Divide by 1-Digit Numbers Download

Transcript
LESSON
4.11
Divide by 1-Digit Numbers
FOCUS
COHERENCE
RIGOR
LESSON AT A GLANCE
F C R Focus:
Common Core State Standards
4.NBT.B.6 Find whole-number quotients and remainders with up to
four-digit dividends and one-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.
Learning Objective
MATHEMATICAL PRACTICES
MP2 Reason abstractly and quantitatively. MP7 Look for and make use of structure.
MP8 Look for and express regularity in repeated reasoning.
Divide multi-digit numbers by 1-digit divisors.
F C R Coherence:
Divide multi-digit numbers by 1-digit divisors.
Language Objective
Materials
MathBoard
Standards Across the Grades
Before
Grade 4 After
3.OA.A.2 4.NBT.B.6 5.NBT.B.5
3.OA.B.6
F C R Rigor:
Level 1: Understand Concepts....................Share and Show (
Checked Items)
Level 2: Procedural Skills and Fluency.......On Your Own
Level 3: Applications..................................Think Smarter and Go Deeper
F C R For more about how GO Math! fosters Coherence
within the Content Standards and Mathematical Progressions
for this chapter, see page 195J.
About the Math
Professional Development
MP2 Reason abstractly and
quantitatively.
In this lesson, students will use reasoning skills to make
predictions, solve problems, and check their solutions.
Guide them to see how the parts of the division algorithm
are interrelated and how the operations of multiplication
and division are used throughout the process.
Students will need to apply previous knowledge of
multiples to predict whether division problems will result
in quotients with remainders. Students will also learn to
recognize when a zero should be placed in a quotient.
It is important that students understand the inverse
relationship between multiplication and division to check
their solutions
Professional Development Videos
259A
Chapter 4
Interactive Student Edition
Personal Math Trainer
Math on the Spot
Animated Math Models
iTools: Algebra
HMH Mega Math
1 ENGAGE
Daily Routines
Common Core
Problem of the Day 4.11
Nora used 20 blocks to build two towers.
The number of blocks used to build each
tower was a multiple of 4. What are
possible numbers of blocks used to make
the towers? Possible answer: 8 blocks and 12 blocks
Vocabulary
Essential Question
How can you divide multidigit numbers and
check your answers?
Making Connections
Invite students to tell you what they know about division of a
two-digit number by a one-digit number.
What is one way to divide 96 by 8? Possible answer: repeated
subtraction or regrouping
Learning Activity
™Interactive Student Edition
™Multimedia eGlossary
Fluency Builder
with the Interactive Student Edition
What is the problem the students are trying to solve? Connect the
story to the problem.
Common Core Fluency
Standard 4.NBT.B.6
Materials Vocabulary Cards
(see eTeacher Resources)
• What problem are you trying to solve? How much a bowl of
spaghetti costs at the diner.
• How much did the diner make in spaghetti sales? $935
• What math operation can you use to find the cost of one bowl of
spaghetti? division
Vocabulary Cards Use vocabulary cards to
help students remember definitions for
review words. Ask students to respond to a
question or statement such as:
The number being divided into parts is
the ___.
Literacy and Mathematics
Choose one or more of the following activities.
• Have students write their own word problem involving division by
5 and discuss how they might solve their problem.
• Have students identify details in the problem that they do and do
not need to solve the problem.
How would you know when a problem
will have a ___?
remainder
dividend
How can you divide
multidigit numbers
and check your
answers?
Lesson 4.11 259B
LESSON
4.11
2 EXPLORE
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies
DO
NOTon
EDIT--Changes
must
be made
through "File
info"the relationship between multiplication and division. Illustrate and
based
place value, the
properties
of operations,
and/or
CorrectionKey=A
explain the calculation by using equations, rectangular arrays, and/or area models
Lesson 4.11
Name
Unlock the Problem
Divide by 1-Digit Numbers
id you know that origami is the Japanese
D
art of paper folding? The goal is to create an
object with folds using one sheet of paper
and no scissors or glue.
Unlock
Unlock the
the Problem
Problem
Students in the third, fourth, and fifth grades made
525 origami animals to display in the library. Each
grade made the same number of animals. How
many animals did each grade make?
Example 1
Example 1 Divide. 525 ÷ 3
After students read the problem, ask:
• Why do we use division to solve this
problem? Possible answer: we know how many
STEP 1 Use place value to place the first digit. Look at
the hundreds in 525. 5 hundreds can be shared among
3 groups without regrouping. The first digit of the
groups there are and want to find how many in
each group.
1
5
Divide. Share _
hundreds equally among
3qw
525 _
3
groups.
–3
3
1 hundred
Multiply. _
× __
2
5 hundreds
3 hundreds
• What will the quotient represent? the
number of origami animals each class made
200, so it is reasonable.
Math
Talk
algorithm.
Use Math Talk to focus on students’
understanding of the division
Possible answer: increase
the number in that place in
the quotient.
Subtract. __ – __.
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) ©Digital Vision/Getty Images
MP1 Make sense of problems and
persevere in solving them. After students
complete the division, ask:
• Is your answer reasonable? How do you
know? Possible answer: 175 is close to the estimate
MATHEMATICAL PRACTICES 8
Use Repeated Reasoning
At the checking step,
what would you do if the
number is greater than
the divisor?
STEP 2 Divide the hundreds.
answer: there are 3 grades: third, fourth, and fifth.
closer to 600 than 300
Math
Talk
hundreds place.
quotient will be in the __
• Why do we use 3 as the divisor? Possible
• Will the quotient be closer to 100 or 200?
Explain. Possible answer: 200, because the dividend is
Number and Operations in Base
Ten—4.NBT.B.6
MATHEMATICAL PRACTICES
MP2, MP7, MP8
Essential Question How can you divide multidigit numbers
and check your answers?
MATHEMATICAL PRACTICES
2
Check. _
hundreds cannot be shared
among 3 groups without regrouping.
STEP 3 Divide the tens.
17
3qw
525
–3
22
–21
1
STEP 4 Divide the ones.
22 tens
Divide. Share __
equally
3
among _
groups.
3 × 7 tens
Multiply. ____
22 tens – __
21 tens
Subtract. __
1 ten cannot be shared
Check. ___
among 3 groups without
____
regrouping.
____
.
15 ones
Divide. Share __
equally
175
3qw
525
–3
22
–21
15
–15
_
0
3
among _
groups.
3 × 5 ones
Multiply. ____
15 ones – __
15 ones
Subtract. __
0 ones
Check. __
are left.
175
So, each class made __
origami animals.
• How does the number you subtract cause
the result to be too large? Possible answer: the
Chapter 4 259
number is not large enough.
• How could you increase the size of the
number you subtract? Possible answer: increase
the number you wrote in the quotient.
MP7 Look for and make use of structure.
• How could you make division of larger
numbers easier? Possible answer: to divide 3-digit
numbers, divide, multiply, subtract, and check starting
with the first place in the quotient and continuing to
the ones place. Use the same steps to divide each place
in larger numbers.
4_MNLESE342217_C04L11.indd 259
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Reteach 4.11
Enrich 4.11
3
2
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1
Lesson 4.11
Reteach
Name What Is Left Over ?
Find the “leftover” in each situation. Then use the code key to see
which letters match each of your answers. Write the letters in order
of the exercises to find the answer to the riddle.
Divide. 766 4 6 5
1​​​​​
​​
Step​1​ Use​place​value​to​place​the​first​digit. ​ ​​​​
​​6​
​​
 
 766​​​​
qw
Think:​7​hundreds​can​be​shared​among​ _
6​groups​without​regrouping.​
Step​3​ There​are​
4​tens​left​over.​
Regroup​4​tens,​now​
there​are​46​ones.​
Divide​the​ones.​
Lesson 4.11
Enrich
Name Divide by 1-Digit Numbers
1​​​​​
Step​2​ There​is​
​​
​​​
​​​
​
​​
6​qw
 
 766​​
2​6​​​
1​hundred​left​over.​
_
16
Regroup​1​hundred,​
now​there​are​16​tens.​
Divide​the​tens.​
​​The​first​digit​is​in​the​
hundreds​place.
1. Jude
​​16​tens
12​​​
12
​​​​
​​​​
6​qw
​
​
 ​​
​
 766​​
​​
​
16​​​​​
​​
​ ​​​
​
​​
212
_​
​​​​
​​46​ones
46
​​
2​6​​​​
__
Step​4​ Check​to​make​sure​that​the​remainder​
is​less​than​the​divisor.​Write​the​answer.
​​​
​​​​​​​​​​16 ​
​
​​
______​
  ​​
​ ​​​​​212  ​
       4
2
​
​​Multiply.​6​3​2​tens
​Subtract.
2. Selena
has a piece of ribbon that is 130 inches long. If she
wants to make bracelets that are 9 inches long, how many
inches of ribbon will be left over?
​​Divide​46​ones​by​6.
127​
127
​​
​ 
​​​
​6​
​​​
 766​​
qw
2​6​​​​​
_
​​​
​ ​​16​
​​
212
_
46
​​​​
​​​​​ ​​ 
​
2​42
4
​
3. Justin
prepares 229 hamburgers for a company picnic. If
buns come in packages of 8, how many will be left over?
​​Multiply.​6​3​7​ones
​Subtract.
_
127 r4 
6​qw
 766​​ 
Step​5​ Use​multiplication​and​addition​to​check​ ​​​
​ 127 
​
​ 
your​answer.​​​
3 6
_
​​​
​ 762​​
 
1 4
_
766
puts 6 lemons in each bag. If he has 170 lemons,
how many will be left over?
​​Divide​16​tens​by​6.
​​12​​​
​​
​ qw
​
 766​​​
6​
 
​​​
​​ ​​ ​​
______
2​6​​​​​​
​
4
5
4​,​6
4. Mrs.
Bradley has $204 to divide equally between her
7 grandchildren. How many dollars will she have left over?
1
​​quotient
​divisor
5. Mr.
White has 115 tulips for bouquets. He puts 9 tulips in
each bouquet. How many tulips will be left over?
​remainder
​dividend
7
Divide and check.  
217
 868​​     
1. 4​qw
  217 
  
 
3
 4
_
868
259 Chapter 4
Chapter Resources
© Houghton Mifflin Harcourt Publishing Company
4_MNLEAN343092_C04R11.indd 25
Differentiated
Instruction
328 r1
 657​​    
2. 2​qw
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3   2
_
  
   
  656 
 
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657
4-25
1,210 r3
3. 7q w
8,473​     
  
  1,210 
 
3      7
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__
8,473 
Reteach
1
2
3
4
5
6
7
8
G
F
E
L
A
N
S
T
What flies around all day but never goes anywhere?
FLAGS
Chapter Resources
© Houghton Mifflin Harcourt Publishing Company
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4_MNLEAN343092_C04E11.indd 26
4-26
Enrich
17/02/14 11:15 PM
Example 2
Division is extended to include 4-digit
dividends. Students will also begin to
understand when to place a zero in the
quotient.
• How is division with a 4-digit dividend
different from division of smaller
dividends? Possible answer: I need to begin with
There are 8,523 sheets of origami paper to be divided
equally among 8 schools. How many sheets of
origami paper will each school get?
Example 2 Divide. 8,523 ÷ 8
STEP 1 Use place value to place the first digit.
Look at the thousands in 8,523.
8 thousands can be shared among
8 groups without regrouping.
The first digit of the quotient will be
thousands place.
in the __
STEP 2 Divide the thousands.
STEP 3 Divide the hundreds.
STEP 4 Divide the tens.
STEP 5 Divide the ones.
1,065 sheets of
So, each school will get _
origami paper.
the thousands place to see if I can divide thousands or
need to regroup.
1, 0 6 5 r 3
8qw
8, 5 2 3
− 8
0 5
− 0
5 2
− 4 8
4 3
− 4 0
3
• In Step 3, why do you place a zero in the
hundreds place? Possible answer: since 5 hundreds
cannot be shared equally among 8 groups without
regrouping, I must write a zero in the hundreds place
in the quotient.
Connect Discuss how to check division.
• How will you know if your answer to a
division problem is correct when you check
by multiplication and addition? Possible answer:
3 sheets left.
There will be _
if the result of the multiplication and addition matches
the dividend, the answer to the division is correct.
connect Division and multiplication are inverse operations. You can
use multiplication to check your answer to a division problem.
Multiply the quotient by the divisor. If there is a remainder, add it to
the product. The result should equal the dividend.
Divide.
Check.
quotient
divisor
→
1,065 r3
→ 8qw
8,523
← remainder
← dividend
← quotient
← divisor
1,065
×
8
__
8,520
+
3
__
8,523
← remainder
← dividend
The check shows that the division is correct.
260
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) Houghton Mifflin Harcourt
Place a zero in the quotient
when a place in the dividend
cannot be divided by the
divisor.
DEEPER
MP3 Construct viable arguments and
critique the reasoning of others. Work
together with students to make a list on the
board of division errors. At the end of the
lesson, have students write a division exercise
and purposely make an error in dividing. Then
exchange with a partner to see if the partner
can find the error.
ELL Strategy:
Identify
Relationships
• Display a color-coded division problem, as
shown below.
Visual / Logical
Partners
Advanced Learners
• Provide students with the following problems.
2qw
128
2qw
6,926
5qw
8,250
5qw
700
• Ask students to analyze the problems to determine
how to tell without dividing if there will be a
remainder.
• Provide students with the following problems.
9qw
171 19
2qw
243 27
9qw
612 68
• Ask students to analyze the problems to determine
a method for knowing, without dividing, if there
will be a remainder when the divisor is 9. Possible
answer: if the divisor is 9 and the sum of the digits of the
dividend is 9, there will be no remainder.
divisor
dividend
quotient
remainder
product
difference
Divide.
1 0 2r1
8qw
81 7
−8
____
0 1 − 0
____
17
−
16
____
1
Check.
102
× 8
___
816
+
1
___
817
• Have students solve several division
problems. Then have them use the correct
terms as they explain the steps in their
solution and in their check.
Lesson 4.11 260
DO NOT EDIT--Changes must be made through "File info"
CorrectionKey=A
Name
3 EXPLAIN
Share
Share and
and Show
Show
MATH
BOARD
1. Ollie used 852 beads to make 4 bracelets. He put the
Share and Show
same number of beads on each bracelet. How many
beads does each bracelet have? Check your answer.
MATH
BOARD
Divide.
The first problem connects to the learning
model. Have students use the MathBoard to
explain their thinking.
2 1 3
4 qw
8 5 2
− 8
0 5
− 4
1 2
− 1 2
0
Math
Talk
Use Math Talk to focus on
students’ understanding of how to
use multiplication to check a division problem.
• What operation undoes division? multiplication
• How can you use multiplication to undo
division? Possible answer: start with the result of
1
Rt I
If
a student misses the checked
exercises
Then
Differentiate Instruction with
• Reteach 4.11
• Personal Math Trainer 4.NBT.B.6
• RtI Tier 1 Activity (online)
On Your Own
If students complete the checked exercises
correctly, they may continue with the
remaining exercises.
COMMON ERRORS
COMMON ERRORS
Error Students do not place a zero in
the quotient. Example 12 r 1
   
​ 8​qw
​
 8 1 7 ​ 
 
∙ 8       
____
 
​
​ 
  
​    1 7 ∙1 6
​  ___​ 
1   
Springboard to Learning Demonstrate
that you cannot divide 1 ten into 8 groups.
Explain that a 0 fills the tens place in the
quotient to show that there are 0 tens. Then
regroup the 1 ten to divide 17 ones.
261 Chapter 4
Possible answer: multiply the
quotient by the divisor. If the
product equals the dividend, the
quotient is correct.
Math
Talk
MATHEMATICAL PRACTICES 7
Identify Relationships
How could you check to
see if your quotient is
correct?
Divide and check.
197
2. 2qw
394
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) Houghton Mifflin Harcourt
2
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) Houghton Mifflin Harcourt
Quick Check
3
1
2 1 3
×
4
8 5 2
213 beads.
So, each bracelet has _
dividing, the quotient, and multiply by the divisor. If the
quotient is correct, the product should be the dividend.
Use the checked exercises for QuickCheck.
In Exercise 3, make sure students place a zero
in the tens place in the quotient. In Exercise 4,
make sure students place the first digit in the
hundreds place.
Check.
197
×
2
_
394
401 r1
3. 2qw
803
401
×
2
_
802
+ 1
_
803
862
4. 4qw
3,448
177 r1
6. 4qw
709
177
× 4
_
708
+
1
_
709
89
7. 3qw
267
862
× 4
_
3,448
On
On Your
Your Own
Own
Divide and check.
408
5. 2qw
816
8.
408
× 2
_
816
89
×
3
_
267
DEEPER
The flower shop received a shipment of
248 pink roses and 256 red roses. The shop owner uses
6 roses to make one arrangement. How many arrangements
can the shop owner make if he uses all the roses?
84 arrangements
Chapter 4 • Lesson 11
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MATHEMATICAL PRACTICES
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4 ELABORATE
Use the table for 9–11.
9.
The Craft Store
SMARTER
Four teachers bought 10 origami
books and 100 packs of origami paper for their
classrooms. They will share the cost of the items
equally. How much should each teacher pay?
Item
$210
10.
MATHEMATICAL
5 Communicate Six students shared equally the
PRACTICE
cost of 18 of one of the items in the chart. Each student paid
$24. What item did they buy? Explain how you found your
answer.
Price
Origami Book
$24 each
Origami Paper
$6 per pack
Origami Kit
$8 each
WRITE
Problem Solving • Applications
MATHEMATICAL PRACTICES
SMARTER
Math
Show Your Work
For Exercise 9, students need to use data from
the table to solve this multistep problem.
origami kits; possible explanation: first, I found how
much they spent altogether: $24 × 6 = $144. Then, I tried
Math on the Spot
Video Tutor
dividing $144 by 8 to see if they bought the origami kits.
144 ÷ 8 = 18, so they bought 18 of the origami kits.
Use this video to help students model and
solve this type of Think Smarter problem.
11. Ms. Alvarez has $1,482 to spend on origami paper. How many
packs can she buy?
Math on the Spot videos are in the Interactive
Student Edition and at www.thinkcentral.com.
247 packs
DEEPER
Evan made origami cranes with red, blue, and
yellow paper. The number of cranes in each color is the same.
If there are 342 cranes, how many of them are blue or yellow?
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) Houghton Mifflin Harcourt
12.
228 cranes
13.
SMARTER
On Monday 336 fourth graders went on
a field trip to a local park. The teachers divided the students
into 8 groups.
Use a basic fact. Estimate the number of students in each
group. Show your work.
32 ÷ 8 = 4, so 320 ÷ 8 = 40. About 40 students will be
in each group.
262
DIFFERENTIATED INSTRUCTION
D
INDEPENDENT ACTIVITIES
MP5 Use appropriate tools strategically.
Encourage students to explain completely how
they decided what computations they needed
to do to solve the problem and how they used
the result of the computations to answer the
question.
SMARTER
Students who are not able to explain how the
estimate in Exercise 13 shows that the answer is
reasonable may not truly understand why they
are asked to estimate an answer before they
complete the division.
5 EVALUATE Formative
Assessment
Essential Question
Using the Language Objective
Differentiated Centers Kit
Activities
Dividend Rolls!
Literature
The Thirst Quencher
Games
Divide to Win
Reflect Have students write a note to an
absent student to answer the Essential
Question.
How can you divide multidigit numbers and
check your answers? Possible answer: I use the steps
to divide, then I multiply the quotient by the divisor and add
any remainder. If the result is the same as the dividend, my
answer is correct.
(BNFT
Students complete
purple Activity Card
9 by dividing 3-digit
numbers by 1-digit
divisors.
Students read
about using
division to find
the number of
bottles to fill a
vending machine.
Students practice
dividing 3-digit
numbers to find
quotients in
given range.
Math Journal
WRITE
Math
Josey got an answer of 167 r4 for 3qw
505 .
Explain and correct Josey’s error.
Lesson 4.11 262
Practice and Homework
Lesson 4.11
Name
Divide by 1-Digit Numbers
COMMON CORE STANDARD—4.NBT.B.6
Use place value understanding and properties
of operations to perform multi-digit arithmetic.
Practice and Homework
Divide and check.
Use the Practice and Homework pages to
provide students with more practice of the
concepts and skills presented in this lesson.
Students master their understanding as they
complete practice items and then challenge
their critical thinking skills with Problem
Solving. Use the Write Math section to
determine student’s understanding of content
for this lesson. Encourage students to use their
Math Journals to record their answers.
318
2qw
636
26
03
22
16
216
0
1.
318
× 2
157 r3
2. 4qw
631
636
113 r2
3. 8qw
906
157
× 4
628
+ 3
631
113
× 8
904
+ 2
906
Problem
Problem Solving
Solving
Use the table for 4 and 5.
4. The Briggs rented a car for 5 weeks. What
was the cost of their rental car per week?
$197
5. The Lees rented a car for 4 weeks. The
Santos rented a car for 2 weeks. Whose
weekly rental cost was lower? Explain.
Rental Car Costs
Family
Lee
Total Cost
$632
Brigg
$985
Santo
$328
Lees; possible explanation: Lees, $632 ÷ 4 = $158; Santos, $328 ÷ 2 = $164; $158 < $164
© Houghton Mifflin Harcourt Publishing Company
6.
Math Josey got an answer of 167 r4 for 3qw
WRITE
505 . Explain
and correct Josey’s error.
Check students’ work.
Chapter 4
Extend the Math
Activity
Choose a Strategy for Dividing
Materials MathBoard, index cards (6 for each pair of students), base-ten
blocks
In this chapter, students have used different strategies to
divide by 1-digit divisors with up to 4-digit dividends.
This activity will help students summarize and apply the
strategy that is most efficient for them to use to divide.
Sample Division. Write this division on the board, and ask
volunteers to give different strategies they could use to
divide. Ask the volunteers to demonstrate their strategy.
5qw
5,055
Possible strategies: • mental math
• Use base-ten blocks
• Distributive Property • partial quotients
• Use place value and steps: divide, multiply, subtract, check (algorithm)
263 Chapter 4
263
Have pairs write each of the strategies they named
and also “Use a basic fact and a pattern” on an index
card. Write 10 exercises with 3- or 4- digit dividends
and 1-digit divisors on slips of paper, turn the slips face
down, and play this game.
Strategy Race
• Partners take turns turning over a slip of paper. Both
students write the exercise on their MathBoard.
• Each partner chooses a different strategy on the
index cards and uses that strategy to complete
the division.
• Partners analyze which strategy was more efficient
and why.
• Partners continue until each student has had the
opportunity to “race” with each strategy.
Lesson Check (4.NBT.B.6)
1. Write an expression that can be used to
check the quotient of 646 ÷ 3.
2. There are 8 volunteers at the telethon. The
goal for the evening is to raise $952. If each
volunteer raises the same amount, what is
the minimum amount each needs to raise
to meet the goal?
Continue concepts and skills practice with
Lesson Check. Use Spiral Review to engage
students in previously taught concepts and
to promote content retention. Common Core
standards are correlated to each section.
Possible answer: (215 × 3) + 1
$119
Spiral Review (4.OA.A.3, 4.NBT.B.5, 4.NBT.B.6)
3. What product is shown by the model?
4. The computer lab at a high school ordered
26 packages of CDs. There were 50 CDs
in each package. How many CDs did the
computer lab order?
5. Write a division problem whose quotient
has its first digit in the hundreds place.
Possible answer: 306 ÷ 2
1,300 CDs
6. Sharon has 64 fluid ounces of juice. She is
going to use the juice to fill as many 6-ounce
glasses as possible. She will drink the
leftover juice. How much juice will
Sharon drink?
4 fluid ounces
© Houghton Mifflin Harcourt Publishing Company
5 × 17 = 85
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Lesson 4.11 264