# Multiplication and Division of Whole Numbers

## Objective

Divide three-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 three-digit dividends and two-digit divisors with one-digit quotients.
2. Use the estimate to approximate 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 one-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.

$256\div47$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic F > Lesson 21Application Problem and Concept Development

Grade 5 Mathematics > Module 2 > Topic F > Lesson 21 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

${369\div46}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic F > Lesson 21Concept Development

Grade 5 Mathematics > Module 2 > Topic F > Lesson 21 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

723 students were divided equally into teams of 94 students for field day. Any students left over after making as many groups of 94 as possible will just be a smaller team. How many students will be on a team smaller than 94, if any?

## Discussion of Problem Set

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• What similarity did you notice between #1c and #1d? Since the quotient was 8 with remainder 7 for both problems, does that mean the two division expressions are equal to each other? Discuss the meaning of the quotient and remainder for both problems.
• In #1, did your estimates need adjusting at times? When? What did you do in order to continue dividing?
• How did you solve #2? How many solutions might there be to this problem? Can you create another solution to it? How did your understanding of the check process help you answer this?
• What steps did you take as you solved #3? Could you have solved in a different way or in a different order of steps? Why?
• Why is estimating a quotient before computing it helpful? How does it make the computation more efficient?

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### Problem 1

${326\div53}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic F > Lesson 21Exit Ticket, Question a

Grade 5 Mathematics > Module 2 > Topic F > Lesson 21 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

Members of the Garner High School yearbook committee need to put 192 student photos in 38 pages in the yearbook. They want to put the same number of student photos on each page. How many student photos will they put on each page in the yearbook?

#### References

Question #3

From EngageNY.org of the New York State Education Department. New York State Testing Program Grade 5 Common Core Mathematics Test Released Questions July 2015. Internet. Available from https://www.engageny.org/resource/released-2015-3-8-ela-and-mathematics-state-test-questions/file/132981; accessed Dec. 7, 2017, 10:56 a.m..

Modified by The Match Foundation, Inc.
EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic F > Lesson 21Exit Ticket, Question b

Grade 5 Mathematics > Module 2 > Topic F > Lesson 21 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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