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.N.2 |
High School |
H.S. Quantitative Reasoning |
Solve problems involving calculations with percentages and interpret the results, such as calculating percentage rates or differentiating between a discount of 30% and two consecutive discounts of 15%. Calculate relative change and explain how it differs from absolute change. Recognize incorrect or deceptive uses of percentages. |

QR.N.3 |
High School |
H.S. Quantitative Reasoning |
Interpret numbers in different forms in terms of authentic contexts to solve real-world problems, such as interpreting a growth rate less than 1%. Compare and precisely communicate with numbers in different forms (including words, fractions, decimals, standard notation, and scientific notation), such as comparing relative and absolute changes in quantities. |

QR.N.4 |
High School |
H.S. Quantitative Reasoning |
Compare magnitudes of numbers in context, such as the population of the US compared to the population of the world. Perform such comparisons when numbers are in different forms (including words, fractions, decimals, standard notation, and scientific notation). |

QR.N.5 |
High School |
H.S. Quantitative Reasoning |
Perform accurate and efficient calculations using large and small numbers in different forms, to an appropriate precision, with and without technology. Include calculations in context, such as ratios representing water use per capita for a large population. |

QR.N.6 |
High School |
H.S. Quantitative Reasoning |
Use estimation skills, and know why, how, and when to estimate results. Identify and use numeric benchmarks for estimating calculations (e.g., using 25% as an estimate for 23%). Identify and use contextual benchmarks for comparison to other numbers (e.g., using US population as a benchmark to evaluate reasonableness of statistical claims or giving context to numbers). Check for reasonableness using both types of benchmarks. |

QR.N.7 |
High School |
H.S. Quantitative Reasoning |
Use dimensional analysis to convert between units of measurements and to solve problems involving multiple units of measurement, such as converting between currencies, calculating the cost of gasoline to drive a given car a given distance, or calculating dosages of medicine. |

QR.P.1 |
High School |
H.S. Quantitative Reasoning |
Determine the nature and number of elements in a finite sample space to model the outcomes of real-world events using counting techniques, and build the sample space by making lists, tables, or tree diagrams. |

QR.P.2 |
High School |
H.S. Quantitative Reasoning |
Determine the number of ways an event may occur using the Fundamental Counting Principle. |

QR.P.3 |
High School |
H.S. Quantitative Reasoning |
Evaluate the validity of claims based on empirical, theoretical, and subjective probabilities. Draw conclusions or make decisions related to risk, pay-off, expected value, and false negatives/positives in various probabilistic contexts. |

QR.P.4 |
High School |
H.S. Quantitative Reasoning |
Use data displays and models, such as two-way tables, tree diagrams, Venn diagrams, and area models, to determine probabilities (including conditional probabilities) and use these probabilities to make informed decisions. |

QR.RP.1 |
High School |
H.S. Quantitative Reasoning |
Solve real-life problems requiring interpretation and comparison of complex numeric summaries which extend beyond simple measures of center, such as problems requiring interpreting and/or comparing weighted averages, indices, coding, and ranking. Evaluate claims based on complex numeric summaries. |

QR.RP.2 |
High School |
H.S. Quantitative Reasoning |
Understand and communicate percentages as rates per 100, and identify uses and misuses of percentages related to a proper understanding of the base in real-world and mathematical problems. |

QR.RP.3 |
High School |
H.S. Quantitative Reasoning |
Solve real-life problems requiring interpretation and comparison of various representations of ratios, (i.e. fractions, decimals, rate, and percentages), such as problems that involve non-standard ratios (e.g., media and risk reporting) or part-to-part versus part-to-whole ratios taken from meaningful context. |

QR.RP.4 |
High School |
H.S. Quantitative Reasoning |
Analyze growth and decay using absolute and relative change and make comparisons using absolute and relative difference. |

QR.RP.5 |
High School |
H.S. Quantitative Reasoning |
Distinguish between proportional and non-proportional situations, and, when appropriate, apply proportional reasoning, such as when solving for an unknown quantity in proportional situations; solving real-life problems requiring conversion of units using dimensional analysis; or applying scale factors to perform indirect measurements (e.g., maps, blueprints, concentrations, dosages, and densities). Recognize when proportional techniques do not apply. |