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

Multiplication and Division of Decimals

Lesson 6

Math

Unit 6

5th Grade

Lesson 6 of 23

Objective

Multiply a decimal by a decimal, reasoning about the placement of the decimal point.

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.5
  • 5.NF.B.4

Criteria for Success

  1. Reason about the placement of the decimal point in cases involving multiplication of a decimal to tenths by a decimal to hundredths, including any of the following lines of reasoning:
    1. Thinking about the product of the smallest base-ten units of each factor (e.g., a tenth times a tenth is a hundredth, so 4.3 × 2.31 will have an entry in the thousandths place),
    2. Thinking of decimals as fractions or as a whole number divided by 10 or 100 (e.g., to compute 4.3 × 2.31, students can use fractions: $$\frac{43}{10}\times\frac{231}{100}=\ \frac{9,933}{1,000}=9.933$$),
    3. Reasoning that when one carries out the multiplication without the decimal point, one has multiplied each decimal factor by 10 or 100, so they will need to divide by those numbers in the end to get the correct answers (e.g., $$4.3\times2.31\ {\rightarrow}\ \left(4.3\times10\right)\times\left(2.31\times100\right)$$$$=43\times231=9,933\ {\rightarrow}\ 9,933\div10\div100=9,933\div1,000=9.933$$), and
    4. Using estimation to reason about the size of numbers (e.g., $$4.3\times2.31\approx4\times2=8$$, so 9.933 is a more reasonable product than 9933, 993.3, 99.33, or 0.9933) (MP.3).

  2. Compute products of decimals to tenths and decimals to hundredths using general methods, including using an area model and/or algorithm (like the partial products algorithm or the standard algorithm).

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Anchor Tasks

25-30 minutes

Problem 1

Elena, Noah, Larae, and Xavier are now trying to compute 3.2 × 2.4. All four of their computations were correct.

Elena’s Method

$$3.2 \times 10 = 32$$

$$2.4 \times 10 = 24$$

$$32 \times 24 = 768$$

$$768 \div 100 = 7.68$$

Noah’s Method

$$3.2 =\frac{32}{10} $$

$$2.4 =\frac{24}{10} $$

  $$\frac{32}{10} \times \frac{24}{10} = \frac{768}{100}$$

   $$\frac{768}{100} = 7.68$$

Larae’s Method

$$\begin{align} 3.2 \times2.4&=34 \ \text{tenths} \times 24 \ \text{tenths} \\ \\ &=768 \ \text{hundredths} \\ \\ &=7.68\end{align} $$

Xavier’s Method

$$3.2 \times 2.4 \approx 3 \times 2$$

$$32 \times 24 = 768$$

So, $$3.2 \times 2.4 = 7.68$$, since it is closest to 6.

a.   Which method of placing the decimal point makes the most sense to you? Why?

b.   If 23 × 651 = 14973, how would each person determine the placement of the decimal in the product 2.3 × 6.51?

Guiding Questions

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Student Response

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References

Open Up Resources Grade 6 Unit 5 Lesson 6 — Activity 2

Grade 6 Unit 5 Lesson 6 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 Sept. 16, 2019, 11:59 a.m..

Modified by Fishtank Learning, Inc.

Problem 2

A common way to find a product of decimals is to calculate a product of whole numbers, then place the decimal point in the product.

a.   Find 78 × 42 using an area model, the partial products algorithm, or the standard algorithm. 

b.   Use the product you found in Part (a) to determine the value of 7.8 × 0.42. Explain why the decimal point of the product is placed where it is using any of the methods from Anchor Task 1.

Guiding Questions

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Student Response

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References

Open Up Resources Grade 6 Unit 5 Lesson 7 — Activity 7.4 Using the Partial Products Method

Grade 6 Unit 5 Lesson 7 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 Sept. 3, 2019, 4:56 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Solve. Show or explain your reasoning for the placement of the decimal point.

a.   0.14 × 0.6

b.   2.4 × 5.03

c.   3.2 × 2.5

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 5 Mathematics > Module 4 > Topic E > Lesson 18 — Concept Development

Grade 5 Mathematics > Module 4 > Topic E > Lesson 18 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

  • What do you notice about the factors in #2a and #2b? What do you notice about their solutions?
  • How did you solve #3? How did you write your solution?
  • How did you find the area of the kitchen in #5? How did you find the area of the living room?

Target Task

5-10 minutes

Solve. Show or explain your work.

a.   $$0.35 \times 0.4$$

b.   $$2.02 \times 4.2 $$

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

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

Lesson 7
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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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