Curriculum  /  Math  /  4th Grade  /  Unit 3: Multi-Digit Division  /  Lesson 9

Multi-Digit Division

Lesson 9

Math

Unit 3

4th Grade

Lesson 9 of 16

Objective

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

Common Core Standards

Core Standards

  • 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

  • 4.NBT.A.1
  • 4.NBT.B.4
  • 4.NBT.B.5
  • 3.OA.C.7

Criteria for Success

  1. Understand how the standard algorithm for division works. 
  2. Solve four-digit dividend division problems using any method to solve, including the standard algorithm. 
  3. Understand that when a remainder is larger than the divisor at any point in the standard algorithm, the quotient should be adjusted up.
  4. Solve one-step division word problems, including those that require the interpretation of the remainder (on the Problem Set and Extra Practice Problems) (MP.4).

Tips for Teachers

The standard algorithm is not an expectation in Grade 4. However, exposure to the standard algorithm here will prepare students well for extending division algorithms to two-digit divisors in Grade 5 and the eventual expectation of being fluent with the standard algorithm in Grade 6. Thus, students are exposed to the standard algorithm in this lesson but allowed to use any method to solve. Note that the standard algorithm relies on students’ ability to find the greatest multiple less than the divisor, so if they are still building that skill or are still making sense of the partial quotients algorithm, you might modify this lesson to continue to focus on that method. If you do decide to modify this lesson, students should see the standard algorithm at some point in Grade 4 to prepare them for Grade 5 so be sure to address it at some point in the year.

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Anchor Tasks

25-30 minutes

Problem 1

a.   Solve 6,479 ÷ 3 using the partial quotients algorithm.

b.   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 6,479 ÷ 3:

Lin arranged the numbers for vertical calculations.

Her plan was to divide each digit of 6,479 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 6,479.

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.

Lin’s method is often called the standard algorithm or long division. How are the standard algorithm and the partial quotients algorithm similar? How are they different?

Guiding Questions

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Student Response

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References

Open Up Resources Grade 6 Unit 5 Lesson 10 — Activity 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 Fishtank Learning, Inc.

Problem 2

Here are three calculations to find the value of 4,968 ÷ 8, but each one is unfinished. Complete at least two of the unfinished calculations.

a.    

b.   

c.   

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 4 Unit 6 Lesson 19 Activity 3

Grade 4 Unit 6 Lesson 19 Activity 3, accessed on Aug. 16, 2022, 4:41 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 3

Use any method to find the following quotients. Then check your work.

a.   5,391 ÷ 4

b.   1,332 ÷ 9

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

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

5-10 minutes

Problem 1

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

$$3,168\div4$$

Student Response

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Problem 2

Complete the following calculation to find the value of the quotient. 

Student Response

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Problem 3

Ms. Ruizdeporras is making gift bags for the fourth- and fifth-grade teachers. She has 3,421 pencils to split into 8 gift bags. Each teacher will get the same number of pencils and 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?

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.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

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.

Lesson 10
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Lesson Map

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

Topic A: Understanding and Interpreting Remainders

Topic B: Division of up to Four-Digit Whole Numbers by One-Digit Whole Numbers

Topic C: Multi-Step Word Problems and Patterns

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