Math g5 m1 Topic F Lesson 16 2

NYS COMMON CORE MATHEMATICS CURRICULUM 5•1
Lesson 16
Objective: Solve word problems using decimal operations.
Suggested Lesson Structure

Fluency Practice (12 minutes)
Application Problem (7 minutes)
Concept Development (31 minutes)
Student Debrief (10 minutes)
Total Time (60 minutes)
Fluency Practice (12 minutes)
 Sprint: Multiply and Divide by Exponents 5.NBT.2 (8 minutes)

 Find the Quotient 5.NBT.7 (4 minutes)
Sprint: Multiply and Divide by Exponents (8 minutes)

Materials: (S) Multiply and Divide by Exponents Sprint
Note: This Sprint helps students build automaticity in dividing decimals by 10 1, 102, 103, and 104.
Find the Quotient (4 minutes)

Materials: (S) Hundreds through thousandths place value chart (Lesson 7 Template), personal white board
Note: This review fluency drill helps students work toward mastery of dividing decimals using concepts
introduced in Lesson 15.
T: (Project the place value chart showing ones, tenths, and hundredths. Write 0.3 ÷ 2 = __.) Use place
value disks to draw 3 tenths on your place value chart. (Allow students time to draw.)
T: (Write 3 tenths ÷ 2 = __ hundredths ÷ 2 = __ tenths __ hundredths on the board.) Solve the division
problem.
S: (Write 3 tenths ÷ 2 = 30 hundredths ÷ 2 = 1 tenth 5 hundredths.)
T: (Write the algorithm below 3 tenths ÷ 2 = 30 hundredths ÷ 2 = 1 tenth 5 hundredths.) Solve using
the standard algorithm. (Allow students time to solve.)
Repeat the process for 0.9 ÷ 5, 6.7 ÷ 5, 0.58 ÷ 4, and 93 tenths ÷ 6.
Lesson 16: Solve word problems using decimal operations.

229
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Application Problem (7 minutes)

Jesse and three friends buy snacks for a hike. They buy trail mix for $5.42, apples for $2.55, and granola bars
for $3.39. If the four friends split the cost of the snacks equally, how much should each friend pay?
Note: Adding and dividing decimals are taught in this module. Teachers may choose to help students draw
the tape diagram before students do the calculations independently.
Concept Development (31 minutes)

Materials: (T/S) Problem Set, pencil
Problem 1
Mr. Frye distributed $126 equally among his 4 children for their weekly allowance. How much money did
each child receive?
As the teacher creates each component of the tape diagram, students should re-create the tape diagram on
their Problem Sets.
T: We will solve Problem 1 on the Problem Set together. (Project the problem on the board.) Read the
word problem together.
S: (Read chorally.)
T: Who and what is this problem about? Let’s identify our variables.
S: Mr. Frye’s money.
T: Draw a bar to represent Mr. Frye’s money. (Draw a rectangle on the board.)
Mr. Frye’s Money
T: Let’s read the problem sentence by sentence and adjust our diagram to match the information in the
problem. Read the first sentence together.
S: (Read.)
T: What is the important information in the first sentence? Turn and talk.
S: $126 and 4 children received an equal amount.

230
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka This work is licensed under a
math.org This file derived from G5-M1-TE-1.3.0-06.2015 Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
T: (Underline the stated information.) How can I represent this information in my diagram?
S: 126 dollars is the total, so put a bracket on top of the bar, and label it.
T: (Draw a bracket over the diagram and label as $126. Have students label their diagrams.)
$126
Mr. Frye’s Money

NOTES ON
MULTIPLE MEANS
T: How many children share the 126 dollars? OF REPRESENTATION:
S: 4 children.
Students may use various approaches
T: How can we represent this information? for calculating the quotient. Some may
S: Divide the bar into 4 equal parts. use place value units 12 tens + 60
tenths. Others may use the division
T: (Partition the diagram into 4 equal sections, and have algorithm. Comparing computation
students do the same.) strategies may help students develop
their mathematical thinking.
$126
Mr. Frye’s Money
T: What is the question?

NOTES ON
S: How much did each child receive?
MULTIPLE MEANS
T: What is unknown in this problem? How will we OF ENGAGEMENT:
represent it in our diagram?
If students struggle to draw a model of
S: The amount of money one of Mr. Frye’s children word problems involving division with
received for allowance is what we are trying to find. decimal values, scaffold their
We should put a question mark inside one of the parts. understanding by modeling an
T: (Write a question mark inside one section of the tape analogous problem substituting
simpler, whole-number values. Then,
diagram.) using the same tape diagram, erase the
$126 whole-number values, and replace
them with the parallel values from the
decimal problem.
Mr. Frye’s Money ?
T: Make a unit statement about your diagram. How many unit bars are equal to $126?
S: Four units is the same as $126.
T: How can we find the value of one unit?
S: Divide $126 by 4.  Use division because we have a whole that we are sharing equally.
T: What is the expression that will give us the amount that each child received?
S: $126 ÷ 4.

231
T: Solve and express your answer in a complete sentence.
$126
Mr. Frye’s Money ?
4 units = $126
1 unit = ?
1 unit = $126 ÷ 4
= $31.50
S: Each child received $31.50 for his weekly allowance.

T: Read Part (b) of Problem 1, and solve using a tape diagram.
S: (Work for 5 minutes.)
As students are working, circulate and be attentive to accuracy and labeling of information in the students’
tape diagrams. Refer to the example student work on the Problem Set for one example of an accurate tape
diagram.
Problem 4
Brandon mixed 6.83 lb of cashews with 3.57 lb of pistachios. After filling up 6 bags that were the same size
with the mixture, he had 0.35 lb of nuts left. What was the weight of each bag?
T: (Project Problem 4.) Read the problem. Identify the variables (who and what), and draw a bar.
S: (Read and draw. Draw a bar on the board.)
Brandon’s Cashews and Pistachios
T: Read the first sentence.

S: (Read.)
T: What is the important information in this sentence? Tell a partner.
S: 6.83 lb of cashews and 3.57 lb of pistachios.
T: (Underline the stated information.) How can I represent this information in the tape diagram?
MP.8 S: Show two parts inside the bar.
T: Should the parts be equal in size?
S: No. The cashews part should be about twice the size of the pistachios part.
6.83 3.57
Brandon’s Cashews/Pistachios

232
T: (Draw and label.) Let’s read the next sentence. How will we represent this part of the problem?
S: We could draw another bar to represent both kinds of nuts together. Then, split the bar into parts
to show the bags and the part that was left over.  We could erase the bar separating the nuts,
put the total on the bar we already drew, and split it into the equal parts. We would have to
remember he had some nuts left over.
T: Both are good ideas. Choose one for your model. I am going to use the bar that I’ve already
drawn. I’ll label my bags with the letter b, and I’ll label the part that wasn’t put into a bag.
T: (Erase the bar between the types of nuts. Draw a bracket over the bar, and write the total. Show
the leftover nuts and the 6 bags.)
10.4
b b b b b b left
0.35
T: What is the question?

S: How much did each bag weigh?
T: Where should we put our question mark?
S: Inside one of the units that is labeled with the letter b.
10.4
? b b b b b left 10.4
? b b left
b b b
0.35 0.35
T: How will we find the value of 1 unit in our diagram?

Turn and talk.
S: Part of the weight is being placed into 6 bags, so we
need to divide that part by 6.  There was a part that
didn’t get put in a bag. We have to take the leftover
part away from the total so we can find the part that
was divided into the bags. Then, we can divide.
T: Perform your calculations, and state your answer in a
complete sentence. (See the solution on the next
page.)

233
10.4 NOTES ON
MULTIPLE MEANS
? b b b b b left OF REPRESENTATION:
The equations pictured to the left are a
0.35 formal teacher solution for Problem 4.
6 units + 0.35 = 10.4 Students should not be expected to
produce such a formal representation of
their thinking. Students are more likely
1 unit = (10.4 – 0.35) ÷ 6 to simply show a vertical subtraction of
the leftover nuts from the total and then
1 unit = 1.675 lb show a division of the bagged nuts into 6
equal portions. There may be other
Each bag contained 1.675 lb of nuts. appropriate strategies for solving
offered by students as well.
Teacher solutions offer an opportunity
T: Complete Problems 2, 3, and 5 on the Problem Set, to expose students to more formal
using a tape diagram and calculations to solve. representations. These solutions might
be written on the board as a way to
Circulate as students work. Listen for sound mathematical translate a student’s approach to solving
reasoning. as the student communicates the
strategy aloud to the class.
Problem Set (10 minutes)
Today’s Problem Set forms the basis of the Concept
Development. Students solve Problems 1 and 4 with
teacher guidance, modeling, and scaffolding.
Problems 2, 3, and 5 are designed to be independent work.
Student Debrief (10 minutes)
Lesson Objective: Solve word problems using decimal

operations.
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.

234
Any combination of the questions below may be used to

lead the discussion.
 How did the tape diagram in Problem 1(a) help you
solve Problem 1(b)?
 In Problem 3, how did you represent the information
using the tape diagram?
 Look at Problem 1(b) and Problem 5(b). How are the
questions different? (Problem 1(b) is partitive division—
groups are known, size of group is unknown. Problem 5(b)
is measurement division—size of group is known, number
of groups is unknown.) Does the difference in the
questions affect the calculation of the answers?
 As an extension or an option for early finishers, have
students generate word problems based on labeled tape
diagrams, or have them create one of each type of division
problem (group size unknown and number of groups
unknown).
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.

235
Number
NumberCorrect:
Correct: _______
_______
A Improvement: _______
Multiply and Divide by Exponents
2
1. 10 × 10 = 23. 3,400 ÷ 10 =
2 2
2. 10 = 24. 3,470 ÷ 10 =
2 2
3. 10 × 10 = 25. 3,407 ÷ 10 =
3 2
4. 10 = 26. 3,400.7 ÷ 10 =
3
5. 10 × 10 = 27. 63,000 ÷ 1,000 =
4 3
6. 10 = 28. 63,000 ÷ 10 =
3
7. 3 × 100 = 29. 63,800 ÷ 10 =
2 3
8. 3 × 10 = 30. 63,080 ÷ 10 =
2 3
9. 3.1 × 10 = 31. 63,082 ÷ 10 =
2
10. 3.15 × 10 = 32. 81,000 ÷ 10,000 =
2 4
11. 3.157 × 10 = 33. 81,000 ÷ 10 =
4
12. 4 × 1,000 = 34. 81,400 ÷ 10 =
3 4
13. 4 × 10 = 35. 81,040 ÷ 10 =
3 4
14. 4.2 × 10 = 36. 91,070 ÷ 10 =
3 2
15. 4.28 × 10 = 37. 120 ÷ 10 =
3 3
16. 4.283 × 10 = 38. 350 ÷ 10 =
4
17. 5 × 10,000 = 39. 45,920 ÷ 10 =
4 3
18. 5 × 10 = 40. 6,040 ÷ 10 =
4 4
19. 5.7 × 10 = 41. 61,080 ÷ 10 =
4 2
20. 5.73 × 10 = 42. 7.8 ÷ 10 =
4 3
21. 5.731 × 10 = 43. 40,870 ÷ 10 =
2
22. 24 × 100 = 44. 52,070.9 ÷ 10 =
B
236
Multiply and Divide by Exponents

2
1. 10 × 10 × 1 = 23. 4,300 ÷ 10 =
2 2
2. 10 = 24. 4,370 ÷ 10 =
2 2
3. 10 × 10 = 25. 4,307 ÷ 10 =
3 2
4. 10 = 26. 4,300.7 ÷ 10 =
3
5. 10 × 10 = 27. 73,000 ÷ 1,000
4 3
6. 10 = 28. 73,000 ÷ 10 =
3
7. 500 ÷ 100 = 29. 73,800 ÷ 10 =
2 3
8. 500 ÷ 10 = 30. 73,080 ÷ 10 =
2 3
9. 510 ÷ 10 = 31. 73,082 ÷ 10 =
2
10. 516 ÷ 10 = 32. 91,000 ÷ 10,000 =
2 4
11. 516.7 ÷ 10 = 33. 91,000 ÷ 10 =
4
12. 6,000 ÷ 1,000 = 34. 91,400 ÷ 10 =
3 4
13. 6,000 ÷ 10 = 35. 91,040 ÷ 10 =
3 4
14. 6,200 ÷ 10 = 36. 81,070 ÷ 10 =
3 2
15. 6,280 ÷ 10 = 37. 170 ÷ 10 =
3 3
16. 6,283 ÷ 10 = 38. 450 ÷ 10 =
4
17. 70,000 ÷ 10,000 = 39. 54,920 ÷ 10 =
4 3
18. 70,000 ÷ 10 = 40. 4,060 ÷ 10 =
4 4
19. 76,000 ÷ 10 = 41. 71,080 ÷ 10 =
4 2
20. 76,300 ÷ 10 = 42. 8.7 ÷ 10 =
4 3
21. 76,310 ÷ 10 = 43. 60,470 ÷ 10 =
2
22. 4,300 ÷ 100 = 44. 72,050.9 ÷ 10 =
Name Date
Solve.

237
1. Mr. Frye distributed $126 equally among his 4 children for their weekly allowance.
a. How much money did each child receive?
b. John, the oldest child, paid his siblings to do his chores. If John pays his allowance equally to his
brother and two sisters, how much money will each of his siblings have received in all?
2. Ava is 23 cm taller than Olivia, and Olivia is half the height of Lucas. If Lucas is 1.78 m tall, how tall are
Ava and Olivia? Express their heights in centimeters.
3. Mr. Hower can buy a computer with a down payment of $510 and 8 monthly payments of $35.75. If he
pays cash for the computer, the cost is $699.99. How much money will he save if he pays cash for the

238
computer instead of paying for it in monthly payments?
4. Brandon mixed 6.83 lb of cashews with 3.57 lb of pistachios. After filling up 6 bags that were the same
size with the mixture, he had 0.35 lb of nuts left. What was the weight of each bag? Use a tape diagram,
and show your calculations.
5. The bakery bought 4 bags of flour containing 3.5 kg each. 0.475 kg of flour is needed to make a batch of
muffins, and 0.65 kg is needed to make a loaf of bread.

239
a. If 4 batches of muffins and 5 loaves of bread are baked, how much flour will be left? Give your
answer in kilograms.
b. The remaining flour is stored in bins that hold 3 kg each. How many bins will be needed to store the
flour? Explain your answer.
Name Date

240
Write a word problem with two questions that matches the tape diagram below, and then solve.
16.23 lb
Weight of John’s Dog
?
Weight of Jim’s Dog ?

241
Name Date
Solve using tape diagrams.
1. A gardener installed 42.6 meters of fencing in a week. He installed 13.45 meters on Monday and
9.5 meters on Tuesday. He installed the rest of the fence in equal lengths on Wednesday through Friday.
How many meters of fencing did he install on each of the last three days?
2. Jenny charges $9.15 an hour to babysit toddlers and $7.45 an hour to babysit school-aged children.
a. If Jenny babysat toddlers for 9 hours and school-aged children for 6 hours, how much money did she
earn in all?
b. Jenny wants to earn $1,300 by the end of the summer. How much more will she need to earn to
meet her goal?

242
3. A table and 8 chairs weigh 235.68 lb together. If the table weighs 157.84 lb, what is the weight of one
chair in pounds?
4. Mrs. Cleaver mixes 1.24 liters of red paint with 3 times as much blue paint to make purple paint. She
pours the paint equally into 5 containers. How much blue paint is in each container? Give your answer
in liters.

243

Math g5 m1 Topic F Lesson 16 2

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NYS COMMON CORE MATHEMATICS CURRICULUM 5•1

Suggested Lesson Structure

Fluency Practice (12 minutes)

 Sprint: Multiply and Divide by Exponents 5.NBT.2 (8 minutes)

Sprint: Multiply and Divide by Exponents (8 minutes)

Find the Quotient (4 minutes)

Lesson 16: Solve word problems using decimal operations.

Application Problem (7 minutes)

Concept Development (31 minutes)

Mr. Frye’s Money

Lesson 16: Solve word problems using decimal operations.

Mr. Frye’s Money

Mr. Frye’s Money

T: What is the question?

Lesson 16: Solve word problems using decimal operations.

T: Solve and express your answer in a complete sentence.

Mr. Frye’s Money ?

S: Each child received $31.50 for his weekly allowance.

Brandon’s Cashews and Pistachios

T: Read the first sentence.

Lesson 16: Solve word problems using decimal operations.

T: What is the question?

T: How will we find the value of 1 unit in our diagram?

Lesson 16: Solve word problems using decimal operations.

Student Debrief (10 minutes)

Lesson Objective: Solve word problems using decimal

Lesson 16: Solve word problems using decimal operations.

Any combination of the questions below may be used to

Exit Ticket (3 minutes)

Lesson 16: Solve word problems using decimal operations.

Multiply and Divide by Exponents

Lesson 16: Solve word problems using decimal operations.

a. How much money did each child receive?

Lesson 16: Solve word problems using decimal operations.

computer instead of paying for it in monthly payments?

Lesson 16: Solve word problems using decimal operations.

Lesson 16: Solve word problems using decimal operations.

Weight of John’s Dog

Lesson 16: Solve word problems using decimal operations.

Solve using tape diagrams.

Lesson 16: Solve word problems using decimal operations.

Lesson 16: Solve word problems using decimal operations.

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