Lesson 6 | Multi-Digit Division | 4th Grade Mathematics

Objective

Solve two-digit dividend division problems with a remainder in the tens and/or 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 a remainder in the tens place.
Solve two-digit dividend division problems with a divisor less than five and a remainder in the tens and 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.
Understand that when there is a remainder in the tens place, you can decompose it into ones to be able to divide and use this reasoning to see why it is more efficient to start with the largest place value when dividing.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

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.)

Lesson Materials

Optional: Base ten blocks (20 ones and 6 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

Starbursts come in packages of 10. Mr. Duffy has 3 packages of Starburst that he wants to share evenly with Ms. Glynn. How many Starbursts will they each get?

Guiding Questions

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Problem 2

This diagram represents 96.

To find 96 ÷ 4, Noah draws the following diagram.

He says, “The quotient is 21 with a remainder of 1 ten and 2 ones.”

a. Explain the error Noah made.

b. Find the correct quotient of 96 ÷ 4.

Guiding Questions

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References

Illustrative Mathematics Grade 4 Unit 6 Lesson 17 Activity 2

Grade 4 Unit 6 Lesson 17 Activity 2, accessed on Nov. 23, 2021, 10:23 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

Solve. Then check your work.

$${82\div3}$$

Guiding Questions

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Problem Set

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

Look at #2. What mistake did Cayman make? How can he correct his work?
What made #3b-d more challenging than #1 or #3a?
Look at #4. How did you find the number? How is this related to the process of checking our work?
Did you use any other strategies from Lesson 4 to solve any problems on today’s Problem Set? For example, #3a?

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. $${75\div3}$$

b. $${66\div4}$$

Student Response

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Problem 2

When 69 is divided by 5 the remainder is 4. Use multiplication to explain why this is true.

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 5

Lesson 7

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

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

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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