# MAFS.7.SP.3.5

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
General Information
Subject Area: Mathematics
Domain-Subdomain: Statistics & Probability
Cluster: Level 1: Recall
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
Assessed: Yes
Test Item Specifications

• Assessment Limits :

N/A

• Calculator :

Neutral

• Context :

Required

Sample Test Items (3)
• Test Item #: Sample Item 1
• Question:

The local weather report stated there is a  chance of rain on Friday. How likely is it to rain?

• Difficulty: N/A
• Type: MC: Multiple Choice

• Test Item #: Sample Item 2
• Question:

The weather report stated there is a  chance of rain on Friday, but it is more likely to rain on Saturday than on Friday.

What is a possible probability of rain on Saturday?

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

• Test Item #: Sample Item 3
• Question:

The local weather report states that there is more than a  chance of rain for Saturday.

What is the likelihood that it will rain on Saturday?

• Difficulty: N/A
• Type: MC: Multiple Choice

## Related Courses

This benchmark is part of these courses.
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1205050: M/J Grade 7 Accelerated Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
2002050: M/J Comprehensive Science 1, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
2002070: M/J Comprehensive Science 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
2002080: M/J Comprehensive Science 2, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
2001020: M/J Earth/Space Science, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
2000020: M/J Life Science, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
2003010: M/J Physical Science (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
2003020: M/J Physical Science, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
1508200: M/J Team Sports - Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2019 (course terminated))
1508300: M/J Outdoor Pursuits/Aquatics - Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2019 (course terminated))
1508700: M/J Comprehensive - Grades 7/8 (Specifically in versions: 2014 - 2015, 2015 - 2019 (course terminated))
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond)
7820016: Access M/J Comprehensive Science 2 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 and beyond)
2002055: M/J Comprehensive Science 1 Accelerated Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
1508020: M/J Team Sports - Grade 7 (Specifically in versions: 2019 - 2022, 2022 and beyond)
1508030: M/J Outdoor Pursuits/Aquatics - Grade 7 (Specifically in versions: 2019 - 2022, 2022 and beyond)
1508070: M/J Comprehensive Physical Education Grade 7/8 (Specifically in versions: 2019 - 2022, 2022 and beyond)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.7.SP.3.AP.5a: Define the probability of related events given a situation of chance.

## Related Resources

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

## Assessments

Sample 3 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

Sample 1 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

## Formative Assessments

Probability or Not?:

Students are asked to determine whether or not a given number could represent the probability of an event.

Type: Formative Assessment

Likely or Unlikely?:

Students are asked to determine the likelihood of an event given a probability.

Type: Formative Assessment

Likelihood of an Event:

Students are asked to determine the likelihood of an event given a probability.

Type: Formative Assessment

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
• Sample sizes

Type: Formative Assessment

## Lesson Plans

Basic Probability Concepts:

This lesson is meant to build on students knowledge of probability. It is designed to teach and reinforce the concept that all probabilities are a number somewhere between zero and one.

Type: Lesson Plan

Tree Diagrams and Probability:

This lesson is designed to develop students' ability to create tree diagrams and figure probabilities of events based on those diagrams. This lesson provides links to discussions and activities related to tree diagrams as well as suggested ways to work them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

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

Probability:

This lesson is designed to develop students' understanding of probability in real life situations. Students will also be introduced to running experiments, experimental probability, and theoretical probability. This lesson provides links to discussions and activities related to probability 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 the current one.

Type: Lesson Plan

When Pigs Fly:

In this lesson students will explore probability and likelihood that an event will occur. They will place both serious and silly events on a number line, once they have assigned a value to that event. They will work with a group and then justify their classifications to their peers.

Type: Lesson Plan

Practically Probable:

In this lesson, students will differentiate between likely and unlikely event, as well as learn the difference between dependent and independent events. Finally, they learn how to compute theoretical probabilities in simple experiments.

Type: Lesson Plan

Planning the perfect wedding:

Students will decide what is the best month to celebrate an outdoor wedding. The couple is looking for the perfect wedding day. What is the definition of a perfect day? It has to be a Saturday or Sunday with a 20% or less probability of rain and sunny but not too hot. Based on the information provided , students will find the month in which the probability of having a rainy day and the probability of having a super hot day (temperature higher than 75ยบ F) are minimal.

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

This activity will allow students to explore the concept of simple probability using a random selection of multi-colored beads.

Type: Lesson Plan

Introduction to Probability:

This resource is designed to introduce students to the concept of probability: the probability of a rare event is represented by a positive number close to zero, the probability of a nearly certain event occurring is represented by a positive number slightly less than one. Students will indicate the approximate probability of events on a number line and determine which events are more likely than others.

Type: Lesson Plan

## Original Student Tutorial

Introduction to Probability:

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

## Perspectives Video: Expert

History of Probability and the Problem of Points:

What was the first question that started probability theory?

Type: Perspectives Video: Expert

The Titanic 1:

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

## 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

The Limits of Probability:

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

Type: Tutorial

Creating the probability of an event by making a sum of 1:

This tutorial will help the learners with their understanding of how to calculate the probability of an event by making a sum of 1.

Type: Tutorial

## Virtual Manipulatives

Hamlet Happens:

The purpose of this manipulative is to help students recognize that (1) unusual events do happen, and (2) it may take a longer time for some of them to happen. The letters are drawn at random from the beginning of Hamlet's soliloquy, "To be, or not to be." Any word made from those letters (such as TO) can be entered in the box. When the start is pressed, letters are drawn and recorded. The process continues until the word appears.

Type: Virtual Manipulative

Fire!!:

In this activity, students burn a simulated forest and adjust the probability that the fire spreads from one tree to the other. This activity allows students to explore the idea of chaos in a simulation of a realistic scenario. 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. This activity would work well in mixed ability groups of two for about 30-35 minutes if you use the provided exploration questions and 10-15 minutes otherwise.

Type: Virtual Manipulative

Spinners:

This virtual manipulative can be used demonstrate random probability and to teach about chance and random choices. Use this free, fully customizable, online spinner to create probability scenarios involving numerous choices, or create advanced, unevenly split spinners to demonstrate and model real life scenarios.

This spinner also incorporates a bar graph to record and model the outcome of each spin.

Type: Virtual Manipulative

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

Probability Models:

Explore probability topics by modeling coin tossing, free throwing shooting, and manufacturing defects with this virtual manipulative.

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

## STEM Lessons - Model Eliciting Activity

Planning the perfect wedding:

Students will decide what is the best month to celebrate an outdoor wedding. The couple is looking for the perfect wedding day. What is the definition of a perfect day? It has to be a Saturday or Sunday with a 20% or less probability of rain and sunny but not too hot. Based on the information provided , students will find the month in which the probability of having a rainy day and the probability of having a super hot day (temperature higher than 75ยบ F) are minimal.

## MFAS Formative Assessments

Likelihood of an Event:

Students are asked to determine the likelihood of an event given a probability.

Likely or Unlikely?:

Students are asked to determine the likelihood of an event given a probability.

Probability or Not?:

Students are asked to determine whether or not a given number could represent the probability of an event.

## Original Student Tutorials Mathematics - Grades 6-8

Introduction to Probability:

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.

## Student Resources

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

## Original Student Tutorial

Introduction to Probability:

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

The Titanic 1:

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

## Tutorial

The Limits of Probability:

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

Type: Tutorial

## Virtual Manipulatives

Hamlet Happens:

The purpose of this manipulative is to help students recognize that (1) unusual events do happen, and (2) it may take a longer time for some of them to happen. The letters are drawn at random from the beginning of Hamlet's soliloquy, "To be, or not to be." Any word made from those letters (such as TO) can be entered in the box. When the start is pressed, letters are drawn and recorded. The process continues until the word appears.

Type: Virtual Manipulative

Spinners:

This virtual manipulative can be used demonstrate random probability and to teach about chance and random choices. Use this free, fully customizable, online spinner to create probability scenarios involving numerous choices, or create advanced, unevenly split spinners to demonstrate and model real life scenarios.

This spinner also incorporates a bar graph to record and model the outcome of each spin.

Type: Virtual Manipulative

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

Probability Models:

Explore probability topics by modeling coin tossing, free throwing shooting, and manufacturing defects with this virtual manipulative.

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.

The Titanic 1:

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

## Virtual Manipulatives

Hamlet Happens:

The purpose of this manipulative is to help students recognize that (1) unusual events do happen, and (2) it may take a longer time for some of them to happen. The letters are drawn at random from the beginning of Hamlet's soliloquy, "To be, or not to be." Any word made from those letters (such as TO) can be entered in the box. When the start is pressed, letters are drawn and recorded. The process continues until the word appears.

Type: Virtual Manipulative

Spinners:

This virtual manipulative can be used demonstrate random probability and to teach about chance and random choices. Use this free, fully customizable, online spinner to create probability scenarios involving numerous choices, or create advanced, unevenly split spinners to demonstrate and model real life scenarios.

This spinner also incorporates a bar graph to record and model the outcome of each spin.

Type: Virtual Manipulative

Probability Models:

Explore probability topics by modeling coin tossing, free throwing shooting, and manufacturing defects with this virtual manipulative.

Type: Virtual Manipulative