Curriculum  /  Math  /  5th Grade  /  Unit 6: Multiplication and Division of Decimals  /  Lesson 7

Multiplication and Division of Decimals

Lesson 7

Math

Unit 6

5th Grade

Lesson 7 of 23

Objective

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

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. Deduce the general pattern about the placement of the decimal point when multiplying decimals, namely that the number of decimal places in the product is the sum of decimal places in each factor (MP.8).
  2. Multiply decimals by decimals or whole numbers in all cases.

Tips for Teachers

  • As a supplement to the Problem Set, students can play an adapted version of the Decimal Product Game, which you can access at the following link: Product Game... again! by Math Hombre. This version involves multiplication of decimals to hundredths that is related to basic facts rather than multi-digit computation, but it can and should be adapted to address the needs of your students.
  • Students can also play an adapted version of Decimal War, which can be found in Number and Operations in Base Ten Multiplication and Division with Decimals Grade 5 Formative Assessment Lesson by the Kentucky Department of Education. Adapt it so students estimate the same product, and whoever has the closest estimate can “win” that hand and play to a certain number (e.g., the first to 10 winning hands wins the game), or students could play a certain number of rounds and the student with the smallest cumulative difference would win the whole game.
  • Students can also solve adapted versions of “Number Puzzles” from the Georgia Standards of Excellence Curriculum Frameworks, Grade 5, Unit 3, which can be found in the Georgia Standard of Excellence Curriculum Frameworks: Mathematics GSE Fifth Grade Unit 3: Multiplying and Dividing with Decimals by The Georgia Department of Education. Adapt them so that they just include multiplication of decimals to hundredths.
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Anchor Tasks

25-30 minutes

Problem 1

a.   Use the fact that 12 × 16 = 192 to solve the following.

  1. 12 × 1.6
  2. 12 × 0.16
  3. 1.2 × 16
  4. 1.2 × 1.6
  5. 1.2 × 0.16
  6. 0.12 × 16
  7. 0.12 × 1.6

b.   What do you notice about the total number of decimal places in the factors and the number of decimal places in the product? Why does that make sense?

c.   Use your work in Parts (a) and (b) to solve the following.

  1. 0.12 × 160
  2. 120 × 0.16
  3. 12,000 × 1.6
  4. 0.12 × 1,600
  5. 0.012 × 0.16

Guiding Questions

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Student Response

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References

Illustrative Mathematics Reasoning about Multiplication and Division and Place Value, Part 1

Reasoning about Multiplication and Division and Place Value, Part 1, accessed on Sept. 28, 2017, 2:48 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

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

a.   4.6 × 3

b.   30 × 2.5

c.   1.25 × 39

d.   0.4 × 0.17

e.   1.5 × 0.32

f.   2.05 × 12.8

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • Which multiplication expression was equivalent to the one given in #1? Were you able to determine that without solving? How?
  • I got 2.25 as a product in #2(c). Do you agree or disagree with my solution? How can you prove me wrong?
  • How can you tell just by looking at Jackson’s and Xavier’s products in #3 that Xavier’s is incorrect?
  • What was the product in each part of #4? How did the given fact help you solve the rest?
  • Which multiplication expressions were equivalent in each part of #7? Were you able to determine that without solving? How?
  • What were the constraints in #8? How did those constraints dictate what values could fill in the blanks?
  • What made #9 challenging? Which equations were particularly difficult to place the decimal point in the product or factors?
  • What was the product you could get that was closest to 50 in #10? Did anyone get a closer product? Can we find an even closer one?
  • Explain the general method that we can use to determine where to place the decimal point in decimal multiplication problems.

Target Task

5-10 minutes

Problem 1

Solve. Show or explain your work.

$$7.25 \times 4.8$$

Student Response

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Problem 2

Use the fact that $$16\times4=64$$ to find the product of 1.6 and 0.04. Explain how you decided where to place the decimal point.

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 in cases that involve basic facts. Estimate quotients of decimal dividends and single-digit whole number divisors by rounding numbers to compatible numbers.

Lesson 8
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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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