Thank you for participating
in Teach It First!
This Teach It First Kit contains a Common Core Support Coach, Foundational
Mathematics teacher lesson followed by the corresponding student lesson. We are
confident that using this lesson will help you achieve your assessment preparation
goals for your entire class.
Common Core Support Coach was built from the ground-up to provide students
with scaffolded support for content required by the Common Core State Standards
for Mathematics (CCSS-M). The program features 20 lessons which focus on
20 critical skills essential to mastery of Common Core State Standards. These
skills were chosen because they are critical components of the mathematical
progressions that connect earlier standards to this grade level and from this grade
level to the next. While each lesson connects to prior foundational skills and
concepts, it can be viewed as an independent unit of instruction. In this way, the 20
lessons allow teachers to differentiate instruction according to the requirements of
each student.
Key to the philosophy behind Common Core Support Coach is the recognition that
math skills and concepts are part of a progression that begins early in students’
lives and continues beyond their current grade level with increased complexity and
depth. For students, achieving true understanding of CCSS-M at any grade level
means mastery of prior content that connects to this grade and mastery of content
that connects within the grade. Often, students who cannot cope with a specific
part of their grade’s curriculum are missing one or more understandings that would
allow mastery. Common Core Support Coach supplies the missing pieces.
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LESSON
14
S
uppor
tCoa
c
h,
Ma
t
he
ma
t
i
c
s
,
T
e
a
c
he
rE
di
t
i
on,
Gr
a
de5
Dividing Unit Fractions and Whole
Numbers
Plug In Multiplying Fractions
FOUNDATIONAL
UNDERSTANDING
Plug In
Multiplying
Fractions
Student Edition .
pp. 134–135
power up
Fractions as
Division
ON-LEVEL
TARGET
ready to go
Dividing Unit
Fractions and
Whole Numbers
MATERIALS
• Math Tool: Fraction
Strips, p. A15 (Student
Edition p. 237)
• Paper clips (suggested)
english language
learners
MP6 ELL students may not
understand why the terms
each and in all indicate
multiplication. Distribute .
2 paper clips to each of .
4 students. Explain that they
each received 2 paper clips
and there are 8 paper clips in
all. Then, have students write
4 3 2 5 8. Repeat, as needed,
to reinforce understanding.
106 Le ss o n 1 4
CC13_Mth_G5_TM_PDF.indd 106
OBJECTIVES
CONCEPTS AND SKILLS
VOCABULARY
• Use a model and write
an equation to multiply
a whole number by a
fraction.
Interpret the product of a fraction
times a whole number using visual
models or by following a sequence
of operations in which the whole
number is renamed as a fraction and
the numerators and denominators
are multiplied. CCSS: 5.NF.4.a
• Show a fraction as
division to solve
problems.
Interpret a fraction as division of
• divisor
the numerator by the denominator. • mixed number
Solve word problems involving
• remainder
division of whole numbers leading
to answers in the form of fractions or
mixed numbers. CCSS: 5.NF.3
• Divide whole numbers
by unit fractions and
unit fractions by whole
numbers using models
and writing equations.
Solve mathematical and real-world
problems involving division of unit
fractions by whole numbers and
division of whole numbers by unit
fractions.
CCSS: 5.NF.7.a, 5.NF.7.b, 5.NF.7.c
• reciprocal
• unit fraction
Build Background
Talk to students about reasons to multiply whole numbers and fractions
1
in real life. For example, Paul has 4 acres of farmland. He plants ​ __
3  ​ of
each acre with corn. How many acres of corn will he plant? Explain that
multiplying fractions helps answer that question. MP4 Have students discuss additional examples of real situations that
involve multiplying whole numbers and fractions.
Tell students they will use models and equations to find the product of a
fraction and a whole number. Introduce and Model
Introduce Concepts Guide students through the information about
multiplying fractions. MP5 Emphasize that the number of rectangles
is the number of wholes and the number of parts in each whole is the
denominator of the fraction. Support Discussion MP3 Have partners discuss briefly before group
discussion. As needed, have students use the previous problems for
reference to help them determine how each number in the problem
should be represented. © 2014 Triumph Learning, LLC
17/05/13 6:00 PM
Tatyanahas5cansofpaint .Each
cancontains1gallonofpaint .
1
Tosolvetheproblemwithout
amodel,writethewhole
number,5,asafraction .
Multiplythenumeratorsand
thedenominators .
Youcanuseamodelto
representtheproblem .
Sheuses__
4ofeachcantomixa
newcolor .Howmanygallonsof
paintdoesshemix?
1
__
4355p
2 __61375
A Youcanuseamodeltomultiplyawholenumbertimesafraction .
1
Multiply:43__
3
3
Writetheproduct .
1
3
1
1
43__
35
134 1
3
1
1
3
4
3
1
1
3
5
4
3
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
WhatcanyoutellAvaabouthermodel?
Possible response: It is not correct. She should have drawn 6 rectangles separated into 4 sections, with one section of each rectangle shaded.
Addtheshadedparts .
Writetheproduct .
1 73__415
1
2
3
1
1
3__
10 5
1
3__
10 15 3
1
1
3 10
5
15
10
15
10
4
7
6
Multiply.
3 63__51
6
1
1
3__
55
6 3 1
1 3 5
5
6
5
4 __313 8
1
__
33
8
1
5
1 3 3
8 3 1
5
8
3
135
Model Application
A Guide students through modeling the number of wholes and the
number of parts in each whole. DO B Monitor students as they find the product. Remind students that
any whole number can be written as a fraction with a denominator of 1.
Practice and Assess
Ask students to complete practice items 1–4 on page 135 independently
or in pairs. Monitor ongoing work.
Observe whether students are writing the whole numbers as fractions
before multiplying. Use the chart below, as needed, to address any
difficulties. Observation
Action
Students do not
multiply the fractions
and whole numbers
correctly.
Have students use Math Tool: Fraction Strips to
model the multiplication rather than draw models. Students should use the whole-number factor to
determine the number of fraction strips and the
fractional factor to determine the size of each strip. Have students compare the model to 1 whole to
determine the product.
CC13_Mth_G5_TM_PDF.indd 107
15
7
Lesson 1 4
© 2014 Triumph Learning, LLC
15
1
Prompt: How many rectangles are there? How many parts are
in each rectangle?
Sentence Starter: Ava’s model is/is not correct because…
DO
1
153__
10 5
Use the model to multiply.
I get it! I can rename a whole
number as a fraction by writing
the whole number as a numerator
over a denominator of 1!
Avadrewthismodeltoshow__
436 .
1
Show4groupsof__
3 .
Multiplythenumeratorsandthe
denominators .
I get it! I can
write a whole
number as a
fraction with a
denominator of 1.
PRACTICE
5
Tatyanamixes__
4 gallons
of paint .
Each shaded section
1
represents __
4 of a gallon.
There are 5 shaded sections.
1
2
1
5
The word
“of” tells me
to multiply.
DO
Renamethewholenumberasa
fraction .
153__
10 5
5__
4
5
1
1
1
1
1
__
__
__
__
__
__
41414141454
CU S S
1
Multiply:153__
10 1
5
1
1
__
43__
1
4355__
135
5____
431
Writeanequationtorepresent
theproblem .
DIS
DO
Multiplying Fractions
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
LESSON
Plug In
B Youcanmultiplyawholenumbertimesafractionwithoutusingamodel .
Lesson 14
14
14 Dividing Unit Fractions and Whole Numbers
Dividing Unit Fractions and
Whole Numbers
spotlight on
mathematical PRACTICES
MP3 Critiquing Others’
Reasoning
Help students think about
Ava’s model critically by asking
probing questions:
What does the number of
rectangles show?
What does the number of
parts in each rectangle show?
What does the number of
shaded parts show?
D ividing U nit F ractions and Whole N umbers 107
17/05/13 6:00 PM
power up Fractions as Division
OBJECTIVES
Plug In
FOUNDATIONAL
UNDERSTANDING
Multiplying
Fractions
power up
Fractions as
Division
Student Edition .
pp. 136–137
ON-LEVEL
TARGET
ready to go
Dividing Unit
Fractions and
Whole Numbers
CONCEPTS AND SKILLS
VOCABULARY
• Use a model and write
an equation to multiply
a whole number by a
fraction.
Interpret the product of a fraction
times a whole number using visual
models or by following a sequence
of operations in which the whole
number is renamed as a fraction and
the numerators and denominators
are multiplied. CCSS: 5.NF.4.a
• Show a fraction as
division to solve
problems.
Interpret a fraction as division of
• divisor
the numerator by the denominator. • mixed number
Solve word problems involving
• remainder
division of whole numbers leading
to answers in the form of fractions or
mixed numbers. CCSS: 5.NF.3
• Divide whole numbers
by unit fractions and
unit fractions by whole
numbers using models
and writing equations.
Solve mathematical and real-world
problems involving division of unit
fractions by whole numbers and
division of whole numbers by unit
fractions.
CCSS: 5.NF.7.a, 5.NF.7.b, 5.NF.7.c
• reciprocal
• unit fraction
Build Background
MATERIALS
• Index cards (suggested)
Talk to students about reasons to divide numbers in real life. For example,
a 3-meter piece of string is cut into 4 equal pieces. How long is each
piece? Explain that dividing 3 4 4 can answer this question.
MP4 Have students discuss additional examples of real situations in
which they divide numbers. Tell students they will divide whole numbers by writing them as fractions. Introduce and Model
SPOTLIGHT ON
MATHEMATICAL PRACTICES
MP3 Critiquing Others’
Reasoning
Help students think about
Ella’s reasoning critically by
asking probing questions:
1
What would a model for __
​ 3 ​ 
look like?
Does this describe each
bar in Ella’s model?
108 Le ss o n 1 4
CC13_Mth_G5_TM_PDF.indd 108
Introduce Concepts and Vocabulary Guide students through the
information about using fractions to divide. Emphasize that the fraction
bar in a fraction is equivalent to a division sign. Use Words to Know to
clarify students’ understanding of vocabulary. Have students explain to a
partner the meaning of divisor, mixed number, and remainder. Support Discussion MP3 MP5 Have partners discuss briefly before
group discussion. Students can use the models in the instruction for
support. As needed, have students draw their own models to compare
against Ella’s model. Prompt: How did Ella represent the divisor, 3?
The dividend, 8?
Sentence Starter: E
lla’s model shows…
© 2014 Triumph Learning, LLC
17/05/13 6:00 PM
14 Dividing Unit Fractions and Whole Numbers
Fractions as Division
Youcanwritethedivision
problemasafraction .The
fractionbarinafraction
representsdivision .The
valueofafractionisequalto
itsnumeratordividedbyits
denominator .
Eachwholerepresents
1 granola bar .Divideeachwhole
into3equalparts .
remainder
divisor
1 friend
1
1
4
__
43__
353 ofagranolabar
1
3
4
So,4435__
3 .
remainder
theamountthatisleftover
afterdivisioniscomplete
divisor
anumberbywhichanother
numberisdivided
5 3 1 R2
5 3 1 R2
3
Elladrewamodeltoshowthat3485__
8 .WhatcanyoutellEllaabouthermodel?
Possible response: Ella should have shaded 3 parts of each whole instead of all 8 parts.
136 Writethequotientasafractionwith
thedividendasthenumeratorand
thedivisorasthedenominator .
3
Interpretthequotient .
4
5
5
Eachfriendwillget
1
Setupadivisionproblem .
2
Dividetowritethefraction
asamixednumber .
3
Interpretthequotient .
5
Thedivisionproblemis 10 4
3 R
3 10
9
5
.
5
4
quartofwater .
Threesistersequallysharethedrivingfora10-hour
trip .Forhowmanyhoursdoeseachsisterdrive?
3
.
I see! Since the
numerator is greater
than the denominator,
I can divide to write
the fraction as a mixed
number!
1
1
10435 3 ____
3
1
Lesson 1 4
Eachsisterwilldrivefor
DIS
CU S S
3 __
3 hours .
25
Keishawantstowritethefraction___
8 asdivision .Whichnumbershouldshewriteasthe
divisor?Whichnumbershouldshewriteasthedividend?
Keisha should write 8 as the divisor and 25 as the dividend.
PRACTICE
Solve.
1 Sixfriendsequallyshareabagofpopcorn .Thebagcontains9cupsofpopcorn .Howmany
cupsofpopcornshouldeachfriendget?
3
1 __
6
2 Charlottecutsa3-foot-longpieceofribboninto4equalpiecestotrimasquarepillow .
Howlongiseachpieceofribbon?
3
__
4 Model Application
DO
4
4
4
1
1
CU S S
2
A fraction greater than
1 can be written as a
mixed number.
1__
6isamixednumber .
DIS
4
Thedivisionproblemis
Setupadivisionproblem .
DO
1
gets1__
3granolabars .
The dividend is greater than
the divisor, so the quotient is a
fraction that is greater than 1!
mixed number
anumberthathasawholenumberpartandafraction
part
Fivefriendsequallyshare4quartsofwater .Howmanyquartsofwaterdoeseachfriendget?
1
B Youcanshowdivisionwithquotientsgreaterthan1asafraction .
1
So,44351__
3,andeachfriend
Eachfriendwillgetfour__
3parts .
Know
1 R1
3 4
3
1
Towritethequotientasa
mixed number,writethe
wholenumber,1,andwritethe
remainderasthenumeratorof
afractionwiththedivisorasthe
denominator .
4
Words
to
DO
4
find__
3 .
4435__
3
I see! A fraction is
another way to write a
division problem!
A Youcanshowdivisionwithquotientslessthan1asafraction .
Youcanuselongdivisionto
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
Thedivisionproblemis:443 .
Youcanuseamodeltoshow
443 .
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
If3friendsshare4granolabars
equally,whatpartofagranola
bardoeseachfriendget?
Lesson 14
POWER uP
A Guide students through finding the quotient. Monitor that
students write the divisor as the denominator.
DO B Explain that since the fraction bar means division, the numerator
can be divided by the denominator to find the quotient. Support Discussion MP6 MP7 Have partners discuss briefly before
group discussion. As needed, point out to students the divisor in a
division problem.
Prompt: Which number is above the fraction bar?
Which number is below the fraction bar?
Sentence Starter: To write the fraction as a division problem,
Keisha should write…
137
english language
learners
MP6 ELL students may
require additional support
for understanding the term
divisor. Explain that many
words in English that end in -or
name the doer of an action, so
the divisor does the dividing. Reinforce with examples such
as an advisor advises and an
inventor invents. Brainstorm
additional examples.
Practice and Assess
Ask students to complete practice items 1 and 2 on page 137
independently or in pairs. Monitor ongoing work.
Observe whether students correctly write and solve the division
problems. Use the chart below, as needed, to address any difficulties. Observation
Action
Students write the
divisor as the numerator
of the fraction.
Write “​ _______
​ 5 ​ __________
 
 ​”
 
on the board. divisor   
denominator
Have students refer to the equation on the board
as they solve the problems.
© 2014 Triumph Learning, LLC
CC13_Mth_G5_TM_PDF.indd 109
dividend
numerator
focus on fluency
MP5 Use index cards
numbered from 1 to 20 to have
students practice division. Place the cards numbered
1–5 in one stack to use as
divisors. Place the remaining
cards in another stack to use
as dividends. Have students
choose a card at random
from each stack and find the
quotient.
D ividing Unit F ractions and Whole Numbers 109
17/05/13 6:00 PM
Unit Fractions and Whole
ready to go Dividing
Numbers
Plug In
FOUNDATIONAL
UNDERSTANDING
Multiplying
Fractions
power up
Fractions as
Division
OBJECTIVES
ON-LEVEL
TARGET
MATERIALS
• Lesson 14 Quiz,
Assessment Manual .
pp. 30–31
• Lesson 14 Quiz Answer
Key, Assessment Manual
VOCABULARY
• Use a model and write
an equation to multiply
a whole number by a
fraction.
Interpret the product of a fraction
times a whole number using visual
models or by following a sequence
of operations in which the whole
number is renamed as a fraction and
the numerators and denominators
are multiplied. CCSS: 5.NF.4.a
• Show a fraction as
division to solve
problems.
Interpret a fraction as division of
• divisor
the numerator by the denominator. • mixed number
Solve word problems involving
• remainder
division of whole numbers leading
to answers in the form of fractions or
mixed numbers. CCSS: 5.NF.3
ready to go • Divide whole numbers
Dividing Unit
Fractions and
Whole Numbers
Student Edition
pp. 138–143
CONCEPTS AND SKILLS
by unit fractions and
unit fractions by whole
numbers using models
and writing equations.
Solve mathematical and real-world
problems involving division of unit
fractions by whole numbers and
division of whole numbers by unit
fractions.
CCSS: 5.NF.7.a, 5.NF.7.b, 5.NF.7.c
• reciprocal
• unit fraction
Build Background
Talk to students about reasons to divide unit fractions in real life. For
example, Marion is expecting 12 guests at a party. She makes 5 cups of
1
punch and pours ​ __
2  ​ cup of punch into each glass. Will she have enough
glasses of punch? Explain that dividing by fractions can be used to
answer this question.
MP4 Have students discuss additional examples of real situations that
require dividing by fractions.
Tell students they will divide whole numbers by unit fractions and unit
fractions by whole numbers.
Introduce and Model
english language
learners
MP6 Enhance students’
understanding of the term
reciprocal by connecting
it with cognates in native
languages.
Spanish: recíproca
French: réciproque
Italian: reciproco
110 Le ss o n 1 4
CC13_Mth_G5_TM_PDF.indd 110
Introduce Concepts and Vocabulary Guide students through the
information about dividing unit fractions. Emphasize that students
should start by modeling the quantity that will be divided (the dividend). Use Words to Know to clarify students’ understanding of vocabulary. Have students explain the meanings of reciprocal and unit fraction, and
give examples of each.
© 2014 Triumph Learning, LLC
17/05/13 6:00 PM
14 Dividing Unit Fractions and Whole Numbers
READY TO gO
Youcanusemodelstohelpyoudividea
unit fractionbyawholenumber .
1
1
1
__
Todivide__
244,startwithamodelfor2 .
Todivide24__
3,startwithamodelfor2wholes .
Divideeachwholeinto3equalparts,orthirds .
Thereareatotalof6equalparts .
1
Divideinto4equalparts .Eachpartis__
8 .
1
2
1
1 1 1 1
8 8 8 8
1
3
Todividewithoutamodel,multiplythedividend
bythereciprocalofthedivisor .
1
1
4
1
1
131
1
__
2445__
24__
15__
23__
45_____
2345__
8
1
3
POWER uP
You can show a fraction as division of the numerator by the denominator.
2
__
55245
3
1
33__
55__
5
138 Solveforn .
gO!
I get it! I can use
what I know about
multiplying and
dividing fractions
and whole numbers
to solve problems.
OVERSET
1
cup
1
cup
1
2
1
2
1
2
3
Renamethewholenumberasafraction:35__1
Writethereciprocalofthedivisor:__
2
Rewriteasmultiplication:__13__
15__
156
1
3
2
6
2
__
1
1
2
1
__
34__
25nisrelatedton3253 .
__ __ __
63__
2513252 53
4
I remember! To write the
reciprocal of a fraction,
switch the numerator
and the denominator.
1
6
1
2
6 2 cup
Usemultiplicationtocheck .
1
1
2
1
So,n56 .
1
6
✓
Themodelsshow3cups .Eachcupisdividedinto
1
2equalparts,orhalves .Thereare6equal__
2parts .
1
A Youcanusemultiplicationtodivideawholenumberbyafraction .
DO
1
1
451 .
4and__
4arereciprocals:43__
must have divided by a fraction, because when a whole number is divided by a fraction, the quotient is greater than the dividend and the divisor.
lEssOn lInk
Plug In
2
1
cup
Therearesix__
2-cupservingsofricein3cupsofrice .
reciprocal
anumberthatgivesaproductof1when
multipliedbyasecondnumber
Morgandivides5byanumberandgetsananswerof20 .BethanysaysthatMorgan’s
answerisincorrectbecausethequotientshouldalwaysbelessthanthedividend .What
can yousaytoBethany?
Possible response: I can tell Bethany that Morgan You can use a model to multiply a fraction by a whole number.
__
Theequation3425nrepresentstheproblem .
3
6
3
233
1
2
13__
15_____
1315__
156
24__
35__
3 cups
1
1
1
3
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
unit fraction
afractionwith1asthenumerator
CU S S
1
3
When dividing a whole number by
a fraction, the quotient is greater
than the dividend and the divisor.
1 1 __
1
1
__
2,__
3,4,and__
5areunitfractions .
DIS
1
3
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
Know
1
3
1
Multiplythedividendbythereciprocalof
thedivisor .
When dividing a fraction
by a whole number, the
quotient is less than the
dividend and the divisor.
Words
to
1
Howmany__
2-cupservingsaretherein3cupsofrice?
Youcanalsouseamodeltodivideawholenumber
byaunitfraction .
Lesson 14
Dividing Unit Fractions and
Whole Numbers
Renamethewholenumberasa
fraction .
2
Writethereciprocalofthedivisor .
3
Rewriteasmultiplication .Writethe
quotient .
4
DIS
1
Divide:24__
5
1
Multiplytocheck .
CU S S
25
2
1
2
1
3
1
__
5
5
1
5
1
2 3 5
1 3 1
1
55
Check: 10 3__
1
5
10
1
5
10
1
1
3__
55
5 10 10
5
5
2
1
___
Wesdivided__
8by3andgotaquotientof24 .Wescheckedhisanswerbymultiplyingthe
quotientbythedivisor .HowwillWesknowifhedividedcorrectly?
1
Possible response: If Wes multiplies the quotient, ___
24 , by the divisor, 3, 1
the product should be the dividend, __
8 .
139
Lesson 1 4
Support Discussion MP3 Have partners discuss briefly before group
discussion. If needed, review the terms quotient and dividend. Prompt: Can you think of a divisor that would result in a
quotient that is greater than 5?
Sentence Starter: Morgan must have divided by a number
that…
lesson link
Connect to Foundational Understanding Skills learned in the Plug In
and Power Up are referenced in the Lesson Link. Explain that fractions
can be divided just like whole numbers and that fraction division uses
the same skills as multiplying fractions. spotlight on
mathematical LANGUAGE
MP6 Support students in
using mathematical language
as they work:
What is the reciprocal of the
divisor?
What is the denominator of
the unit fraction?
Write the reciprocal of the
unit fraction.
Teach/Instruction Guide students through the information about
solving word problems. Explain that in this problem, the dividend is a
whole number and the divisor is a fraction. DO A Monitor students as they write the whole number as a fraction and
the reciprocal of the divisor before they multiply. Support Discussion MP2 Have partners discuss briefly before group
discussion. As needed, have students identify the quotient, dividend,
and divisor before discussion. Prompt: What numbers will Wes multiply? What should his
answer be?
Sentence Starter: If Wes multiplies the quotient by the divisor,
his answer…
© 2014 Triumph Learning, LLC
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14 Dividing Unit Fractions and Whole Numbers
READY TO gO
PRACTICE
Write an equation to solve. Use multiplication to check. Variables may vary.
Use models to solve. 1 __41435
1
6 Howmany__81-foot-longtilesmustIsobelplaceinarowifshewantstherowtobe3feetlong?
HINT
The divisor tells you how many equal parts to 1
divide __
4 .
12
1
4
3
1
__
8 4
5
t
24 tiles
1 1 1 1 1 1 1 1 1 1 1 1
12 12 12 12 12 12 12 12 12 12 12 12
7 If6peopleequallyshare__21gallonofmilk,howmuchmilkwilleachpersonreceive?
1
2 64__415 24
1
1
1
1
1
1
__
2
4
1
__
2 gallon(s)
6
5
m 8 Craigused__41cupofsugartomake12cookies .
1
15
4 44__715 28
5 24__915 18
140 REMEMBER
Multiply the quotient by the divisor to check your work.
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
Divide.
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
Howmuchsugarwasineachcookie?
3 __51435
I know! I can write
an equation to
solve each problem.
Solve.
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
1
___
48 cup
12
9 Meganbought4ouncesofcheese .Thecheese
1
wascutinto__
3-ounceslices .Howmanyslices
ofcheesedidshebuy? DIS
CU S S
Check That It’s Reasonable 1
oliviadivided6by__
2andgotaquotientof3 .
Isolivia’squotientlessthanorgreaterthanthedividend,6? less than
Whenyoudivideawholenumberbyaunitfraction,youarefindingthenumberofpiecesinthewhole
number .Shouldthequotientbelessthanorgreaterthanthewholenumber? greater than
1 Possible response: Olivia multiplied Whaterrordidoliviamakewhenshedivided6by__
2?
1
1
2 .
6 3 __
2 instead of dividing 6 by __
1
Whatis6dividedby__
2? 12
141
Less o n 1 4
ADDITIONAL PRACTICE
Provide students with
additional practice to model
and solve:
1
1
1
1
__ ​  4 5
 
5 4 ​ __
4
3 ​​ 
__ ​  4 8
6 4 ​ __
 
5 ​​ 
2
Support Independent Practice
1–5 Remind students to read the HINT and REMEMBER. If needed,
ask: Which number is the divisor? What is the reciprocal of the divisor?
6–7 Ensure that students are writing the whole number as a fraction.
8–9 How do you know which number is the divisor and which number is
the dividend?
Support Discussion MP2 Have partners discuss briefly before group
discussion. As needed, have students draw models to show the division.
Prompt: What is the relationship between 6 and 3?
Sentence Starter: The relationship between 6 and 3 is…
Problem Solving
Model the Four-Step Method MP4 MP6 Guide students through the
four-step method using think-aloud strategies. 1
Think Aloud Kara has 3 feet of ribbon. Each piece is __
​ 6 ​ foot long. I need to
1
find the number of times __
​ 6 ​ goes into 3.
Support Problem-Solving Practice Have students use the Checklist as
they complete each step.
Prompt: How can you find the number of laps Max ran?
Prompt: Did Alisha practice for more than or less than 4 hours?
Prompt: How many sandwiches will Jervaise make?
112 Le ss o n 1 4
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14 Dividing Unit Fractions and Whole Numbers
READY TO gO
READ
PlAn
Rewrite division as
multiplication using
the reciprocal of
the divisor.
PRACTICE
Use the problem-solving steps to help you.
ribboN cuttiNG
1 Maxranatotalof5milesaroundatrack .Eachlap
1
was__
8 mile .Zacharyran36lapsaroundthetrack .
Who ran morelaps?
Karaneeds16piecesofribbonforaquilt .Shecuta3-foot-longred
1
ribboninto__
6-foot-longpieces .Doesshehaveenoughpiecesofribbon?
CHECKLIST
READ
Max
PLAN
• Whatistheproblemaskingyoutofind?
SoLVE
pieces
WhetherKarahasenough
Lesson 14
PROblEm sOlvIng
ofribbon
CHECK
• Whatdoyouneedtoknowtosolvethisproblem?
3
Thelengthoftheredribbonis
feet .
1
__
6
Thelengthofeachpieceis
foot .
2 Lastmonth,Lauriepracticedpianofor__41houreachdayfor
• Howcanyousolvetheproblem?
Dividethelengthofthe
sOlvE
ribbon
pieces
bythelengthofthe
atotalof4hours .Alishapracticedpianoon15days .
Whopracticedonmoredays?
.
3
4
1
SoLVE
CHECK
5r
6
READ
PLAN
Laurie
Writeanequation .Letr5thenumberofpiecesofribbon .
CHECKLIST
3
1
3
6
1
5
3 3 6
1 3 1
5
18
1
r5 18
Thereare 18 piecesofredribbon .
ChECk
Multiplythenumberofpiecesofribbonbythelengthofeachpiece .
Theproductshouldequalthelengthoftheribbonbeforeitwascut .
18 3
1
6
5
18
1
3
1
6
5
18 3 1
1
3 6
5
18
6
5
3
feet
DoesKarahaveenoughpiecesofribbon? yes
142 Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
Solve .
3 Jervaiseneedstomake20sandwichesforaparty .Hehas
1
6poundsofturkeyandheisusing__
3poundofturkeyfor
eachsandwich .Willhemakeenoughsandwiches?
No
CHECKLIST
READ
PLAN
SoLVE
CHECK
143
Lesson 1 4
Explore Student Thinking MP4 Invite students to explain how they
solved the problems. Have partners compare their work on a problem
and describe their results.
COMMON ERRORS
Students may write the
reciprocal of the wrong
fraction. Emphasize that they
should write the reciprocal of
the divisor. In each problem,
have students identify the
divisor and then write its
reciprocal.
Assess
Use the table below to observe whether students accurately divide unit
fractions and whole numbers and to address any difficulties, as needed,
before the quiz.
When students are ready, assign the Lesson 14 Quiz.
1
Observation
Errors in division are frequent; general
confusion about dividing unit fractions and
whole numbers.
Action
Have students draw pictures to model all computations. Have
them write an equation below the models.
2
Observation
Makes occasional errors when dividing;
some understanding of dividing unit
fractions and whole numbers.
Observation
Writes, models, and solves problems
involving division of unit fractions and
whole numbers accurately.
Action
Provide additional practice problems for dividing unit
fractions and whole numbers. Encourage students to model
the computations. Action
Assign the Lesson 14 Quiz.
3
© 2014 Triumph Learning, LLC
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14
Dividing Unit Fractions and
Whole Numbers
Plug In
Multiplying Fractions
Tatyana has 5 cans of paint. Each
can contains 1 gallon of paint. 1
To solve the problem without a model, write the whole number, 5, as a fraction. Multiply the numerators and the denominators.
You can use a model to
represent the problem. She uses ​ __
4 ​  of each can to mix a
new color. How many gallons of
paint does she mix?
5
1
1
__
__
​ 4 ​  3 5 5 ​ __
4 ​  3 ​ 1 ​ 
135
​ 5 ​ ____
4 3 1  
5
5 ​ __
4 ​
5
Tatyana mixes ​ __
4 ​ gallons
Write an equation to represent
the problem. 1
​ __
4 ​  3 5 5 p
5
1
1
1
1
1
__
__
__
__
__
​ 4 ​  1 ​ __
4  ​ 1 ​ 4 ​  1 ​ 4  ​ 1 ​ 4  ​ 5 ​ 4 ​
The word
“of” tells me
to multiply.
of paint.
I get it! I can rename a whole
number as a fraction by writing
the whole number as a numerator
over a denominator of 1!
Each shaded section
 ​41  ​of a gallon.
represents __
There are 5 shaded sections.
DIS
CU S S
1
Ava drew this model to show ​ __
4  ​ 3 6.
What can you tell Ava about her model?
A You can use a model to multiply a whole number times a fraction.
DO
1
Multiply: 4 3 ​ __
3 ​ 
1
1
Show 4 groups of ​ __
3 ​. 
2
Add the shaded parts.
3
Write the product.
1
3
1
1
4 3 ​ __
3 ​  5
134 1
1
5
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
LESSON
S
uppor
tCoa
c
h,
Ma
t
he
ma
t
i
c
s
,
S
t
ude
ntE
di
t
i
on,
Gr
a
de5
L e ss o n 1 4
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14 Dividing Unit Fractions and Whole Numbers
B You can multiply a whole number times a fraction without using a model.
DO
1
Multiply: 15 3 ​ __
10   ​
1
Rename the whole number as a
fraction.
2
Multiply the numerators and the
denominators.
3
Write the product.
1
1
15 3 ​ __
10   ​ 5
1
1
3 ​ __
10   ​ 5
1
I get it! I can
write a whole
number as a
fraction with a
denominator of 1.
3 ​ __
10   ​
3
5
3
1
15 3 ​ __
10   ​ 5
PRACTICE
Use the model to multiply.
1 7 3 ​ __41  ​ 5
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
2 ​ __61  ​ 3 7 5
Multiply.
3 6 3 ​ __51  ​ 1
3 __
​ 5  ​5
3
5
3
4 ​ __31 ​  3 8
1
__
​ 3 ​ 3
5
3
5
3
135
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Fractions as Division
If 3 friends share 4 granola bars
equally, what part of a granola
bar does each friend get?
The division problem is: 4 4 3.
You can write the division
problem as a fraction. The
fraction bar in a fraction
represents division. The
value of a fraction is equal to
its numerator divided by its
denominator.
You can use a model to show 4 4 3.
You can use long division to 4
find ​ __
3 ​.
Each whole represents
1 granola bar. Divide each whole
into 3 equal parts.
1 R1
3 4
3
1
To write the quotient as a
mixed number, write the
whole number, 1, and write the
remainder as the numerator of
a fraction with the divisor as the
denominator.
4
4 4 3 5 ​ __
3 ​
remainder
divisor
1 friend
1
Each friend will get four ​ __
3  ​ parts.
1
I see! A fraction is
another way to write a
division problem!
4
__
4 3 ​ __
3  ​ 5 ​ 3 ​ of a granola bar
Know
mixed number
a number that has a wholenumber part and a fraction part
1
1​ __
6  ​ is a mixed number.
DIS
136 CU S S
1
So, 4 4 3 5 1​ __
3 ​,  and each friend
1
gets 1​ __
3 ​  granola bars.
4
So, 4 4 3 5 ​ __
3 ​.
The dividend is greater than
the divisor, so the quotient is a
fraction that is greater than 1!
Words
to
1
3
remainder
the amount that is left over after division is complete
5 3 1 R2
3
A fraction greater than
1 can be written as a
mixed number.
divisor
a number by which another
number is divided
5 3 1 R2
Ella drew a model to show that 3 4 8 5 ​ __
8 ​. What can you tell Ella about her model?
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POWER UP
L e ss o n 1 4
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14 Dividing Unit Fractions and Whole Numbers
A You can show division with quotients less than 1 as a fraction.
DO
Five friends equally share 4 quarts of water. How many quarts of water does each friend get?
The division problem is
1
Set up a division problem.
2
Write the quotient as a fraction with
the dividend as the numerator and
the divisor as the denominator.
3
4
Interpret the quotient.
4
4
Each friend will get
quart of water. Three sisters equally share the driving for a 10-hour
trip. For how many hours does each sister drive?
1
Set up a division problem.
2
Divide to write the fraction
as a mixed number.
3
Interpret the quotient.
The division problem is
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
4
.
I see! Since the
numerator is greater
than the denominator,
I can divide to write
the fraction as a mixed
number!
3 R
3 10
9
10 4 3 5
​ ____  ​
Each sister will drive for
CU S S
DIS
.
5
B You can show division with quotients greater than 1 as a fraction.
DO
5
hours.
25
Keisha wants to write the fraction ​ ___
8   ​ as division. Which number should she write as the
divisor? Which number should she write as the dividend?
PRACTICE
Solve.
1 Six friends equally share a bag of popcorn. The bag contains 9 cups of popcorn. How many
cups of popcorn should each friend get?
2 Charlotte cuts a 3-foot-long piece of ribbon into 4 equal pieces to trim a square pillow. How long is each piece of ribbon?
137
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Dividing Unit Fractions and
Whole Numbers
READY TO GO
You can use models to help you divide a unit fraction by a whole number.
1
You can also use a model to divide a whole number
by a unit fraction.
1
1
__ 
To divide ​ __
2 ​  4 4, start with a model for ​ 2 ​. To divide 2 4 ​ __
3 ​,  start with a model for 2 wholes. Divide each whole into 3 equal parts, or thirds. There are a total of 6 equal parts.
1
Divide into 4 equal parts. Each part is ​ __
8 ​. 
1
2
1
1 1 1 1
8 8 8 8
1
3
To divide without a model, multiply the dividend
by the reciprocal of the divisor.
1
1
4 __
1
1
131
1
__
__
__
_____
__
​ 2  ​ 4 4 5 ​ __
2 ​  4 ​ 1 ​  5 ​ 2 ​  3 ​ 4 ​  5 ​ 2 3 4  ​  5 ​ 8  ​
1 1 __
1
1
__
__
​ 2 ​,  ​ __
3 ​,  ​ 4 ​,  and ​ 5 ​  are unit fractions.
1
3
1
2
3
6
233
__ __ _____​ 5 ​ __ ​  5 6
2 4 ​ __
1
3 ​  5 ​ 1 ​  3 ​ 1 ​  5 ​ 1 3 1  
reciprocal
a number that gives a product of 1 when
multiplied by a second number 1
1
__
4 and ​ __
4 ​  are reciprocals: 4 3 ​ 4 ​  5 1.
Morgan divides 5 by a number and gets an answer of 20. Bethany says that Morgan’s
answer is incorrect because the quotient should always be less than the dividend. What
can you say to Bethany?
lesSon link
Plug In
You can use a model to
multiply a fraction by a
whole number.
POWER UP
You can show a fraction as
division of the numerator by
the denominator.
2
__
​ 5 ​ 5 2 4 5
1
3
__
3 3 ​ __
5  ​ 5 ​ 5 ​
138 1
3
When dividing a whole number by
a fraction, the quotient is greater
than the dividend and the divisor.
unit fraction
a fraction with 1 as the numerator CU S S
DIS
1
3
GO!
I get it! I can use
what I know about
multiplying and
dividing fractions
and whole numbers
to solve problems.
OVERSET
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
Know
1
3
Multiply the dividend by the reciprocal of the divisor.
When dividing a fraction
by a whole number, the
quotient is less than the
dividend and the divisor.
Words
to
1
3
1
L e ss o n 1 4
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14 Dividing Unit Fractions and Whole Numbers
1
How many ​ __
2 ​-  cup servings are there in 3 cups of rice?
3 cups
1
1
__
The equation 3 4 ​ 2 ​  5 n represents the problem.
2
Solve for n.
1
cup
1
cup
1
cup
1
2
1
2
1
2
3
Rename the whole number as a fraction: 3 5 ​ __1  ​
Write the reciprocal of the divisor: ​ __
2 ​  
Rewrite as multiplication: ​ __1 ​  3 ​ __1 ​  5 ​ __1 ​  5 6
So, n 5 6.
1
3
3
2
1
2
1
I remember! To write the
reciprocal of a fraction,
switch the numerator
and the denominator.
1
__
3 4 ​ __
2  ​ 5 n is related to n 3 ​ 2  ​ 5 3.
__ __ __
6 3 ​ __
2 ​  5 ​ 1 ​  3 ​ 2  ​ 5 ​ 2 ​ 5 3
6
1
2
6 2 cup
Use multiplication to check.
1
1
2
1
4
6
2
​ __1 ​ 
1
6
✓
The models show 3 cups. Each cup is divided into
1
2 equal parts, or halves. There are 6 equal ​ __
2 ​  parts.
1
There are six ​ __
2 ​-  cup servings of rice in 3 cups of rice.
A You can use multiplication to divide a whole number by a fraction.
DO
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
1
1
Divide: 2 4 ​ __
5 ​ 
Rename the whole number as a
fraction.
2
Write the reciprocal of the divisor.
3
Rewrite as multiplication. Write the
quotient.
4
25
2
2
3
Multiply to check.
CU S S
1
5
2 3
5
5
3
Check:
DIS
1
​ __
5  ​ 1
3 ​ __
5 ​  5
1
3 ​ __
5 ​  5
5
1
___
Wes divided ​ __
8 ​  by 3 and got a quotient of ​ 24   ​. Wes checked his answer by multiplying the
quotient by the divisor. How will Wes know if he divided correctly?
139
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Ready to Go
practice
Use models to solve.
HINT
The divisor tells
you how many
equal parts to
1
divide ​ __
4  ​.
1 ​ __41  ​ 4 3 5
1
4
2 6 4 ​ __41  ​ 5
1
1
1
1
1
Divide.
3
1
​ __
5 ​  4 3 5
4 4 4 ​ __71  ​ 5
5 2 4 ​ __91  ​ 5
140 REMEMBER
Multiply the
quotient by the
divisor to check
your work.
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
1
L e ss o n 1 4
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14 Dividing Unit Fractions and Whole Numbers
Write an equation to solve. Use multiplication to check.
6 How many ​ __81 ​-  foot-long tiles must Isobel place in a row if she wants the row to be 3 feet long?
4
5
tiles
7 If 6 people equally share ​ __21 ​  gallon of milk, how much milk will each person receive?
4
5
gallon(s)
I know! I can write
an equation to
solve each problem.
Solve.
8 Craig used ​ __41 ​  cup of sugar to make 12 cookies. Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
How much sugar was in each cookie?
9 Megan bought 4 ounces of cheese. The cheese
1
was cut into ​ __
3 ​-  ounce slices. How many slices
of cheese did she buy? CU S S
DIS
Check That It’s Reasonable
1
Olivia divided 6 by ​ __
2 ​  and got a quotient of 3.
Is Olivia’s quotient less than or greater than the dividend, 6?
When you divide a whole number by a unit fraction, you are finding the number of pieces in the whole
number. Should the quotient be less than or greater than the whole number?
1
What error did Olivia make when she divided 6 by ​ __
2  ​?
1
What is 6 divided by ​ __
 
2 ​?
141
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Ready to Go
Problem solving
RIBBON CUTTING
READ
Kara needs 16 pieces of ribbon for a quilt. She cut a 3-foot-long red
1
ribbon into ​ __
6 ​-  foot-long pieces. Does she have enough pieces of ribbon?
PLAN
• What is the problem asking you to find?
Whether Kara has enough
of ribbon
• What do you need to know to solve this problem?
The length of the red ribbon is
feet.
The length of each piece is
foot.
• How can you solve the problem?
Divide the length of the
SOLVE
by the length of the
. Write an equation. Let r 5 the number of pieces of ribbon. 5r
4
3
3
5
5
3
r5
There are
CHECK
pieces of red ribbon. Multiply the number of pieces of ribbon by the length of each piece. The product should equal the length of the ribbon before it was cut.
3
3
5
3
5
5
3
Does Kara have enough pieces of ribbon?
142 5
feet
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Solve.
L e ss o n 1 4
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14 Dividing Unit Fractions and Whole Numbers
practice
Use the problem-solving steps to help you.
Rewrite division as
multiplication using
the reciprocal of
the divisor.
1 Max ran a total of 5 miles around a track. Each lap
1
was ​ __
8 ​  mile. Zachary ran 36 laps around the track. Who ran more laps?
CHECKLIST
Read
Plan
Solve
Check
2 Last month, Laurie practiced piano for ​ __41 ​  hour each day for
a total of 4 hours. Alisha practiced piano on 15 days. Who practiced on more days?
CHECKLIST
Read
Plan
Solve
Duplicating any part of this book is prohibited by law. © 2014 Triumph Learning, LLC
Check
3 Jervaise needs to make 20 sandwiches for a party. He has
1
6 pounds of turkey and he is using ​ __
3 ​  pound of turkey for
each sandwich. Will he make enough sandwiches?
CHECKLIST
Read
Plan
Solve
Check
143
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