Curriculum  /  Math  /  5th Grade  /  Unit 6: Multiplication and Division of Decimals  /  Lesson 16

Multiplication and Division of Decimals

Lesson 16

Math

Unit 6

5th Grade

Lesson 16 of 24

Objective

Divide with decimals in all cases, 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.6
  • 5.NF.B.3

Criteria for Success

  1. Deduce the general pattern about the placement of the decimal point when dividing decimals, namely that when the decimal point in the divisor is moved to make a whole number, the decimal point in the dividend should be moved the same number of places (MP.8).
  2. Divide decimals in all cases.
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Anchor Tasks

25-30 minutes

Problem 1

a.   Which of the following expressions are equivalent to 1.33 ÷ 0.7?

  1. 0.133 ÷ 0.07
  2. 1.33 ÷ 0.07
  3. 0.133 ÷ 0.7
  4. 13.3 ÷ 0.7
  5. 1.33 ÷ 7
  6. 13.3 ÷ 7
  7. 13.3 ÷ 70
  8. 133 ÷ 70

b.   What do you notice about the equivalent expressions in Part (a)? What do you wonder?

c.   Use one of the expressions you chose in Part (a) to find the quotient 1.33 ÷ 0.7.

Guiding Questions

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Student Response

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Problem 2

Solve. Show or explain your work.

a.   51 ÷ 6

b.   45.2 ÷ 5

c.   3.7 ÷ 20

d.   14.04 ÷ 52

e.   0.9 ÷ 0.25

f.   27.54 ÷ 3.4

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • Which division expression was equivalent to the one given in #1? Were you able to determine that without solving? How?
  • How can you tell just by looking at Jessica’s quotient in #3 that she is incorrect? Why is her answer unreasonable?
  • What was the quotient in each part of #4? How did the given fact help you solve the rest?
  • Why are both Gil and Miriam’s methods in #5 correct? Which one do you gravitate toward with similar problems? Why?
  • How did you decide on what values to fill in the blanks in #8 to make the expression have the largest possible value? How did you decide on what values to fill in the blanks in the challenge in #3 to make the expression have a value as close to 30 as possible?
  • Explain the general method that we can use to determine where to place the decimal point in decimal division problems.

Target Task

5-10 minutes

Problem 1

Which expressions are equal to 9.45 ÷ 3.5? Select the two correct answers. 

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Student Response

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Problem 2

Use the fact that $$288 \div 36 = 8$$ to find the quotient of 28.8 and 0.36. 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

Solve real-world problems that require interpretation of the remainder involving all possible cases, including further decomposition into a decimal.

Lesson 17
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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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