Multiplication and Division of Whole Numbers

Lesson 18

Math

Unit 2

5th Grade

Lesson 18 of 20

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

  • 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.

Foundational Standards

  • 4.NBT.B.4
  • 4.NBT.B.6
  • 5.NBT.A.1
  • 5.NBT.A.2

Criteria for Success


  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 an answer using estimation and/or the relationship between multiplication and division to check answers (MP.1).
  6. Solve word problems involving division, including those that require interpretation of the remainder (MP.1, MP.4).
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Anchor Tasks


Problem 1

Estimate the following quotient. Then compute it.

$$6,247\div29$$

Guiding Questions

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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

Solve. Then check your answer using multiplication.

a.   $${4,289\div52}$$

b.   $$6,649\div63$$

Guiding Questions

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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:

a.   Answer to the word problem is 170

b.   Answer to the word problem is 171

c.   Answer to the word problem is 5

d.   CHALLENGE: Answer to the word problem is 11

Guiding Questions

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Problem Set


Answer Keys

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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?

Target Task


Problem 1

Solve. Show or explain your work. 

$${1,368 \div 47}$$

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?

Student Response

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Student Response

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Additional Practice


The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 17

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Lesson 19

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Writing and Interpreting Numerical Expressions

Topic B: Multi-Digit Whole Number Multiplication

Topic C: Multi-Digit Whole Number Division

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