Multiplication and Division of Decimals

Lesson 6

Math

Unit 6

5th Grade

Lesson 6 of 24

Objective


Multiply a decimal 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 decimals to tenths 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.
  3. Reason about the placement of the decimal point in cases involving multiplication of a decimal to tenths by a decimal to hundredths, including any of the following lines of reasoning:
    1. Thinking about the product of the smallest base-ten units of each factor (e.g., a tenth times a tenth is a hundredth, so 4.3 × 2.31 will have an entry in the thousandths place),
    2. Thinking of decimals as fractions or as a whole number divided by 10 or 100 (e.g., to compute 4.3 × 2.31, students can use fractions: $$\frac{43}{10}\times\frac{231}{100}=\ \frac{9,933}{1,000}=9.933$$),
    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., $$4.3\times2.31\ {\rightarrow}\ \left(4.3\times10\right)\times\left(2.31\times100\right)$$$$=43\times231=9,933\ {\rightarrow}\ 9,933\div10\div100=9,933\div1,000=9.933$$), and
    4. Using estimation to reason about the size of numbers (e.g., $$4.3\times2.31\approx4\times2=8$$, so 9.933 is a more reasonable product than 9933, 993.3, 99.33, or 0.9933) (MP.3).
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Anchor Tasks


Problem 1

The fifth graders are planting vegetables in the school garden. They want to know how big one of the garden beds is. They measure its length and width and find that it is 3.2 feet long and 2.4 feet wide. How many square feet is the garden bed?

Guiding Questions

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References

San Francisco Unified School District Math Department 5.5 LS1 Day 2 Decimal Multiplication with Base-10 Blocks Student

5.5 LS1 Day 2 Decimal Multiplication with Base-10 Blocks Student is made available by the San Francisco Unified School District Math Department as a part of their SFUSD Math Core Curriculum under a CC BY 4.0 license. Accessed Oct. 7, 2019, 1:35 p.m..

Problem 2

a.   Label the area diagram to represent 7.8 × 0.42 and to find that product.

Decompose 7.8 and 0.42 into its base-ten units and write them in the corresponding boxes of the model.

  1. Label regions A–D with their areas. Show your reasoning.
  2. Find the product that the area diagram represents. Show your reasoning.

b.   Here are two ways to calculate 7.8 × 0.42. Each number with a box gives the area of one or more regions in the area diagram.

  1. In the boxes next to each number, write the letter(s) of the corresponding region(s).
  2. In Calculation B, which two numbers are being multiplied to obtain 0.156? Which two are being multiplied to obtain 3.12? 

Guiding Questions

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References

Open Up Resources Grade 6 Unit 5 Lesson 7Activity 7.4 Using the Partial Products Method

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 reasoning for the placement of the decimal point.

a.   0.14 × 0.6

b.   2.4 × 5.03

c.   3.2 × 2.5

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 4 > Topic E > Lesson 18Concept Development

Grade 5 Mathematics > Module 4 > Topic E > Lesson 18 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem Set


Answer Keys

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Discussion of Problem Set

  • What do you notice about the factors in #2a and #2b? What do you notice about their solutions?
  • How did you solve #3? How did you write your solution?
  • How did you find the area of the kitchen in #5? How did you find the area of the living room?

Target Task


Solve. Show or explain your work.

a.   $$0.35 \times 0.4$$

b.   $$2.02 \times 4.2 $$

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 5

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Lesson 7

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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