# Multi-Digit Division

## Objective

Solve two-digit dividend division problems with no remainder or a remainder in the ones place with smaller 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.

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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 no remainder, where the quotient is less than 20.
2. Solve two-digit dividend division problems with a remainder in the ones place, where the quotient is less than 20.
3. Check the work of a division calculation by multiplying the quotient and divisor and adding the remainder to see if it equals the dividend.

## Tips for Teachers

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• The following material is needed for today's lesson: base ten blocks
• This lesson allows for flexible use of models, depending on what students have gravitated towards in previous lessons and units. Later in the unit, students will more explicitly be pointed towards the use of an area model, the partial quotients algorithm, and the standard algorithm. However, since students may find base ten block representations helpful as they develop an understanding of division, the models shown as examples here use this model. If students are comfortable with area models, you may choose to jump straight to that model. None of the Anchor Tasks, Problem Set tasks, or Homework tasks in this lesson ask students to use a particular strategy to allow for that flexible use of model.
• “Language plays an enormous role in thinking conceptually about the standard division algorithm. More adults are accustomed to the “goes into” language that is hard to let go. For the problem $583 \div 4$, here is some suggested language:
• I want to share 5 hundreds, 8 tens, and 3 ones among these 4 sets. There are enough hundreds for each set to get 1 hundred. That leaves 1 hundred that I can’t share.
• I’ll trade the remaining hundred for 10 tens. That gives me a total of 18 tens. I can give each set 4 tens and have 2 tens left over. Two tens are not enough to go around the 4 sets.
• I can trade the 2 tens for 20 ones and put those with the 3 ones I already had. That makes a total of 23 ones. I can give 5 ones to each of the four sets. That leaves me with 3 ones as a remainder. In all, I gave each group 1 hundred, 4 tens, and 5 ones, with 3 ones left over.” (Van de Walle, Teaching Student-Centered Mathematics, Grades 3—5, vol. 2, p. 191).
• Throughout this lesson, students may want to divide starting with the smallest place value. This strategy will work in this lesson, but students will see in Lesson 5 why starting with the largest place value first is the most effective way to divide. Therefore, model starting with the largest place value here, but don’t force students to do so. In Lesson 5, they will develop that understanding.

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 1 and Anchor Task 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

There are 3 packages of 10 pencils and 6 loose pencils. Ms. Banta, Ms. Kosowsky, and Ms. Mullen want to share them evenly. How many pencils will they each get?

#### Guiding Questions

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#### References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic E > Lesson 16Concept Development

Grade 4 Mathematics > Module 3 > Topic E > Lesson 16 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

Solve.

${45\div4}$

#### Guiding Questions

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#### References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic E > Lesson 16Concept Development

Grade 4 Mathematics > Module 3 > Topic E > Lesson 16 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

1. Priya wrote 13 for the value of $28\div2$. Check her answer by multiplying it by 2. What product do you get and what does it tell you about Priya’s answer?
2. Find $58\div5$. Then use multiplication to check your answer.

#### Guiding Questions

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#### References

Open Up Resources Grade 6 Unit 5 Lesson 1010.3 "Dividing Whole Numbers"

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 The Match Foundation, Inc.

## Problem Set & Homework

#### Discussion of Problem Set

• Review any of the computational problems with which students seemed to struggle.
• Look at #2. How did you find the unknown number? What division equations are each of these multiplication equations related to?
• Look at #4. How are the quotient and remainder of $58\div5$ related to the equation in part (a)? Why?
• Did you use any other strategies from Lesson 4 to solve any problems on today’s Problem Set?

## Target Task

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### Problem 1

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

1.      ${48\div4}$                  2.       $27\div2$

### Problem 2

Enter the unknown number that makes the equation true.

$38 = 12 \times 3 +$ _____

Choose the division equation below that corresponds with the multiplication equation in Part A.

1. $12 \div 2$
2. $38\div2$
3. $12\div3$
4. $38\div3$

### Mastery Response

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## Additional Practice

#### Unit Practice

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