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.CO.6 |
High School |
H.S. Trigonometry |
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. |

TR.ID.1 |
High School |
H.S. Trigonometry |
Prove the Pythagorean identity sin^2(x) + cos^2(x) = 1 and use it to find trigonometric ratios, given sin(x), cos(x), or tan(x), and the quadrant of the angle. |

TR.ID.2 |
High School |
H.S. Trigonometry |
Verify trigonometric identities and simplify expressions using trigonometric identities. |

TR.ID.3 |
High School |
H.S. Trigonometry |
Prove the addition and subtraction identities for sine, cosine, and tangent. Use the identities to solve problems. |

TR.ID.4 |
High School |
H.S. Trigonometry |
Prove the double- and half-angle identities for sine, cosine, and tangent. Use the identities to solve problems. |

TR.PC.1 |
High School |
H.S. Trigonometry |
Understand and use complex numbers, including real and imaginary numbers, on the complex plane in rectangular and polar form, and explain why the rectangular and polar forms of a given complex number represent the same number. |

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

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

TR.PC.4 |
High School |
H.S. 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. 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. 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. Trigonometry |
Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. |

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

TR.PF.5 |
High School |
H.S. 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. 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. |