Lesson 5 | Multi-Digit Division | 4th Grade Mathematics

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

The core standards covered in this lesson

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.

Number and Operations in Base Ten

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

The foundational standards covered in this lesson

4.NBT.A.1

Number and Operations in Base Ten

4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
4.NBT.B.4

Number and Operations in Base Ten

4.NBT.B.4 — Fluently add and subtract multi-digit whole numbers using the standard algorithm.
4.NBT.B.5

Number and Operations in Base Ten

4.NBT.B.5 — Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
3.OA.C.7

Operations and Algebraic Thinking

3.OA.C.7 — Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Solve two-digit dividend division problems with a divisor less than five and no remainder.
Solve two-digit dividend division problems with a divisor less than five and a remainder in the ones place.
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

Suggestions for teachers to help them teach this lesson

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 flexiblility.
“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 groups. There are enough hundreds for each group 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 group 4 tens and have 2 tens left over. Two tens are not enough to go around the 4 groups.
- 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 groups. 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 6 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 6, they will develop that understanding.

Lesson Materials

Optional: Base ten blocks (9 ones and 9 tens per student or small group) — Students might not need these depending on their reliance on concrete materials.

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

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 16 — Concept 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 Fishtank Learning, Inc.

Problem 2

Ingomar draws a base-ten diagram to find the value of $$85\div4$$. A rectangle represents 10. A small square represents 1.

Use the diagram (or actual blocks) to help Ingomar complete the division. Explain or show your reasoning.

Guiding Questions

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References

Illustrative Mathematics Grade 4 Unit 6 Lesson 17 Activity 1

Grade 4 Unit 6 Lesson 17 Activity 1, accessed on Nov. 17, 2021, 11:35 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 3

a. 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?

b. Find $$97\div3$$. Then use multiplication to check your answer.

Guiding Questions

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References

Open Up Resources Grade 6 Unit 5 Lesson 10 — 10.3 "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 Fishtank Learning, Inc.

Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

How did #1a and #1b differ? What about #1c and #1d?
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

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

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

a. $${48\div4}$$

b. $$67\div2$$

Student Response

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Problem 2

Enter the unknown number that makes the equation true.

$$38 = 12 \times 3 \ +$$ _____

Problem 3

Choose the division expression below that corresponds with the multiplication equation in Problem 2.

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Student Response

An example response to the Target Task at the level of detail expected of the students.

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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.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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

Lesson 4

Lesson 6

Lesson Map

Topic A: Understanding and Interpreting Remainders

Solve division word problems with remainders.

4.OA.A.3

Solve division word problems that require the interpretation of the remainder.

4.OA.A.3

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

Divide multiples of 10, 100, and 1,000 by one-digit numbers.

4.NBT.B.6

Divide two-, three-, and four-digit numbers by one-digit numbers using a variety of mental strategies.

4.NBT.B.6

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

4.NBT.B.6

Solve two-digit dividend division problems with a remainder in the tens and/or ones place with smaller divisors and quotients.

4.NBT.B.6

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

4.NBT.B.6

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

4.NBT.B.6

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

4.NBT.B.6

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.

4.NBT.B.6

Topic C: Multi-Step Word Problems and Patterns

Apply the formulas for area and perimeter in real-world and mathematical problems involving all four operations.

4.MD.A.3 4.OA.A.3

Solve two-step word problems involving all four operations, including those involving interpreting the remainder.

4.NBT.B.6 4.OA.A.3

Solve multi-step word problems involving all four operations.

4.MD.A.3 4.NBT.B.6 4.OA.A.3

Identify and extend growing number patterns.

4.OA.C.5

Identify and extend growing shape patterns.

4.OA.C.5

Identify and extend repeating shape patterns.

4.OA.C.5

Multi-Digit Division

Objective

Common Core Standards

Core Standards

Number and Operations in Base Ten

Foundational Standards

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

Operations and Algebraic Thinking

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Student Response

Problem 2

Problem 3

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

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