Multiplication and Division of Whole Numbers

Lesson 11

Objective

Divide multiples of powers of ten by multiples of ten without remainders. Estimate multi-digit quotients by rounding numbers to their largest place value.

Materials and Resources

Common Core Standards

Core Standards

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  • 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

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  • 4.NBT.B.6

  • 5.NBT.A.1

  • 5.NBT.A.2

Criteria for Success

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  1. Divide multiples of powers of ten by multiples of ten (e.g., $$2,400\div60$$). (Note: they will only encounter examples in which the computation involved is a basic fact, i.e., they will not encounter a problem such as $$4,500\div70$$.) 
  2. Look for patterns in division of multiples of powers of ten (MP.8).
  3. Estimate products by rounding values to their largest place value. (Note: they will only see problems in which rounding to the largest place value results in a quotient that is easy to compute once the values are rounded to their largest place value, e.g., $$402\div19\rightarrow 400\div 20 = 20$$.) 

Tips for Teachers

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  • Throughout Lessons 11—19, students see and make use of structure (MP.7) and attend to precision (MP.6) as they decompose numbers into sums of multiples of base-ten units to multiply or divide them. 

  • In the book Teaching Student-Centered Mathematics, Grades 3-5, vol.1, John A. Van de Walle writes, “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 $${583\div4}$$, here is some suggested language:

    • I want to share 5 hundreds, 8 tens, and 3 ones among these 4 sets. There are enough hundreds for each set 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 set 4 tens and have 2 tens left over. Two tens are not enough to go around the 4 sets. 
    • 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 sets. 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).

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Anchor Tasks

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Problem 1

1. Solve.

a.     $${24\div6=}$$ __________

b.     $${240\div6=}$$  __________

c.     $${240\div60=}$$  __________

d.     $${2,400\div60=}$$  __________

2. What do you notice about Problem 1? What do you wonder?

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic E > Lesson 16Concept Development

Grade 5 Mathematics > Module 2 > 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 The Match Foundation, Inc.

Problem 2

Solve.

a.     $$40\div8=$$  __________

b.     $$400\div80=$$  __________

c.     $$4,000\div80=$$ __________

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic E > Lesson 17Concept Development

Grade 5 Mathematics > Module 2 > Topic E > Lesson 17 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 The Match Foundation, Inc.

Problem 3

Estimate the following quotients.

  1. $$402\div19$$
  2. $$4,028\div19$$
  3. $$239\div41$$

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic E > Lesson 17Concept Development

Grade 5 Mathematics > Module 2 > Topic E > Lesson 17 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 The Match Foundation, Inc.

Discussion of Problem Set

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  • Look at #1a and 1b. What do you notice about the problems and their solutions? 
  • Look at #1f. If I got 800, what mistake did I make? 
  • Look at #3. Who was correct? What error did the other person make? 
  • Look at #4b and 4c. Do you think the actual quotients would be greater or less than the estimate? Why? What about #4d and #4e? 
  • How are the correct answers in #5 Part A related to the correct answers in #5 Part B? 

Target Task

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Problem 1

Compute the quotient for the following problems:

$${120\div40}$$

$${4,800\div60}$$

Problem 2

Estimate the quotient for the following problems:

$${608\div23}$$

$${9,136\div31}$$

References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic E > Lesson 17Exit Ticket

Grade 5 Mathematics > Module 2 > Topic E > Lesson 17 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 The Match Foundation, Inc.

Mastery Response

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