Lesson 9 | Multiplication and Division of Decimals | 5th Grade Mathematics

Objective

Divide a decimal by a single-digit whole number.

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

Number and Operations in Base Ten

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

The foundational standards covered in this lesson

5.NBT.A.1

Number and Operations in Base Ten

5.NBT.A.1 — Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NBT.A.2

Number and Operations in Base Ten

5.NBT.A.2 — Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
5.NBT.B.6

Number and Operations in Base Ten

5.NBT.B.6 — Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Divide a decimal to the hundredths place by a whole number in which the smallest place value unit does not need to be decomposed using general methods, including using a base ten diagram and/or algorithms.
Check the answer to a division problem by using inverse operations, multiplying the quotient by the divisor and seeing if the product is equivalent to the dividend.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

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.
This lesson can be split over two days.

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

Elena and Zack want some change to buy penny candy. Their mom keeps rolls of 10 pennies to give to them for just this purpose. Their mom gives them 5 rolls and 4 loose pennies. How can Zack and Elena split the change they got from their mom evenly?

Guiding Questions

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Problem 2

Elena used base-ten diagrams to find 3.72 ÷ 3. She started by representing 3.72.

She made three groups, each with 1 one. Then, she put the tenths and hundredths in each of the three groups. Here is her diagram for 3.72 ÷ 3.

a. Elena’s diagram for 3.72 has 7 tenths. The one for 3.72 ÷ 3 has only 6 tenths. Why?

b. Where did the extra hundredths (small squares) come from?

c. How would Elena calculate 95.6 ÷ 4?

Guiding Questions

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References

Open Up Resources Grade 6, Unit 5, Lesson 9 — Activity 9.2 Using the Partial Quotients Method to Calculate Quotients

Grade 6, Unit 5, Lesson 9 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 Dec. 13, 2018, 3:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Andre calculated 95.6 ÷ 4 using a method that was different from Elena’s method.

He started by writing the dividend, 95.6, and the divisor, 4.	He then subtracted 4 groups of different amounts from 95.6, starting with 4 groups of 20...	…then 4 groups of 3, and then 4 groups of 0.9.	Andre calculated 20 + 3 + 0.9 and then wrote 23.9.

a. Andre subtracted 80.0 from 95.6. What does the 80 represent?

b. Andre wrote 3.0 above the 20.0 and then subtracted 12.0 from 15.6. How is the 12.0 related to the 3.0?

c. What do the numbers 20.0, 3.0, and 0.9 represent?

d. What is the meaning of the 0.0 at the bottom of Andre’s work?

Guiding Questions

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References

Open Up Resources Grade 6, Unit 5, Lesson 9 — Activity 9.2 Using the Partial Quotients Method to Calculate Quotients

Modified by Fishtank Learning, Inc.

Problem 4

Solve. Show or explain your work.

a. 0.96 ÷ 6 = ___________

b. 9.85 ÷ 5 = ___________

c. 24.08 ÷ 8 = ___________

d. 64.8 ÷ 6 = ___________

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 — Concept Development

Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 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

Problem Set

Answer Keys

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Discussion of Problem Set

Look at #1. How did a basic fact help you solve? Where did you decide to place the decimal point in the quotient?
Look at #2. How did you determine what values should go in the blanks? How did you know to write 0.60 instead of 6 or 0.06 in the first blank? How would it be written if you were using long division?
How much money did Esperanza save per avocado? How did you solve?
How are dividing decimals and dividing whole numbers similar? How are they different?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Solve. Show or explain your work.

a. 0.85 ÷ 5

b. 5.76 ÷ 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.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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Lesson 8

Lesson 10

Lesson Map

Topic A: Multiplying Decimals

Multiply a single-digit whole number by a decimal in cases that involve basic facts. Estimate the product of a single-digit whole number with a decimal by rounding numbers to their largest place.

5.NBT.B.7

Multiply a single-digit whole number by a decimal.

5.NBT.B.7

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

5.NBT.B.7

Multiply a multi-digit whole number by a decimal.

5.NBT.B.7

Multiply a decimal by a decimal in cases that involve basic facts. Estimate the product of two decimals by rounding numbers to their largest place.

5.NBT.B.7

Multiply a decimal by a decimal.

5.NBT.B.7

Multiply with decimals in all cases, reasoning about the placement of the decimal point.

5.NBT.B.7

Topic B: Dividing Decimals

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

5.NBT.B.7

Divide a decimal by a single-digit whole number.

5.NBT.B.7

Divide a decimal by a single-digit whole number that requires decomposition in the smallest place.

5.NBT.B.7

Divide a decimal by a two-digit whole number.

5.NBT.B.7

Divide a decimal by a two-digit whole number that requires decomposition in the smallest place.

5.NBT.B.7

Divide a whole number or a decimal by 1 tenth or 1 hundredth.

5.NBT.B.7

Divide a whole number or a decimal by a decimal in cases that involve basic facts. Estimate quotients with decimal divisors by rounding numbers to compatible numbers.

5.NBT.B.7

Divide a whole number or a decimal by a decimal.

5.NBT.B.7

Divide with decimals in all cases, reasoning about the placement of the decimal point.

5.NBT.B.7

Topic C: Decimal Expressions and Real-World Problems

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

5.NBT.B.7

Solve real-world problems involving multiplication and division with decimals.

5.NBT.B.7 5.OA.A.2

Write and evaluate numerical expressions involving multiplication and division with decimals.

5.NBT.B.7 5.OA.A.1 5.OA.A.2

Topic D: Measurement Conversion and Real-World Problems

Express measurements in a whole number of larger units or mixed units in terms of a smaller unit.

5.MD.A.1

Express measurements in a fractional or decimal number of larger units in terms of a smaller unit.

5.MD.A.1

Express measurements in a whole number of smaller units in terms of a larger unit.

5.MD.A.1

Express measurements in a fractional or decimal number of smaller units in terms of a larger unit.

5.MD.A.1

Solve real-world problems involving measurement conversions.

5.MD.A.1

Multiplication and Division of Decimals

Objective

Common Core Standards

Core Standards

Number and Operations in Base Ten

Foundational Standards

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

References

Problem 4

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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