Curriculum  /  Math  /  5th Grade  /  Unit 6: Multiplication and Division of Decimals  /  Lesson 15

Multiplication and Division of Decimals

Lesson 15

Math

Unit 6

5th Grade

Lesson 15 of 23

Objective

Divide a whole number or a decimal by a decimal.

Common Core Standards

Core Standards

  • 5.NBT.B.7 — Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Foundational Standards

  • 5.NBT.A.1
  • 5.NBT.A.2
  • 5.NBT.B.6
  • 5.NF.B.3

Criteria for Success

  1. Understand that shifting the decimal point in both the dividend and divisor the same number of places to the left or the right will result in an equivalent quotient (e.g., 6 ÷ 2 = 60 ÷ 20 as well as 0.6 ÷ 0.2), and use this understanding to rewrite equivalent decimal division computations to be whole-number computations (MP.8).
  2. Estimate quotients of whole numbers or decimals divided by decimals by finding nearby compatible numbers, using that estimate to approximate the leading value in the actual quotient.
  3. Adjust an estimate when the estimate would yield too large or too small a result.
  4. Divide a whole number or decimal to the hundredths place by decimals using general methods.
  5. Check the answer to a division problem by using inverse operations, multiplying the quotient by the divisor, and seeing if it is equivalent to the dividend.
  6. Reason about why it’s only necessary to rewrite a division problem as an equivalent one so that there is no longer a decimal in the divisor, regardless of whether there is a decimal in the dividend (MP.3).
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Anchor Tasks

25-30 minutes

Problem 1

a.   Solve

  1. 520 ÷ 40
  2. 52 ÷ 4

b.   What do you notice about the dividends, divisors, and quotients in Part (a)? What do you wonder?

c.   Use what you noticed in Parts (a) and (b) to solve 5.2 ÷ 0.4 and 0.52 ÷ 0.04.

Guiding Questions

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Student Response

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Problem 2

Solve. Show or explain your work.

a.   34.8 ÷ 0.6

b.   7.32 ÷ 0.08

c.   4.55 ÷ 0.7

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 5 Mathematics > Module 4 > Topic G > Lesson 31 — Concept Development

Grade 5 Mathematics > Module 4 > Topic G > Lesson 31 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 Fishtank Learning, Inc.

Problem 3

Solve. Show or explain your work.

a.   40.8 ÷ 4.8

b.   205.8 ÷ 0.98

c.   14.56 ÷ 2.8

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • In #1(a) and #1(b), is your actual quotient close to your estimated quotients?
  • Explain why there are more stations in #2(a) than in #2(b).
  • How did you determine the quotients in #3? What made Part (c) more challenging than Parts (a) and (b)?
  • I think the answer in #4 is 5.4. Do you agree or disagree? Why? 
  • How did you solve #5? Did you draw a tape diagram to help you solve?

Target Task

5-10 minutes

Solve. Show or explain your work.

a.   4.62 ÷ 0.07

b.   51.2 ÷ 0.08

c.   2.91 ÷ 0.6

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.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Divide with decimals in all cases, seeing the general pattern for the placement of the decimal point in the quotient.

Lesson 16
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Lesson Map

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

Topic A: Multiplying Decimals

Topic B: Dividing Decimals

Topic C: Decimal Real-World Problems

Topic D: Measurement Conversion

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