Lesson 10 | Multiplication and Division of Decimals | 5th Grade Mathematics

Objective

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

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 needs 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.

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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

Josie makes 1.7 liters of lemonade. Josie’s mom tells her to split it evenly with her brother. How much lemonade, in liters, will Josie and her brother each get?

Guiding Questions

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Problem 2

Here is how Mai used base-ten diagrams to calculate 0.62 ÷ 5. She started by representing 0.62.

She then made 5 groups, each with 1 tenth. There was 1 tenth left. She unbundled it into 10 hundredths and distributed the hundredths into 5 groups. Here is her diagram for 0.62 ÷ 5.

a. Mai should have a total of 12 hundredths, but her diagram shows only 10. Why?

b. She did not originally have thousandths, but in her diagrams each group has 4 thousandths. Why?

c. What value has Mai found for 0.62 ÷ 5? Explain your reasoning.

Guiding Questions

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References

Open Up Resources Grade 6 Unit 5 Lesson 11 — Activity 11.2 Keep Dividing

Grade 6 Unit 5 Lesson 11 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. 22, 2019, 11:03 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Here is how Lin calculated 0.62 ÷ 5.

Lin wrote the dividend, 0.62, and the divisor, 5.

She subtracted 5 groups of different amounts from 0.62, starting with 5 groups of 0.10, then 5 groups of 0.02.

Lin wrote 0 to the right of the 2, which made 0.020.

Lastly, she subtracted 5 times 0.004 from 0.020, which left no remainder.

Then she added 0.100 + 0.020 + 0.004, which gave a quotient of 0.124.

a. Lin put a 0 after the remainder of 0.02. Why? Why does this 0 not change the value of the quotient?

b. What value did Lin find for 0.62 ÷ 5?

Guiding Questions

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Problem 4

Solve. Show or explain your work.

a. 27 ÷ 6

b. 0.84 ÷ 8

c. 18.03 ÷ 6

d. 3 ÷ 4

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 1 > Topic F > Lesson 15 — Concept Development

Grade 5 Mathematics > Module 1 > Topic F > Lesson 15 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

Will a whole number divided by a whole number always result in a whole number?
What was different about #3(f) compared to the rest of the computations in #3?

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. 0.7 ÷ 5

b. 1.5 ÷ 4

c. 45 ÷ 6

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

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Word Problems and Fluency Activities

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Lesson 9

Lesson 11

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

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

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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