**Number:**MA.7.DP.2

**Title:**Develop an understanding of probability. Find and compare experimental and theoretical probabilities.

**Type:**Standard

**Subject:**Mathematics (B.E.S.T.)

**Grade:**7

**Strand:**Data Analysis and Probability

## Related Benchmarks

## Related Access Points

## Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Perspectives Video: Experts

## Problem-Solving Tasks

## Text Resource

## Tutorials

## Student Resources

## Original Student Tutorial

Learn how to calculate the probability of simple events, that probability is the likeliness of an event occurring, and that some events may be more likely than others to occur in this interactive tutorial.

Type: Original Student Tutorial

## Problem-Solving Tasks

This task asks students to calculate probabilities using information presented in a two-way frequency table.

Type: Problem-Solving Task

The purpose of this task is to provide students with the opportunity to determine experimental probabilities by collecting data. The cylindrical objects used in this task typically have three different resting positions but not all of these may be equally likely and some may be extremely unlikely or impossible when the object is tossed. Furthermore, obtaining the probabilities of the outcomes is perhaps only possible through the use of long-run relative frequencies. This is because these cylinders do not have the same types of symmetries as objects that are often used as dice, such as cubes or tetrahedrons, where each outcome is equally likely.

Type: Problem-Solving Task

This resource involves a simple data-gathering activity which furnishes data that students organize into a table. They are then asked to refer to the data and determine the probability of various outcomes.

Type: Problem-Solving Task

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). In the task built around an election poll scenario, the population is the entire seventh grade class, the unknown characteristic (parameter) of interest is the proportion of the class members voting for a specific candidate, and the sample summary (statistic) is the observed proportion of voters favoring the candidate in a random sample of class members. Variation 2 leads students through a physical simulation for generating sample proportions by sampling, and re-sampling, marbles from a box.

Type: Problem-Solving Task

This task is intended as a classroom activity. Students pool the results of many repetitions of the random phenomenon (rolling dice) and compare their results to the theoretical expectation they develop by considering all possible outcomes of rolling two dice. This gives them a concrete example of what we mean by long term relative frequency.

Type: Problem-Solving Task

The purpose of this task is for students to compute the theoretical probability of a seating configuration. There are 24 possible configurations of the four friends at the table in this problem. Students could draw all 24 configurations to solve the problem but this is time consuming and so they should be encouraged to look for a more systematic method.

Type: Problem-Solving Task

## Tutorials

This video demonstrates several examples of finding probability of random events.

Type: Tutorial

This video discusses the limits of probability as between 0 and 1.

Type: Tutorial

This video compares theoretical and experimantal probabilities and sources of possible discrepancy.

Type: Tutorial

This video demonstrates how to find the probability of a simple event.

Type: Tutorial

Watch the video as it predicts the number of times a spinner will land on a given outcome.

Type: Tutorial

## Parent Resources

## Problem-Solving Tasks

This task asks students to calculate probabilities using information presented in a two-way frequency table.

Type: Problem-Solving Task

The purpose of this task is to provide students with the opportunity to determine experimental probabilities by collecting data. The cylindrical objects used in this task typically have three different resting positions but not all of these may be equally likely and some may be extremely unlikely or impossible when the object is tossed. Furthermore, obtaining the probabilities of the outcomes is perhaps only possible through the use of long-run relative frequencies. This is because these cylinders do not have the same types of symmetries as objects that are often used as dice, such as cubes or tetrahedrons, where each outcome is equally likely.

Type: Problem-Solving Task

This resource involves a simple data-gathering activity which furnishes data that students organize into a table. They are then asked to refer to the data and determine the probability of various outcomes.

Type: Problem-Solving Task

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). In the task built around an election poll scenario, the population is the entire seventh grade class, the unknown characteristic (parameter) of interest is the proportion of the class members voting for a specific candidate, and the sample summary (statistic) is the observed proportion of voters favoring the candidate in a random sample of class members. Variation 2 leads students through a physical simulation for generating sample proportions by sampling, and re-sampling, marbles from a box.

Type: Problem-Solving Task

This task is intended as a classroom activity. Students pool the results of many repetitions of the random phenomenon (rolling dice) and compare their results to the theoretical expectation they develop by considering all possible outcomes of rolling two dice. This gives them a concrete example of what we mean by long term relative frequency.

Type: Problem-Solving Task

The purpose of this task is for students to compute the theoretical probability of a seating configuration. There are 24 possible configurations of the four friends at the table in this problem. Students could draw all 24 configurations to solve the problem but this is time consuming and so they should be encouraged to look for a more systematic method.

Type: Problem-Solving Task