Unit 4

Size of Divisor and Size of Quotient

Lesson 1

Dividing Fractions

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Expressions and Equations

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Let’s explore quotients of different sizes.

Unit 4 ● Lesson 1

Learning

Goal

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Size of Dividend and Divisor

Unit 4 ● Lesson 1 ● Activity 1

Find the value of each expression mentally.

5,000 ÷ 5

5,000 ÷ 2,500

5,000 ÷ 10,000

5,000 ÷ 500,000

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Warm-up: Number Talk

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Size of Dividend and Divisor

Unit 4 ● Lesson 1 ● Activity 1

• What do you notice about the value of each expression as the divisor (the number we use to divide) gets larger?”
• Why is the value of the expression getting smaller each time?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

All Stacked Up

Unit 4 ● Lesson 1 ● Activity 2

1. Here are several types of objects. For each type of object, estimate how many are in a stack that is 5 feet high. Be prepared to explain your reasoning.

Cardboard boxes Notebooks

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Bricks Coins

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

All Stacked Up

Unit 4 ● Lesson 1 ● Activity 2

2. A stack of books is 72 inches tall. Each book is 2 inches thick. Which expression tells us how many books are in the stack? Be prepared to explain your reasoning.
• 72 • 2
• 72 - 2
• 2 ÷ 72
• 72 ÷ 2
3. Another stack of books is 43 inches tall. Each book is ½-inch thick. Write an expression that represents the number of books in the stack.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

All Stacked Up

Unit 4 ● Lesson 1 ● Activity 2

• How did your estimates for the number of objects change as the object got thinner?
• Why might that be?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

All in Order

Unit 4 ● Lesson 1 ● Activity 3

Your teacher will give you two sets of papers with division expressions.

1. Without computing, estimate the quotients in each set and order them from greatest to least. Be prepared to explain your reasoning.

Pause here for a class discussion.

Record the expressions in each set in order from the greatest value to the least.

• Set 1
• Set 2
2. Without computing, estimate the quotients and sort them into the following three groups. Be prepared to explain your reasoning.

• Close to 0 • Close to 1 • Much larger than 1

30 ÷ ½ 9 ÷ 10 18 ÷ 19 15,000 ÷ 1,500,000

30 ÷ 0.45 9 ÷ 10,000 18 ÷ 0.18 15,000 ÷ 14,500

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

All in Order

Unit 4 ● Lesson 1 ● Activity 3

• How did you decide that a quotient is close to 0?
• How did you decide that a quotient is close to 1?
• Is there a way to tell if a quotient is less than 1 or more than 1?
• Suppose a divisor is less than the dividend. How can we tell if the quotient is just a little larger than 1 or much larger than 1?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Size of Divisor and Size of Quotient

Unit 4 ● Lesson 1

• What happens to the quotient when we divide by smaller and smaller numbers?
• Which would result in a smaller quotient: dividing a number by 0.5 or dividing it by 5? Why?
• What can we say about the quotient when the divisor is much smaller than the dividend?
• What about when we divide a number by another number that is much larger?
• What can we say about the quotient when the divisor and dividend are about the same size?

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Unit 4 ● Lesson 1

When dividing, I know how the size of a divisor affects the quotient.

Learning Targets

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Result of Division

Unit 4 ● Lesson 1 ● Activity 4

Without computing, decide whether the value of each expression is much smaller than 1, close to 1, or much larger than 1.

1. 1,000,001 ÷ 99
2. 3.7 ÷ 4.2
3. 1 ÷ 835
4. 100 ÷
5. 0.006 ÷ 6,000
6. 50 ÷ 50

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Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.

All curriculum excerpts are under the following licenses:

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

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