# Multiplication and Division of Whole Numbers

## Objective

Divide two-digit dividends by two-digit divisors with one-digit quotients and remainders in the ones place.

## 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 of two-digit dividends and two-digit divisors with one-digit quotients.
2. Use the estimate to approximate the leading value in the quotient.
3. Adjust an estimate when the estimate would yield too large a result.
4. Divide two-digit dividends by two-digit divisors with one-digit quotients and remainders in the ones place.
5. Assess the reasonableness of an answer by rounding and/or using the relationship between multiplication and division to check answers (MP.1).
6. Solve word problems involving division, including those that require the interpretation of the remainder (MP.1, MP.4).

## Tips for Teachers

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In Lesson 15, students first encounter a case that requires the need to adjust an estimate, since it is the first time they are estimating not just the dividend but also the divisor and using that estimate to compute. As noted in the Progressions, “even if students round the dividend appropriately, the resulting estimate may need to be adjusted up or down. Sometimes multiplying the ones of a two-digit divisor composes a new thousand, hundred, or ten. These newly composed units can be written as part of the division computation, added mentally, or as part of a separate multiplication computation” (NBT Progression, p. 18).

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Estimate the following quotient. Then compute it.

$66\div21$

### Problem 2

${84\div23}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic F > Lesson 20Concept Development

Grade 5 Mathematics > Module 2 > Topic F > Lesson 20 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

A ferry can hold 19 cars. How many trips will it have to make to carry 83 cars across the lake?

## Discussion of Problem Set

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• Did your initial estimates work for every example in #1? Why or why not?
• In #2, what would you tell Linda in order to help her solve the problem? What lesson does Linda need to learn? What is another way that Linda could have estimated that would have eliminated the issue she encountered in the standard algorithm?
• Explain your thought process as you set up and began to solve #3 and #4. What was challenging or unique about them?
• Talk about the importance of estimation when dividing with two-digit divisors.

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### Problem 1

${78\div21}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic F > Lesson 20Exit Ticket, Question a

Grade 5 Mathematics > Module 2 > Topic F > Lesson 20 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 2

Sam played arcade games and won 89 tickets. You can buy 1 prize for every 37 tickets earned. Sam bought as many prizes as he could with his tickets. How many prizes was Sam able to buy?

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic F > Lesson 20Exit Ticket, Question b

Grade 5 Mathematics > Module 2 > Topic F > Lesson 20 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.

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