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

Multiplication and Division of Decimals

Lesson 5

Math

Unit 6

5th Grade

Lesson 5 of 23

Objective

Multiply a decimal by a decimal in cases that involve basic facts. Estimate the product of two decimals by rounding numbers to their largest place.

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.A.4
  • 5.NBT.B.5
  • 5.NF.B.4

Criteria for Success

  1. Multiply a decimal by a decimal in cases that involve basic facts using fraction equivalence.
  2. Multiply a decimal by a decimal in cases that involve basic facts using the whole number basic fact, then moving the decimal point the relevant number of spaces based on the place value of the original values (e.g., 0.4 × 0.02 = 4 × 2 × 0.1 × 0.01 = 8 × 0.1 × 0.01 = 0.8 × 0.01 = 0.008).  
  3. Estimate the product of two decimals by rounding each decimal to its largest place.
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Anchor Tasks

25-30 minutes

Problem 1

a.   Helen, Ramiro, and Jackie all have square garden plots in their community garden.

  1. Helen plants 0.1 of her garden with flowers. Of those flowers, 0.1 of them are tulips. How much of Helen’s garden is tulips?
  2. Ramiro plants 0.3 of his garden with flowers. Of those flowers, 0.1 of them are tulips. How much of Ramiro’s garden is tulips?  
  3. Jackie plants 0.3 of her garden with flowers. Of those flowers, 0.2 of them are tulips. How much of Jackie’s garden is tulips?

b.   Write equations to represent each problem in Part (a) above. What do you notice? What do you wonder?

Guiding Questions

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Student Response

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Problem 2

a.   Select all expressions that are equivalent to $$0.4 \times 0.02$$.

  1. $$4 \times 0.1 \times 2 \times 0.01$$
  2. $$4 \times 0.1 \times 2 \times 0.1$$
  3. $$4 \times \frac{1}{10} \times 2 \times \frac{1}{100}$$
  4. $$4 \times \frac{1}{100} \times 2 \times \frac{1}{1,000}$$
  5. $$4 \times 2 \times 0.01 \times 0.01$$
  6. $$4 \times 2 \times \frac{1}{10} \times \frac{1}{100}$$
  7. $$\frac{4}{10} \times \frac{2}{100}$$

b.   Find the value of $$0.4 \times 0.02$$. Show your reasoning.

Guiding Questions

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Student Response

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References

Open Up Resources Grade 6 Unit 5 Lesson 5 — Activity 5.3 Fractionally Speaking: Multiples of Powers of Ten

Grade 6 Unit 5 Lesson 5 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. 18, 2019, 3:32 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Find the value of each product below. Show or explain your work.

a.   0.09 × 0.3 = _________

b.   0.7 × 0.6 = _________

c.   0.8 × 0.05 = _________

Guiding Questions

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Student Response

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Problem 4

Estimate the following products. Determine whether the actual product will be greater or less than the estimated product or whether it’s difficult to determine.

a.   6.23 × 8.4

b.   5.4 × 0.79

c.   0.34 × 0.56

d.   0.21 × 0.03

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • I think the area model in #1 represents 0.8 × 0.4, which isn’t one of the options listed. What mistake did I make?
  • My estimate in #2d is 0.04 because 8 × 5 is 40, and our answer should be to the hundredths place since tenths times tenths are hundredths. Do you agree or disagree? Why?
  • I think the Boy Scout used 0.5 meter of the rope for the knot in #3. Do you agree or disagree? Why?
  • How does #4a help you solve #4c?
  • My estimate in #5f is 0.48 because 6 × 8 is 48, and I know my answer needs to be less than 0.84. Do you agree or disagree with my estimate?

Target Task

5-10 minutes

Problem 1

Which equation shows a correct strategy and product for the expression shown?

$$0.04 \times 0.8$$

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Student Response

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Problem 2

Estimate $$0.5 \times 0.63$$. 

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

Lesson 6
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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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