Multi-Digit Division

Lesson 7

Objective

Solve two-digit dividend division problems with a remainder in any place with larger divisors and quotients.

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 dividend division problems with a large divisor and/or dividend with a remainder in any place using an area model and equations. 
  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 $$84\div3$$, 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, using any strategy, understanding that an area model can be used to solve equal groups and comparison problems (MP.4).

Tips for Teachers

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  • Throughout the remainder of the topic, the main visual model used is the area model. If students seem to be struggling with place value understanding or don’t yet seem ready for the area model for some other reason, you might extend the work from the prior two days until students seem ready for the area model.
  • As noted in Lesson 5 Anchor Task #2, because many of the computations in this lesson involve a remainder when computing the partial quotient in the ones place, the computation has been recorded using the partial quotients algorithm to avoid writing the “R” notation after an equal sign. If you’d like to postpone the introduction of the partial quotient notation, you could either record the computation in a way that is similar to Lesson 5 Anchor Task #1 but in such a way to avoid confusion regarding the equality of a computation with its quotient and remainder. (See the Tips for Teachers section of Lesson 1 to read more.) The partial quotients algorithm will be discussed in detail in Lesson 8.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 2 (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

Ms. Roll gets some butcher paper from the teacher supply room to put up on her bulletin board. The butcher paper has an area of 60 square feet and a height of 6 square feet. When she puts it on her bulletin board, she realizes she needs a little more to fully cover its width. The extra piece she needed has an area of 18 square feet and a height of 6 feet. 

  1. How many square feet of butcher block paper did Ms. Roll put on her bulletin board? 
  2. What was the total length and width of the space Ms. Roll ended up covering?

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic E > Lesson 20Concept Development

Grade 4 Mathematics > Module 3 > Topic E > Lesson 20 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

Ayana starts to draw an area model to solve $$93\div7$$, which is shown below. 

  1. What is the value of A? How do you know? 
  2. How much of the dividend still needs to be divided by 7? How do you know? 
  3. Complete the area model by extending the one Ayana started above. 
  4. Write the quotient and remainder for $$93\div7$$. Where are those values represented in the area model above? 
  5. Use multiplication to check your answer. 

Guiding Questions

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References

Open Up Resources Grade 6 Unit 5 Lesson 7 (Teacher Version)7.2 "Connecting Area Diagrams to Calculations with Whole Numbers"

Grade 6 Unit 5 Lesson 7 (Teacher Version) 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, 4:05 p.m..

Modified by The Match Foundation, Inc.

Problem 3

Jada and Andre both used an area model to find $$85\div 3$$, but they did the calculations differently, as shown here. 

   

  1. How is Jada’s work similar to and different from Andre’s work? 
  2. Write the quotient and remainder for $$85\div 3$$. Then 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 4

  1. Solve each of the following word problems. Show or explain your work.
    1. The price of a video game is $78. The price of the video game is 3 times as much as the price of a jigsaw puzzle. What is the price of the jigsaw puzzle? 
    2. Ms. Needham made 85 ounces of juice. She wants to pour it into cups that hold 6 ounces each. How many cups will Ms. Needham need to hold all the juice?
  2. Did you use an area model to represent either or both problems above? If not, could you have? Why or why not?

Guiding Questions

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Problem Set & Homework

Discussion of Problem Set

  • What do you notice about the dividends, divisors, and quotients in #1c and #1d? What do you wonder? 
  • Look at #2. How did you figure out the division problem that Alfonso was trying to solve? How is the equation you wrote related to the distributive property?
  • How did the zero effect your division in #4b? 
  • Look at #5. How did you solve for the unknowns in the area model? 
  • Look at #6. What did you get for an answer? How did you interpret the remainder? 
  • Did you use any other strategies from Lesson 4 to solve any problems on today’s Problem Set? For example, #4d?

Target Task

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Problem 1

Damon is using the area model below to solve a problem.

Write the problem represented by the whole area model, including its quotient and remainder.

Problem 2

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

$$92\div4$$

Problem 3

Molly has a total of 95 pieces of candy to share with her two friends. Any pieces they can’t share evenly they’ll give to Molly’s mom. How many pieces of candy will Molly’s mom get?

Mastery Response

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