Curriculum  /  Math  /  5th Grade  /  Unit 6: Multiplication and Division of Decimals  /  Lesson 13

Multiplication and Division of Decimals

Lesson 13

Math

Unit 6

5th Grade

Lesson 13 of 23

Objective

Divide a whole number or a decimal by 1 tenth or 1 hundredth.

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.7

Criteria for Success

  1. Divide a decimal to the hundredths place by one tenth or one hundredth using an understanding of number of groups unknown division (also called quotitive, measurement, or equal-sharing division).
  2. Reason about the placement of the decimal point in cases involving division of a number by one tenth or one hundredth by thinking about the problem as number of groups unknown division in which one partitions some number of units into an unknown number of groups of equal size, and then using any of the following lines of reasoning:
    1. E.g., $$7\div0.1$$ can be thought of as determining how many tenths are in 7, and since there are 10 tenths in 1, there must be 7 times as many tenths in 7, so $$7 \div 0.1 = 7 \times10 = 70$$,
    2. Determining how many tenths are in 7 by noting that 7 is 70 tenths, so asking how many tenths are in 7 is the same as asking how many tenths are in 70 tenths, which is 70), or
    3. Rewriting a division computation as a fraction to create an equivalent division expression, e.g., $$7 \div 0.1 = \frac{7}{0.1} = \frac{7 \times 10}{0.1 \times 10} = \frac{70}{1} = 70$$ (MP.3).
  3. Explain why the quotient of a number divided by 1 tenth or 1 hundredth is 10 or 100 times as large as the dividend, respectively (MP.3).
  4. 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

“Students can first examine the cases of dividing by 0.1 and 0.01 to see that the quotient becomes 10 times or 100 times as large as the dividend. … For example, students can view 7 ÷ 0.1 = â–¡ as asking how many tenths are in 7. Because it takes 10 tenths to make 1, it takes 7 times as many tenths to make 7, so 7 ÷ 0.1 = 7 × 10 = 70. Or students could note that 7 is 70 tenths, so asking how many tenths are in 7 is the same as asking how many tenths are in 70 tenths, which is 70. In other words, 7 ÷ 0.1 is the same as 70 ÷ 1. So dividing by 0.1 moves the number 7 one place to the left, the quotient is ten times as big as the dividend” (NBT Progression, p. 20).

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Anchor Tasks

25-30 minutes

Problem 1

a.   Find each quotient. Be prepared to explain your reasoning.

  1. 2 ÷ 0.1 = _________
  2. 2 ÷ 0.01 = _________

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

Guiding Questions

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Student Response

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Problem 2

Solve. Show or explain your work.

a.   7 ÷ 0.1

b.   7.4 ÷ 0.1

c.   7.46 ÷ 0.1

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 5 Mathematics > Module 4 > Topic G > Lesson 29 — Concept Development

Grade 5 Mathematics > Module 4 > Topic G > Lesson 29 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.   8 ÷ 0.01

b.   8.3 ÷ 0.01

c.   8.37 ÷ 0.01

Guiding Questions

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Student Response

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Problem 4

a.   Solve.

  1. 5 ÷ 0.1
  2. 50 ÷ 1

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

c.   Solve.

  1. 9 ÷ 0.01
  2. 900 ÷ 1

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

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • In #1, did you notice the relationship between (a) and (c), (b) and (d), (e) and (g), and (f) and (h)?
  • In #1, did you notice the relationship between (a) and (e), (b) and (f), (c) and (g), and (d) and (h)?
  • What is the relationship between #3(a) and #3(b)?
  • Do you agree with Carrie, Garret, both of them, or neither of them in #4? Why?
  • What strategy did you use to solve #5?
  • How did you answer #6?
  • How is this lesson similar to the work we did in Unit 1? How is it different?

Target Task

5-10 minutes

Problem 1

Which of the following expressions is equivalent to 7 ÷ 0.1? Circle the three correct answers.

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Student Response

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Problem 2

Solve. Show or explain your work.

$$76.02 \div 0.01$$

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 whole number or a decimal by a decimal in cases that involve basic facts. Estimate quotients with decimal divisors by rounding numbers to compatible numbers.

Lesson 14
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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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