Download Algebra • Fractions and Properties of Addition

LESSON
7.9
Algebra • Fractions and
Properties of Addition
FOCUS
COHERENCE
RIGOR
LESSON AT A GLANCE
F C R Focus:
Common Core State Standards
4.NF.B.3c Understand a fraction a/b with a > 1 as a sum of fractions
1/b. Add and subtract mixed numbers with like denominators, e.g., by
replacing each mixed number with an equivalent fraction, and/or by using properties of
operations and the relationship between addition and subtraction.
MATHEMATICAL PRACTICES
MP2 Reason abstractly and quantitatively. MP7 Look for and make use of structure.
F C R Coherence:
Standards Across the Grades
Before
Grade 4 After
3.NF.A.1 4.NF.B.3c 5.NF.A.1
5.NF.A.2
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
Learning Objective
Use the properties of addition to add fractions.
Language Objective
Students present to a partner a step-by-step
demonstration of how you can add fractions
with like denominators using the properties of
addition.
Materials
MathBoard
FC R
For more about how GO Math! fosters Coherence
within the Content Standards and Mathematical Progressions
for this chapter, see page 383J.
About the Math
Professional Development
Why Teach This
When students apply the Commutative and Associative
Properties of Addition to fractions, they discover they can
use mental math to add some fractions. For example, they
can use the properties to change the order or grouping of
addends so the sum of two fractions is 1.
Encourage students to look in each exercise for fractions
that have a sum of 1. Then have them decide how to use
the properties to change the order or grouping of the
fractions so that the mixed numbers whose fractions have
a sum of 1 are next to each other or added first.
Professional Development Videos
435A
Chapter 7
Interactive Student Edition
Personal Math Trainer
Math on the Spot
1 ENGAGE
Daily Routines
Common Core
Problem of the Day 7.9
Jess is laying down tiles in rows. She will
have more than 4 rows, but less than
10 rows. She wants to lay down the same
number of tiles in each row. She starts with
63 tiles. What numbers of rows could have
the same number of tiles? 7 and 9 rows
Vocabulary
™Interactive Student Edition
™Multimedia eGlossary
with the Interactive Student Edition
Essential Question
How can you add fractions with like denominators
using the properties of addition?
Making Connections
Ask students to tell what they know about addition properties.
• What are some addition properties? Possible answer: Commutative
and Associative Properties of Addition
• How can the Commutative and Associative Properties help you add
25 + 86 + 75 mentally? Possible answer: The Commutative Property
lets me change the order of 86 and 75. The Associative Property lets me
group 25 and 75 to get 100. Then I just have to add 100 + 86 to get 186.
Learning Activity
What is the problem the students are trying to solve? Connect the
story to the problem. Ask the following questions.
Vocabulary Builder
Use this activity to remind students of the
Commutative Property of Addition and the
Associative Property of Addition. Write each
of the following equalities on the board.
Have students name the property that is
shown. Then ask students to explain how
the property makes it easier to find the sum
of the fractions. Possible explanation: the two
fractions that have a sum of 1 are next to each other or
added first.
__ + 1
__ + 3
__ = 5
__ + 3
__ + 1
__ Commutative
1. 5
• Suppose you are trying to find the sum of 3 fractions mentally. If
possible, what sum do you think would be helpful to make with 2
of the fractions? Possible answer: 1
• What is the relationship between the numerator and denominator
of a fraction that is equivalent to 1? They are the same.
Literacy and Mathematics
View the lesson opener with the students. Then, have students
complete the following activity.
• Have students work in small groups to create a table that lists the
Commutative and Associative Properties of Addition, explains each
property, and provides a whole number and a fraction example
for each property.
8
8
8
8
8
8
1
11
5
1
5 Associative
___
___
___
___
___) + ___
2.
+ ( + ) = ( + 11
12
12
12
12
12
12
1 + ___
7 = ___
3 + ___
7 + ___
1 Commutative
3 + ___
3. ___
10
10
10
10
10
10
__ + 7
__) + 2
__ = 8
__ + (7
__ + 2
__) Associative
4. (8
9
9
9
9
9
9
How can you add
fractions with like
denominators using the
proper ties of addition?
Lesson 7.9
435B
LESSON
7.9
2 EXPLORE
4.NF.B.3c Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Add and subtract mixed numbers with like
DO
NOT EDIT--Changes
must beeach
made
through
“Filewith
info”an equivalent fraction, and/or by using properties of operations
denominators,
e.g., by replacing
mixed
number
CorrectionKey=B
and the relationship between addition and subtraction.
Connect
Essential Question How can you add fractions with like denominators
using the properties of addition?
connect The Associative and Commutative Properties of Addition
can help you group and order addends to find sums mentally. You can
use mental math to combine fractions that have a sum of 1.
ELL Strategy:
Develop Meanings
•
The Commutative Property of Addition states that when
the order of two addends is changed, the sum is the
same. For example, 4 + 5 = 5 + 4.
•
The Associative Property of Addition states that when the
grouping of addends is changed, the sum is the same. For
example, (5 + 8) + 4 = 5 + (8 + 4).
The terms Commutative Property of Addition
and Associative Property of Addition may be
unfamiliar academic words.
The map shows four lighthouses in the Florida Keys
and their distances apart in miles. The Dry Tortugas
Lighthouse is the farthest west, and the Alligator
Reef Lighthouse is the farthest east.
5 + 43 ___
6 + 34 ___
5
Add. 70 ___
10
10
5
70__
5
34__
6
43__
10
10 ) + _
10
= (_
+_
6
43__
Use the Commutative
Property to order the
addends so that the fractions
with a sum of 1 are together.
Use the Associative Property
to group the addends that
you can add mentally.
Add the grouped numbers,
and then add the other
mixed number.
105 ) + _
10
= (_
6
___
148
10
=_
Write the sum.
So, the distance from the Dry Tortugas Lighthouse to the
Alligator Reef Lighthouse, traveling between the four lighthouses,
6
148___
10 miles.
is _
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Reteach 7.9
Enrich 7.9
3
2
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1
Lesson 7.9
Reteach
Name Use addition properties to help you solve each problem.
1.
6135316
The Associative Property of Addition states that when the
grouping of addends is changed, the sum is the same.
(3 1 6) 1 4 5 3 1 (6 1 4)
7 1 65
3 1 4_
_.
Use the properties and mental math to add 10 _
8
8
8
_ 1 47
_ 1 65
_
10 3
8
8
8
Step 2 Use the Commutative Property to order the
addends so that the fractions
3 1 6_
5 1 47
_
_ 1 47
_ 1 65
_ 5 10 _
with a sum of 1 are together.
10 3
8
8
8
8
8
8
3 1 6_
7
5 ​1 4 _
Step 3 Use the Associative Property to group
5 10 __
8
8
8
the addends that you can add mentally.
(
3.
)
_
5 (17) 1 4 7
8
Step 5 Write the sum.
_
5 21 7
8
Robyn cut a length of ribbon into
four pieces to wrap four gifts. The
7
lengths she cut were 16 __
12 inches,
3
9
2
__
__
10 __
12 inches, 4 12 inches, and 10 12
inches. If she used the whole ribbon,
how long was her ribbon?
Ben’s family likes bananas. On
Monday, they ate 1 3_4 pounds of
bananas. On Tuesday, they ate 2 2_4
pounds. On Wednesday, they ate
2 1_4 pounds. On Thursday, they
ate 1 2_4 pounds. How many pounds of
bananas did Ben’s family eat during
the four days?
(
1
5
)
2
5
(
4
5
(
)
11
12
5
12
7
12
​ ​​​1​3​​___​​​1​1​​___
​ ​​​
4. ​ 2​​___
11
7 __
12
Chapter Resources
© Houghton Mifflin Harcourt Publishing Company
4_MNLEAN343122_C07R09.indd 21
)
4
10
7
10
3
10
​ ​​​​1​6​​___
2. ​ 5​​___
​ ​​​1​1​​___
​ ​​​
2
9_
5
4
13 __
10
7
8
(
3
8
)
1
8
5. 4​​__​1​​ 6​​__​1​​__​ ​
3
11 _
8
7-21
Emily enjoys riding her bike. During a
five-day biking trip, she rode 8 1_8 miles,
4 3_8 miles, 5 4_8 miles, 2 7_8 miles, and 6 _18
miles. How many miles in all did she
ride during the trip?
4.
Ms. Cleary runs a catering business.
She is buying fruit to make a large order
3
for fruit salad. She buys 5 __
10 pounds
4
of apples, 3 __
10 pounds of oranges,
1
3
__
2 __
10 pounds of bananas, 4 10 pounds of
4
__
green grapes, and 5 10 pounds of red
grapes. How many pounds of fruit did
Ms. Cleary buy in all?
27 miles
5 pounds
20__
10
8 pounds
Use the properties and mental math to find the sum.
1. ​ 3​​__​1​1​​__​ ​1​4​​__​
2.
9 inches
41__
12
Step 1 Look for fractions that combine to make 1.
Step 4 Add the grouped numbers and then add
the other mixed number.
Lesson 7.9
Enrich
Mixing Properties
Properties of addition can help you group and order addends so you can
use mental math to find sums.
The Commutative Property of Addition states that when the
order of two addends is changed, the sum is the same.
3
4
)
(
1
4
3. 7​​__​1​​ 5​1​3​​__​ ​
5.
16
2
6
(
1
6
Explain how you used the commutative and associative
properties to help you add the mixed numbers.
Possible answer: I first looked for fractions
that had a sum of 1. I then ordered and
)
4
6
6. 9​​__​1​​ 4​​__​1​7​​__​ ​
Differentiated
Instruction
Name
Algebra • Fractions and Properties of Addition
any two numerators equals the denominator of the
fractions.
435 Chapter 7
10
5
5
6
70__
34__
43__
6 + 34 ___
5 + 43 ___
5 =_
10
10
10
70 ___
+_
+_
10
10
10
10 ​ = 1
5 + 5 = 10 and ​ __
10
need to use the Commutative Property first because  
4
6
__
​ __
10  ​ + ​ 10  ​ make a sum of 1, which is easy to add mentally.
34 150
Use the properties to order and group.
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (tr) ©Danita Delimont/Alamy
MATHEMATICAL PRACTICES
MP6 Attend to precision.
5  ​ 
__
• How would your first step change if 70​ 10
4
__
was 70​ 10  ​ instead? Possible answer: I would not
43 160
70 150
What is the distance from the Dry Tortugas Lighthouse
to the Alligator Reef Lighthouse, traveling between the
four lighthouses?
Unlock the Problem
MP8 Look for and express regularity in
repeated reasoning.
• When adding three mixed numbers with
like denominators, how do you know if you
can reorder and/or regroup the addends
so that the fractions with a sum of 1 are
together? Possible answer: check if the sum of
Number and Operations—
Fractions—4.NF.B.3c
MATHEMATICAL PRACTICES
MP2, MP7, MP8
Unlock
Unlock the
the Problem
Problem
• Write both terms on the board.
• Have students draw cars driving around.
Tell them the cars are commuting. Have
them write Commutative Property of
Addition under the picture and write an
example of it.
• Then have students draw people they
associate (socialize) with. Tell them the
people are associating, or are spending
time together in a group. Have them write
Associative Property of Addition under the
picture and write an example of it.
How can you find the distance between
lighthouses in the Florida Keys? Read the
problem to find out.
Encourage students to think about how the
properties can help them add mentally.
• Which fractions in the expression have a
5
5
__
sum of 1? How do you know? ​ __
10  ​ + ​ 10  ​;
Lesson 7.9
Fractions and Properties of Addition
Remind students of the definitions of each
property they will use in this lesson. It may
help to discuss the common meanings of
commute and associate.
ALGEBRA
Name
_
21 1
6
grouped the addends so the fractions with a
sum of 1 were together.
Reteach
Chapter Resources
© Houghton Mifflin Harcourt Publishing Company
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Enrich
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Try This!
Make sure students understand why the
Commutative Property was used first.
• Why is the order of 2 and 3​ _23 ​changed? The
Try This! Use the properties and mental math to solve. Show each
step, and name the property used.
order is changed so that the mixed numbers whose fraction parts add to 1 are next to each other.
1 1_3 + (2 + 3 2_3 )
(
)
_ + 32
_+2
11
Commutative Property of Addition
(
Associative Property of Addition
3
3
_ + 32
_ +2
11
3
3
)
• Why is the Associative Property used to
change the way the numbers are grouped?
The grouping was changed so that we add 1​ _13 ​ and 3​ _23 ​ first to get the sum, 4 + 1.
(1 + 4) + 2
5+2=7
Share
Share and
and Show
Show
Math
Talk
Use Math Talk to focus on
students’ understanding of how
to use the Commutative and Associative
Properties to add 3 mixed numbers.
MATH
BOARD
1. Complete. Name the property used.
(3104 + 5102 ) + 106 = (5102 + 3104 ) + _
= 5 2 + (3 4 + _)
10
10
____
____
____
____
____
____
____
6
__
10
6
__
10
2 +
= 5 ____
4
10 _
Commutative Property of Addition
_____
Associative Property of Addition
_____
Math
Talk
2 or 91
_
9__
=_
5
10
Possible description: use the Commutative Property to order
the mixed numbers so that the fractions that have a sum of
1 are together and then add 2 5_8 . (1 1_3 + 1 2_3 ) + 2 5_8 = 3 + 2 5_8 = 5 5_8
3 EXPLAIN
MATHEMATICAL PRACTICES 2
Reason Abstractly
Describe how you could
use the properties to find
the sum 1 1_3 + 2 5_8 +1 2_3 .
Share and Show
Use the properties and mental math to find the sum.
(278 + 382) + 118
__
__
3.
(
)
__ + 1 + 3
__
12
5
5 3
4.
__
15 5
__ or 71
__
72
5.
6
6
6
4
8
6
3
1 + 11
__) + 2 __
(1__
4
4
4
__
51
4
6.
5
2) + 3 __
4 + 1 __
(12 __
9
9
9
2
17 __
9
7.
9)
8 + ____
3 + (1____
____
12 12
12
2
8 or 2__
2 ___
3
12
436
4_MNLESE342255_C07L09.indd 436
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Advanced Learners
Logical
Individual
•For the following sums, have students work
backward to write at least two addends
for each sum. They should use at least two
properties when finding the addends.
1​ 
1. 7​__
5​ 
2. 8​__
3
8
__​ 
3. 15
4. 4​2
5
Possible answer for Exercise 1:
1​ =
1​ 
7​__
  6 + 1​__
3
3
1​ 
= 2 + 3 + 1 + 1​__
3
2
1
__ ​ = 2 + 3 + __
​ ​ +
  __
​ ​ +
  1​1
3
3
2
1
__
__
= 2 + ​3​ +
  3 + ​ ​ +
 
3
2
1
__
__
1
= 2​3​ +
  3 ​ ​ +
  1​__​ 
3
3
3
__​ 
1​1
BOARD
The first problem connects to the learning
model.
Use the checked exercises for Quick Check.
__ + (5 5
__ + 4 3
__)
53
© Houghton Mifflin Harcourt Publishing Company
__
© Houghton Mifflin Harcourt Publishing Company
2.
MATH
Quick Check
Quick Check
If
If
Then
3
2
31
2
1
Rt I
Rt I
a student misses the checked
exercises
Differentiate Instruction with
• Reteach 7.9
• Personal Math Trainer 4.NF.B.3c
• RtI Tier 1 Activity (online)
COMMON ERRORS
Error Students may not recognize pairs of
COMMON
fractions
that have a sumERRORS
of 1.
Example In the expression
2​ _95 ​∙ (1​ _91  ​∙ 3​ 9_4 ​), the ease of adding ​ _95 ​
and ​ _94 ​is not recognized.
Springboard to Learning Use examples
to demonstrate that when the sum of the
numerators of two fractions with like denominators is the same as the denominators, the sum of the fractions is 1.
3
Lesson 7.9 436
Name
On
On Your
Your Own
Own
On Your Own
Use the properties and mental math to find the sum.
If students complete the checked exercises
correctly, they may continue with the
remaining exercises. Suggest to students that
they circle the fraction pairs in Exercises 8–10
that have a sum of 1.
8.
(451_3 + 61_3) + 382_3
(
9. _1 + 103 1_ + 12
2
2
116
1
90 _
3
4 ELABORATE
11.
DEEPER
Pablo is training for a marathon.
He ran 5 4_8 miles on Friday, 6 5_8 miles on
Saturday, and 7 4_8 miles on Sunday. How
many miles did he run on all three days?
Problem Solving • Applications
)
12.
(
)
5 + 10 + 11__
5
10. 3 __
10
10
25
DEEPER
At lunchtime, Dale’s Diner served
a total of 2 2_6 pots of vegetable soup, 3 5_6 pots
of chicken soup, and 4 3_6 pots of tomato soup.
How many pots of soup were served in all?
10 2_3 pots
19 5_8 miles
MATHEMATICAL PRACTICES
OqnakdlRnkuhmf¤@ookhb`shnmr
OqnakdlRnkuhmf¤@ookhb`shnmr
SMARTER
Use the expressions in the box for 13–14.
Exercise 14 is a multistep problem that requires
students to find the value of four expressions
and then compare those values. Have
volunteers describe how they can find the
value of expression C, which has fractions with
different denominators.
13. Which property of addition would you use to
8
Associative
SMARTER
14.
Which two expressions have the
(
Math on the Spot videos are in the Interactive
Student Edition and at www.thinkcentral.com.
© Houghton Mifflin Harcourt Publishing Company
Use this video to help students model and
solve this type of Think Smarter problem.
SMARTER
D 1_ + 4_ + 2_
3
3 2_5 + (5 4_5 + 2 1_5 ) = 3 2_5 + (2 _51 + 5 4_5 )
(1 _18
+ 3 _56 ) + 2 2_6
+
_5 ) + 3 3_
8
8
3
3
Match the equation with the property used.
6
6
3
6
6
3
__
__
__
__
__
__
12 + ( 12 + 12 ) = ( 1 2 + 12 ) + 12
(4 _16
)
C _37 + _12 + 4_7
same value?
15.
)
8
B _1 + 2
2
A and C
Math on the Spot
Video Tutor
(
A 1_ + _78 + 4_
regroup the addends in Expression A?
= (3 _56
= 1 _18
+ 4 _1 ) + 2 2_
+ ( 8_5
6
+ 3 _38 )
6
•
•
•
•
•
•
Commutative Property
Associative Property
Chapter 7 • Lesson 9
SMARTER
For Exercise 15, students must understand
the difference in the application of the
Commutative Property and the Associative
Property. If students classify all four equations
incorrectly, they may have switched the
definitions of the two properties. If students
classify some of the equations correctly and
others incorrectly, they may not understand
the meaning of the properties themselves.
437 Chapter 7
437
MATHEMATICAL PRACTICES
ANALYZEt-00,'034536$563&t13&$*4*0/
Pose a Problem
DEEPER
Costumes are being made for the
high school musical. The table at the right
shows the amount of fabric needed for the
costumes of the male and female leads. Alice
uses the expression 7 3_8 + 1 5_8 + 2 4_8 to find the total
amount of fabric needed for the costume of the
female lead.
16.
Pose a Problem
Costume Fabric (in Yards)
Female Lead
Costume
Male Lead
Costume
Silk
7 3_8
1 2_8
Felt
1 5_8
2 3_8
Cotton
2 4_8
5 6_8
Material
To find the value of the expression using mental
math, Alice used the properties of addition.
Have students read Exercise 16 and describe
the steps Alice followed to solve the
problem. Ask a volunteer to record each step
on the board.
DEEPER
__ + 15
__ + 24
__ = 73
__ + 15
__ + 24
__
73
8
8
8
8
8
8
(
)
Challenge your advanced learners to write
addition problems with three addends that
are mixed numbers, such that the fraction
parts of two of the three mixed numbers
have a sum of 1. Their problems should be
able to be solved by using the Commutative
and Associative Properties. Invite volunteers
to share their work with the class.
MP7 Look for and make use of structure.
• When adding three mixed numbers, how
does grouping addends whose fractions
have a sum of 1, if possible, make it easier
to add the mixed numbers mentally?
Alice added 7 + 1 and was able to quickly add
3_ and 5_ to the sum of 8 to get 9. She added 24
_
8
8
8
to 9, so her answer was 114_.
8
So, the amount of fabric needed for the costume of the female lead
actor is 114_ yards.
8
Write a new problem using the information for the costume for
the male lead actor.
Solve your problem. Check your solution.
Pose a Problem
Possible problem: Alice used the
expression
1 _28
+
2 _38
+
5 _68
to find the
total amount of fabric needed for the
costume of the male lead. What is the
total amount of fabric needed for the
Possible solution: Alice rewrote the
expression as (1 2_8 + 5 6_8 ) + 2 3_8 and
simplified it by adding the wholenumber parts and the fraction parts in
the parentheses. Then she added the
mixed number: (1 + 5 + 1) + 2 3_8 = 9 3_8 .
So, the male lead’s costume needed
9 3_8 yards of fabric.
Possible answer: only one fraction is left in the
addends, so it can just be written in the sum. Three
whole numbers are left to add.
•
MATHEMATICAL
7 Identify Relationships Explain how using the properties of
PRACTICE
addition makes both problems easier to solve.
Possible explanation: the properties make the problems easier to solve because you can
rearrange the mixed numbers so that their fraction parts add to 1.
© Houghton Mifflin Harcourt Publishing Company
costume?
438
5 EVALUATE
Formative
Assessment
Essential Question
Using the Language Objective
DIFFERENTIATED INSTRUCTION
D
INDEPENDENT ACTIVITIES
Properties of Addition to change the order and grouping
of the addends so the mixed numbers whose fractions
have a sum of 1 are next to each other or are added first.
Differentiated Centers Kit
Activities
Fraction
Bingo!
Literature
Sleeping Half the Day
Away
Reflect Have students present to a partner a
step-by-step demonstration to answer the
Essential Question.
How can you add fractions with like
denominators using the properties of
addition? I can use the Commutative and Associative
Games
Fraction
Concentration
Math Journal
WRITE
Math
Describe how the Commutative and
Associative Properties of Addition can make
adding mixed numbers easier.
(BNFT
Students complete
purple Activity
Card 6 by creating
pictorial models
of fractions and
finding equivalent
fractions.
Students read
about what
fraction of the day
different kinds of
animals sleep.
Students practice
adding and
subtracting
fractions and
mixed numbers to
reveal a hidden
picture.
Lesson 7.9
438
Practice and Homework
Lesson 7.9
Name
Fractions and Properties of Addition
COMMON CORE STANDARD—4.NF.B.3c
Build fractions from unit fractions by applying
and extending previous understandings of
operations on whole numbers.
Use the properties and mental math to find the sum.
Practice and Homework
2 1 1 1__
__ 1 2 __
1. 5 1
3
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.
(
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Problem
Problem Solving
Solving
7. Nate’s classroom has three tables of different
lengths. One has a length of 4 1_2 feet, another
has a length of 4 feet, and a third has a length
of 2 1_2 feet. What is the length of all three
tables when pushed end to end?
8. Mr. Warren uses 2 1_4 bags of mulch for his
garden and another 4 1_4 bags for his front
yard. He also uses 3_4 bag around a fountain.
How many total bags of mulch does
Mr. Warren use?
© Houghton Mifflin Harcourt Publishing Company
11 feet
9.
_ bags
71
4
Math Describe how the Commutative and Associative
WRITE
Properties of Addition can make adding mixed numbers easier.
Check students’ work.
Chapter 7
439 Chapter 7
439
Lesson Check (4.NF.B.3c)
1. A carpenter cut a board into three pieces.
One piece was 2 5_6 feet long. The second
piece was 3 1_6 feet long. The third piece was
1 5_6 feet long. How long was the board?
5 feet
7_
6
2. Harry works at an apple orchard. He
picked 45 7_8 pounds of apples on Monday.
He picked 42 3_8 pounds of apples on
Wednesday. He picked 54 1_8 pounds of
apples on Friday. How many pounds of
apples did Harry pick those three days?
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.
_ pounds
1423
8
Spiral Review (4.OA.B.4, 4.NBT.B.5, 4.NBT.B.6, 4.NF.B.3c)
3. There were 6 oranges in the refrigerator.
Joey and his friends ate 3 2_3 oranges.
How many oranges were left?
4. Darlene was asked to identify which of the
following numbers is prime:
2, 12, 21, 39
Which number should she choose?
5. A teacher has 100 chairs to arrange for an
2
6. Nic bought 28 folding chairs for $16 each.
assembly into equal rows. Write one way
the chairs could be arranged. Include the
number of rows and the number of chairs in
each row.
How much money did Nic spend on chairs?
Possible answer: 10 rows of 10 chairs
$448
© Houghton Mifflin Harcourt Publishing Company
1
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FOR MORE PRACTICE
GO TO THE
440
Personal Math Trainer
Lesson 7.9
440