Lesson 10 | Multi-Digit Division | 4th Grade Mathematics

Objective

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.

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, three-digit, and four-digit by one-digit division problems using any method.
Understand what to do when there is a zero in a remainder partway through, a zero in the quotient, or a zero in the dividend.
Critique the reasoning of others regarding any of the above cases (MP.3).
Assess the reasonableness of answers using mental computation and estimation strategies including rounding, and/or using the relationship between multiplication and division to check answers (MP.1).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Because “cases involving 0 in division may require special attention” (NBT Progression, p. 16), the purpose of this lesson is to solidify students’ skills with all computational cases, giving special attention to cases involving 0.

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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

Geraldo is solving $${{83\div2}}$$. His work is below.

He says he is done because he got a remainder of 0.

a. Explain the error that Geraldo made when computing $${{83\div2}}$$.

b. Determine the correct answer.

Guiding Questions

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Problem 2

Solve. Show or explain your work.

$${618\div3}$$

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic G > Lesson 30 — Concept Development

Grade 4 Mathematics > Module 3 > Topic G > Lesson 30 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 3

Solve. Then assess the reasonableness of your answer.

$${8,028 \div 4}$$

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic G > Lesson 30 — Concept Development

Modified by Fishtank Learning, Inc.

Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Look at #3. What mistake did Yari make? What was the correct answer?
In #4c, did anyone get 128? How did you know that was wrong?
In #4d, the whole had consecutive zeros. How does your place value knowledge help you to keep track of where you are dividing?
Look at #6. Can you think of a problem that would satisfy the first claim? Why or why not?
Look at #7. How did you decide on your quotient and divisor? Is there more than one right answer? Why?
Look at #6. How did you decide on your quotient and divisor? Is there more than one right answer? Why?

Target Task

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

Problem 1

Solve. Assess the reasonableness of your answer.

a. $${92\div3}$$

b. $${5,010\div3}$$

Student Response

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Problem 2

Geraldo says the solution to $$725\div6 $$ is 12 with a remainder of 5.

What error do you think Geraldo made? Why do you think he made that error?
Determine the correct answer.

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

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Lesson 9

Lesson 11

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

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Student Response

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

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