Unit 5

Using Long Division

Lesson 10

Arithmetic in Base Ten

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Expressions and Equations

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Let’s use long division.

Unit 5 ● Lesson 10

Learning

Goal

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Estimating Quotients

Unit 5 ● Lesson 10 ● Activity 1

Estimate these quotients mentally.

500 ÷ 7

1,394 ÷ 9

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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.

Lin Uses Long Division

Unit 5 ● Lesson 10 ● Activity 2

Lin has a method of calculating quotients that is different from Elena’s method and Andre’s method. Here is how she found the quotient of �657 ÷ 3:

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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.

Lin Uses Long Division

Unit 5 ● Lesson 10 ● Activity 2

1. Discuss with your partner how Lin’s method is similar to and different from drawing base-ten diagrams or using the partial quotients method.
1. Lin subtracted 3 • 2 then 3 • 1, and lastly 3 • 9. Earlier, Andre subtracted 3 • 200 then 3 • 10, and lastly 3 • 9. Why did they have the same quotient?

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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.

Lin Uses Long Division

Unit 5 ● Lesson 10 ● Activity 2

• (Continued…) Discuss with your partner how Lin’s method is similar to and different from drawing base-ten diagrams or using the partial quotients method.
• In the third step, why do you think Lin wrote the 7 next to the remainder of 2 rather than adding 7 and 2 to get 9?

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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.

Lin Uses Long Division

Unit 5 ● Lesson 10 ● Activity 2

2. Lin’s method is called long division. Use this method to find the following quotients. Check your answer by multiplying it by the divisor.
1. 846 ÷ 3
2. 1,816 ÷ 4
3. 768 ÷ 12

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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.

Lin Uses Long Division

Unit 5 ● Lesson 10 ● Activity 2

• Let’s take 1,816 ÷ 4 as an example. If we were using base-ten diagrams, we would have 1 piece representing a thousand. How would we divide that piece into 4 groups?
• How can we apply the same idea to long division? If there is not enough thousands to divide into 4 groups, what can we do?
• How many hundreds would go into each group if we divide 18 hundreds into 4 groups?
• Where should we write the 4? Why?
• How do we deal with the 2 hundreds?

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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.

Dividing Whole Numbers

Unit 5 ● Lesson 10 ● Activity 3

1. Find each quotient.
1. 633 ÷ 3
2. 1,001÷ 7
3. 2,996 ÷ 14
2. Here is Priya’s calculation of 906 ÷ 3.
• Priya wrote 320 for the value of 906 ÷ 3. Check her answer by multiplying it by 3. What product do you get and what does it tell you about Priya’s answer?
• Describe Priya’s mistake, then show the correct calculation and answer.

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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.

Dividing Whole Numbers

Unit 5 ● Lesson 10 ● Activity 3

• How did you deal with the 0’s in 1,001? Would they cause any difficulty when doing long division?
• How can you check your answer to a division problem such as 1,001 ÷ 147?
• What happens if you check Priya’s answer for �906 ÷ 3?

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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.

Using Long Division

Unit 5 ● Lesson 10

• How is dividing using long division similar to dividing by drawing base-ten diagrams?
• How is long division similar to and different from the partial quotients method?
• Which method for finding quotients do you think is the most efficient?

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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 5 ● Lesson 10

I can use long division to find a quotient of two whole numbers when the quotient is a whole number.

Learning Targets

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Dividing by 15

Unit 5 ● Lesson 10 ● Activity 4

Use long division to find the value of 1,875 ÷ 15.

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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.

long division

Unit 5 ● Lesson 10

Long division is a way to show the steps for dividing numbers in decimal form. It finds the quotient one digit at a time, from left to right.

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For example, here is the long division for 57 ÷ 4.

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Glossary

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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.

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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