Multiplication and Division of Whole Numbers

Lesson 13

Math

Unit 2

5th Grade

Lesson 13 of 20

Objective


Divide two-digit, three-digit, and four-digit dividends by one-digit divisors.

Common Core Standards


Core Standards

  • 5.NBT.B.6 — Find whole-number quotients of whole numbers with up to four-digit dividends and two-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

  • 4.NBT.B.4
  • 4.NBT.B.6
  • 5.NBT.A.1
  • 5.NBT.A.2

Criteria for Success


  1. Compute two-digit by one-digit, three-digit by one-digit, and four-digit by one-digit quotients using the area model, the partial quotients algorithm, and the standard algorithm.
  2. Relate the area model, the partial quotients algorithm, and the standard algorithm.
  3. Estimate two-digit by one-digit, three-digit by one-digit, and four-digit by one-digit quotients.
  4. Use the relationship between multiplication and division to check whether one’s answer is correct.

Tips for Teachers


Students divided up to four-digit by one-digit whole numbers using the area model, the partial quotients algorithm, and/or the standard algorithm in Grade 4. The intention of this lesson it to solidify the standard algorithm with these cases before moving onto new, more cognitively complex cases in later lessons.

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Anchor Tasks


Problem 1

a.   Shani calculated $$81\div3$$ using an area model by finding the length of a rectangle whose area is 81 square units and width is 3 units.

  1. The value being divided has 8 tens. The area model has only 6 tens in the leftmost region. Why?
  2. Where did the 21 ones come from in the area model?

b.   Albie calculated $$81\div3$$ using a method that was different from Shani’s.

  1. Albie subtracted 60 from 81. What does the 60 represent?
  2. Albie wrote 7 above the 20, and then subtracted 21 from 21. How is the 21 related to the 7?
  3. What do the numbers 20 and 7 represent?

c.   Kimiko has a method of calculating quotients that is different from Shani’s method and Albie’s method. Here is how she found the quotient $$81\div3$$.

  1. How is Kimiko’s method similar to and different from Shani’s method and Albie’s method?
  2. Kimiko subtracted $$3\times2$$, then $$3\times7$$. Earlier, Albie subtracted $$3\times20$$, then $$3\times7$$. Why did they have the same quotient?
  3. Why do you think Kimiko wrote 1 next to the remainder of 2 rather than adding 1 and 2 to get 3? 

Guiding Questions

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References

Open Up Resources Grade 6, Unit 5, Lesson 9

Grade 6, Unit 5, Lesson 9 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. 13, 2018, 3:15 p.m..

Modified by Fishtank Learning, Inc.
Open Up Resources Grade 6 Unit 5 Lesson 10

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 2

Estimate each quotient, then solve using any method. Then assess the reasonableness of your answer.

a.   $$97 \div2$$

b.   $$1,216\div4$$

c.   $$4,309\div7$$

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • Look at #1. Which problems were particularly difficult? Why?
  • How did you determine what division problem was being solved in #2? 
  • Look at #4. Are there other division problems with the same quotient and remainder? How do you know?
  • Look at #5. What if Mr. Jones has 163 books? How would this change the answer to the question? 

Target Task


Problem 1

Solve. Show or explain your work.

a.   $$72\div6$$

b.   $$3,809\div5$$

Student Response

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Problem 2

Alyssa is using the area model below to solve a problem. 

Write the problem represented by the whole area model, including its quotient and remainder.

Student Response

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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

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 12

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Lesson 14

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Writing and Interpreting Numerical Expressions

Topic B: Multi-Digit Whole Number Multiplication

Topic C: Multi-Digit Whole Number Division

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