# MAFS.7.SP.3.6Archived Standard Export Print
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. 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.
General Information
Subject Area: Mathematics
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 of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications

• Assessment Limits :

Long-run frequency should be greater than or equal to 300.

• Calculator :

Neutral

• Context :

Required

Sample Test Items (2)
• 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

This benchmark is part of these courses.
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Probabilities Cubed:

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.

Type: Formative Assessment

Hen Eggs:

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

Type: Formative Assessment

Game of Chance:

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.

Type: Formative Assessment

## Image/Photograph

Clipart ETC: Probability:

Clipart images that relate to probability.

Type: Image/Photograph

## Lesson Plans

Genetics and Proportions Design Challenge:

Students will explore principles of heredity through an activity where they design a themed Potato Head toy set.

Type: Lesson Plan

Let's Flip Out:

This lesson is designed to follow a lesson that teaches theoretical probability. The students should have a strong foundation in theoretical probability, understanding how to find theoretical probability for a given situation. In this lesson students will roll a number cube and flip a coin to find the relative frequency for a given simulation.

Type: Lesson Plan

Garbage Can Hoops:

This lesson guides students through an experiment to learn about relative frequencies and probability of events occurring. Students discover what happens when repeatedly tossing a paper ball (balled up paper) from:

• a relatively short distance (5 ft.) from a garbage can;
• a relatively medium distance (10 ft.) from the garbage can;
• a relatively long distance (15 ft.) from the garbage can.

Students participate in the experiment and compare their predictions to the experimental outcomes of others. They propose and refine conjectures about relative frequency probability.

Type: Lesson Plan

This lesson unit addresses common misconceptions relating to probability of simple and compound events. The lesson will help you assess how well students understand concepts of equally likely events, randomness and sample sizes.

Type: Lesson Plan

This lesson is designed to introduce students to random numbers and fairness as a precursor to learning about probability. The lesson provides links to discussions and activities related to probability and fairness as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with this one.

Type: Lesson Plan

Roll of the Dice and Some Turkey Fun!:

Students will conduct experiments on their own to see the difference between experimental and theoretical probabilities.

Type: Lesson Plan

A Roll of the Dice:

What are your chances of tossing a particular number on a number cube? Students collect data by experimenting and then converting the data in terms of probability. By the end of the lesson, students should have a basic understanding of simple events.

Type: Lesson Plan

Marble Mania:

In this lesson, "by flipping coins and pulling marbles out of a bag, students begin to develop a basic understanding of probabilities, how they are determined, and how the outcome of an experiment can be affected by the number of times it is conducted." (from Science NetLinks)

Type: Lesson Plan

Who Would Have Figured? (Probability):

"Students discover what happens when a coin is tossed a few times versus when a coin is tossed many times. They discover the answer to "What is the probability of heads, and does it change as you toss the coin more times?" from Beacon Learning Center.

Type: Lesson Plan

## Original Student Tutorial

Predicting Outcomes at the Carnival:

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

Type: Original Student Tutorial

## Perspectives Video: Experts

How Math Models Help Insurance Companies After a Hurricane Hits:

Hurricanes can hit at any time! How do insurance companies use math and weather data to help to restore the community?

Type: Perspectives Video: Expert

Probabilistic Weather Modeling:

Meteorologist from Risk Management discusses the use of probability in predicting hurricane tracks.

Type: Perspectives Video: Expert

Tossing Cylinders:

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.

Rolling Dice:

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.

## Text Resource

Shuffling Shenanigans:

This informational text resource is intended to support reading in the content area. A student in love with magic card tricks asks and answers his own math questions after pursuing a career as a mathematician in order to solve them. How many times must a deck be shuffled to achieve a truly random mix of cards? The answer lies within.

Type: Text Resource

## Tutorials

Making Predictions with Probability:

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

Type: Tutorial

Constructing Probability Model from Observations:

This video demonstrates development and use of a probability model.

Type: Tutorial

## Virtual Manipulatives

Spinner:

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

Interactive Marbles:

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

Random Drawing Tool - Individual Trials (Probability Simulation):

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

## MFAS Formative Assessments

Game of Chance:

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.

Hen Eggs:

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

Probabilities Cubed:

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

Predicting Outcomes at the Carnival:

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

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorial

Predicting Outcomes at the Carnival:

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

Type: Original Student Tutorial

Tossing Cylinders:

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.

Rolling Dice:

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.

## Tutorials

Making Predictions with Probability:

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

Type: Tutorial

Constructing Probability Model from Observations:

This video demonstrates development and use of a probability model.

Type: Tutorial

## Virtual Manipulatives

Spinner:

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

Interactive Marbles:

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

Random Drawing Tool - Individual Trials (Probability Simulation):

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

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.