Multiplication and Division of Whole Numbers

Lesson 11

Math

Unit 2

5th Grade

Lesson 11 of 20

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.

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.6
  • 5.NBT.A.1
  • 5.NBT.A.2

Criteria for Success


  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


  • 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 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


Problem 1

a.   Solve.

  1. $${24\div6=}$$ __________
  2. $${240\div6=}$$  __________
  3. $${240\div60=}$$  __________
  4. $${2,400\div60=}$$  __________
  5. $${24,000\div60=}$$  __________

b.   What do you notice about Part (a)? What do you wonder?

Guiding Questions

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Problem 2

a.   Solve.

  1. $$40\div8=$$  __________
  2. $$400\div80=$$  __________
  3. $$4,000\div80=$$  __________

b.   What do you notice about Part (a)? What do you wonder?

Guiding Questions

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Problem 3

Estimate the following quotients.

a.   $$403\div18$$

b.   $$4,038\div18$$

c.   $$253\div49$$

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • 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


Problem 1

Compute the quotient for the following problems:

a.   $${120\div40}$$

b.   $$4,800\div60$$

Student Response

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Problem 2

Estimate the quotient for the following problems:

a.   $${603\div28}$$

b.   $${8,792\div31}$$

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 10

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Lesson 12

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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