Multiplication and Division of Whole Numbers

Lesson 12

Objective

Estimate multi-digit quotients by rounding numbers to compatible numbers.

Common Core Standards

Core Standards

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  • 5.NBT.B.6 — Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Foundational Standards

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  • 4.NBT.B.4

  • 4.NBT.B.6

  • 5.NBT.A.1

  • 5.NBT.A.2

Criteria for Success

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  1. Estimate quotients by finding nearby compatible numbers (e.g., $$132\div71\rightarrow140\div7$$).
  2. Understand that finding nearby compatible numbers is likely the best way to estimate quotients, as opposed to rounding the values to a particular place value.

Tips for Teachers

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As noted in the Progressions, “estimating the quotients if a new aspect of dividing by a two-digit number” (NBT Progression, p. 18). Thus, Lesson 12 focuses on the idea of estimating quotients with compatible numbers before computing them in future lessons.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 2 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Tasks

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Problem 1

Martin and LuAnn are trying to estimate the quotient $${132\div71}$$. Martin uses $${100\div 70}$$ to estimate the quotient. LuAnn uses $${140\div 70 }$$ to estimate the quotient. Whose estimate do you agree with? Explain. If you don’t agree with either, explain how you would estimate in this problem.

Guiding Questions

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References

Achievement First Grade 5 Unit 3 Lesson 3 Estimate by Rounding to Compatible Numbers"Think About It" Task

Grade 5 Unit 3 Lesson 3 Estimate by Rounding to Compatible Numbers is made available by Achievement First as a part of their Open Source web portal under a CC BY 4.0 license. Copyright © 1999-2017 Achievement First. Accessed Dec. 5, 2017, 4:06 p.m..

Modified by The Match Foundation, Inc.

Problem 2

Estimate the following quotients.

  1.   $$4,212\div52$$
  2.  $$1,232\div28$$
  3.   $$5,427\div81$$

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic E > Lesson 18Concept Development

Grade 5 Mathematics > Module 2 > Topic E > Lesson 18 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem 3

Estimate the following quotient.

$${9,215 \div95}$$

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic E > Lesson 18Concept Development

Grade 5 Mathematics > Module 2 > Topic E > Lesson 18 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem Set & Homework

Discussion of Problem Set

  • Look back at the divisors in #1i, 1j, and 1k. What did you notice about them? How did the 5 in the ones place affect the way you rounded?
  • In #1l, did anyone leave the divisor $${11}$$ unrounded? Is it always necessary to round? 
  • Do we follow our typical rounding rules when estimating with division? Why not?
  • How can you justify your answer in #3?

Target Task

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Estimate the quotient for the following problems:

1.     $${151\div39}$$

2.     $${481\div68}$$

3.     $${3,704\div53}$$

4.     $${4,819\div68}$$

References

Mastery Response

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