Curriculum  /  Math  /  5th Grade  /  Unit 6: Multiplication and Division of Decimals  /  Lesson 2

Multiplication and Division of Decimals

Lesson 2

Math

Unit 6

5th Grade

Lesson 2 of 23

Objective

Multiply a single-digit whole number by a decimal.

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 single-digit whole numbers and decimals to hundredths using general methods, including using a base ten block diagram, an area model and/or the partial products algorithm.
  2. Relate a base ten block diagram, an area model, and the partial products algorithm when multiplying a decimal by a single-digit whole number.
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Anchor Tasks

25-30 minutes

Problem 1

Tyler says he can use base-ten blocks to find the value of 4 × 3.17 because he knows 4 × 3, 4 × 0.1, and 4 × 0.07. He says this diagram proves his thinking.

Do you agree or disagree? Explain your reasoning.

Guiding Questions

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Student Response

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References

Open Up Resources Grade 3 Unit 4 Lesson 14 — Activity 1

Grade 3 Unit 4 Lesson 14 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 Nov. 14, 2024, 1:22 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

a.   Thalia says you can use area diagrams to represent products of decimals. Here is what she draws to represent 4 × 3.17: 

  1. Label each region with its area.

  2. Find the value of 4 × 3.17. Show your reasoning.

  3. How are the partial products in the area model related to the base ten blocks in Anchor Task 1? 

b.   Here is another way of calculating 4 × 3.17. 

  1. How are each of the partial products obtained? For instance, where does the 0.28 come from? 

  2. How are the partial products related to the numbers in the area model? In the base ten block diagram in 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 7.3 Connecting Area Diagrams to Calculations with Decimals

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 work.

a.   4 × 0.67

b.   2.09 × 6

c.   8 × 12.5

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • How did you determine the multiplication problem the area model represented in #1(a)? How did you find the product?
  • What was the product in #2(f)? What made this problem more challenging than the previous ones in #2?
  • What was Miles’s error in #3? What was the correct product?
  • Extension: Seven times what number gives the product 14.42? In other words, what multiplication problem would Miles have the correct solution for? 

Target Task

5-10 minutes

Find the following products. Show or explain your work.

a.   $$6\times 3.5$$

b.   $$9.63 \times 3$$

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

Construct viable arguments and critique the reasoning of others regarding the placement of the decimal point in computations that involve multiplying a whole number by a decimal.

Lesson 3
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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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