Multi-Digit Division

Lesson 8

Objective

Solve three-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 three-digit dividend division problems using an area model and the partial quotients algorithm. 
  2. Understand that while the most efficient way to solve a division problem involves finding the greatest multiple less than the divisor for each place value starting with the largest one, there are many ways in which partial quotients can be computed. For example, to solve $$84\div 3$$, one might compute with the greatest multiple less than the divisor for each place value starting with the largest one to get the partial quotients $$ (60 \div 3) + (24 \div 3)$$ or one might use less efficient partial quotients, such as $$(30 \div 3) + (30 \div 3) + (24 \div 3)$$, among many other possibilities.
  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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  • This lesson covers a lot of ground, introducing students to the partial quotients algorithm and having students compute three-digit by one-digit division problems in all cases. Thus, you may decide to spend two days on this lesson. You could split it up in a variety of ways:
    • Postponing the discussion of the partial quotients algorithm in Anchor Tasks #1 and #2 and the corresponding tasks on the Problem Set and Homework to a later day, 
    • Postponing Anchor Task #3 and the corresponding tasks on the Problem Set and Homework to a later day, or
    • Splitting up tasks (both Anchor Tasks as well as Problem Set/Homework ones) according to how often and in what places remainders exist in the division process, among other possibilities.
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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

Elena used an area model to find the value of $$796\div 6$$

  1. Determine the number that each letter in the model represents, then write the quotient and remainder for $$796\div 6$$
  2. Andrea calculated $$796\div 6$$ in a different way, as shown below. 

  1. Andre subtracted 600 from 796. What does the 600 represent? 
  2. Andre wrote 30 above the 100, and then subtracted 180 from 196. How is the 180 related to the 30? 
  3. What do the numbers 100, 30, and 2 represent? 
  4. What is the meaning of the 4 at the bottom of Andre’s work? 

Guiding Questions

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References

Open Up Resources Grade 6, Unit 5, Lesson 9Activity 9.2, "Using the Partial Quotients Method to Calculate Quotients"

Grade 6, Unit 5, Lesson 9 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. 13, 2018, 3:15 p.m..

Modified by The Match Foundation, Inc.

Problem 2

Yasmin and Osvaldo both found $$951\div4$$ using the partial quotients method, but they did the calculations differently, as shown here. 

  1. How is Yasmin’s work similar to and different from Osvaldo’s work? 

  2. Explain why they have the same answer. 

Guiding Questions

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References

Open Up Resources Grade 6 Unit 5 Practice ProblemsLesson 9, 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

Use any method to solve. Then check your work.

$$648\div8$$

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 #5a? What do you wonder?  
  • How did you solve #1b? What made it more difficult? What about #5d?
  • Look at #2. How did you find the missing value? How is that related to how you might use the partial quotient algorithm to solve that division problem?
  • Look at #4. What did you get for an answer? How did you interpret the remainder? 
  • How did the zero effect your division in #5c? 
  • Did you use any other strategies from Lesson 4 to solve any problems on today’s Problem Set? For example, #1b or #5d?
  • Look at #6. How did you use the partial quotients algorithm to solve differently? 
  • What changed when we moved from dividing two-digit wholes to three-digit wholes? Would the same process we’re using for three-digit wholes work for four-digit wholes? Five digits? Six digits? A million digits? 

Target Task

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Problem 1

Here is an incomplete calculation of $$534\div6$$. Write the missing numbers (marked with “?”) that would make the calculation complete. 

References

Open Up Resources Grade 6 Unit 5 Practice ProblemsLesson 9, Problem #4

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 2

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

$$596\div3$$

Problem 3

Chris baked 128 cookies to bring to school. He put the cookies in boxes that can each hold 6 cookies. What is the fewest number of boxes he’ll need to bring the cookies to school? 

Mastery Response

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Additional Practice

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