Lesson 27 5 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 27
Objective: Divide decimal dividends by two-digit divisors, estimating
quotients, reasoning about the placement of the decimal point, and making
connections to a written method.
Suggested Lesson Structure
Fluency Practice

Application Problem

Concept Development

Student Debrief

Total Time
(12 minutes)
(5 minutes)
(33 minutes)
(10 minutes)
(60 minutes)
Fluency Practice (12 minutes)
 Divide Decimals by Multiples of 10 5.NBT.7
(3 minutes)
 Unit Conversions 5.MD.1
(4 minutes)
 Divide Decimals by Two-Digit Numbers 5.NBT.7
(5 minutes)
Divide Decimals by Multiples of 10 (3 minutes)
Materials: (S) Personal white board
Note: This fluency activity reviews Lesson 24 content.
Repeat the process from Lesson 25 using the following possible sequence: 1.2 ÷ 6, 1.2 ÷ 60, 8.4 ÷ 4, 8.4 ÷ 40,
6 ÷ 3, 6 ÷ 30, 0.32 ÷ 4, and 0.32 ÷ 40.
Unit Conversions (4 minutes)
Materials: (S) Personal white board
Note: This fluency activity reviews unit conversions and prepares students for problem solving in Lessons 28
and 29.
T:
S:
(Write 1 liter = ____ mL.) How many milliliters are in 1 liter?
1,000 milliliters.
Repeat the process for 1 ft = ____ in, 1 kg = ____ g, and 1 lb = ____ oz.
Lesson 27:
Divide decimal dividends by two-digit divisors, estimating quotients,
reasoning about the placement of the decimal point, and making
connections to a written method.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G5-M2-TE-1.3.0-07.2015
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This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 27 5 2
NYS COMMON CORE MATHEMATICS CURRICULUM
T:
S:
(Write 0.732 liters = ____ mL.) On your personal white board, write an equation to solve, and then
show how many milliliters are in 0.732 liters.
(Write 0.732 × 1,000 = 732 and 0.732 liters = 732 mL.)
Repeat the process using the following possible sequence: 0.037 liters = ____ mL, 0.537 kg = ____ g, and
0.04 kg = ____ g.
Divide Decimals by Two-Digit Numbers (5 minutes)
Materials: (S) Personal white board
Note: This fluency activity reviews Lesson 26 content.
T:
S:
T:
(Write 83.03 ÷ 23.) On your personal white board, write a division equation to estimate the
quotient.
(Write 80 ÷ 20 = 4.)
Use the algorithm to solve.
Repeat the process using the following possible sequence: 6.76 ÷ 13, 12.43 ÷ 11, and 65.94 ÷ 21.
Application Problem (5 minutes)
Michael has 567 pennies, Jorge has 464 pennies, and
Jaime has 661 pennies. If the pennies are shared equally
by the 3 boys and 33 of their classmates, how much
money will each classmate receive? Express your final
answer in dollars.
Note: This problem invites different ways of working with the quantities, either as decimals or whole
numbers, at different stages of the problem. Students might place the decimal point at the very end of their
work or as they add from the beginning. Have them share their approach and express their dollar amounts as
decimal units, too.
Concept Development (33 minutes)
Materials: (S) Personal white board
Problem 1
In a 77-kilometer relay race, each of 22 team members will run an
equal distance. How many kilometers will each team member run?
77 ÷ 22
T:
S:
Write a division expression to solve for the number of
kilometers run by each team member.
(Work.) 77 ÷ 22.
Lesson 27:
Divide decimal dividends by two-digit divisors, estimating quotients,
reasoning about the placement of the decimal point, and making
connections to a written method.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G5-M2-TE-1.3.0-07.2015
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This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 27 5 2
NYS COMMON CORE MATHEMATICS CURRICULUM
T:
S:
T:
S:
T:
S:
T:
S:
T:
S:
T:
S:
T:
S:
T:
S:
T:
S:
T:
S:
T:
S:
T:
S:
(Using the standard algorithm, write 77 ÷ 22 on the board.) Let’s solve together. Tell how you’ll
estimate.
60 ones ÷ 20 = 3 ones.
(Record each step in the algorithm.) What is 3 ones
times 22?
NOTES ON
66 ones.
MULTIPLE MEANS
How many ones remain?
OF ACTION AND
11 ones.
EXPRESSION:
Decompose 11 ones into tenths. How many tenths is
Students should continue to be
that?
encouraged to interpret remainders
and decimal portions of quotients.
110 tenths.
Challenge students with the following
Tell your neighbor how you’ll show the zero tenths in
questions:
the whole.
 How many kilometers would need to
I’ll write a decimal point and a zero in the tenths place
be added to the race for each runner
next to the 7 ones in 77.
to run a 4-kilometer distance?
A 4.5-kilometer distance?
Now, divide 110 tenths by 22. Tell me how you’ll
A 5-kilometer distance?
estimate.
 Change the context of the problem
100 tenths ÷ 20 = 5 tenths.
so that the interpretation of the
What is 5 tenths × 22?
remainder must change.
110 tenths.
 77 students need to board buses.
The buses have 22 seats. How
How many tenths remain?
many buses are needed?
Zero tenths.
 22 students will share 77 t-shirts.
What is our quotient?
How many students could
3.5.
receive more than 1 shirt?
So, how many kilometers will each team member run
during the race?
Each team member will run 3 and 5 tenths kilometers.
Is your answer reasonable? What is 5 tenths kilometer as meters?
500 meters!
What fraction of a kilometer is 500 meters?
Half!  So, each runner ran 3 and a half kilometers.  3.5 kilometers is the same as 3 kilometers
and 500 meters, or 3 and a half kilometers.
Lesson 27:
Divide decimal dividends by two-digit divisors, estimating quotients,
reasoning about the placement of the decimal point, and making
connections to a written method.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G5-M2-TE-1.3.0-07.2015
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This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 27 5 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Problem 2
A vial contains 14.7 mL of serum that is then split equally into 21 tiny containers. How much serum is in each
new container?
14.7 ÷ 21
T:
Work with a partner to write a division
expression that matches this story problem.
S: (Work.) 14.7 ÷ 21.
T: (Using the standard algorithm, write 14.7 ÷ 21 on
the board.) Before dividing, let’s reason about
what our quotient might be. Will there be more
than 1 mL in each container or less than 1 mL?
Justify your thinking.
S: It will have to be less than 1 mL because there are
more containers than mL of serum.  To have 1 mL in
NOTES ON
each container, there would have to be 21 mL of
MULTIPLE MEANS
serum. We only have about 15.
OF ACTION AND
T: Great reasoning. Now, tell me how you will estimate
EXPRESSION:
14.7 ÷ 21 numerically.
Many lessons, including this one,
S: 140 tenths ÷ 20 = 7 tenths.
require students to understand and
use precise vocabulary. Teachers can
T: Work with a partner to solve.
help students gain familiarity with new
T: What is the quotient?
words by displaying them on posters.
S: 0.7.
There are several ways to make
posters more effective:
T: Is our actual quotient reasonable? Does the placement
 Be judicious when deciding how
of the decimal make sense?
many posters to display. If there are
S: Yes, it’s the exact same as the estimated quotient.
too many, students tend to not see
 We said we should have less than 1 mL, and we do.
them.
If the decimal was behind the 7, it wouldn’t make
 Place the posters in odd places, such
sense because that would be 7 mL in each container.
as on the floor in the doorway or in
 It couldn’t have been 7 hundredths. If the divisor
the washroom. This may capture
had been 2, then the answer would be 7. We had 21,
attention.
which is about 10 times as large, so we had to divide by
 Try to use pictures or graphics
10, which is 7 tenths, not 7 hundredths.
instead of wordy definitions.
T: Did you check your work?
 When a student is struggling for a
S: Yes.
precise word, point to a poster. This
shows students that posters can be
T: Answer the question using a complete sentence.
support materials.
S: Zero and 7 tenths milliliters of serum is in each tiny
container.
The same context may be repeated for the following: 22.47 ÷ 21. This problem requires the recording of a
zero in the quotient.
Lesson 27:
Divide decimal dividends by two-digit divisors, estimating quotients,
reasoning about the placement of the decimal point, and making
connections to a written method.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G5-M2-TE-1.3.0-07.2015
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Lesson 27 5 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Problem 3
The surface area of a rectangular piece of construction paper is 140.25 square inches. If the paper’s length is
17 inches, what is the width?
140.25 ÷ 17
T:
S:
T:
S:
T:
T:
S:
T:
S:
What expression would you use to solve this problem?
(Work.) 140.25 ÷ 17.
(Using the standard algorithm, write 140.25 ÷ 17 on the
board.) Before dividing, let’s reason about what our
quotient might be. Tell me how you’ll estimate
140.25 ÷ 17.
140 ones ÷ 20 = 7 ones.
Work independently to solve this problem. Share your
work with a neighbor after each step in the division
process.
What is the quotient?
8.25.
Answer the question using a complete sentence.
The width of the paper was 8 and 25 hundredths inches long.
Problem Set (10 minutes)
Students should do their personal best to complete the
Problem Set within the allotted 10 minutes. For some
classes, it may be appropriate to modify the assignment by
specifying which problems they work on first. Some
problems do not specify a method for solving. Students
should solve these problems using the RDW approach
used for Application Problems.
Student Debrief (10 minutes)
Lesson Objective: Divide decimal dividends by two-digit
divisors, estimating quotients, reasoning about the
placement of the decimal point, and making connections
to a written method.
The Student Debrief is intended to invite reflection and
active processing of the total lesson experience.
Invite students to review their solutions for the Problem
Set. They should check work by comparing answers with a
partner before going over answers as a class.
Look for misconceptions or misunderstandings that can be
addressed in the Debrief. Guide students in a conversation
to debrief the Problem Set and process the lesson.
Lesson 27:
Divide decimal dividends by two-digit divisors, estimating quotients,
reasoning about the placement of the decimal point, and making
connections to a written method.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G5-M2-TE-1.3.0-07.2015
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 27 5 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Any combination of the questions below may be used to lead the discussion.




When dividing a decimal by a two-digit divisor,
when is it useful to think of decimals in various
units? (During estimation, it can be easier to
think of a whole number as an equivalent amount
of smaller units.)
Discuss the multi-step problems in the Problem
Set. Ask students to explain how they knew their
placement of the decimal point was reasonable,
how they knew their quotient was reasonable,
and how to interpret the decimal portion of the
quotient.
The quotients for Problems 1(d) and (e) are the
same. Divide them again. This time, do not go
beyond the ones place. Compare the whole
number remainders. What do you notice? Are
the division equations equal to each other?
Why or why not?
We expressed our remainders today using
decimals. Does it always make sense to do this?
Give an example of a situation where a whole
number remainder makes more sense. Do you
notice a pattern to these examples?
Exit Ticket (3 minutes)
After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help with
assessing students’ understanding of the concepts that were presented in today’s lesson and planning more
effectively for future lessons. The questions may be read aloud to the students.
Lesson 27:
Divide decimal dividends by two-digit divisors, estimating quotients,
reasoning about the placement of the decimal point, and making
connections to a written method.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G5-M2-TE-1.3.0-07.2015
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
Lesson 27 Problem Set 5 2
Date
1. Divide. Check your work with multiplication.
a. 5.6 ÷ 16
b. 21 ÷ 14
c. 24 ÷ 48
d. 36 ÷ 24
e. 81 ÷ 54
f.
15.6 ÷ 15
g. 5.4 ÷ 15
h. 16.12 ÷ 52
i.
2.8 ÷ 16
Lesson 27:
Divide decimal dividends by two-digit divisors, estimating quotients,
reasoning about the placement of the decimal point, and making
connections to a written method.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G5-M2-TE-1.3.0-07.2015
368
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 27 Problem Set 5 2
2. 30.48 kg of beef was placed into 24 packages of equal weight. What is the weight of one package
of beef?
3. What is the length of a rectangle whose width is 17 inches and whose area is 582.25 in2?
Lesson 27:
Divide decimal dividends by two-digit divisors, estimating quotients,
reasoning about the placement of the decimal point, and making
connections to a written method.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G5-M2-TE-1.3.0-07.2015
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 27 Problem Set 5 2
4. A soccer coach spent $162 dollars on 24 pairs of socks for his players. How much did five pairs of socks
cost?
5. A craft club makes 95 identical paperweights to sell. They collect $230.85 from selling all the
paperweights. If the profit the club collects on each paperweight is two times as much as the cost to
make each one, what does it cost the club to make each paperweight?
Lesson 27:
Divide decimal dividends by two-digit divisors, estimating quotients,
reasoning about the placement of the decimal point, and making
connections to a written method.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G5-M2-TE-1.3.0-07.2015
370
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NYS COMMON CORE MATHEMATICS CURRICULUM
Name
Lesson 27 Exit Ticket 5 2
Date
Divide.
a. 28 ÷ 32
b. 68.25 ÷ 65
Lesson 27:
Divide decimal dividends by two-digit divisors, estimating quotients,
reasoning about the placement of the decimal point, and making
connections to a written method.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G5-M2-TE-1.3.0-07.2015
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
Lesson 27 Homework 5 2
Date
1. Divide. Check your work with multiplication.
a. 7 ÷ 28
b. 51 ÷ 25
c. 6.5 ÷ 13
d. 132.16 ÷ 16
e. 561.68 ÷ 28
f.
604.8 ÷ 36
2. In a science class, students water a plant with the same amount of water each day for 28 consecutive
days. If the students use a total of 23.8 liters of water over the 28 days, how many liters of water did they
use each day? How many milliliters did they use each day?
Lesson 27:
Divide decimal dividends by two-digit divisors, estimating quotients,
reasoning about the placement of the decimal point, and making
connections to a written method.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G5-M2-TE-1.3.0-07.2015
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 27 Homework 5 2
3. A seamstress has a piece of cloth that is 3 yards long. She cuts it into shorter lengths of 16 inches each.
How many of the shorter pieces can she cut?
4. Jenny filled 12 pitchers with an equal amount of lemonade in each. The total amount of lemonade in the
12 pitchers was 41.4 liters. How many liters of lemonade would be in 7 pitchers?
Lesson 27:
Divide decimal dividends by two-digit divisors, estimating quotients,
reasoning about the placement of the decimal point, and making
connections to a written method.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G5-M2-TE-1.3.0-07.2015
373
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.