MA.7.DP.2.2

Given the probability of a chance event, interpret the likelihood of it occurring. Compare the probabilities of chance events.

Clarifications

Clarification 1: Instruction includes representing probability as a fraction, percentage or decimal between 0 and 1 with probabilities close to 1 corresponding to highly likely events and probabilities close to 0 corresponding to highly unlikely events.

Clarification 2: Instruction includes P(event) notation.

Clarification 3: Instruction includes representing probability as a fraction, percentage or decimal.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 7
Strand: Data Analysis and Probability
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Event
  • Theoretical Probability

 

Vertical Alignment

Previous Benchmarks

Next Benchmarks

 

Purpose and Instructional Strategies

In grade 7, students interpret the probability of a chance event and the likelihood of it occurring. In grade 8, students will solve problems involving probabilities related to single or repeated experiments, including making predictions based on theoretical probability. 
  • An event is a set of outcomes.
    • For example, if the experiment is to roll a six-sided die, possible events could be:
      • “rolling a 3 or a 4;”
      • “rolling an even number;” or
      • “not rolling a 2.”
  • Instruction includes the understanding that some events can have a probability of 1 or 0. Students should understand that if an event has a probability of zero, the event is impossible or will not occur. If an event has a probability of one, the event is certain or must occur.
    • For example, in the experiment of rolling a 6-sided die, the event of rolling a 1, 2, 3, 4, 5 or 6 would have a probability of 1.
    • For example, when rolling a 6-sided fair die, the event of rolling a 7 would have a probability of 0.
  • Instruction includes having students use probabilities of 1, 0.5 and 0 as benchmark probabilities to interpret the likelihood of other events.
    • For example, if a student wants to interpret the likelihood represented by the probability of 80%, they can compare 80% to the benchmark probabilities of 50% and 100%.
  • If an event has a probability of 0.5, it can be interpreted that is has the same likelihood as its opposite.
    • For example, in the experiment of picking a card from a standard 52-card deck, the event of picking a red card has a probability of 0.5, which can be interpreted as having the same likelihood as the opposite event, which is picking a black card.

 

Common Misconceptions or Errors

  • Students may invert the meaning of an event and an experiment.
  • Students may confuse the mathematical meaning of a word like “event” with the everyday meaning.
  • Students may incorrectly convert forms of probability between fractions and percentages. To address this misconception, scaffold with more familiar values initially to facilitate the interpretation.
  • Students may incorrectly interpret a value with a negative sign as a possible probability.
    • For example, −12 cannot represent a probability since negative values are less than 0.

 

Strategies to Support Tiered Instruction

  • Teacher creates and posts an anchor chart with visual representations of probability terms to assist students in correct academic vocabulary when solving real-world problems.
  • Teacher provides opportunities for students to use a 100 frame to review place value for and the connections to decimal, fractional and percentage forms of probabilities.
  • Instruction includes the use of a 100 frame to review place value for tenths, hundredths, and if needed, thousandths and the connections for decimal and fractional forms of probabilities.
  • When students incorrectly convert from one form to another (i.e, fraction to percentage), the teacher scaffolds with more familiar values initially to facilitate the interpretation.

 

Instructional Tasks

Instructional Task 1 (MTR.1.1)
Determine which of the following could represent the probability of an event. For those that can, provide a possible event that would fit the probability given.
Table representing Probabilities

 

Instructional Items

Instructional Item 1
In each scenario, a probability is given. Describe each event as likely, unlikely or neither.
  • a. The probability of a hurricane being within 100 miles of a location in two days is 40%.
  • b. The probability of a thunderstorm being located within 5 miles of your house sometime tomorrow is 910
  • c. The probability of a given baseball player getting at least three hits in the game today is 0.08.

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 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.
MA.7.DP.2.AP.2: Given the probability of a simple chance event written as a fraction, percentage or decimal between 0 and 1, determine how likely is it that an event will occur.

Related Resources

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

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

Lesson Plans

Probability of Being Summoned for Jury Duty:

Students will explore how an individual’s personal experience may impact their interpretation of the likelihood of a specific event by comparing theoretical and experimental probabilities in the context of being summoned for jury duty in this integrated lesson.

Type: Lesson Plan

Experimental and Theoretical Probability:

Students will compare experimental and theoretical probability using a standard deck of cards.  Then, given fictional data from the population of 3 counties in Florida, they will compare the theoretical probability of an individual being summoned for jury service in each county to the experimental probability based on individual experiences.  Finally, students will evaluate the impact of sample size on this comparison and explore the importance of a random jury summons process in our judicial system in this integrated lesson.

Type: Lesson Plan

What is the Likelihood?:

Students will develop an understanding of likelihood based on calculated probabilities and relate these concepts to being called for jury duty in this integrated lesson.

Type: Lesson Plan

Genetics Has Gone to the Dogs!:

This lesson uses pooches to teach about pedigrees and the impact of artificial selection on individuals and populations as well as to drive home math concepts already discussed in lessons on Punnet squares.

Type: Lesson Plan

Genetics can be a Monster!:

In this lesson, students will use Punnett squares to calculate the probabilities of different genotypes and phenotypes produced by genetic crosses.

Type: Lesson Plan

Independent Compound Probability:

During this lesson, students will use Punnett Squares to determine the probability of an offspring's characteristics.

Type: Lesson Plan

Casino Royale:

Students examine games of chance to determine the difference between dependent and independent conditional probability.

Type: Lesson Plan

Chancy Candy:

In this lesson students will use candy to find the probability of independent compound events, determining the sample space from a tree diagram. They will then conduct an experiment to test the theoretical probability. Once the experiment is complete, the students will compare the theoretical and experimental probability.

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 75º F) are minimal.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Probabilities and Punnett Squares:

Students simulate the process of meiosis for an alien society. The students choose physical characteristics for hair, nose and eyes corresponding to genes and then generate two alien babies. Then pictures of the parents and babies are drawn, with similarities and differences noted and explained.

Type: Lesson Plan

Beads in a Bowl:

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: 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?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

History of Probability and the Problem of Points:

What was the first question that started probability theory?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Problem-Solving Task

The Titanic 1:

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

Type: Problem-Solving Task

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

Tutorial

The Limits of Probability:

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

Type: Tutorial

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 75º F) are minimal.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

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

Problem-Solving Task

The Titanic 1:

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

Type: Problem-Solving Task

Tutorial

The Limits of Probability:

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

Type: Tutorial

Parent Resources

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

Problem-Solving Task

The Titanic 1:

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

Type: Problem-Solving Task