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.
PS.DA.9

High School

H.S. Probability & Statistics

Understand statistics and use sampling distributions as a process for making inferences about population parameters based on a random sample from that population.

PS.DA.10

High School

H.S. Probability & Statistics

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

PS.DA.11

High School

H.S. Probability & Statistics

Find linear models by using median fit and least squares regression methods to make predictions. Decide which among several linear models gives a better fit. Interpret the slope and intercept in terms of the original context. Informally assess the fit of a function by plotting and analyzing residuals.

PS.DA.12

High School

H.S. Probability & Statistics

Evaluate reports based on data by considering the source of the data, the design of the study, the way the data are analyzed and displayed, and whether the report confuses correlation with causation. Distinguish between correlation and causation.

PS.ED.1

High School

H.S. Probability & Statistics

Formulate questions that can be addressed with data. Collect, organize, and display relevant data to answer the questions formulated.

PS.ED.2

High School

H.S. Probability & Statistics

Use election theory techniques to analyze election data. Use weighted voting techniques to decide voting power within a group.

PS.ED.3

High School

H.S. Probability & Statistics

Construct simulated sampling distributions of sample proportions and use sampling distributions to identify which proportions are likely to be found in a sample of a given size.

PS.ED.4

High School

H.S. Probability & Statistics

Use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions.

PS.ED.5

High School

H.S. Probability & Statistics

Model and solve real-world problems using the geometric distribution or waiting-time distribution, with or without technology.

PS.ED.6

High School

H.S. Probability & Statistics

Model and solve real-world problems involving patterns using recursion and iteration, growth and decay, and compound interest.

PS.ED.7

High School

H.S. Probability & Statistics

Understand and apply basic ideas related to the design, analysis, and interpretation of surveys and sampling, such as background information, random sampling, causality and bias.

PS.ED.8

High School

H.S. Probability & Statistics

Understand how basic statistical techniques are used to monitor process characteristics in the workplace.

PS.ED.9

High School

H.S. Probability & Statistics

Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each.

PS.P.1

High School

H.S. Probability & Statistics

Understand and use the addition rule to calculate probabilities for mutually exclusive and non mutually exclusive events.

PS.P.2

High School

H.S. Probability & Statistics

Understand and use the multiplication rule to calculate probabilities for independent and dependent events. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.