Curriculum  /  Math  /  5th Grade  /  Unit 6: Multiplication and Division of Decimals  /  Lesson 9

Multiplication and Division of Decimals

Lesson 9

Math

Unit 6

5th Grade

Lesson 9 of 23

Objective

Divide a decimal by a single-digit whole number.

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

Criteria for Success

  1. Divide a decimal to the hundredths place by a whole number in which the smallest place value unit does not need to be decomposed using general methods, including using a base ten diagram and/or the partial quotients algorithm.
  2. Check the answer to a division problem by using inverse operations, multiplying the quotient by the divisor and seeing if the product is equivalent to the dividend.

Tips for Teachers

  • Fifth graders are expected to “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”. However, the standards do not specify exactly which cases of decimal division this entails. For example, should students be dividing by two-digit decimal divisors, as they do with whole number divisors (5.NBT.B.6)? Should they only divide in cases for which they can compute the equivalent fraction division (i.e., equivalent to a unit fraction divided by a whole number or vice versa, meaning $$6 \div 0.2$$ is permissible (since it is equivalent to $$ 6 \div \frac{1}{5} $$ but $$6 \div 0.3$$ is not)? This curriculum takes an inclusive approach to these and all likely cases, but it would be worthwhile to see if your state or its assessment consortium include more information about grade-level expectations, in which case certain lessons or Anchor Tasks may be cut or modified.
  • This lesson can be split over two days.
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Anchor Tasks

25-30 minutes

Problem 1

Elena and Zack want some change to buy penny candy. Their mom keeps rolls of 10 pennies to give to them for just this purpose. Their mom gives them 5 rolls and 4 loose pennies. How can Zack and Elena split the change they got from their mom evenly?

Guiding Questions

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Student Response

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Problem 2

Elena used base-ten diagrams to find 3.72 ÷ 3. She started by representing 3.72.

She made three groups, each with 1 one. Then, she put the tenths and hundredths in each of the three groups. Here is her diagram for 3.72 ÷ 3.

a.   Elena’s diagram for 3.72 has 7 tenths. The one for 3.72 ÷ 3 has only 6 tenths. Why?

b.   Where did the extra hundredths (small squares) come from?

c.   How would Elena calculate 95.6 ÷ 4?

Guiding Questions

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Student Response

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References

Open Up Resources Grade 6, Unit 5, Lesson 9 — Activity 9.2 Using the Partial Quotients Method to Calculate Quotients

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.

Problem 3

Andre calculated 95.6 ÷ 4 using a method that was different from Elena’s method.

He started by writing the dividend, 95.6, and the divisor, 4. He then subtracted 4 groups of different amounts from 95.6, starting with 4 groups of 20... …then 4 groups of 3, and then 4 groups of 0.9. Andre calculated 20 + 3 + 0.9 and then wrote 23.9.

a.   Andre subtracted 80.0 from 95.6. What does the 80 represent?

b.   Andre wrote 3.0 above the 20.0 and then subtracted 12.0 from 15.6. How is the 12.0 related to the 3.0?

c.   What do the numbers 20.0, 3.0, and 0.9 represent?

d.   What is the meaning of the 0.0 at the bottom of Andre’s work?

Guiding Questions

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Student Response

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References

Open Up Resources Grade 6, Unit 5, Lesson 9 — Activity 9.2 Using the Partial Quotients Method to Calculate Quotients

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.

Problem 4

Solve. Show or explain your work.

a.   0.96 ÷ 6 = ___________

b.   9.85 ÷ 5 = ___________

c.   24.08 ÷ 8 = ___________

d.   64.8 ÷ 6 = ___________

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 — Concept Development

Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 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 Set

15-20 minutes

Discussion of Problem Set

  • Look at #1. How did a basic fact help you solve? Where did you decide to place the decimal point in the quotient?
  • Look at #2. How did you determine what values should go in the blanks? How did you know to write 0.60 instead of 6 or 0.06 in the first blank? How would it be written if you were using long division?
  • How much money did Esperanza save per avocado? How did you solve?
  • How are dividing decimals and dividing whole numbers similar? How are they different?

Target Task

5-10 minutes

Solve. Show or explain your work.

a.   0.85 ÷ 5

b.   5.76 ÷ 4

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 a decimal by a single-digit whole number that requires decomposition in the smallest place.

Lesson 10
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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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