# Multiplication and Division of Whole Numbers

## Objective

Divide four-digit dividends by two-digit divisors with two- and three-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 four-digit dividends and two-digit divisors with two- and three-digit quotients.
2. Use the estimate to approximate each value in the quotient, adjusting when the estimate is either too high or too low.
3. Divide four-digit dividends by two-digit divisors with two- and three-digit quotients and remainders in the ones place.
4. Check that the solution to a division problem is correct by using inverse operations, multiplying the quotient by the divisor and adding the remainder, seeing if it is equivalent to the dividend.
5. Assess the reasonableness of a solution by rounding to estimate or by checking a solution using multiplication (MP.1).
6. Solve word problems involving division, including those that require interpretation of the remainder (MP.1, MP.4).

## Tips for Teachers

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### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 2 and 3 (benefit from worked examples). 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

Estimate the following quotient. Then compute it.

$6,247\div29$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic F > Lesson 23Concept Development

Grade 5 Mathematics > Module 2 > Topic F > Lesson 23 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 2

1. ${4,289\div52}$
2. $6,649\div63$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic F > Lesson 23Concept Development

Grade 5 Mathematics > Module 2 > Topic F > Lesson 23 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 3

Write different word problems that involve the equation $2,725\div16=?$ and fit the following criteria:

1. Answer to the word problem is 170
2. Answer to the word problem is 171
3. Answer to the word problem is 5
4. CHALLENGE: Answer to the word problem is 11

## Problem Set & Homework

### Discussion of Problem Set

• What pattern did you notice between #1d and 1f? Since the quotient was 70 with a remainder of 14 for both problems, does that mean these division expressions are equal?
• When dividing, did your estimate need to be adjusted at times? When? What did you do in order to continue dividing?
• Compare your quotients in #1. What did you notice in #1a, 1b, and 1c? Will a four-digit total divided by a two-digit divisor always result in a three-digit quotient? How does the relationship between the divisor and the whole impact the number of digits in the quotient? Can you create a problem that will result in a two-digit quotient? A three-digit quotient?
• How did you decide on a dividend and divisor in #2? Are both of your actual values greater than their estimates, less than their estimates, or is one greater than and the other less than? Could you ever come up with a dividend and divisor that are both less than their estimated values and still have the quotient be between 1,000 and 1,200? Why or why not?

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### Problem 1

${1,056 \div 37}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic F > Lesson 23Exit Ticket, Question b

Grade 5 Mathematics > Module 2 > Topic F > Lesson 23 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 2

A store is celebrating its 19th year of being in business by giving away a prize to every 19th online customer. A total of 8,281 customers bought something.

a.   What is the total number of prizes they gave away?

b.   How many additional customers would need to have bought something for one more prize to be given away?