Multiplication and Division of Decimals

Lesson 2

Math

Unit 6

5th Grade

Lesson 2 of 24

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 an area model and/or algorithm (like the partial products algorithm or the standard algorithm).
  2. Relate the area model, the partial products algorithm, and the standard algorithm.
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Anchor Tasks


Problem 1

Mr. Wynn, the art teacher, is creating a mural on the side of the school building. The mural will be 2 meters tall and 6 meters long. After finishing the mural, he decided he wants to add a small section to the side of it, and the new section is also 2 meters tall but just 0.4 meters long.

a.   How many square meters is Mr. Wynn’s mural?

b.   What was the total length of the mural Mr. Wynn created?

Guiding Questions

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Problem 2

a.   You can use area diagrams to represent products of decimals. Here is an area diagram that represents $$3.17 \times 4$$.

  1. Label each region with its area.
  2. Find the value of $$3.17 \times 4$$. Show your reasoning.

b.   Here are two ways of calculating $$3.17 \times 4$$.

  1. In Calculation A, how are each of the partial products obtained? For instance, where does the 0.28 come from? How are the partial products in Calculation A related to the numbers in the area model?
  2. How is Calculation B similar to Calculation A? How is it different?
  3. What are the advantages and disadvantages of the partial products method shown in Calculation A? What about of the standard algorithm method shown in Calculation B?

Guiding Questions

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References

Open Up Resources Grade 6 Unit 5 Lesson 7Activity 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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Problem Set


Answer Keys

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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 Mike’s error in #3? What was the correct product?
  • Extension: Seven times what number gives the product 14.42?

Target Task


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.

Extra Practice Problems

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 1

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Lesson 3

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Multiplying Decimals

Topic B: Dividing Decimals

Topic C: Decimal Expressions and Real-World Problems

Topic D: Measurement Conversion and Real-World Problems

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