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

PS.P.3 |
High School |
H.S. Probability & Statistics |
Understand the multiplication counting principle, permutations, and combinations; use them to solve real-world problems. Use simulations with and without technology to solve counting and probability problems. |

PS.P.4 |
High School |
H.S. Probability & Statistics |
Calculate the probabilities of complementary events. |

PS.P.5 |
High School |
H.S. Probability & Statistics |
Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. |

PS.P.6 |
High School |
H.S. Probability & Statistics |
Analyze decisions and strategies using probability concepts. Analyze probabilities to interpret odds and risk of events. |

PS.P.7 |
High School |
H.S. Probability & Statistics |
Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. |

PS.P.8 |
High School |
H.S. Probability & Statistics |
Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; Compute and interpret the expected value of random variables. |

PS.P.9 |
High School |
H.S. Probability & Statistics |
Derive the binomial theorem by combinatorics. Use combinatorial reasoning to solve problems. |

PS.P.10 |
High School |
H.S. Probability & Statistics |
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events. |

QR.M.1 |
High School |
H.S. Quantitative Reasoning |
Analyze and critique mathematical models and be able to describe their limitations, including distinguishing between correlation and causation and determine whether interpolation and/or extrapolation are appropriate. |

QR.M.2 |
High School |
H.S. Quantitative Reasoning |
Use models, including models created with spreadsheets or other tools, to estimate solutions to contextual questions, such as functional models to estimate future population or spreadsheets to model financial applications (e.g. credit card debt, installment savings, amortization schedules, mortgage and other loan scenarios). Identify patterns and identify how changing parameters affect the results. |

QR.M.3 |
High School |
H.S. Quantitative Reasoning |
Choose and create, with and without technology, linear, exponential, logistic, or periodic models and curves of best fit for bivariate data sets. Use the models to answer questions and draw conclusions or make decisions, addressing limitations and long-term ramifications of chosen models when appropriate. Recognize when a change in model is needed. |

QR.M.4 |
High School |
H.S. Quantitative Reasoning |
Analyze real-world problem situations and use variables to construct and solve equations involving one or more unknown or variable quantities to answer questions about the situations, such as creating spreadsheet formulas to calculate prices based on percentage mark-up or solving formulas for specified values. Demonstrate understanding of the meaning of a solution. Identify when there is insufficient information given to solve a problem. |

QR.M.5 |
High School |
H.S. Quantitative Reasoning |
Apply geometric concepts to model situations and solve problems such as those arising in art, architecture, and other fields. |

QR.M.6 |
High School |
H.S. Quantitative Reasoning |
The student uses a variety of network models represented graphically to organize data in quantitative situations, make informed decisions, and solve problems, such as in scheduling or routing situations that can be modeled using different methods, e.g., vertex-edge graphs using critical paths, Euler paths, or minimal spanning trees. |

QR.N.1 |
High School |
H.S. Quantitative Reasoning |
Represent quantities in equivalent forms (fractions, decimals, and percentages) to investigate and describe quantitative relationships and solve real-world problems in a variety of contexts. Compare the size of numbers in different forms arising in authentic real-world contexts, such as growth expressed as a fraction versus as a percentage. Interpret the meaning of numbers in different forms, such as the meaning of a fraction or the meaning of a percentage greater than 100 and its validity in a given context. Recognize incorrect or deceptive uses of fractions, decimals, or percentages. |