Curriculum  /  Math  /  5th Grade  /  Unit 6: Multiplication and Division of Decimals  /  Lesson 8

Multiplication and Division of Decimals

Lesson 8

Math

Unit 6

5th Grade

Lesson 8 of 23

Objective

Divide a decimal by a single-digit whole number in cases that involve basic facts. Estimate quotients of decimal dividends and single-digit whole number divisors by rounding numbers to compatible numbers.

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.A.4
  • 5.NBT.B.6

Criteria for Success

  1. Divide a decimal by a whole number in cases that involve basic facts using using an understanding of group size unknown division.
  2. Explain why the quotient of a decimal divided by a whole number is 1 tenth or 1 hundredth as large as its related basic fact (e.g., $$0.8 \div 2$$ is 0.4, which is 1 tenth as large as $$8 \div 2$$) (MP.3).
  3. Estimate the quotient of a decimal divided by a whole number by finding nearby compatible numbers (e.g., $$1.32 \div 7 \rightarrow 1.4 \div 7$$).

Tips for Teachers

  • Fifth graders are expected to “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”. However, the standards do not specify exactly which cases of decimal division this entails. For example, should students be dividing by two-digit decimal divisors, as they do with whole number divisors (5.NBT.B.6)? Should they only divide in cases for which they can compute the equivalent fraction division (i.e., equivalent to a unit fraction divided by a whole number or vice versa, meaning $$6 \div 0.2$$ is permissible (since it is equivalent to $$ 6 \div \frac{1}{5} $$) but $$6 \div 0.3$$ is not)? This curriculum takes an inclusive approach to these and all likely cases, but it would be worthwhile to see if your state or its assessment consortium include more information about grade-level expectations, in which case certain lessons or Anchor Tasks may be cut or modified.
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Anchor Tasks

25-30 minutes

Problem 1

a.   Find each quotient. Be prepared to explain your reasoning.

  1. 8 ÷ 2 = _________
  2. 0.8 ÷ 2 = _________
  3. 0.08 ÷ 2 = _________

b.   What is the relationship between the quotients in Parts (i) and (ii) above? Between Parts (i) and (iii)?

Guiding Questions

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Student Response

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Problem 2

Compute.

a.   0.06 ÷ 3 = ___________

b.   0.24 ÷ 4 = ___________

Guiding Questions

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Student Response

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Problem 3

Estimate each of the following quotients.

a.   7.92 ÷ 4

b.   3.6 ÷ 5

c.   0.52 ÷ 6

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • What did you estimate was the quotient in #4e? How did you come up with that estimate?
  • My estimate for #4f is 0.5, since 2.88 is close to 3.0, and 3.0 ÷ 6 is 0.5. Do you think 3 ÷ 6 would also be 0.5? What does that make you think about dividing whole numbers that results in a decimal?
  • In #5(a), what mistake is being made that would produce 5.6 ÷ 7 = 8?
  • Change the dividends in #5 so that all of the quotients are correct. Is there a pattern to the changes that you must make?
  • Which estimated quotients will be greater than their actual ones in #6? Less than? How do you know?

Target Task

5-10 minutes

Problem 1

What is the value of $$0.24 \div 3$$?

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Student Response

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Problem 2

Estimate $$3.46 \div 4$$.

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

Divide a decimal by a single-digit whole number.

Lesson 9
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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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