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.PF.3 |
High School |
H.S. Trigonometry |
Construct the inverse trigonometric functions of sine, cosine, and tangent by restricting the domain. |

TR.PF.4 |
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.PF.5 |
High School |
H.S. Trigonometry |
Prove the addition and subtraction formulas for sine, cosine, and tangent. Use the formulas to solve problems. |

TR.PF.6 |
High School |
H.S. Trigonometry |
Prove the double- and half-angle formulas for sine, cosine, and tangent. Use the formulas to solve problems. |

TR.PF.7 |
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. |

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

TR.UC.2 |
High School |
H.S. Trigonometry |
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. |

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

TR.V.1 |
High School |
H.S. Trigonometry |
Solve problems involving velocity and other quantities that can be represented by vectors. |

TR.V.2 |
High School |
H.S. Trigonometry |
Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy). |

TR.V.3 |
High School |
H.S. Trigonometry |
Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0). |