# Multiplication and Division of Whole Numbers

## Objective

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

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Estimate the following quotient. Then compute it.

$590\div17$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic F > Lesson 22Concept Development

Grade 5 Mathematics > Module 2 > Topic F > Lesson 22 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

a.      ${987\div16}$

b.      $859\div21$

### Problem 3

A farmer’s chickens laid a total of 779 eggs. He packs the eggs into cartons of 24. After fully packing as many cartons as possible, he has one partially-filled carton. How many more eggs are needed to fill that carton?

## Discussion of Problem Set

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• In #1, was it ever necessary to adjust your quotients after estimating? If so, what did you do in order to continue dividing?
• While checking your work today, did anyone discover an error in his or her division? If so, how did you fix it? How did you know what to do?
• For #1f, I got 4 remainder 14. What mistake did I make?
• Talk to your partner about how you set up and solved #2. What was your thinking like?

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### Problem 1

${413\div19}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic F > Lesson 22Exit Ticket, Question a

Grade 5 Mathematics > Module 2 > Topic F > Lesson 22 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..

### Problem 2

Cement is shipped in bags. Each bag weighs 67 pounds. A construction worker needs 708 pounds of cement to complete a job. What is the total number of bags of cement that should be shipped for the construction worker to complete the job?

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic F > Lesson 22Exit Ticket, Question b

Grade 5 Mathematics > Module 2 > Topic F > Lesson 22 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.
Massachusetts Department of Elementary and Secondary Education Spring 2015 Grade 5 Mathematics TestQuestion #3

Spring 2015 Grade 5 Mathematics Test is made available by the Massachusetts Department of Elementary and Secondary Education. © 2017 Commonwealth of Massachusetts. Accessed Dec. 5, 2017, 4:12 p.m..

Modified by The Match Foundation, Inc.

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