Lesson 15 | Multiplication and Division of Decimals | 5th Grade Mathematics

Objective

Divide a whole number or a decimal by a decimal.

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.
5.NF.B.3

Number and Operations—Fractions

5.NF.B.3 — Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Criteria for Success

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

Understand that shifting the decimal point in both the dividend and divisor the same number of places to the left or the right will result in an equivalent quotient (e.g., 6 ÷ 2 = 60 ÷ 20 as well as 0.6 ÷ 0.2), and use this understanding to rewrite equivalent decimal division computations to be whole-number computations (MP.8).
Estimate quotients of whole numbers or decimals divided by decimals by finding nearby compatible numbers, using that estimate to approximate the leading value in the actual quotient.
Adjust an estimate when the estimate would yield too large or too small a result.
Divide a whole number or decimal to the hundredths place by decimals using general methods.
Check the answer to a division problem by using inverse operations, multiplying the quotient by the divisor, and seeing if it is equivalent to the dividend.
Reason about why it’s only necessary to rewrite a division problem as an equivalent one so that there is no longer a decimal in the divisor, regardless of whether there is a decimal in the dividend (MP.3).

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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

a. Solve

520 ÷ 40
52 ÷ 4

b. What do you notice about the dividends, divisors, and quotients in Part (a)? What do you wonder?

c. Use what you noticed in Parts (a) and (b) to solve 5.2 ÷ 0.4 and 0.52 ÷ 0.04.

Guiding Questions

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Problem 2

Solve. Show or explain your work.

a. 34.8 ÷ 0.6

b. 7.32 ÷ 0.08

c. 4.55 ÷ 0.7

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 4 > Topic G > Lesson 31 — Concept Development

Grade 5 Mathematics > Module 4 > Topic G > Lesson 31 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 3

Solve. Show or explain your work.

a. 40.8 ÷ 4.8

b. 205.8 ÷ 0.98

c. 14.56 ÷ 2.8

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

In #1(a) and #1(b), is your actual quotient close to your estimated quotients?
How did you determine the quotients in #2? What made Part (c) more challenging than Parts (a) and (b)?
How did you solve #4?
How did you solve #5? Did you draw a tape diagram to help you solve?

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. 4.62 ÷ 0.07

b. 51.2 ÷ 0.08

c. 2.91 ÷ 0.6

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

Answer Keys

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Word Problems and Fluency Activities

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Lesson 14

Lesson 16

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

Number and Operations—Fractions

Criteria for Success

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

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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