Curriculum  /  Math  /  5th Grade  /  Unit 6: Multiplication and Division of Decimals  /  Lesson 4

Multiplication and Division of Decimals

Lesson 4

Math

Unit 6

5th Grade

Lesson 4 of 23

Objective

Multiply a whole number 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. Compute products of whole numbers and decimals using general methods, including the standard algorithm. 

  2. Reason about the placement of the decimal point in cases involving multiplication of a decimal by a multi-digit whole number, including any of the following lines of reasoning:

    1. Thinking about the product of the smallest base-ten units of each factor (e.g., one times a hundredth is a hundredth, so 43 × 2.31 will have an entry in the hundredths place),
    2. Thinking of decimals as fractions or as a whole number divided by 10 or 100 (e.g., to compute 43 × 2.31, students can use fractions: $$43\times\frac{231}{100}=\ \frac{9,933}{100}=99.33$$),
    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., $$43\times2.31\ {\rightarrow}43\times\left(2.31\times100\right)=43\times231=9,933{\rightarrow9,933\div100=99.33}$$), and
    4. Using estimation to reason about the size of numbers (e.g., $$43\times2.31\approx40\times2=80$$, so 99.33 is a more reasonable product than 9933, 993.3, 9.933, or 0.9933) (MP.3).
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Anchor Tasks

25-30 minutes

Problem 1

Namrata says you can find the product of decimals by finding the product whole numbers, then place the decimal point in the product. She wants to compute 8 × 4.27, so she starts to compute 8 × 427 using the standard algorithm below:

Finish Namrata’s computation, then determine where to place the decimal point in the product of 8 × 4.27. 

Guiding Questions

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Student Response

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Problem 2

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

a.   68 × 0.05

b.   6.5 × 8

c.   602 × 5.99

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • Look at #1(c). What made this problem more difficult than the previous ones? What about #1(d)?
  • Some students think Pedro should buy 2 meters of shelving in #2. Others think 3. Which is better? Why? 
  • Look at #3. What do you notice about the size of the factors in each problem and the size of the product? How is that related to what we saw with analogous fraction computations?
  • Look at #3(d). Where did you place the decimal point? Why?
  • Did Greg have enough money to pay for his gas in #4? If so, how much change would he get? If not, how much more would he need? Why might estimation give Greg the false impression that he has enough money?
  • Look at #5(d). Did anyone solve using the standard algorithm? Did you write 2.88 as the “top” number in the algorithm? Why?
  • What error did Michelle make in #6?
  • Look at #7(a). What is similar about this problem and #7(b)? What is different?
  • How does being fluent in whole-number multi-digit multiplication help you multiply decimals? After finding the analogous whole number product, how can you then determine where to place the decimal point?

Target Task

5-10 minutes

Problem 1

Solve. Show or explain your work.

$$1.07 \times 54$$

Student Response

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Problem 2

Arthur computes 485 × 3.4 and gets a product of 164.9.

  • What was Arthur’s mistake?
  • Find the correct product.
  • Show your work or explain your answer.

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

Lesson 5
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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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