MidSchoolMath 1

It is important for students to understand that although many events can’t be predicted with total certainty, we can use a number between 0 and 1 to estimate their likelihood. In Extraterrestrial Existence, sisters Sonia and Misha are discussing the chances, or the probability, that there might be life on other planets. Sonia says there is a probability of 0.5 that there is life on other planets. Misha isn’t quite sure what that means. The data provided is an image of Sonia and Misha looking up at the sky, with Sonia stating that the probability of life on other planets is 0.5, and Misha asking, "What does that mean?"

LESSON: EXTRATERRESTRIAL EXISTENCEWith a probability of 0.5, is life on other planets likely or unlikely?

Extraterrestrial Existence

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.

The Math SimulatorTM

ImmersionPlay Extraterrestrial Existence Immersion video, whole-class. Restate the question: With a probability of 0.5, is life on other planets likely or unlikely?Facilitate classroom discussion; ask students: "What are your ideas?"

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2 Data & ComputationPrint the Data Artifact and distribute to students. Allow students work time. Ask students: "Does your answer make sense?"Consider using a sharing protocol leading to mathematical insights and/or highlighting misconceptions. Allow students to revise their work.

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3 ResolutionPlay Extraterrestrial Existence Resolution video, whole-class. Prepare and give brief lecture (Teacher Instruction).

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Download the Detailed Lesson PlanAvailable on the Teacher Dashboard

+ Simulation TrainerAssign the Simulation Trainer.Use protocols that encourage students to help each other.Use Progress Monitoring to access real-time data for the classroom.Provide individual help for students who are not making progress.

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(Use student headphones.)

7.SP.C.5Statistics & Probability

MidSchoolMath Extraterrestrial Existence

Clicker QuizLaunch the Clicker Quiz, whole-class.

7.SP.C.5Statistics & Probability

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Gladys: Consider hosting a discussion about probability or the chances that something will happen. Get students to use their intuition and to think about this concept before formally introducing it.

Kevin: It may be helpful to review skills around fractions, decimals and percents, as probabilities can be expressed in various ways. Help students connect that for probabilities, fractions and decimals will be between 0 and 1, which means the percents will be between 0% and 100%.

Megan: Consider having students draw a probability continuum and place events along the continuum, using only their ideas or experience with such events.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #5Standard Math Procedures

Instruction at a Glance

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Find the sum of the probabilities.

Select the appropriate answer.

0.76 + 0.34 = 1.1

B: No

A total of 1.1 implies a probability greater than "certain." There is no probability greater than 1. The sum of any valid probability model will be 1.

2 Interpret the total.

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EXTRATERRESTRIAL EXISTENCEWith a probability of 0.8, is life on other planets likely or unlikely?At the same time Sonia and Misha were discussing life on other planets, so were extraterrestrials on a far away planet. One extraterrestrial thought the probability of life on other planets might be 0.8. His extraterrestrial friend wasn’t quite sure what that meant.

With a probability of 0.8, is life on other planets likely or unlikely?

7.SP.C.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.

About this standard

Date PeriodName

MidSchoolMath Extraterrestrial Existence 1 of 2

With a probability of 0.8, is life on other planets likely or unlikely?

Explain your reasoning.

Likely Unlikely

APPLYING THE STANDARD

MidSchoolMath 2 of 2

Date PeriodName

How might this standard appear on a test?

Extraterrestrial Existence

Using the spinner, describe the likelihood of each event. On each line write either likely, unlikely, neither unlikely nor likely, certain or impossible.

1)

Fill in the blanks with the vocabulary words below to make the statement true.2)

Write the probability of each event as a fraction or decimal, and then label the event likely, unlikely, neither likely nor unlikely, certain, or impossible.

3)

Michael was on a game show and made it to the fi nal round. In order to win the grand prize, he had to correctly guess which of 4 doors the prize was hidden behind. He had a or 0.25 probability of guessing the correct door.

4)

The probability of rolling a 6 on a normal six-sided number cube.a)

Is it likely or unlikely that Michael will win?a)

What is the probability that Michael will NOT choose the correct door?b)

The probability of rolling a 7 on a normal six-sided number cube.b)

The probability of rolling an even number on a normal six-sided number cube.c)

The probability of rolling a 1, 2, 3, 4, 5, or 6 on a normal six-sided number cube.d)

a) Spinner lands on 1: ____________________

c) Spinner lands on 0: ____________________

e) Spinner lands on a number ≥ 1: ____________________

b) Spinner lands on an even number: ____________________

d) Spinner lands on an odd number: ____________________

f) Spinner lands on a number ≤ 3: ____________________

The probability of a chance event is a numberbetween ______________and ______________. Thisnumber expresses the ______________ that an eventwill occur. Larger numbers indicate ______________likelihood. Numbers closer to 0 indicate that an eventis ______________.

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Check out my worked example #1f

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