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Skills available for Virginia high school math standards

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Virginia Curriculum Framework: Algebra I Virginia Curriculum Framework: Algebra I
Virginia Curriculum Framework: Algebra II Virginia Curriculum Framework: Algebra II
Virginia Curriculum Framework: Algebra, Functions and Data Analysis Virginia Curriculum Framework: Algebra, Functions and Data Analysis
Virginia Curriculum Framework: Geometry Virginia Curriculum Framework: Geometry
Virginia Curriculum Framework: Mathematical Analysis Virginia Curriculum Framework: Mathematical Analysis
Virginia Curriculum Framework: Probability and Statistics Virginia Curriculum Framework: Probability and Statistics
Virginia Curriculum Framework: Trigonometry Virginia Curriculum Framework: Trigonometry
Virginia Standards of Learning (2016): Algebra I Virginia Standards of Learning (2016): Algebra I
Virginia Standards of Learning (2016): Algebra II Virginia Standards of Learning (2016): Algebra II
Virginia Standards of Learning (2016): Algebra, Functions and Data Analysis Virginia Standards of Learning (2016): Algebra, Functions and Data Analysis
Virginia Standards of Learning (2016): Geometry Virginia Standards of Learning (2016): Geometry
Virginia Standards of Learning (2016): Mathematical Analysis Virginia Standards of Learning (2016): Mathematical Analysis
Virginia Standards of Learning (2016): Probability and Statistics Virginia Standards of Learning (2016): Probability and Statistics
Virginia Standards of Learning (2016): Trigonometry Virginia Standards of Learning (2016): Trigonometry
Virginia College and Career Ready Performance Expectations Virginia College and Career Ready Performance Expectations
Virginia Standards of Learning (2023): Algebra 1 Virginia Standards of Learning (2023): Algebra 1
Virginia Standards of Learning (2023): Algebra 2 Virginia Standards of Learning (2023): Algebra 2
Virginia Standards of Learning (2023): Algebra, Functions and Data Analysis Virginia Standards of Learning (2023): Algebra, Functions and Data Analysis
Virginia Standards of Learning (2023): Discrete Mathematics Virginia Standards of Learning (2023): Discrete Mathematics
Virginia Standards of Learning (2023): Geometry Virginia Standards of Learning (2023): Geometry
Virginia Standards of Learning (2023): Mathematical Analysis Virginia Standards of Learning (2023): Mathematical Analysis
Virginia Standards of Learning (2023): Probability and Statistics Virginia Standards of Learning (2023): Probability and Statistics
Virginia Standards of Learning (2023): Trigonometry Virginia Standards of Learning (2023): Trigonometry

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PS.DC Data in Context

PS.DC.1 The student will use a statistical cycle to formulate questions, describe types of data, data sources, and constraints within the context of a problem.
- PS.DC.1.a Define the stages of the statistical cycle and how each stage relates to the others.
- PS.DC.1.b Formulate questions and conclusions based on context.
- PS.DC.1.c Understand the type of data relevant to the question at hand.
- PS.DC.1.d Compare and contrast population and sample, and parameter and statistic.
- PS.DC.1.e Identify and explain constraints of the statistical approach.
PS.DC.2 The student will compare and contrast data collection methods to plan and conduct an observational study.
- PS.DC.2.a Investigate and describe sampling techniques.
- PS.DC.2.b Determine which sampling technique is best, given a particular context.
- PS.DC.2.c Investigate and explain biased influences inherent within sampling methods and various forms of response bias.
  - Identify biased samples (PC-FF.1)
- PS.DC.2.d Use the statistical cycle to plan and conduct an observational study to answer a question or address a problem.
PS.DC.3 The student will utilize the principles of experimental design to plan and conduct a well-designed experiment.
- PS.DC.3.a Describe the principles of experimental design, including: treatment/control groups; blinding/placebo effects; experimental units/subjects; and blocking/matched pairs and completely randomized designs.
  - Experiment design (PC-FF.8)
- PS.DC.3.b Evaluate the principles of experimental design to address comparison, randomization, replication, and control within the context of the problem.
- PS.DC.3.c Compare and contrast controlled experiments and observational studies and the conclusions that may be drawn from each.
- PS.DC.3.d Use the statistical cycle to plan and conduct a well-designed experiment to answer a question or address a problem.
- PS.DC.3.e Select a data collection method appropriate for a given context.
  - Experiment design (PC-FF.8)

PS.DS Descriptive Statistics

PS.DS.1 The student will represent and analyze data visualizations of univariate quantitative data, including dot plots, stemplots, boxplots, cumulative frequency graphs, and histograms, to identify and describe patterns and departures from patterns, using central tendency, spread, clusters, gaps, and outliers, within the context of a problem.
- PS.DS.1.a Create and interpret graphical displays of data, including dot plots, stemplots, boxplots, cumulative frequency graphs, and histograms, using appropriate technology.
- PS.DS.1.b Examine the graphs within the context of the problem by analyzing: shape; measures of center; spread; and unusual features of the data.
PS.DS.2 The student will represent and analyze numerical characteristics of univariate quantitative data sets to describe patterns and departures from patterns within the context of a problem.
- PS.DS.2.a Interpret measures of central tendency: mean, median, and mode.
  - Mean, median, mode, and range (A1-II.2)
- PS.DS.2.b Interpret measures of spread: range, interquartile range, variance, and standard deviation.
- PS.DS.2.c Identify possible outliers, using an algorithm.
  - Identify an outlier (PC-FF.3)
- PS.DS.2.d Investigate and explain the influence of outliers on a univariate data set.
  - Identify an outlier and describe the effect of removing it (PC-FF.4)
- PS.DS.2.e Investigate and explain ways in which standard deviation addresses variability by examining the formula for standard deviation.
  - Variance and standard deviation (PC-FF.2)
PS.DS.3 The student will represent, compare, and analyze distributions of two or more univariate quantitative data sets, numerically and graphically.
- PS.DS.3.a Create graphical displays of data, including back-to-back stemplots, parallel dot plots, parallel boxplots, and histograms, using appropriate technology.
- PS.DS.3.b Compare and contrast two or more univariate data sets, numerically and graphically, within the context of a problem by analyzing: shape; measures of center; measures of spread; and unusual features of the data.
PS.DS.4 The student will represent and analyze categorical data, using two-way tables and other graphical displays, to describe patterns and relationships.
- PS.DS.4.a Create and interpret graphical displays of univariate categorical data, including bar graphs within the context of the problem, using appropriate technology.
  - Create bar graphs (A1)
  - Interpret bar graphs (A1)
- PS.DS.4.b Create and interpret graphical displays comparing distributions of two or more univariate categorical data sets including segmented and side-by-side bar graphs within the context of the problem, using appropriate technology.
- PS.DS.4.c Generate and interpret a two-way table as a summary of the information obtained from two categorical variables.
- PS.DS.4.d Calculate and interpret marginal, relative, and conditional frequencies to analyze data in a two-way table within the context of a problem.
  - Create relative frequency tables (G)
PS.DS.5 The student will represent and analyze quantitative bivariate data with scatterplots to identify and describe the relationship between two variables.
- PS.DS.5.a Create scatterplots, using appropriate technology.
  - Create scatter plots (A1)
- PS.DS.5.b Examine and interpret scatterplots in the context of the problem by analyzing: the form of relationship for linear and nonlinear trends; the direction of the relationship for positive, negative, or no association; the strength of the relationship such as strong, moderate, or weak; and the presence of unusual features within the data.
PS.DS.6 The student will create and interpret a linear model using the least squares regression method to assess the relationship between two quantitative variables.
- PS.DS.6.a Create the least squares regression model using technology to interpret the contextual meaning of the slope and y-intercept.
  - Find the equation of a regression line (PC-GG.4)
  - Interpret regression lines (PC-GG.5)
- PS.DS.6.b Using technology, calculate and interpret the correlation coefficient, r, within the context of a problem.
  - Match correlation coefficients to scatter plots (PC-GG.2)
  - Calculate correlation coefficients (PC-GG.3)
- PS.DS.6.c Using technology, calculate and interpret the coefficient of determination, r², within the context of a problem.
- PS.DS.6.d Use regression lines to make predictions, and identify the limitations of the predictions, such as extrapolation.
  - Analyze a regression line of a data set (PC-GG.6)
  - Analyze a regression line using statistics of a data set (PC-GG.7)
- PS.DS.6.e Calculate and interpret a residual to understand the error of a prediction.
- PS.DS.6.f Using technology, calculate and interpret the standard deviation of the residuals, s.

PS.P Probability

PS.P.1 The student will organize information and apply probability rules to compute probabilities of events within the context of a problem.
- PS.P.1.a Given two or more events, determine whether the events are complementary, dependent, independent, and/or mutually exclusive, and compute the probability of those events.
  - Probability of mutually exclusive events and overlapping events (A2)
  - Identify independent events (PC-CC.5)
- PS.P.1.b Represent and calculate probabilities using Venn diagrams, tree diagrams, and two-way tables.
- PS.P.1.c Apply the addition rule, the multiplication rule, and complementary rule to calculate probabilities.
  - Calculate probabilities of events (PC-CC.1)
  - Find probabilities using the addition rule (PC-CC.9)
- PS.P.1.d Calculate conditional probabilities to determine the association or independence of two events.
  - Find conditional probabilities (PC-CC.6)
  - Independence and conditional probability (PC-CC.7)
PS.P.2 The student will represent and interpret situations using discrete random distributions, including binomial distributions.
- PS.P.2.a Identify discrete random variables and create a table to represent valid discrete probability distributions within the context of a problem.
  - Identify discrete and continuous random variables (PC-DD.2)
  - Write a discrete probability distribution (PC-DD.3)
- PS.P.2.b Calculate and interpret the mean (expected value) and standard deviation for a discrete random variable within the context of a problem.
- PS.P.2.c Determine if a discrete random variable satisfies the conditions for a binomial distribution.
- PS.P.2.d Design and conduct a simulation of a binomial distribution.
- PS.P.2.e Calculate and interpret probabilities from a binomial distribution within the context of a problem.
  - Find probabilities using the binomial distribution (PC-EE.1)
- PS.P.2.f Calculate the mean and standard deviation for binomial distributions.
  - Mean, variance, and standard deviation of binomial distributions (PC-EE.2)
- PS.P.2.g Describe the center, shape, and spread of a discrete random variable within the context of a problem.
PS.P.3 The student will represent and interpret situations using normal distributions.
- PS.P.3.a Compare and contrast discrete and continuous distributions.
  - Identify discrete and continuous random variables (PC-DD.2)
- PS.P.3.b Represent probability as the area under the curve of a normal distribution using the Empirical Rule and graphing technology.
  - Find probabilities using the normal distribution I (PC-EE.3)
- PS.P.3.c Describe the center, shape, and spread of normal distributions within the context of a problem.
- PS.P.3.d Compare and contrast two or more sets of normally distributed data using z-scores, percentiles, or probabilities within the context of a problem.
- PS.P.3.e Standardize a data value from a normal distribution and interpret the z-score within the context of a problem.
  - Find z-values (PC-EE.5)
  - Find values of normal variables (PC-EE.6)
- PS.P.3.f Calculate and interpret probabilities of a normal distribution using technology within the context of a problem.

PS.IS Inferential Statistics

PS.IS.1 The student will apply properties of sampling distributions and inference procedures to make decisions about population proportions.
- PS.IS.1.a Describe the shape, center, and spread of the sampling distribution of a proportion within the context of a problem.
- PS.IS.1.b Given a problem, construct a one sample z confidence interval:
  - PS.IS.1.b.i identify the basic conditions for inference: random sample, independence, and normality;
    - Identify representative, random, and biased samples (A2)
  - PS.IS.1.b.ii calculate a confidence interval using technology; and
    - Find confidence intervals for population proportions (PC-FF.6)
  - PS.IS.1.b.iii interpret the interval within the context of the problem.
- PS.IS.1.c Explain how changes in confidence level and sample size affect width of the confidence interval and margin of error.
- PS.IS.1.d Calculate and interpret a point estimate and margin of error of a confidence interval for a proportion within the context of the problem.
- PS.IS.1.e Explain how and why the hypothesis testing procedure allows one to reach a statistical decision.
- PS.IS.1.f Given a problem, apply the one sample z hypothesis testing procedures:
  - PS.IS.1.f.i construct appropriate null and alternate hypotheses;
  - PS.IS.1.f.ii identify the basic conditions for inference: random sample; independence, and normality;
  - PS.IS.1.f.iii calculate and interpret the p-value using technology;
  - PS.IS.1.f.iv determine and justify whether to reject the null hypothesis; and
  - PS.IS.1.f.v interpret the results within the context of the problem.
- PS.IS.1.g Use the statistical cycle to plan and conduct a statistical study about a proportion to answer a question or address a problem with inference.
PS.IS.2 The student will apply properties of sampling distributions and inference procedures to make decisions about populations.
- PS.IS.2.a Describe the shape, center, and spread of the sampling distribution of a mean within the context of a problem.
  - Distributions of sample means (PC-EE.7)
- PS.IS.2.b Calculate and interpret a point estimate and a margin of error for a confidence interval of a mean within the context of a problem.
- PS.IS.2.c Describe the use of the Central Limit Theorem in satisfying the assumptions and conditions for inference about a mean.
  - The Central Limit Theorem (PC-EE.8)
- PS.IS.2.d Identify the properties of a t distribution.
- PS.IS.2.e Given a problem, construct a one sample t confidence interval:
  - PS.IS.2.e.i identify the basic conditions for inference: random sample, independence, and approximate normality;
    - Identify representative, random, and biased samples (A2)
  - PS.IS.2.e.ii calculate a confidence interval using technology; and
    - Find confidence intervals for population means (PC-FF.5)
  - PS.IS.2.e.iii interpret the interval within the context of the problem.
    - Interpret confidence intervals for population means (PC-FF.7)
    - Analyze the results of an experiment using simulations (PC-FF.9)
- PS.IS.2.f Given a problem, apply the one sample t hypothesis testing procedures:
  - PS.IS.2.f.i construct appropriate null and alternate hypotheses;
  - PS.IS.2.f.ii identify the basic conditions for inference: random sample, independence, and approximate normality;
  - PS.IS.2.f.iii calculate and interpret the p value using technology;
  - PS.IS.2.f.iv determine and justify whether to reject the null hypothesis; and
  - PS.IS.2.f.v interpret the results within the context of the problem.

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PS.DC Data in Context

PS.DC.1 The student will use a statistical cycle to formulate questions, describe types of data, data sources, and constraints within the context of a problem.

PS.DC.1.a Define the stages of the statistical cycle and how each stage relates to the others.

PS.DC.1.b Formulate questions and conclusions based on context.

PS.DC.1.c Understand the type of data relevant to the question at hand.

PS.DC.1.d Compare and contrast population and sample, and parameter and statistic.

PS.DC.1.e Identify and explain constraints of the statistical approach.

PS.DC.2 The student will compare and contrast data collection methods to plan and conduct an observational study.

PS.DC.2.a Investigate and describe sampling techniques.

PS.DC.2.b Determine which sampling technique is best, given a particular context.

PS.DC.2.c Investigate and explain biased influences inherent within sampling methods and various forms of response bias.

PS.DC.2.d Use the statistical cycle to plan and conduct an observational study to answer a question or address a problem.

PS.DC.3 The student will utilize the principles of experimental design to plan and conduct a well-designed experiment.

PS.DC.3.a Describe the principles of experimental design, including: treatment/control groups; blinding/placebo effects; experimental units/subjects; and blocking/matched pairs and completely randomized designs.

PS.DC.3.b Evaluate the principles of experimental design to address comparison, randomization, replication, and control within the context of the problem.

PS.DC.3.c Compare and contrast controlled experiments and observational studies and the conclusions that may be drawn from each.

PS.DC.3.d Use the statistical cycle to plan and conduct a well-designed experiment to answer a question or address a problem.

PS.DC.3.e Select a data collection method appropriate for a given context.

PS.DS Descriptive Statistics

PS.DS.1.a Create and interpret graphical displays of data, including dot plots, stemplots, boxplots, cumulative frequency graphs, and histograms, using appropriate technology.

PS.DS.1.b Examine the graphs within the context of the problem by analyzing: shape; measures of center; spread; and unusual features of the data.

PS.DS.2 The student will represent and analyze numerical characteristics of univariate quantitative data sets to describe patterns and departures from patterns within the context of a problem.

PS.DS.2.a Interpret measures of central tendency: mean, median, and mode.

PS.DS.2.b Interpret measures of spread: range, interquartile range, variance, and standard deviation.

PS.DS.2.c Identify possible outliers, using an algorithm.

PS.DS.2.d Investigate and explain the influence of outliers on a univariate data set.

PS.DS.2.e Investigate and explain ways in which standard deviation addresses variability by examining the formula for standard deviation.

PS.DS.3 The student will represent, compare, and analyze distributions of two or more univariate quantitative data sets, numerically and graphically.

PS.DS.3.a Create graphical displays of data, including back-to-back stemplots, parallel dot plots, parallel boxplots, and histograms, using appropriate technology.

PS.DS.3.b Compare and contrast two or more univariate data sets, numerically and graphically, within the context of a problem by analyzing: shape; measures of center; measures of spread; and unusual features of the data.

PS.DS.4 The student will represent and analyze categorical data, using two-way tables and other graphical displays, to describe patterns and relationships.

PS.DS.4.a Create and interpret graphical displays of univariate categorical data, including bar graphs within the context of the problem, using appropriate technology.

PS.DS.4.b Create and interpret graphical displays comparing distributions of two or more univariate categorical data sets including segmented and side-by-side bar graphs within the context of the problem, using appropriate technology.

PS.DS.4.c Generate and interpret a two-way table as a summary of the information obtained from two categorical variables.

PS.DS.4.d Calculate and interpret marginal, relative, and conditional frequencies to analyze data in a two-way table within the context of a problem.

PS.DS.5 The student will represent and analyze quantitative bivariate data with scatterplots to identify and describe the relationship between two variables.

PS.DS.5.a Create scatterplots, using appropriate technology.

PS.DS.6 The student will create and interpret a linear model using the least squares regression method to assess the relationship between two quantitative variables.

PS.DS.6.a Create the least squares regression model using technology to interpret the contextual meaning of the slope and y-intercept.

PS.DS.6.b Using technology, calculate and interpret the correlation coefficient, r, within the context of a problem.

PS.DS.6.c Using technology, calculate and interpret the coefficient of determination, r², within the context of a problem.

PS.DS.6.d Use regression lines to make predictions, and identify the limitations of the predictions, such as extrapolation.

PS.DS.6.e Calculate and interpret a residual to understand the error of a prediction.

PS.DS.6.f Using technology, calculate and interpret the standard deviation of the residuals, s.

PS.P Probability

PS.P.1 The student will organize information and apply probability rules to compute probabilities of events within the context of a problem.

PS.P.1.a Given two or more events, determine whether the events are complementary, dependent, independent, and/or mutually exclusive, and compute the probability of those events.

PS.P.1.b Represent and calculate probabilities using Venn diagrams, tree diagrams, and two-way tables.

PS.P.1.c Apply the addition rule, the multiplication rule, and complementary rule to calculate probabilities.

PS.P.1.d Calculate conditional probabilities to determine the association or independence of two events.

PS.P.2 The student will represent and interpret situations using discrete random distributions, including binomial distributions.

PS.P.2.a Identify discrete random variables and create a table to represent valid discrete probability distributions within the context of a problem.

PS.P.2.b Calculate and interpret the mean (expected value) and standard deviation for a discrete random variable within the context of a problem.

PS.P.2.c Determine if a discrete random variable satisfies the conditions for a binomial distribution.

PS.P.2.d Design and conduct a simulation of a binomial distribution.

PS.P.2.e Calculate and interpret probabilities from a binomial distribution within the context of a problem.

PS.P.2.f Calculate the mean and standard deviation for binomial distributions.

PS.P.2.g Describe the center, shape, and spread of a discrete random variable within the context of a problem.

PS.P.3 The student will represent and interpret situations using normal distributions.

PS.P.3.a Compare and contrast discrete and continuous distributions.

PS.P.3.b Represent probability as the area under the curve of a normal distribution using the Empirical Rule and graphing technology.

PS.P.3.c Describe the center, shape, and spread of normal distributions within the context of a problem.

PS.P.3.d Compare and contrast two or more sets of normally distributed data using z-scores, percentiles, or probabilities within the context of a problem.

PS.P.3.e Standardize a data value from a normal distribution and interpret the z-score within the context of a problem.

PS.P.3.f Calculate and interpret probabilities of a normal distribution using technology within the context of a problem.

PS.IS Inferential Statistics

PS.IS.1 The student will apply properties of sampling distributions and inference procedures to make decisions about population proportions.

PS.IS.1.a Describe the shape, center, and spread of the sampling distribution of a proportion within the context of a problem.

PS.IS.1.b Given a problem, construct a one sample z confidence interval:

PS.IS.1.b.i identify the basic conditions for inference: random sample, independence, and normality;

PS.IS.1.b.ii calculate a confidence interval using technology; and

PS.IS.1.b.iii interpret the interval within the context of the problem.

PS.IS.1.c Explain how changes in confidence level and sample size affect width of the confidence interval and margin of error.

PS.IS.1.d Calculate and interpret a point estimate and margin of error of a confidence interval for a proportion within the context of the problem.

PS.IS.1.e Explain how and why the hypothesis testing procedure allows one to reach a statistical decision.

PS.IS.1.f Given a problem, apply the one sample z hypothesis testing procedures:

PS.IS.1.f.i construct appropriate null and alternate hypotheses;