Multi-Digit Division

Lesson 10

Objective

Solve two-, three-, and four-digit dividend problems, including the special cases of having a 0 in the quotient or dividend, and assess the reasonableness of the quotient.

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 two-digit, three-digit, and four-digit by one-digit division problems using the standard algorithm. 
  2. Understand what to do when there is a zero in a remainder partway through, a zero in the quotient, or a zero in the dividend. 
  3. Critique the reasoning of others regarding any of the above cases (MP.3).
  4. Assess the reasonableness of answers using mental computation and estimation strategies including rounding, and/or using the relationship between addition and subtraction to check answers (MP.1).

Tips for Teachers

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Because “cases involving 0 in division may require special attention” (NBT Progression, p. 16), the purpose of this lesson is to solidify students’ mastery with all computational cases, giving special attention to cases involving 0.

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.

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Anchor Tasks

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Problem 1

Geraldo is solving $${{83\div2}}$$. His work is below. 

He says he is done because he got a remainder of 0.

  • Explain the error that Geraldo made when computing $${{83\div2}}$$
  • Determine the correct answer.

Guiding Questions

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Problem 2

Solve. Show or explain your work. 

$${618\div3}$$

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic G > Lesson 30Concept Development

Grade 4 Mathematics > Module 3 > Topic G > Lesson 30 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

Solve. Then assess the reasonableness of your answer. 

$${8,028 \div 4}$$

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic G > Lesson 30Concept Development

Grade 4 Mathematics > Module 3 > Topic G > Lesson 30 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 Set & Homework

Discussion of Problem Set

  • In #3c, did anyone get 128? How did you know that was wrong? 
  • In #3d, the whole had consecutive zeros. How does your place value knowledge help you to keep track of where you are dividing? 
  • Look at #2. What mistake did William make? What was the correct answer? 
  • Look at #4. Can you think of a problem that would satisfy the first claim? Why or why not? 
  • Look at #5. How did you decide on your quotient and divisor? Is there more than one right answer? Why?
  • Look at #6. How did you decide on your quotient and divisor? Is there more than one right answer? Why?

Target Task

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Problem 1

Solve. Assess the reasonableness of your answer. 

a.      $${92\div3}$$                           b.       $${7,040\div4}$$

References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic G > Lesson 30Exit Ticket

Grade 4 Mathematics > Module 3 > Topic G > Lesson 30 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

Geraldo is solving $${{725 ÷ 6}}$$. His work is below. 

He says he is done because he got a remainder of 0. 

  • Explain the error that Geraldo made when computing $${{725 ÷ 6}}$$.
  • Determine the correct answer. 

Mastery Response

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