Standard #: MAFS.7.SP.3.6 (Archived Standard)


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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
Grade: 7
Domain-Subdomain: Statistics & Probability
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

Test Item Specifications

    N/A

    Assessment Limits :

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

     

    Calculator :

    Neutral

    Context :

    Required



Sample Test Items (2)

Test Item # Question Difficulty Type
Sample Item 1

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?

N/A EE: Equation Editor
Sample Item 2

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?

N/A EE: Equation Editor


Related Courses

Course Number1111 Course Title222
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 Resources

Formative Assessments

Name Description
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.

Hen Eggs

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

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.

Image/Photograph

Name Description
Clipart ETC: Probability Clipart images that relate to probability.

Lesson Plans

Name Description
Genetics and Proportions Design Challenge

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

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.

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.

Evaluating Statements About Probability 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.
Ideas that Lead to Probability
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.
Roll of the Dice and Some Turkey Fun!

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

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.

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)

Original Student Tutorial

Name Description
Predicting Outcomes at the Carnival

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

Perspectives Video: Experts

Name Description
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?

Download the CPALMS Perspectives video student note taking guide.

Probabilistic Weather Modeling

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

Download the CPALMS Perspectives video student note taking guide.

Problem-Solving Tasks

Name Description
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

Name Description
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.

Tutorials

Name Description
Making Predictions with Probability

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

Constructing Probability Model from Observations

This video demonstrates development and use of a probability model.

Virtual Manipulatives

Name Description
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.

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.

Plinko Probability

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.

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.

Student Resources

Original Student Tutorial

Name Description
Predicting Outcomes at the Carnival:

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

Problem-Solving Tasks

Name Description
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

Name Description
Making Predictions with Probability:

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

Constructing Probability Model from Observations:

This video demonstrates development and use of a probability model.

Virtual Manipulatives

Name Description
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.

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.

Plinko Probability:

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.

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.



Parent Resources

Problem-Solving Tasks

Name Description
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.



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