Lesson 7 | Multi-Digit Division | 4th Grade Mathematics

Objective

Solve two-digit dividend division problems with a remainder in any place with larger 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 large divisor and/or dividend with a remainder in any place using an area model and equations.
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.
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

Suggestions for teachers to help them teach this lesson

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

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

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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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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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.

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?
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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Problem Set

Problem Set

Answer Keys

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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

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

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.

Problem 2

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

$$92\div4$$

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

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 6

Lesson 8

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

References

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Problem 3

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

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