Lesson 4 | Probability | 7th Grade Mathematics

Objective

Use probability to predict long-run frequencies.

Common Core Standards

Core Standards

The core standards covered in this lesson

7.SP.C.6 — 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.

Statistics and Probability

7.SP.C.6 — 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.

Foundational Standards

The foundational standards covered in this lesson

7.RP.A.3

Ratios and Proportional Relationships

7.RP.A.3 — Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Use experimental and theoretical probabilities to make predictions of long-run frequencies or larger populations.
Understand that long-run frequencies tend to approximate theoretical probability.
Understand that predictions are reasonable estimates and not exact measures.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Students draw on their ratio and proportion reasoning skills to make predictions of long-run frequencies. This is a good opportunity to review or re-engage students in ratio reasoning skills from Units 1 and 5.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

a. Alexander flips a coin 3 times. It lands on heads 0 times. Do you think this is a fair coin? Explain why or why not.

b. Alexander flips the same coin 100 times. It lands on heads 47 times.

Do you think this is a fair coin? Explain why or why not.
If Alexander were to flip the coin 500 times, about how many times would you expect the coin to land on heads?

c. Taylah flips a coin and creates the graph below to represent her results.

Explain what the graph tells you about Taylah’s experiment.
Does it appear that Taylah used a fair coin? Explain your answer.

Guiding Questions

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References

Academo Statistics of Rolling Dice

Statistics of Rolling Dice is made available by Academo. © Academo.org 2016. Accessed April 5, 2018, 2:06 p.m..

EngageNY Mathematics Grade 7 Mathematics > Module 5 > Topic B > Lesson 8 — Image from Example 1e

Grade 7 Mathematics > Module 5 > Topic B > Lesson 8 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

On a game show, contestants spin a wheel to determine which game, of four options, they will play to win a prize. The games of the last several contestants are shown below.

Game	Frequency
Guess the Price	16
Match the Brand	7
Throw the Darts	5
Race the Clock	12

About how many of the next 200 contestants do you expect will play Race the Clock? Explain your reasoning.

Guiding Questions

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Problem 3

A six-sided number cube includes the numbers 1, 3, 5, and 7, as shown below.

Han predicts that out of 150 rolls of the number cube, the number 1 will appear exactly 50 times.

Do you agree with Han? Explain your reasoning.

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

A spinner with letters A through E is shown below.

About how many times will the spinner land on the letter A after 300 spins? Explain your reasoning.

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Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Dan Meyer's Three-Act Math Yellow Starbursts
EngageNY Mathematics Grade 7 Mathematics > Module 5 > Topic B > Lesson 8 — Exit Ticket
Open Up Resources Grade 7 Unit 8 Practice Problems — Lesson 4

Lesson 3

Lesson 5

Lesson Map

Topic A: Probability Models of Simple Events

Understand the probability of an event happening is a number between 0 and 1, ranging from impossible to certain.

7.SP.C.5

Define probability and sample space. Estimate probabilities from experimental data.

7.SP.C.6 7.SP.C.7

Determine the probability of events.

7.SP.C.7.A 7.SP.C.7.B

Use probability to predict long-run frequencies.

7.SP.C.6

Design and conduct simulations to model real-world situations.

7.SP.C.7

Topic B: Probability Models of Compound Events

Conduct simulations with multiple events to determine probabilities.

7.SP.C.8 7.SP.C.8.C

List the sample space for compound events using organized lists, tables, or tree diagrams.

7.SP.C.8.B

Determine the probability of compound events.

7.SP.C.8

Design and conduct simulations to model real-world situations for compound events.

7.SP.C.8.C

Probability

Objective

Common Core Standards

Core Standards

Statistics and Probability

Foundational Standards

Ratios and Proportional Relationships

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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