Curriculum  /  Math  /  4th Grade  /  Unit 3: Multi-Digit Division  /  Lesson 7

Multi-Digit Division

Lesson 7

Math

Unit 3

4th Grade

Lesson 7 of 16

Objective

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

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. 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

  • Throughout the remainder of the topic, the main pictorial 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.
  • Because there will be a remainder when computing the partial quotient in the ones place here, the computations in this lesson have been recorded using a shorthand written method to avoid writing the “R” notation after an equal sign. (See the Tips for Teachers section of Lesson 1 to read more.)
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Anchor Tasks

25-30 minutes

Problem 1

Ms. Roll is making a mural using square tiles. She has 96 tiles and wants the mural to be 8 tiles tall.

a.   How many tiles long will Ms. Roll’s mural be?

b.   Write one or more equations to show how you solved this problem.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 4 Unit 6 Lesson 15 Activity 1

Grade 4 Unit 6 Lesson 15 Activity 1, accessed on Nov. 23, 2021, 11:09 a.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 2

Ayana starts to draw an area model to solve $$79\div3$$, which is shown below.

a.   Why did Ayana make a rectangle with an area of 60 and a length of 20?

b.   How much of the dividend still needs to be divided by 3? How do you know?

c.   Complete the area model by extending the one Ayana started above.

d.   Write the quotient and remainder for $$79\div3$$. Where are those values represented in the area model above?

e.   Use multiplication to check your answer.

Guiding Questions

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Student Response

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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 Fishtank Learning, Inc.

Problem 3

a.   Solve each of the following word problems. Show or explain your work.

  1. The price of a video game is $52. A video game costs 2 times as much as a jigsaw puzzle. What is the price of the jigsaw puzzle? 
  2. Ms. Needham squeezed 85 ounces of orange juice. She wants to pour it into glasses that hold 6 ounces each. How many glasses will Ms. Needham need to hold all the juice?

b.   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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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 #1c and #1d? What do you wonder? 
  • Look at #2. How did you figure out the division problem that Alfonso was trying to solve? What expression did you write to match Alfonso's area model?
  • 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

5-10 minutes

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.

Student Response

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Problem 2

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

$$92\div4$$

Student Response

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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?

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

Lesson 8
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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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