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

PC.QPR.4 |
High School |
H.S. Precalculus: Algebra |
Know and apply the Remainder Theorem and the Factor Theorem. |

PC.QPR.5 |
High School |
H.S. Precalculus: Algebra |
Understand the Fundamental Theorem of Algebra. Find a polynomial function of lowest degree with real coefficients when given its roots. |

PC.QPR.6 |
High School |
H.S. Precalculus: Algebra |
Graph rational functions with and without technology. Identify and describe features such as intercepts, domain and range, and asymptotic and end behavior. |

PC.SS.1 |
High School |
H.S. Precalculus: Algebra |
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. |

PC.SS.2 |
High School |
H.S. Precalculus: Algebra |
Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms. |

PC.SS.3 |
High School |
H.S. Precalculus: Algebra |
Find partial sums of arithmetic and geometric series and represent them using sigma notation. |

PC.SS.4 |
High School |
H.S. Precalculus: Algebra |
Model and solve real-world problems involving applications of sequences and series, interpret the solutions and determine whether the solutions are reasonable. |

PS.DA.1 |
High School |
H.S. Probability & Statistics |
Create, compare, and evaluate different graphic displays of the same data, using histograms, frequency polygons, cumulative frequency distribution functions, pie charts, scatterplots, stem-and-leaf plots, and box-and-whisker plots. Draw these with and without technology. |

PS.DA.2 |
High School |
H.S. Probability & Statistics |
Compute and use mean, median, mode, weighted mean, geometric mean, harmonic mean, range, quartiles, variance, and standard deviation. Use tables and technology to estimate areas under the normal curve. Fit a data set to a normal distribution and estimate population percentages. Recognize that there are data sets not normally distributed for which such procedures are inappropriate. |

PS.DA.3 |
High School |
H.S. Probability & Statistics |
Understand the central limit theorem and use it to solve problems. |

PS.DA.4 |
High School |
H.S. Probability & Statistics |
Understand hypothesis tests of means and differences between means and use them to reach conclusions. Compute and use confidence intervals to make estimates. Construct and interpret margin of error and confidence intervals for population proportions. |

PS.DA.5 |
High School |
H.S. Probability & Statistics |
Recognize how linear transformations of univariate data affect shape, center, and spread. |

PS.DA.6 |
High School |
H.S. Probability & Statistics |
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. |

PS.DA.7 |
High School |
H.S. Probability & Statistics |
Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. |

PS.DA.8 |
High School |
H.S. Probability & Statistics |
Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable. |