*For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.*

**Subject Area:**Mathematics

**Grade:**7

**Domain-Subdomain:**Statistics & Probability

**Cluster:**Level 2: Basic Application of Skills & Concepts

**Cluster:**Investigate chance processes and develop, use, and evaluate probability models. (Supporting Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved - Archived

**Assessed:**Yes

**Assessment Limits :**Long-run frequency should be greater than or equal to 300.

**Calculator :**Neutral

**Context :**Required

**Test Item #:**Sample Item 1**Question:**A spinner is divided into equal parts 1-5. George spun the spinner 300 times. A table of outcomes is shown.

Based on the table, what is an estimated probability of the spinner landing on an even number?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 2**Question:**A spinner is divided into blue, green, and red parts. George spins the spinner 300 times. A table of outcomes is shown.

Based on this data, what is the estimated probability of the spinner landing on red?

**Difficulty:**N/A**Type:**EE: Equation Editor

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Image/Photograph

## Lesson Plans

## Original Student Tutorial

## Perspectives Video: Experts

## Problem-Solving Tasks

## Text Resource

## Tutorials

## Virtual Manipulatives

## MFAS Formative Assessments

Students are asked to estimate the frequency of an event given its probability and explain why an expected frequency might differ from an observed frequency.

Students are asked to estimate the probability of a chance event based on observed frequencies.

Students are asked to estimate the frequency of an event given its probability and explain why an expected frequency might differ from an observed frequency.

## Original Student Tutorials Mathematics - Grades 6-8

Learn how to use probability to predict expected outcomes at the Carnival in this interactive tutorial.

## Student Resources

## Original Student Tutorial

Learn how to use probability to predict expected outcomes at the Carnival in this interactive tutorial.

Type: Original Student Tutorial

## Problem-Solving Tasks

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 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

## Tutorials

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

Type: Tutorial

This video demonstrates development and use of a probability model.

Type: Tutorial

## Virtual Manipulatives

In this activity, students adjust how many sections there are on a fair spinner then run simulated trials on that spinner as a way to develop concepts of probability. A table next to the spinner displays the theoretical probability for each color section of the spinner and records the experimental probability from the spinning trials. This activity allows students to explore the topics of experimental and theoretical probability by seeing them displayed side by side for the spinner they have created. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

This online manipulative allows the student to simulate placing marbles into a bag and finding the probability of pulling out certain combinations of marbles. This allows exploration of probabilities of multiple events as well as probability with and without replacement. The tabs above the applet provide access to supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.

Type: Virtual Manipulative

The students will play a classic game from a popular show. Through this they can explore the probability that the ball will land on each of the numbers and discover that more accurate results coming from repeated testing. The simulation can be adjusted to influence fairness and randomness of the results.

Type: Virtual Manipulative

This virtual manipulative allows one to make a random drawing box, putting up to 21 tickets with the numbers 0-11 on them. After selecting which tickets to put in the box, the applet will choose tickets at random. There is also an option which will show the theoretical probability for each ticket.

Type: Virtual Manipulative

## Parent Resources

## Problem-Solving Tasks

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 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