# Multiplication and Division of Whole Numbers

## 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.

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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.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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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.

#### 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.   $5,427\div81$

#### 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.

${9,215 \div95}$

#### 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?

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Estimate the quotient for the following problems:

 1.     ${151\div39}$ 2.     ${481\div68}$ 3.     ${3,704\div53}$ 4.     ${4,819\div68}$

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