Math Learning Progressions

[S] Statistics and Probability

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Math Learning Progressions   HS Math Concepts

[S] Statistics and Probability

K 1 2 3 4 5 6 7 8
[MD] Measurement and Data [SP] Statistics and Probability

Students’ prior knowledge includes:

  • Students investigate patterns of association in bivariate data (grade 8)
  • Students use random sampling to draw inferences about a population (grade 7)
  • Students draw informal comparative inferences about two populations (grade 7)
  • Students investigate chance processes and develop, use, and evaluate probability models (grade 7)
  • Students develop an understanding of statistical variability (grade 6)
  • Students summarize and describe distributions (grade 6)
Interpreting Categorical and Quantitative Data
  • Summarize, represent, and interpret data on a single count or measurement variable.
  • Summarize, represent, and interpret data on two categorical and quantitative variables.
  • Interpret linear models.
Making Inferences and Justifying Conclusions
  • Understand and evaluate random processes underlying statistical experiments.
  • Make inferences and justify conclusions from sample surveys, experiments and observational studies.
Conditional Probability and the Rules of Probability
  • Understand independence and conditional probability and use them to interpret data.
  • Use the rules of probability to compute probabilities of compound events in a uniform probability model.
Using Probability to Make Decisions
  • Calculate expected values and use them to solve problems.
  • Use probability to evaluate outcomes of decisions.

MAT-HS.S [S] Overview: Statistics and Probability

MAT-HS.S-ID Domain: [S-ID] Interpreting Categorical and Quantitative Data

    • MAT-HS.S-ID.01 Represent data with plots on the real number line
    • MAT-HS.S-ID.02 Use statistics to compare center and spread of two or more data sets
    • MAT-HS.S-ID.03 Interpret differences in shape/center/spread of data, accounting for outliers
    • MAT-HS.S-ID.04 Use the mean and standard deviation of a data set for normal distribution
    • MAT-HS.S-ID.05 Summarize categorical data for two categories in twoway frequency tables
    • MAT-HS.S-ID.06 Represent data on two quantitative variables on a scatter plot
      • S-ID.06.a Fit a function to the data to solve problems
      • S-ID.06.b Informally assess the fit of a function by plotting and analyzing residuals
      • S-ID.06.c Fit a linear function for a scatter plot that suggests a linear association
    • MAT-HS.S-ID.07 interpret the Slope and the Intercept of a linear model in context of data
    • MAT-HS.S-ID.08 Compute and interpret the correlation coefficient of a linear fit
    • MAT-HS.S-ID.09 Distinguish between correlation and causation

 

MAT-HS.S-IC Domain: [S-IC] Making Inferences and Justifying Conclusions

    • MAT-HS.S-IC.01 Understand statistics as a process for making inferences based on random sample
    • MAT-HS.S-IC.02 Decide if a model is consistent with results from a data-generating process
    • MAT-HS.S-IC.03 Compare the purposes of surveys/experiments/observational studies
    • MAT-HS.S-IC.04 Use data from a sample survey to estimate a population mean or proportion
    • MAT-HS.S-IC.05 Use data from a randomized experiment to compare two treatments
    • MAT-HS.S-IC.06 Evaluate reports based on data

 

MAT-HS.S-CP Domain: [S-CP] Conditional Probability and the Rules of Probability

    • MAT-HS.S-CP.01 Describe events as subsets of a sample space using characteristics
    • MAT-HS.S-CP.02 Using probabilities, understand and show that two events are independent
    • MAT-HS.S-CP.03 Understand the conditional probability of A given B as P(A and B)/P(B
    • MAT-HS.S-CP.04 Construct and interpret two-way frequency tables of data
    • MAT-HS.S-CP.05 Recognize and explain the concepts of conditional probability and independence
    • MAT-HS.S-CP.06 Find the probability of A given B as the fraction of B??s outcomes belong to A
    • MAT-HS.S-CP.07 Apply and interpret the Addition Rule of probability
    • MAT-HS.S-CP.08 Apply the general Multiplication Rule in a uniform probability model
    • MAT-HS.S-CP.09 Use permutations and combinations to compute probabilities

 

MAT-HS.S-MD Domain: [S-MD] Using Probability to Make Decisions

    • MAT-HS.S-MD.01 Define a random variable for a quantity of interest by assigning a numerica
    • MAT-HS.S-MD.02 Calculate the expected value of a random variable; interpret it as the mean
    • MAT-HS.S-MD.03 Develop a probability distribution for a random variable defined for a samp
    • MAT-HS.S-MD.04 Develop a probability distribution for a random variable defined for a samp
    • MAT-HS.S-MD.05 Weigh outcomes of a decision by assigning probabilities to payoff values
      • S-MD.05.a Find the expected payoff for a game of chance
      • S-MD.05.b Evaluate and compare strategies on the basis of expected values
    • MAT-HS.S-MD.06 Use probabilities to make fair decisions
    • MAT-HS.S-MD.07 Analyze decisions and strategies using probability concepts

 

A Sample of HS Math Concept Statistics and Probability your child will be learning

Interpreting Categorical and Quantitative Data

  • Summarize, represent, and interpret data on a single count or measurement variable.
  • Summarize, represent, and interpret data on two categorical and quantitative variables.
  • Interpret linear models.

Making Inferences and Justifying Conclusions

  • Understand and evaluate random processes underlying statistical experiments.
  • Make inferences and justify conclusions from sample surveys, experiments and observational studies.

Conditional Probability and the Rules of Probability

  • Understand independence and conditional probability and use them to interpret data.
  • Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Using Probability to Make Decisions

  • Calculate expected values and use them to solve problems.
  • Use probability to evaluate outcomes of decisions.