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Skills available for Colorado high school math standards

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9-12.1 Number Sense, Properties, and Operations

9-12.2 Patterns, Functions, and Algebraic Structures

9-12.3 Data Analysis, Statistics, and Probability

  • 9-12.3.1 Visual displays and summary statistics condense the information in data sets into usable knowledge

    • 9-12.3.1.a Summarize, represent, and interpret data on a single count or measurement variable

    • 9-12.3.1.b Summarize, represent, and interpret data on two categorical and quantitative variables

      • 9-12.3.1.b.i Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

      • 9-12.3.1.b.ii Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

        • 9-12.3.1.b.ii.1 Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

        • 9-12.3.1.b.ii.2 Informally assess the fit of a function by plotting and analyzing residuals.

        • 9-12.3.1.b.ii.3 Fit a linear function for a scatter plot that suggests a linear association.

    • 9-12.3.1.c Interpret linear models

      • 9-12.3.1.c.i Interpret the slope and the intercept of a linear model in the context of the data.

      • 9-12.3.1.c.ii Using technology, compute and interpret the correlation coefficient of a linear fit.

      • 9-12.3.1.c.iii Distinguish between correlation and causation.

  • 9-12.3.2 Statistical methods take variability into account supporting informed decisions making through quantitative studies designed to answer specific questions

    • 9-12.3.2.a Understand and evaluate random processes underlying statistical experiments

      • 9-12.3.2.a.i Describe statistics as a process for making inferences about population parameters based on a random sample from that population.

      • 9-12.3.2.a.ii Decide if a specified model is consistent with results from a given data-generating process.

    • 9-12.3.2.b Make inferences and justify conclusions from sample surveys, experiments, and observational studies

      • 9-12.3.2.b.i Identify the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

      • 9-12.3.2.b.ii Use data from a sample survey to estimate a population mean or proportion.

      • 9-12.3.2.b.iii Develop a margin of error through the use of simulation models for random sampling.

      • 9-12.3.2.b.iv Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

      • 9-12.3.2.b.v Define and explain the meaning of significance, both statistical (using p-values) and practical (using effect size).

      • Evaluate reports based on data.

  • 9-12.3.3 Probability models outcomes for situations in which there is inherent randomness

    • 9-12.3.3.a Understand independence and conditional probability and use them to interpret data

      • 9-12.3.3.a.i Describe events as subsets of a sample space using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events.

      • 9-12.3.3.a.ii Explain 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.

      • 9-12.3.3.a.iii Using the conditional probability of A given B as P(A and B)/P(B), interpret the independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

      • 9-12.3.3.a.iv 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.

      • 9-12.3.3.a.v Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

    • 9-12.3.3.b Use the rules of probability to compute probabilities of compound events in a uniform probability model

      • 9-12.3.3.b.i Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.

      • 9-12.3.3.b.ii Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.

    • 9-12.3.3.c Analyze the cost of insurance as a method to offset the risk of a situation

9-12.4 Shape, Dimension, and Geometric Relationships