Curriculum  /  Math  /  5th Grade  /  Unit 2: Multiplication and Division of Whole Numbers  /  Lesson 12

Multiplication and Division of Whole Numbers

Lesson 12

Math

Unit 2

5th Grade

Lesson 12 of 20

Objective

Estimate multi-digit quotients using compatible numbers.

Common Core Standards

Core Standards

  • 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

  • 4.NBT.B.4
  • 4.NBT.B.6
  • 5.NBT.A.1
  • 5.NBT.A.2

Criteria for Success

  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

As noted in the Progressions, “estimating the quotients is 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.

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Anchor Tasks

25-30 minutes

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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Student Response

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References

Achievement First Grade 5 Unit 3 Lesson 3 — "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 Fishtank Learning, Inc.

Problem 2

Estimate the following quotients.

a.   $$431\div62$$

b.   $$1,912\div28$$

c.   $$984\div24$$

Guiding Questions

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Student Response

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Problem 3

Aliya is trying to estimate $${9,215 \div95}$$. She says that she can estimate the divisor to be 90, 95, or 100. 

a.   Using each of the possible divisors, estimate the quotient.

b.   Pick one of the estimates you made in Part (a). Do you expect the actual quotient to be greater or less than that estimate? Explain.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic E > Lesson 18 — Concept 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 Fishtank Learning, Inc.

Problem Set

15-20 minutes

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

5-10 minutes

Estimate the quotient for the following problems:

a.   $${151\div39}$$

b.   $${481\div68}$$

c.   $${3,704\div53}$$

d.   $${4,819\div68}$$

Student Response

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Divide two-digit, three-digit, and four-digit dividends by one-digit divisors.

Lesson 13
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Writing and Interpreting Numerical Expressions

Topic B: Multi-Digit Whole Number Multiplication

Topic C: Multi-Digit Whole Number Division

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