MidSchoolMath 1

The real world requires that we represent rational numbers in different ways depending on the context of a situation. During Grandpa’s Journey, Kate is sent on a hiking journey when she reads a letter her grandpa left behind. He listed all distances as frac-tions of miles, but Kate’s GPS reads decimals, so she must convert the fractional distances to decimals. The data provided is a letter from Grandpa that lays out the hiking route with fractional distances.

LESSON: GRANDPA'S JOURNEYWhat decimals should Kate enter into the GPS?

Grandpa's Journey

Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

The Math SimulatorTM

ImmersionPlay Grandpa's Journey Immersion video, whole-class. Restate the question: What decimals should Kate enter into the GPS?Facilitate classroom discussion; ask students: "What are your ideas to help Kate?"

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2 Data & ComputationPrint the Data Artifact, cut into halves, 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 Grandpa's Journey 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.NS.A.2dThe Number System

MidSchoolMath 2Grandpa's Journey

7.NS.A.2dThe Number System

Clicker QuizLaunch the Clicker Quiz, whole-class.

Gladys: You may want to combine the 7.NS.A.2b Debt Division results (-22/3 = -7.3333...) with the results seen in Grandpa's Journey to illustrate the dif-ference between decimals that terminate in 0s and those that infinitely repeat. Terminating decimals have an exact location on the number line, whereas infinitely repeating ones don't.

Kevin: When indicating repeating numerals in a dec-imal expansion, remind students the bar is written only over those digits that repeat.

Megan: When appropriate, bring students' attention to denominators that lead to repeating decimal ex-pansions and denominators that lead to terminating decimal expansions. See if they can conjecture when a fraction will terminate or repeat.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #2Standard Math Procedures

Instruction at a Glance

1 Convert the fractions to decimals.

A: 0.55

C: 0.6666D: 0.428571

B: 0.5555

A: 0.552 Select the answer option that terminates.

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GRANDPA’S JOURNEYWhat decimals should Kate enter into the GPS?Kate’s grandpa left her a second letter, encouraging her to go on another hiking journey through the mountains. The letter gave her the directions and distances that she should walk to reach the destination.

The distances were given in fractions, but Kate’s GPS uses decimals.

Help Kate convert each fractional distance to its equivalent decimal distance.

7.NS.A.2d

Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

About this standard

Date PeriodName

MidSchoolMath Grandpa’s Journey 1 of 2

3mi =7

mi =

7

9

mi =12

165

mi =81

APPLYING THE STANDARD

Each of the following rational numbers has a decimal equivalent that infi nitely repeats. Rewrite each decimal using a vinculum (horizontal line above the number or numbers) to indicate the repetition.

Convert each rational number to decimal form. Continue the decimal until it either terminates in 0 or until it begins to repeat.

MidSchoolMath Grandpa’s Journey 2 of 2

Date PeriodName

How might this standard appear on a test?

6) 7)5) 8)

1) 59 = 0.555555.... 3) = 1.08333....2) 4)

1324

1522

24311

1554

1511

= 1.363636.... 1312

512

= 0.416666....

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For each rational number, use the denominator to help you determine whether its decimal equivalent will terminate in 0 or repeat infi nitely. Write each rational number under the appropriate column.

9)

Terminates in 0 Repeats Infi nitely

1720

325

143

-511

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34

- 49

56

78

- 85

Check out my worked example #8

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