Mathematics: Probability

• Standard 1: Problem Solving
• Standard 2: Communication
• Standard 3: Reasoning
• Standard 4: Connections
• Standard 5: Estimation & Computation
• Standard 6: Numeration & Number Theory
• Standard 7: Geometry
• Standard 8: Measurement
• Standard 9: Statistics
• Standard 11: Algebra
• Standard 12: Patterns, Relations, Functions
• Introduction to Mathematics
• Table of Contents - All Standards

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Content Standard: Probability

Students will demonstrate knowledge of probability concepts to make decisions about real world situations involving uncertainty.

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Fourth Grade Performance Standards: Probability

By the end of grade Four, students will:

Work with data in the context of real-world situations by

• formulating questions that lead to data collection and analysis
• determining what data to collect and when and how to collect them
• collecting, organizing, and displaying data
• drawing reasonable conclusions based on data

Describe a set of data using

• high and low values, and range
• most frequent value (mode)
• middle value of a set of ordered data (median)

In problem-solving situations, read, extract, and use information presented in graphs, tables, or charts

Determine if future events are more, less, or equally likely, impossible, or certain to occur

Predict outcomes of future events and test predictions using data from a variety of sources

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Eighth Grade Performance Standards: Probability

By the end of grade Eight, students will:

Work with data in the context of real-world situations by

• formulating questions that lead to data collection and analysis
• designing and conducting a statistical investigation
• using technology to generate displays, summary statistics, and presentations

Organize and display data from statistical investigations using

• appropriate tables, graphs, and/or charts (e.g., circle, bar or line for multiple sets of data)
• appropriate plots (e.g., line, stem-and-leaf, box, scatter)

Extract, interpret, and analyze information from organized and displayed data by using

• frequency and distribution, including mode and range
• central tendencies of data (mean and median)
• indicators of dispersion (e.g., outliers)

Use the results of data analysis to

• make predictions
• develop convincing arguments
• draw conclusions

Compare several sets of data to generate, test, and, as the data dictate, confirm or deny hypotheses

Evaluate presentations and statistical analyses from a variety of sources for

• credibility of the source
• techniques of collection, organization, and presentation of data
• missing or incorrect data
• inferences
• possible sources of bias

Determine the likelihood of occurrence of simple events by

• using a variety of strategies to identify possible outcomes (e.g., lists, tables, tree diagrams)
• conducting an experiment
• designing and conducting simulations
• applying theoretical notions of probability (e.g., that four equally likely events have a 25% chance of happening)

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Grade Level Performance Standards: Grade Six: Probability

The student will:

Construct a sample space and calculate the numerical probability.

Determine the probability of events occurring from a sample space and predict the number of times events will occur in given situations.

Develop an algorithm for the number of combinations possible in sets of at least four objects.

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Grade Level Performance Standards: Grade Seven: Probability

The student will:

Use technology to determine probabilities in complex situations.

Simulate real life probability problems and predict future outcomes based on probability experiments.

Construct sample spaces to determine theoretical probabilities of real life situations.

Determine combinations and permutations for situations involving at least four variables.

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Grade Level Performance Standards: Grade Eight: Probability

The student will:

Use tables of outcomes from sample spaces to predict the probability of future events.

Construct area models to determine expected values of probability situations.

Predict the theoretical probability of an event occurring after analyzing trial data.

Compare trial data and technology-simulated results to theoretical probabilities.

Determine combinations and permutations for situations involving at least four variables.

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Twelfth Grade Performance Standards: Probability

By the end of grade Twelve, students will:

Work with data in the context of real-world situations by

• formulating hypotheses that lead to collection and analysis of one- and two-variable data
• designing a data collection plan that considers random sampling, control groups, the role of assumptions, etc.
• conducting an investigation based on that plan
• using technology to generate displays, summary statistics, and presentations

Organize and display data from statistical investigations using

• frequency distributions
• percentiles, quartiles, deciles
• line of best fit (estimated regression line)
• matrices

Interpret and analyze information from organized and displayed data when given

• measures of dispersion, including standard deviation and variance
• measures of reliability
• measures of correlation

Analyze, evaluate, and critique the methods and conclusions of statistical experiments reported in journals, magazines, news media, advertising, etc.

Determine the likelihood of occurrence of complex events by

• using a variety of strategies (e.g., combinations) to identify possible outcomes
• conducting an experiment
• designing and conducting simulations
• applying theoretical probability

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