Multi-Digit Division

Lesson 9

Objective

Solve four-digit dividend division problems with a remainder in any place.

Common Core Standards

Core Standards

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  • 4.NBT.B.6 — Find whole-number quotients and remainders with up to four-digit dividends and one-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

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  • 4.NBT.A.1

  • 4.NBT.B.4

  • 4.NBT.B.5

  • 3.OA.C.7

Criteria for Success

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  1. Solve four-digit dividend division problems using an area model and the standard algorithm. 
  2. Understand that when a remainder is larger than the divisor at any point in the standard algorithm, the quotient should be adjusted up.
  3. Solve one-step division word problems, including those that require the interpretation of the remainder (on the Problem Set and Homework) (MP.4).

Tips for Teachers

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The supporting work of gaining familiarity with factors and multiples (4.OA.4) supports the major work here, particularly the standard algorithm’s dependence on students’ ability to find the greatest multiple less than the divisor.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 1 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Tasks

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Problem 1

Lin has a method of calculating quotients that is different from the ones we have explored so far. Here is how she found the quotient of $$4,314 ÷ 6$$

Lin arranged the numbers for vertical calculations.

Her plan was to divide each digit of 6,439 into 3 groups starting with the 6 thousands.

There are 3 groups of 2 in 6, so Lin wrote 2 at the top and subtracted 6 from the 6, leaving 0. 

Then, she brought down the 4 hundreds of 6,439. 

There are 3 groups of 1 in 4, so she wrote 1 at the top and subtracted 3 from 4, which left a remainder of 1.

 

She brought down the 7 tens and wrote it next to the 1, which made 17.

There are 3 groups of 5 in 17, so she wrote 5 at the top and subtracted 15 from 17, which left a remainder of 2. 

She brought down the 9 ones and wrote it next to the 2, which made 29. 

There are 3 groups of 9 in 29, so she wrote 9 at the top and subtracted 27 from 29, which left a remainder of 2.

Study Lin's work and determine whether the strategy she used works. 

Guiding Questions

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References

Open Up Resources Grade 6 Unit 5 Lesson 10Activity 10.2, "Lin Uses Long Division"

Grade 6 Unit 5 Lesson 10 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Jan. 29, 2019, 2:12 p.m..

Modified by The Match Foundation, Inc.

Problem 2

Solve. Then check your work.

$$5,391\div4$$

Guiding Questions

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Problem 3

Stefan is solving the following problem using the standard algorithm.

Stefan thinks he did something wrong, since 9 is greater than 7. Do you agree? How can he fix it? 

Guiding Questions

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Problem Set & Homework

Discussion of Problem Set

  • What do you notice about the dividends, divisors, and quotients in #1a and #1b? What do you wonder?  
  • Look at #2. What division problem did you write? Is there more than one correct answer? How many possible answers, with one-digit divisors, are there? How do you know? 
  • Look at #3. What did you get for an answer? How did you interpret the remainder? 
  • Look at #4. What did you get for an answer? How did you interpret the remainder? 
  • What do you notice about the dividends, divisors, and quotients in #5a and #5b? What do you wonder?  
  • I think the quotient in #5d is 43 R 7. Do you agree or disagree? Why? 
  • Did you use any other strategies from Lesson 4 to solve any problems on today’s Problem Set? For example, #5b?
  • Look at #6. What mistake did Han make? How can you tell, even before multiplying, that his answer is incorrect? 

Target Task

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Problem 1

Solve. Show or explain your work. Then check your work.

$$1,773\div3$$

References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic G > Lesson 29Exit Ticket

Grade 4 Mathematics > Module 3 > Topic G > Lesson 29 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

Here is a calculation of $$8,472\div5$$.

  1. There’s a 5 under the 8 in 8,472. What does this 5 represent?
  2. What does the subtraction of 5 from 8 mean?
  3. Why is a 4 written next to the 3 from 8 – 5? 

References

Open Up Resources Grade 6 Unit 5 Practice ProblemsLesson 10, Practice Problem #2

Grade 6 Unit 5 Practice Problems is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Dec. 14, 2018, 10:06 a.m..

Modified by The Match Foundation, Inc.

Problem 3

Ms. Ruizdeporras is making gift bags for the fourth- and fifth-grade teachers. She has 3,421 pencils to split evenly into 8 gift bags. Ms. Ruizdeporras will keep any extra pencils. How many pencils will each teacher get? How many more pencils would Ms. Ruizdeporras need in order to give teachers one more pencil?

Mastery Response

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Additional Practice

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