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 |
---|---|---|---|

QR.RP.6 |
High School |
H.S. Quantitative Reasoning |
Determine the constant of proportionality in proportional situations (both real-life and mathematical), leading to a symbolic model for the situation (i.e. an equation based upon a rate of change, y = kx). |

QR.S.1 |
High School |
H.S. Quantitative Reasoning |
Analyze statistical information from studies, surveys, and polls (including when reported in condensed form or using summary statistics) to make informed judgments as to the validity of claims or conclusions, such as when interpreting and comparing the results of polls using margin of error. |

QR.S.2 |
High School |
H.S. Quantitative Reasoning |
Identify limitations, strengths, or lack of information in studies, including data collection methods (e.g. sampling, experimental, observational) and possible sources of bias, and identify errors or misuses of statistics to justify particular conclusions. |

QR.S.3 |
High School |
H.S. Quantitative Reasoning |
Create (with and without technology) and use visual displays of real world data, such as charts, tables and graphs. |

QR.S.4 |
High School |
H.S. Quantitative Reasoning |
Interpret and analyze visual representations of data, and describe strengths, limitations, and fallacies of various graphical displays. |

QR.S.5 |
High School |
H.S. Quantitative Reasoning |
Read, interpret, and make decisions about data summarized numerically using measures of center and spread, in tables, and in graphical displays (line graphs, bar graphs, scatterplots, and histograms), e.g., explain why the mean may not represent a typical salary; explain the difference between bar graphs and histograms; critique a graphical display by recognizing that the choice of scale can distort information. |

QR.S.6 |
High School |
H.S. Quantitative Reasoning |
Summarize, represent, and interpret data sets on a single count or measurement variable using plots and statistics appropriate to the shape of the data distribution to represent it. |

QR.S.7 |
High School |
H.S. Quantitative Reasoning |
Compare center, shape, and spread of two or more data sets and interpret the differences in context. |

QR.S.8 |
High School |
H.S. Quantitative Reasoning |
Use properties of distributions, including uniform and normal distributions, to analyze data and answer questions. |

QR.S.9 |
High School |
H.S. Quantitative Reasoning |
Recognize when data are normally distributed and use the mean and standard deviation of the data to fit it to a normal distribution. |

TR.ID.1 |
High School |
H.S. Precalculus: 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. Precalculus: Trigonometry |
Verify trigonometric identities and simplify expressions using trigonometric identities. |

TR.ID.3 |
High School |
H.S. Precalculus: 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. Precalculus: 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. Precalculus: 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. |