: Trigonometry |
Graph trigonometric functions with and without technology. Use the graphs to model and analyze periodic phenomena, stating amplitude, period, frequency, phase shift, and midline (vertical shift). |

TR.PF.2 |
High School |
H.S. Precalculus: Trigonometry |
Model a data set with periodicity using a sinusoidal function and explain the parameters of the model. |

TR.PF.3 |
High School |
H.S. Precalculus: Trigonometry |
Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. |

TR.PF.4 |
High School |
H.S. Precalculus: Trigonometry |
Construct the inverse trigonometric functions of sine, cosine, and tangent by restricting the domain. |

TR.PF.5 |
High School |
H.S. Precalculus: Trigonometry |
Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. |

TR.T.1 |
High School |
H.S. Precalculus: Trigonometry |
Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right triangles and the coordinates on the unit circle. |

TR.T.2 |
High School |
H.S. Precalculus: Trigonometry |
Solve real-world problems with and without technology that can be modeled using right triangles, including problems that can be modeled using trigonometric ratios. Interpret the solutions and determine whether the solutions are reasonable. |

TR.T.3 |
High School |
H.S. Precalculus: Trigonometry |
Explain and use the relationship between the sine and cosine of complementary angles. |

TR.T.4 |
High School |
H.S. Precalculus: Trigonometry |
Prove the Laws of Sines and Cosines. |

TR.T.5 |
High School |
H.S. Precalculus: Trigonometry |
Understand and apply the Laws of Sines and Cosines to solve real-world and other mathematical problems involving right and non-right triangles. |

TR.T.6 |
High School |
H.S. Precalculus: Trigonometry |
Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line. Use the formula to find areas of triangles. |

TR.UC.1 |
High School |
H.S. Precalculus: Trigonometry |
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. |