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6-8 Accelerated 6 Unit 3 Lesson 9

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•Accelerated 6 Accelerated 7

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Unit 1 Unit 2 •Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 •Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21 Lesson 22 Lesson 23

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Curriculum

IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Lesson 9

9.1 Warm-up 9.2 Activity 9.3 Activity 9.4 Activity Student Lesson Summary

Unit 3, Lesson 9

Fractional Lengths

Accelerated 6

9.1

Warm-up

Which three go together? Why do they go together?

A string that is meter long is cut into 15 equal pieces. How long is each piece? 
 
A driver drove km from home to a gas station and then drove 15 times as far to go to work. What is the distance between the gas station and his work?
Mai built a tower that is 21 inches tall by stacking -inch tall cubes. How many cubes did she use?

9.2

Activity

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the problem card:

Silently read your card, and think about what information you need to answer the question.
Ask your partner for the specific information that you need. “Can you tell me ?”
Explain to your partner how you are using the information to solve the problem. “I need to know because . . . .”
Continue to ask questions until you have enough information to solve the problem.
Once you have enough information, share the problem card with your partner, and solve the problem independently.
Read the data card, and discuss your reasoning.

If your teacher gives you the data card:

Silently read your card. Wait for your partner to ask for information.
Before telling your partner any information, ask, “Why do you need to know ?”
Listen to your partner’s reasoning and ask clarifying questions. Only give information that is on your card. Do not figure out anything for your partner!
These steps may be repeated.
Once your partner says there is enough information to solve the problem, read the problem card, and solve the problem independently.
Share the data card, and discuss your reasoning.

9.3

Activity

Write a division expression that can help answer each question. Then find the answer and show your reasoning. You can draw a tape diagram if you find it helpful.

A young giraffe is 4 meters tall. An adult giraffe is meters tall.
1. How many times as tall as the young giraffe is the adult giraffe?
2. What fraction of the adult giraffe’s height is the young giraffe’s height?
1. A runner ran miles on Monday and miles on Tuesday. How many times her Monday’s distance was her Tuesday’s distance?
2. A cyclist planned to ride miles but only managed to travel miles. What fraction of his planned trip did he travel?

9.4

Activity

The photo shows a situation that involves fractions.

<p>3 short cardboard tubes lined up horizontally. 1 long cardboard tube below. Long tube starts at the same spot as the first short tube and ends about half way down the third short tube. </p>

Complete the sentences. Be prepared to explain your reasoning.
1. The length of the long tube is about times the length of a short tube.
2. The length of a short tube is about times the length of the long tube.
If the length of the long paper roll is inches, what is the length of each short paper roll?

Student Lesson Summary

Division can help us solve comparison problems in which we find out how many times as large or as small one number is compared to another. For example, a student is playing two songs for a music recital. The first song is minutes long. The second song is minutes long.

Double number line. Top line, first song. 1 and the fraction 1 over 2 units long. Labeled 1 and the fraction 1 over 2 minutes. Bottom line, second song. 3 and the fraction 3 over 4 units long. Labeled 3 and the fraction 3 over 4 minutes.

We can ask two different comparison questions and write different multiplication and division equations to represent each question.

How many times as long as the first song is the second song?

What fraction of the second song is the first song?

We can use the algorithm we learned to calculate the quotients.

This means the second song is times as long as the first song.

This means the first song is as long as the second song.

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