Chapter 5 - Macmillan/McGraw-Hill

Transcription

CHAPTE R
5
Add and Subtract Decimals
Planner
Skills Trace
The
BIG Idea
Vertical Alignment
Students begin by estimating decimal sums and differences through the use of
rounding and compatible numbers. Students develop an understanding of and
fluency with adding and subtracting decimals through models, place value, and
properties. Students check the reasonableness of their results, including
real-world problems.
Targeted Standards
GLE 0506.1.2 Apply and adapt a variety of appropriate strategies to problem
solving, including estimation, and reasonableness of the solution.
GLE 0506.2.5 Develop fluency in solving multi-step problems using whole
numbers, fractions, mixed numbers, and decimals.
Previous Grade
In the previous grade, students learned to:
• Use decimals to name numbers between whole numbers.
• Estimate decimal amounts in real-world problems.
This Grade
During this chapter, students learn to:
• Represent addition and subtraction of decimals by using
models, place value, and properties.
• Add and subtract decimals and verify the reasonableness
of results, including problem situations.
• Solve non-routine problems using the work backward
strategy.
• Estimate decimal sums and differences by using various
techniques.
After this chapter, students learn to:
• Estimate fraction sums and differences by using various
techniques.
• Solve real-world problems and check for reasonableness
of the results.
Next Grade
Print and Online Professional Development
articles can be found in the Teacher Resource
Handbook. These articles on current issues
will allow you to implement new mathematical
strategies and enhance your classroom
performance.
In the next grade, students learn to:
• Explain and justify procedures for multiplying and
dividing decimals.
• Solve real-world problems involving multiplication and
division of decimals.
• Use reasoning about multiplication and division to solve
ratio and rate problems.
Digital Videos The McGraw-Hill
Professional Development Video
Library provides short videos that support
McGraw-Hill’s Math Connects. For
support for this chapter, the following video
is available.
Problem Solving Strategies
Other videos, program walkthroughs, online courses, and video
workshops are available at mhpdonline.com.
192A Add and Subtract Decimals
Vertical Alignment and Backmapping
McGraw-Hill’s Math Connects program was conceived
and developed with the final results in mind: student success
in Algebra 1 and beyond. The authors developed this brand-new
series by backmapping from Algebra 1 concepts, and vertically
aligning the topics so that they build upon prior skills and
concepts and serve as a foundation for future topics.
Chapter at a Glance
Multi-Part
Lesson
1
Lesson
Pacing
Estimate Sums and
Differences
3 Days
Days
Resources
Materiials
Materials
l and
d Ma
Manipulatives
nipul
i latives
i
markers, take-out pizza menus, base-ten blocks
Get ConnectED
A
Round Decimals
GLE 0506.2.5
B
Estimate Sums and Differences
GLE 0506.1.2
C
Problem-Solving Investigation:
GLE 0506.1.2
Leveled Worksheets
Lesson Animations
Daily Transparencies
Problem of the Day
Self-Check Quiz
Personal Tutor
Estimate or Exact
Multi-Part
Lesson
A
2
3 Days
Add Decimals
Add Decimals Using
Base-Ten Blocks
B
GLE 0506.2.5
Add Decimals Using Models GLE 0506.2.5
Add Decimals
GLE 0506.2.5
D
Addition Properties
GLE 0506.2.5
A
3
Subtract Decimals Using
Base-Ten Blocks
GLE 0506.2.5
GLE 0506.2.5
Models
C
Subtract Decimals
GLE 0506.2.5
D
Problem-Solving Strategy:
GLE 0506.1.2
Work Backward
Leveled Worksheets
Explore Worksheets
Lesson Animations
Problem of the Day
Self-Check Quiz
3 Days
Subtract Decimals
B
Materials and Manipulatives
place-value chart, base-ten blocks, grid paper, colored pencils, empty milk
carton, empty orange juice carton,
carton
carton empty cereal box,
box bunch of bananas,
bananas play
money, index cards
Get ConnectED
C
Multi-Part
Lesson
Virtual Manipulatives
eGames
Hands-On Activity Tools and Resources
Personal Tutor
eGames
Graphic Novel Animation
Materials and Manipulatives
place-value chart, base-ten blocks, grid paper, double-9 dominos
Get ConnectED
Leveled Worksheets
Explore Worksheets
Lesson Animations
Problem of the Day
Self-Check Quiz
Personal Tutor
eGames
Real-World Problem Solving
Readers
Chapter at a Glance
192B
CHAPTE R
5
Vocabulary and Language Connections
Planner
Math Vocabulary
Glossary
The following math vocabulary words are listed in the glossary of the Student Edition.
Get ConnectED
Find interactive definitions in 13 languages in the eGlossary and review
vocabulary eGames at connectED.mcgraw-hill.com.
Associative Property of Addition Property
that states that the way in which numbers
are grouped does not change the sum.
Example: (7 + 2) + 8 = 7 + (2 + 8)
Commutative Property of Addition
Property that states that the order in which
numbers are added does not change the
sum.
Example: 16 + 4 = 4 + 16
compatible numbers Numbers in a problem
that are easy to work with mentally.
Example: 810 and 90 are compatible
numbers because 81 ÷ 9 = 9.
estimate A number close to an exact value.
Example: A mile can be estimated as
1.6 kilometers.
Identity Property of Addition Property
that states that the sum of any number
and 0 equals the number.
Example: 15 + 0 = 15
rounding To find the approximate value of
a number.
Example: 237 rounded to the nearest
hundred is 200.
Activity
Hang three sheets of large paper on the board or
the wall. Label them Commutative Property of
Addition, Associative Property of Addition, and
Identity Property of Addition. Students write a
different number sentence to model each
property on individual index cards. Students trade
sets of cards with another student and then tape
the card that models the property below the
correct property. When all the cards are posted,
allow students to observe the similarities and
differences in the number sentences that their
classmates wrote.
Visual Vocabulary Cards
Use Visual Vocabulary Cards to reinforce the vocabulary in
this chapter in English and Spanish. (The Define/Example/Ask
routine is printed on the back of each card.)
ISBN: 978-0-02-101742-3
MHID: 0-02-101742-5
Copyright © by The McGraw-Hill
Companies, Inc.
All rights reserved.
MM'12_VVC_G5_cov_
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VVC G5
101742-5.indd 1
12/3/09 2:48 PM
192C Add and Subtract Decimals
ELL
Support
Multi-Part
Lesson
1
Estimate Sums and Differences of Decimals
Level
Activity
Modality
Word Recognition
Visual, Social, Kinesthetic
AL
Beginning
OL
Intermediate Recognize and Act It Out
BL
Advanced
Internalize Language
Interpersonal, Linguistic, Auditory
Extend
Cooperative Learning
On and Beyond Level
Multi-Part
Lesson
2
Visual, Kinesthetic, Social
Multi-Part Lesson 2
Phonemics
Auditory, Social, Visual
Pigs Will Be Pigs
Amy Axelrod
OL
Intermediate Scaffold
BL
Advanced
Academic Vocabulary
Interpersonal, Visual, Auditory
Extend
Whole Group Instruction
On and Beyond Level
Interpersonal, Visual, Kinesthetic
Math Man
Teri Daniels
Multi-Part Lesson 3
Spaghetti and Meatballs for All
Marilyn Burns and Gordon Silveria
Subtract Decimals
Level
Activity
Word Recognition
Modality
Auditory, Social, Visual
AL
Beginning
OL
Intermediate Speak and Pass
Testing Language
Advanced
Social, Auditory, Linguistic
Extend
On and Beyond Level
BL
Sold! A Mathematics Adventure
Nathan Zimelman
Modality
Beginning
3
Coyotes All Around
Stuart J. Murphy
Activity
AL
Multi-Part
Lesson
Multi-Part Lesson 1
If You Hopped Like a Frog
David M. Schwartz
Add Decimals
Level
Check with your school library or your local
public library for these titles. ✔ 0506.1.9
Cooperative Learning
Interpersonal, Visual, Linguistic
Real-World Problem
Solving Reader ✔ 0506.1.9
Math and Social Studies: A Growing Nation
Use these leveled books to reinforce
ce
and extend problem-solving skills
and strategies.
K
1
2
3
4
5
*
*
Ma tem
Get ConnectED
Find other English Language Learner strategies.
ELL Resources
• “English Learners and Mathematics:
Best Practices for Effective Instruction”
by Kathryn Heinze (pp. TR32–TR33)
• “Engaging English Language Learners
in Your Classroom” by Gladis Kersaint
(pp. TR34–TR35)
• Multilingual eGlossary
• Visual Vocabulary Cards
y cie nci
as
Ma tem
átic
y est udi as
os soc
iale
Leveled for:
OL On Level
AL Approaching Level
BL Beyond Level
SP Spanish
CVR_B
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5LEV_
SPA_1
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The Professional Development articles listed below can be found in print
and online in the Teacher Resource Handbook.
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• Language Alerts (pp. 198, 204, 218)
• ELL Guide (pp. 8–9, 22–23)
Reading and Language Arts Support
For activities to connect reading and language arts to this
chapter’s math concepts, see Reading and Language Arts
Support in the Grade 5 Math Connects Program Overview.
Leveled Reader Database
Get ConnectED
connectED.mcgraw-hill.com
Search by
• Content Area
• Guided Reading Level
• Lexile Score
• Benchmark Level
192D
CHAPTE R
5
Learning Stations
Planner
group
What Did You Buy?
• Read Math Man by Teri Daniels or a similar book by yourself
or as a group.
• What if your group went on a shopping trip?
• Each person invents one item to buy. Add up how much in
total your group will have to spend at the cash register.
Jared: sneakers $7
4.99
Louise: jeans $64.
99
Valerie: purse $8
2.75
Tom: shirt $24.01
Lisa: hat $16.89
SOCIAL
Materials:
• paper
• pencils
• Math Man by Teri
Daniels
• How would you estimate the amount?
• What is the actual amount?
25
individual
pair
Art Appreciation
VISUAL
Materials:
The Starry Night by Vincent Van Gogh is 73.66 centimeters tall and
92.08 centimeters wide. 100 Soup Cans by Andy Warhol is
208.28 centimeters tall and 132.08 wide.
• Which work of art is closest to a square? Starry Night
• What is the approximate perimeter (the distance around) of 100 Soup
Cans? 680.7 cm
You can see these works of art online. See which one is your favorite, and
then make your own work of art. About how many centimeters tall and wide
is your picture, rounded to the nearest tenth?
• paper
• pencil
26
individual
Music Counts
Key
Use the key to solve these musical puzzles.
+ + + + + +
3.375 + 2.25 = 5.625
+ + +
+
27
+ +
2 + 0.25 + 0.125 = 2.375
0.5 +1 + 0.75 - 0.375 = 1.875
+ +
-
0.75 - 0.125 = 0.625
0.375 + 0.75 + 1 + 0.125 = 2.25
( + + + + + + )-( + + + )
(hint: add inside both parenthesis first, then subtract)
(1 + 1 + 1 + 1 + 1 + 0.25 + 0.375) - (1 + 1 + 1 + 0.125) = 5.625 - 3.125 = 2.5
192E Add and Subtract Decimals
Materials:
=1
• paper
= 0.75
• pencil
= 0.5
= 0.375
= 0.25
= 0.125
LOGICAL
individual
Space Travel from Earth
Lost in Space
Use the table to answer the questions.
• How much longer will it take you to travel to the Sun than to the
Moon? 503.72 s
• Find the difference between the time it takes to travel to the Moon
at light speed and the time it takes to travel to Venus. 149.01 s
• How much longer will it take you to travel to Mars than to the Moon?
238.64 s
• Would it be faster to travel to the Sun or to Mercury and back?
28 How much faster? Sun; 94.68 s
Destination
Light-Speed Time
(seconds)
Moon
LOGICAL
Materials:
• paper
• pencil
1.2
Sun
504.92
Mercury
299.8
Venus
150.21
Mars
239.84
SOCIAL
group
On Your Mark, Get Set, Go!
Materials:
• Write these distances (given in miles) on the sections of a spinner.
12.34 15.8 9.53 10.04 21.6 18.67 7.91 19.2
• blank spinner
• markers
• Your group has entered a 150-mile cross-country bike race.
• Take turns spinning the spinner. Each spin represents a distance
you have ridden.
19.2
12.34
• Add each decimal distance to the previous sum.
7.91
15.8
• The first player to reach or exceed 150 miles wins the race.
18.67
9.53
21.6 10.04
29
pair
Florida Counties
All Around the Area
The table shows the areas of six Florida counties.
County
• Use this information to write 5 estimation word problems.
• Write the answers on a separate sheet of paper to use as a key.
• Trade papers and solve your partner’s word problems. Then,
return the papers and check the answers.
• What key words were used in the problems to indicate that
the answer should be an estimate?
30
LOGICAL
Area
(square miles)
Alachua
874.25
Bay
763.68
Charlotte
693.6
Indian River
503.23
Orange
907.45
Sarasota
571.55
Materials:
• paper
• pencil
192F
CHAPTER
5
Introduce the Chapter
E
Essential Questions
CHAPTE R
5
Add and Subtract
Decimals
connectED.mcgraw-hill.com
• What is an example of how decimals are used in
the real world? Sample answer: gas prices, money,
running times are usually expressed to the nearest
hundredth, etc.
• Describe when you might estimate decimals to find
their sum or difference. Sample answer: I estimate
the costs of items I want to purchase and then add the
estimates to find the total cost. I might subtract the sum
from the amount of money I have to determine if I have
enough.
WRITE MATH
• Have students set up a KWL chart.
• As they look through the chapter, have students record
what they already know in the K (Know) column.
• In the W (Want to Know) column, have students record
the new concepts or ideas they think they will learn in
this chapter.
• Have students refer back to the chart and complete the
L (Learn) column as they work through the chapter.
Dinah Zike’s
Foldables®
BIG Idea
Investigate
How do I add and
subtract decimals
accurately?
Animations
Vocabulary
Math Songs
Multilingual
eGlossary
Learn
Personal Tutor
E
The
Virtual
Manipulatives
Make this Foldable to
help you organize
information about
addition and
subtraction.
Foldables
Practice
Self-Check Practice
eGames
Key Vocabulary
Introduce the key vocabulary in the chapter using the
following routine.
Define: A number close to an exact value; an estimate
indicates about how much.
Example: 12.3 is about 12.
Ask: What are some strategies for estimating a number?
Student Glossary
Graphic Organizer
Notetaking
192
Review Vocabulary
the approximate value
Round redondear To find
of a number.
t hundred is 500.
524 rounded to the neares
Worksheets
Review Vocabulary
Assessment
English
decimal
addend
Go to connectED.mcgraw-hill.com to provide
students with directions to create their own Foldables
graphic organizers for this chapter. Students may also
use their Foldables to study and review for chapter
assessments.
When to Use It Multi-Part Lessons 1, 2, and 3 (Additional
instructions for using the Foldable with these lessons are
found in the Mid-Chapter Check and Chapter Study Guide
and Review.)
Subtrac
Add
t
ate
imalss
Estims and s Decimals Decim
m
e
u
c
S eren
f
Dif
Audio
sum
Español
decimal
sumando
suma
192
0192_0194_C05CO_101808.indd 192
Chapter Project
Food Drive
• Organize students in small groups and have them work together to plan a food drive
for a local food bank.
• One group creates a poster showing what items the food bank needs, another group
estimates the dollar value of each item, and a third group determines the amount of
each item they plan to collect. Students may invite other classes to participate.
• The donations are recorded on the poster.
• At the end of the chapter, students assess whether they reached their goal and
estimate the total dollar value of the items.
• Each student writes a summary of the project and creates a bar graph or pictograph to
display the results.
Refer to Chapter Resource Masters for a rubric to assess students’ progress on this project.
12/7/09 12:05
When Will I Use This?
When Will I Use This?
Filling a Phone
Read the story. You may wish to use the blank Graphic
Novels provided in Hands-On Activity Tools and Resources
to help develop writing and speech skills.
• Have students read the graphic novel in small groups,
each student reading one frame.
• What do you need to do before you can find the
solution? add before subtracting
✔ 0506.1.9 Use age-appropriate books, stories, and videos to
convey ideas of mathematics.
For additional reading and language arts activities,
including support for reading a graphic novel, see Reading
and Language Arts Support in the Grade 5 Math Connects
Program Overview.
Visit connectED.mcgraw-hill.com to
download the animated version of “Filling
a Phone.”
Your Turn!
his
You will solve thi
errr.
problem in the chapte
192_0194_C05CO_101808.indd 193
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In Lesson 2C, students will learn more about Desiree’s cell
phone and solve the problem posed in the graphic novel.
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• Read the Math at Home letter found in the
Chapter Resource Masters with the class
and have each student sign it. A Spanish versionn
is also included. Use the Spanish letter for
Spanish-speaking parents or guardians who
do not read English fluently.
9 3:25:39
3 11/24/0
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193
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• Add and
Grade 5
Decimals
Print er PDF
Available in
For more information about parent involvement,
English • Spanish
read the article, “The Role of Parents and Guardians
in Young Children Learning Mathematics” by
Paul Giganti, Jr. See the Teacher Resource Handbook pp. TR44–TR45.
193
Diagnostic Assessment
1 ASSESS
You have two options for checking Prerequisite Skills for this chapter.
Text Option
“Are You Ready for the Chapter?”
SE
Student Edition
O
Online Option
Are You Ready
You have two options for checking
Prerequisite Skills for this chapter.
for the Chapter?
Text Option
Take the Quick Check below. indicates multi-step problem
Take the Online Readiness Quiz.
Name the place-value position of each underlined digit.
1. 52 tens
2. 138 ones
3. 4.3 tenths
4. 901 hundreds
5. 1.216 hundredths
6. 2,785 thousands
Round each number to the underlined place.
8. 681 680
7. 19 20
9. 735 700
10. 3,705 4,000
11. 106,950 107,000
12. 5,750 5,800
13. 24,921 25,000
14. 692,300 690,000
Add.
15. 38 + 716 754
16. 151 + 218 369
17. 260 + 398 658
18. 235 + 68 303
19. 27 + 48 + 62 137
20. 18 + 98 + 112 228
21. The Pham family and the Weber family
have many pets. How many more
pets does the Pham family have
than the Weber family? 4 pets
Online Option
Pets
Pham
Weber
3 dogs
2 dogs
1 cat
3 gerbils
6 fish
1 turtle
Take the Online Readiness Quiz.
194 Add and Subtract Decimals
0192_0194_C05CO_101808.indd 194
194
12/14/09 1:32 PM
3 REASSESS
2 DIAGNOSE AND PRESCRIBE
RtI (Response to Intervention)
Administer the Diagnostic
Assessment.
Based on the results of the Diagnostic Assessment, use the charts below to address
individual needs before beginning the chapter.
TIER
1
Diagnostic Assessment.
001_015_C05_101837.indd
On Level
OL
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for the Chapter?
Practice
2. 296
Name the place-valu
e position of each underlined
digit.
3. 14.63
ones
1. 63
TE
2. 0.2
tenths
5. 1,389
hundreds
3. 5,107
4. 27
thousands
4. 8.24 hundredths
Add.
Learning Stations
(pp. 192E–192F)
7. 59 + 34 =
93
10. 143 + 17 =
160
25
8. 18 + 7 =
9. 40 + 26 =
66
12. 18 + 6 + 7 =
31
14. 976
980
630
10. 4 + 11
15. 428
400
1,800
16. 3,159
3,160
19. 2,816
2,820
8.
15
9.
17
15
10.
11. 3 + 6 + 2
12. 12 + 4 + 5
18. 1,837
12
7.
9. 3 + 14
3 pairs
17. 625
thousands
hundredths
7. 5 + 7
8. 9 + 6
22
11. 9 + 5 + 8 =
Round each number
to the underlined place.
Copyright © Macmillan/McGraw
Self-Check Quiz
tens
5.
Add.
13. Allie has 3 pairs of
white socks, 5 pairs of
blue socks, and 2 pairs
pink socks. Wade has
of
8 pairs of white socks,
1 pair of brown socks,
and 4 pairs of black socks.
How many more pairs
of socks does
Wade have than Allie?
-Hill, a division of The McGraw-Hill
Get ConnectED
tenths
13. Nadia has 4 board
games, 3 sets of marbles,
and
6 stuffed animals. Robert
has 8 video games, 1
set of
toy cars, and 7 model
airplanes. How many
more toys
does Robert have than
Nadia?
11.
11
12.
21
13.
Copyright © Macmillan/McG
raw-Hill, a division of The
Are You Ready? Practice
ones
hundreds
6.
6. 5.943
tens
6. 95
1.
2.
3.
4.
5. 8,594
choose a resource:
Companies, Inc.
Then
Name the place-value
position of each underlin
ed digit.
1. 83
Are You Ready
students miss three to six in Exercises 1–21,
Date
Diagnostic Assessment
Name __________________
_________
__ Date ________________
If
/Volumes/121/GO00398/GO
00398_Math_Connects_CR
M_NA_G5%0/XXXXXXXXX
XXXX_SE/Appli...
XXXX_S
Name
3 toys
McGraw-Hill Companies,
Round each number
to the underlined place.
14. 39
Grade 5 • Add and Subtract
Decimals
15. 268
5
17. 54,176
40
15.
270
16.
9,000
17.
54,200
Inc.
16. 9,340
14.
8
TIER
2
If
Decimals
Strategic Intervention
approaching grade level
AL
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XXXXXXXXXXX_SE/Appli...
Name __________________
_________
__ Date ________________
Are You Ready
for the Chapter?
students miss seven to thirteen in Exercises 1–21,
Review
Addition
Step 1
Add the ones.
1
Then
choose a resource:
Strategic Intervention Guide
185
+ 347
2
Add. 5 ones + 7 ones
= 12 ones
12 ones = 1 ten and
2 ones
Write a 2 in the ones
place of the sum.
Regroup the tens.
Step 2
Add the tens.
Add. 1 ten + 8 tens +
4 tens = 13 tens
13 tens = 1 hundred
and 3 tens.
Write a 3 in the tens place
of the sum.
Regroup the hundreds.
11
185
+ 347
32
(pp. T12–T13)
Step 3
Add the hundreds.
Add. 1 hundred + 1 hundred
+ 3 hundreds = 5 hundreds
Write a 5 in the hundreds
place of the sum.
11
185
+ 347
532
Are You Ready? Review
Add.
Lesson Animations
1.
2
+9
2.
6
+8
3.
4.
48
+ 45
5.
28
+ 16
6.
95
+ 27
8.
529
+ 192
9.
321
+ 113
11
14
44
405
+ 221
626
122
721
6
8
+4
12
Companies, Inc.
93
7.
Get ConnectED
434
Decimals
TIER
3
If
Then
Intensive Intervention
2 or more years below grade level
students miss fourteen or more in Exercises 1–21,
use Math Triumphs, an intensive math intervention
program from McGraw-Hill
Chapter 7 Decimals
Beyond Level
BL
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XXXXXXXXXXX
X_SE/Appli...
Name __________________
_________
__ Date ________________
If
Are You Ready
for the Chapter?
students miss two or less in Exercises 1–21,
Apply
Solve.
choose a resource:
(p. 192)
Are You Ready? Apply
Get ConnectED
eGames: Number Voyage
Companies, Inc.
Chapter Project
TE
$1
Then
1. Tyrell spent $4 on
a sandwich, $2 on
chips, and $2 on a drink.
Jackson spent
$3 on a vegetable, $3
on a salad, and
$1 on a drink. How much
more did
Tyrell spend than Jackson?
3. Nick’s batting average
during last year’s
baseball season was .318.
What is the
place-value position of
the 1 in .318?
hundredths
5. Su Ling likes the rock-climbi
ng wall at
the gym. Her highest
climb so far is
8.47 meters. What is the
place-value
position of the 8 in 8.47?
ones
2. The Orta family has
5 fish, 2 birds, and
1 dog. The Phillips family
has 1 cat,
1 dog, and 3 fish. How
many more
pets does the Orta family
have than
the Phillips family?
3 pets
4. Alonda jogs 5.92 miles
each day.
What is the place-value
position of
the 9 in 5.92?
tenths
6. Jannelle made sandwiches
for a party.
She made 11 chicken
sandwiches,
8 cheese sandwiches,
and 8 peanut
butter sandwiches. How
many
sandwiches did she make
in all?
27 sandwiches
7. Virgil practiced the
piano 28 minutes
on Wednesday and 25
minutes on
Friday. How many minutes
did he
practice in all?
53 min
Decimals
8. Karen opens a bag
of mixed nuts to
eat for a snack. She counts
4 pecans,
5 almonds, and 14 peanuts.
How
many nuts does Karen
count in all?
23 nuts
7
194A
Multi-Part
Lesson
1
Planner
PART
A Round Decimals
PART
PART
A
Round Decimals
Title/Objective
B
(pp. 195–197)
(pp. 198–201)
B
C
Problem-Solving Investigation :
Estimate or Exact
Standards
Round decimals.
Estimate sums and differences by
rounding.
GLE 0506.2.5
GLE 0506.1.2
markers
take-out pizza menus
Vocabulary
E
Essential Question
How is estimating with rounding different from
estimating with compatible numbers? Sample
answer: Rounding implies that you “round up”
or “round down” based on place value, such
as to the nearest ten or the nearest hundred.
When estimating with compatible numbers,
you round to find numbers that are easy to
work with mentally. For example, 734 ÷ 94
might be estimated as 730 ÷ 90 based on
rounding to the tens place. However, if you
use compatible numbers you would estimate
734 ÷ 94 to be 720 ÷ 90.
Materials/
Manipulatives
base-ten blocks
Resources
Get ConnecttED
✔ 0506.1.9
Focus on Math Background
Get ConnecttED
Leveled Worksheets
Leveled Worksheets
Lesson Animations
Lesson Animations
Problem of the Day
Problem of the Day
Self-Check Quiz
Self-Check Quiz
Personal Tutor
Personal Tutor
VVirtual Manipulatives
Remind students that, unlike using
compatible numbers, rounding uses specific
rules. When instructed to use rounding to
estimate numbers, all students will arrive at
the same estimate. When compatible
numbers are used, or when the estimation
strategy is left to student choice, the final
estimate will vary depending on the strategy
and numbers used.
eGames: Robo Works
Blended Approach
IWB
All digital assets are Interactive
Whiteboard ready.
195a Add and Subtract Decimals
Suggested Pacing
Multi-Part Lessons
1
(11 Days)
2
PART
A
B
C
Days
1
1
1
A
B
1
3
C
D
1
1
A
B
1
Assess
C
D
SGR
PCT
1
1
1
1
PART
Notes
C
Problem-Solving Investigation:
Estimate or Exact
Title/Objective
(pp. 202–203)
Determine whether a problem needs an
estimate or an exact answer.
Standards
GLE 0506.1.2
Vocabulary
Materials/
Manipulatives
Get ConnecttED
Leveled Worksheets
Resources
✔ 0506.1.9
Lesson Animations
Problem of the Day
Personal Tutor
Blended Approach
195b
Differentiated Instruction
Approaching Level
On Level
AL
Option 1
Use with 1B
OL
Option 1
Use with 1A
Hands-On Activity
Materials: 11 × 17 paper
Hands-On Activity
Materials: number cubes
• Arrange two sets of five chairs in a row across the front of the
room. Tape a sheet of 11 × 17 paper showing a decimal point
on the middle chair of each set so that it is visible to the class.
• In small groups or pairs, students
take turns rolling a number cube.
• Give each student a sheet of 11 × 17 paper, and instruct
them to write any digit, 1 through 9, on the sheet of paper
large enough so that everyone can see it from the front of
the classroom.
• Call eight students with their number cards to the front of the
room, and allow them to sit in any chair. Students should hold
their number cards so that the remaining students can see
the digits.
• Guide the class to round the decimal number to the nearest
whole number and find the estimated sum or difference.
• After each roll, each student uses a
pen to secretly record the digit in
the tens, ones, tenths, or hundredths
place on his or her paper.
5.
• After a number is written in a place
value, it may not be moved. After
four rolls, the decimal number is complete.
• The teacher calls out a place value, and each student
rounds the secret number to that place.
• The student with the highest estimate earns one point.
• Repeat the activity with different students.
Option 2
Use with 1B
Materials: assorted grocery store sales fliers
• Provide each small group of students a sales flier.
• Each group must buy at least five different items and spend as
close to $20 as possible, without going over. Direct each
group to list the items they will purchase, the estimated cost
of each item, and how many of each item they will buy.
Option 2
Use with 1B
• Write two decimal numbers on the board. Point to a digit, and
ask students to identify the place value.
• Have students add the estimates to make sure that they have
not exceeded the $20 limit.
• Have students add the exact amount to see whether it is
actually less than $20.
• Have students round both numbers to that place value. Then
have students find the sum or difference of the estimates.
• Compare the exact sum or difference with the estimated
answer.
Other Options
TE
Learning Station Card 30
Get ConnectED
Other Options
TE
Get ConnectED
195c
Personal Tutor, Lesson Animations, Virtual
Manipulatives, eGames: Robo Works
Manipulatives, eGames: Robo Works
Beyond Level
English Language Learners
BL
Option 1
Use with 1A
Hands-On Activity
Materials: Internet
• Have students locate real-world information on the Internet
that uses estimated decimal numbers and exact decimal
numbers.
• Allow students to share their findings with the class.
• Encourage students to hypothesize why estimates or exact
values were used in the various situations.
Option 2
Use with 1C
• Sequentially number a set
of index cards to equal twice
the number of students in
your class.
• Give each student two cards.
Have students write a decimal
story problem that uses
estimation on one card and
another problem that uses an
exact answer on the other
card. Have students write the
answers on the back of the
correct card.
• Students should tape their problems at various locations
around the room. Allow students to circulate around the
room, solving the various problems.
• When everyone has finished, direct students to retrieve their
cards. Have students read the answers to their problems
aloud while each student checks his or her own work.
Other Options
TE
Learning Station Cards 26, 30
Get ConnectED
ELL
This strategy helps English Learners use the language required to
estimate sums and differences of decimals.
Find Core Vocabulary and Common Use Verbs in the online
EL strategies to help students grasp the math skills; use
Language Alerts at point of use in the Teacher Edition.
Beginning
Word Recognition Understand the mathematical meaning of
the word round.
AL
• Draw a number line
from 10 to 20 inside an
open foil or plastic wrap box
lid. Place box on a fulcrum
m at 15. Put
a marble on 14. Say, “round down” as the marble rolls to 10.
Repeat for round up, starting on 18. Repeat.
• Pairs create models (fold paper trough to stabilize the marble
and place a bead at 15 as a fulcrum). Prompt and restate
vocalization of terms as pairs experiment.
Intermediate
Recognize and Act It Out Use kinesthetic cues to reinforce the
mathematical meaning of the word round.
OL
• Draw a number line from 0–20 on the board. Draw circles
around 0–4, 5–10, 11–14, and 15–20.
• Give EL sticky notes with numbers 1–20. Have students round
their numbers and place their notes under the rounded
figures on the number line. Have students describe answers
by using this sentence frame: “My number rounds to __ .”
Repeat for all students as time permits.
Advanced
Internalize Language Distinguish between correct and
incorrect estimates.
BL
• Provide several problems and solutions to bilingual pairs.
• Have pairs determine whether the solution is correct, and
then present and explain their reasoning.
Lesson Animations, eGames: Robo Works
Extend
In bilingual pairs, have each English speaker write a five-digit
number and circle one digit. Have each student round his or her
partner’s number to the circled digit. English speakers then
describe the rounding process used by their partners. Repeat
with students using their native language. Allow peers to tutor
language.
195d
Research
To become good problem solvers, it
is important for students to acquire a
“mathematical point of view.” This can
be achieved by creating a community of
mathematical practice in the classroom,
characterized by collaboration and
discussion. Discussing solutions to routine
problems can provide students with
“learnable and usable” problem-solving
strategies. Discussions about problem
solving should exhibit several
characteristics:
• Explicit explanation of processes;
• Student involvement in discussions
about processes;
• Balanced focus on both qualitative
understanding and knowledge of specific
procedures; and
• Guided practice.
Adapted from Research Base of Effective
Mathematics Instruction: McGraw-Hill’s
Math Connects Kindergarten through Algebra
Series, p. 7
Get ConnectED Find more information
on Formative and Summative Research on
our programs.
The I
of In mpor tan
str uc
c
Estim
tion e
in
ation
Calcula
to
utilized rs and compu
te
in class
room in rs are increas
these t
ing
ec
str
explora hnological too uction. Althou ly
tion of
ls allow
gh
inc
algorith
fo
ms, stu reasingly com r expanded
dents m
plex
the me
ay
an
workin ing of the num not always gr
g with.
asp
bers th
Pr
e
studen
ts with actice in estim y are
a to
ation p
answer
rovides
is reaso ol to evaluat
e
n
ability t
o evalu able or not. W whether an
ate the
it
may ha
solution hout the
ve
s, stude
solution greater diffic
nts
ult
e
reasona xpectations a y expressing t
nd judg
heir
b
in
through leness of solu
tions ar g the
techno
riv
logical
assistan ed at
ce.
Notes
Multi-Part
Lesson
1
PART
Multi-Part
Lesson
A
Main Idea
I will round decimals.
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, and decimals.
B
C
D
1
A
PART
E
PART
Round Decimals
A
Remember that numbers that have digits in the tenths place,
hundredths place, and beyond are called decimals. When you
round a decimal, you find its approximate value.
B
C
Round Decimals
Objective
Round decimals.
Resources
L
LOBSTER
A new species of
lobster
that measures 5.9 inches
l
long was discovered in the
South Pacific Ocean. Round
the length of the lobster to
the nearest whole number.
Materials: markers
Leveled Worksheets
Get ConnectED
GLE 0506.2.5 Develop fluency in solving multi-step
problems using whole numbers, fractions, mixed numbers,
and decimals.
One Way:
1 INTRODUCE
Use a Number Line
5.9
5
5.5
Activity Choice 1: Hands-On
6
5.9 is between 5 and 6. It is closer to 6. So, round 5.9 to 6.
Another Way:
Use Rounding Rules
Step 1 Underline the digit in the ones place, 5
Step 2
5.9
Look at the digit to the right of 5. It is 9.
Step 3 If this digit is 5 or greater, round to
the next whole number.
5.9
5.9
6
To the nearest whole number, 5.9 rounds to 6.
Lesson 1A Estimate Sums and Differences
195_0197_C05L01_103031.indd 195
195
• Divide the class into 2 teams. Write the digits 0–9 on
sheets of notebook paper, using markers. Hand out one
digit to each student. If there are more than 10 students
per team, give them extra zeros.
• Have each team send five students from the other team
to the front of the room. Ask each team to make the
largest number possible with their digits.
• Check that each team made the largest number
possible. Send all students back, and repeat, this time
asking students to make the smallest number possible.
• Challenge teams to round their numbers to place
values that you name. For example, if a team creates
the number 40,788, you may ask them to round it to
the nearest ten, hundred, and thousand. 40,790;
40,800; 41,000
2/26/10 10:39 AM
Activity Choice 2: Rhyme
• Have students work in teams of three or four.
• Challenge teams to write a rhyme, jingle, or rap
explaining the rules for rounding.
• Allow teams to teach their rhyme, jingle, or rap
to the class.
Building Math Vocabulary
Have students write a sentence in their Math Journals that uses
the vocabulary word, round, in its everyday meaning. For
example, “the ball is round.” Then have them write a sentence
that uses round in its mathematical meaning. For example,
“round your answer to the nearest tens.” Students should
illustrate their sentences.
195
2 TEACH
Round Decimals
Round 46.73 to the nearest tenth. Is it closer to 46.7
or 46.8?
Scaffolding Questions
Explain that students may find it helpful to underline the
place value to which they are rounding. Write 12,549 and
9.57 on the board.
• Round 12,549 to the nearest thousand. 13,000
Step 1
Underline the digit in the tenths place, 7.
46.73
Step 2
Look at 3, the digit to the right of 7.
46.73
Step 3
If the digit is 4 or less, do not change 46.73 → 46.7
the underlined digit. Drop the digit
after the underlined digit.
• Round 9.57 to the nearest whole number. 10
You can use a number
line to check if the
answer is reasonable.
So, 46.73 rounds to 46.7. On the number line, 46.73 is closer
to 46.7 than to 46.8. So, the answer is reasonable.
46.73
The largest spider in the world is the goliath
birdeater. If a goliath birdeater is 9.4 inches
long, what is its length to the nearest whole
number? 9 inches
46.7
Round 910.36 to the nearest tenth. Is it closer
to 910.3 or 910.4? 910.4; On the number line,
910.36 is closer to 910.4.
46.75
46.8
Round each decimal to the underlined place.
place See Examples 1 and 2
IWB INTERACTIVE WHITEBOARD READY
1. 8.74 9
2. 4.23 4.2
3. 5.476 5.48
4. 983.625 983.63
Round each decimal to the place indicated. See Examples 1 and 2
As a class, have students complete the Check What You
Know Exercises as you observe their work.
E
TALK MATH Use the Talk Math Exercise to assess
student comprehension before assigning the practice
exercises.
AL
5. 28.6; ones 29
6. 4.35; tenths 4.4
7. 110.079; hundredths 110.08
8. 67.142; ones 67
9. What is the length of the 10-dollar bill
to the nearest whole number? 16 cm
15.6 cm
Alternate Teaching Strategy
If
Then
1
AL
10. An ice sheet that covers most of
Antarctica is about 1.34 miles thick.
To the nearest tenth of a mile, how
thick is the ice? 1.3 mi
E TALK MATH Explain how to round 74.685 to the nearest
hundredth. See margin.
students have difficulty rounding
numbers . . .
11.
assign one of these reteach options:
Reteach Worksheet
0195_0197_C05L01_101808.indd 196
!
2 Use a Number Line Draw a number line from
0 to 9 with empty boxes at both ends. Write
12.58 on the board. Write the underlined digit in
the box next to the 0. Add 1 to the underlined
digit and write that number in the empty box
next to the 9. Graph the digit to the right of the
underlined digit on the number line. Round the
underlined digit to the number in the closest
box. Then change all digits to the right of the
underlined digit to zero.
5
0
1
2
3
4
5
6
7
8
9
• To which square is the 8 closer? 6
• What is 12.58 rounded to the nearest
tenth? 12.6
196
COMMON ERROR!
Exercise 5 Crossing over the decimal may be daunting for some
students. Explain that rounding across a decimal is done the same
as rounding to any other place.
6
Additional Answer
11. Sample answer: Underline 8, since it is in the place being rounded. Since the
number to the right of 8 equals 5, add 1 to the 8. Then drop the 5. So, 74.685
rounded to the nearest hundredth is 74.69.
12/7/09 1:00
EXTRA
%
#E
4) C
!# TI
2 AC
0R
P
Begins on page EP2.
Round
R
d each
h decimal
d i l to
t the
th underlined
d li d place.
l
See Examples 1 and 2
12. 1.8 2
13. 6.2 6
14. 7.358 7.36
15. 37.05 37.1
16. 48.32 48
17. 0.39 0.4
18. 249.217 249.22
19. 6.923 6.92
3 PRACTICE
Differentiate practice using these leveled assignments for
the exercises in Practice and Problem Solving.
Level
Round each decimal to the place indicated. See Examples 1 and 2
20. 6.2; ones 6
21. 8.17; tenths 8.2
22. 0.053; hundredths 0.05
23. 19.25; ones 19
24. 36.81; ones 37
25. 9.045; tenths 9.0
26. 2.526; hundredths 2.53
27. 57.009; hundredths 57.01
28. The minimum bicycle mass at the
Tour de France is 6.8 kilograms. What
is the minimum bicycle mass rounded
to the nearest whole number? 7 kg
29. The African bush elephant weighs
between 4.4 tons and 7.7 tons. What
are its least weight and greatest
weight, rounded to the nearest ton?
4 T and 8 T
WV
KY
Georgia is the 24th largest state in the U.S. in total
area. Use the information in the table to solve.
AR
Round each number to the place indicated.
Place
Area (square miles)
Florida
65,754.59
Georgia
59,424.77
Alabama
52,419.02
South Carolina
32,020.20
13–29 odd, 30–34
OL
On Level
12–28 even, 30–34
BL
Beyond Level
12–30 even, 32–34
Have students discuss and
complete the Higher Order Thinking problems. If students
are not sure how to explain their answers, provide them
with base-ten blocks.
Homework Practice Worksheet
Problem-Solving Practice Worksheet
GA
LA
30. What is the area of Florida rounded to the
nearest tenth? 65,754.6 sq mi
31. What is the area of Georgia rounded
to the nearest whole number?
59,425 sq mi
AL
Approaching Level
WRITE MATH Have students complete the Write
Math Exercise in their Math Journals. You may choose to
use this exercise as an optional formative assessment.
SC
MS
AL
E
VA
NC
TN
Assignment
FL
4 ASSESS
Formative Assessment
Write 5,123 and 3.48 on the board.
• Round 5,123 to the nearest thousand. Explain.
5,000; Sample answer: Since the digit 1 is 4 or less, do
not change the 5. Replace all digits after the 5 with
zeros.
32. OPEN ENDED Write two different numbers that when rounded to
the nearest tenth will give you 18.3. Sample answer: 18.29 and 18.31
33. NUMBER SENSE Explain what happens when you round
9,999.999 to any place. The number always rounds to 10,000.
34.
E
• Round 3.48 to the nearest tenth. Explain. 3.5; Sample
answer: Since 8 is 5 or greater, add 1 to the 4 to get 5.
Drop the digit in the hundredths place.
WRITE MATH Describe two real-world situations in which
it makes sense to round numbers. See margin.
195_0197_C05L01_101808.indd 197
197
Are students continuing to struggle
with rounding whole numbers and
decimals?
11/17/09 1:56 PM
Give students the following
number: 13,579.246. Ask them to tell how to round to the
nearest hundred
h d d andd the
h nearest hundredth.
During Small Group Instruction
If Yes
AL
AL
Additional Answer
34. Sample answer: to express large numbers like population, or to express numbers
that have more decimal places than are needed, like average rainfall per year
If No
OL
OL
BL
BL
Strategic Intervention Guide (pp. T12–T13 )
Skills Practice Worksheet
Differentiated Instruction Option 1 (p. 195c)
Differentiated Instruction Option 1 (p. 195d)
Enrich Worksheet
197
Multi-Part
Lesson
1
PART
PART
B
B
A
C
D
E
Estimate Sums
and Differences
Objective
Estimate sums and differences by rounding.
Resources
Materials: take-out pizza menus
Manipulatives: base-ten blocks
Hands-On Activity Tools and Resources (p. 90)
Leveled Worksheets
Get ConnectED
Multi-Part
Lesson
1
PART
A
Main Idea
I will estimate sums
and differences by
rounding.
Get ConnectED
GLE 0506.1.2 Apply
and adapt a variety of
appropriate strategies to
problem solving, including
estimation, and reasonableness
of the solution. SPI 0506.1.2
Estimate fraction and decimal
sums or differences. Also
addresses GLE 0506.2.5,
SPI 0506.2.5.
Checks for Understanding
✔ 0506.2.5 Make reasonable
estimates of fraction and decimal
sums and differences.
GLE 0506.1.2 Apply and adapt a variety of
appropriate strategies to problem solving, including estimation,
and reasonableness of the solution. SPI 0506.1.2 Estimate
fraction and decimal sums or differences. Also addresses
GLE 0506.2.5, SPI 0506.2.5.
B
C
Estimate Sums
and Differences
When you do not need an exact answer or when you want to
check whether an answer is reasonable, you can estimate. One
way to estimate is to use rounding.
Estimate Sums
Estimate 5.26 + 1.93 by rounding.
Round each decimal to the nearest whole number. Then add.
5.26
+ 1.93
−−−−−
5 5.26 is closer to 5 than 6.
+ 2 1.93 is closer to 2 than 1.
−−−
7
So, 5.26 + 1.93 is about 7.
X-GAMES The results of a recent skateboard competition
X
are
a shown. About how many more points did Steamer have
than Dal Santo?
Elissa Steamer
Marisa Dal Santo
Amy Caron
• Provide students with an invented menu from a pizza
parlor or use real take-out menus. Ask students to
estimate the cost of a large pepperoni pizza and a
garden salad. Answers will vary.
87.83
81.50
80.00
Round each decimal to the nearest ten. Then subtract.
• Ask students to estimate the difference in cost between
a large and a small vegetable pizza. Answers will vary.
90 87.83 is closer to 90 than 80.
- 80 81.50 is closer to 80 than 90.
−−−−
10
So, Steamer scored about 10 more points than Dal Santo.
87.83
- 81.50
−−−−−−
• Ask students to choose two items that they would
order for lunch, then estimate the total cost.
Answers will vary.
• Have students write a story that uses both estimates
and exact numbers. For example, students could write
about estimating how much money to save for a
shopping trip and compare the estimate with the actual
amount spent.
E
Estimate Differences
1 INTRODUCE
Activity Choice 2: Story Telling
D
0198_0201_C05L01_103031.indd 198
• Allow students to share their stories with the class.
• Have the listeners identify which numbers are estimates
and which are exact values.
ELL
Activating Prior Knowledge: Real World Context
Students may benefit by using real menus to help
connect the lesson information to their experiences
in the United States. Consider adapting the menu to
one from an ethnicity of your students.
198
Have students imagine that a creature from outer space has just
landed on Earth. Today is the alien’s first day of school. Have
students explain the term estimate to the newcomer. Have
them write their explanation of the vocabulary word in their
Math Journals.
2/26/10 10:38 A
2 TEACH
You can round numbers to any place value when you estimate.
If you round numbers to a lesser place value, you are likely to
get an estimate that is closer to the exact answer.
Write the following problem on the board: 582.3 - 39.18
• If you want to estimate the difference, what
could you do first? Sample answer: Find
compatible numbers.
TEMPERATURE The average January temperature for
T
Knoxville,
Tennessee, is 37.6°F. In Newark, New Jersey,
K
the average is 31.3°F. Estimate the difference in average
temperatures.
You can also use
compatible numbers
to estimate sums and
differences.
23.8 →
7
- 13.−
−−−−
25
- 15
→ −−−
−
One Way
Another Way
Round to the nearest ten.
40
37.6
- 30
31.3
−−−
−−−−
10
Round to the nearest whole
number.
38
37.6
31
31.3
−−−
−−−−
7
10
• What two numbers would be compatible?
580 and 40
• Why is it easier to use 580 and 40? It is easier to
subtract tens.
• Estimate the difference. 580 - 40 = 540
The difference in temperatures is about 10°F or about 7°F. The
actual difference is 6.3°F. So, rounding to the nearest whole
number gave the more accurate estimate.
Estimate 9.23 - 4.15 by rounding. about 5
Gareth’s dog weighs 49.3 pounds. Dieter’s dog
weighs 28.9 pounds. Estimate how many more
pounds Gareth’s dog weighs than Dieter’s
dog. 50 - 30 = 20 pounds
1–10. Sample answers are given.
The average yearly rainfall for Orlando, Florida,
is 50.6 inches. The record for the most rainfall
received in a single year is 68.7 inches. Estimate
the difference between the two rainfalls. about
18 inches or about 20 inches
Estimate each sum or difference.
difference See Examples 1–3
1 3
1.
2.8 3 + 1 = 4
+ 1.3
−−−−
2.
4. 10.4 + 32.8 10 + 33 = 43
7. 32.56 + 6.7
33 + 7 = 40
5.98 6 - 1 = 5
- 1.03
−−−−−
5. 2.65 - 0.766 3 - 1 = 2
8. 25.21 - 12.47
25 - 12 = 13
E
6. 37.58 - 21.25
38 - 21 = 17
9. 475.6 - 58.5
480 - 60 = 420
11. The weights of Marisa’s pets are shown in the table.
About how much more does Marisa’s dog weigh
than her cat? Sample answer: 26 - 11 = 15 lb
12.
3. 10.08 10 + 6 = 16
+5.60
______
TALK MATH Tell when it might be appropriate to
10. 751.2 + 82.3
750 + 80 = 830
Pet Weights
Pet
Weight (pounds)
dog
25.6
cat
11.3
estimate rather than get the exact answer. Give a
real-world example. See margin.
Lesson 1B Estimate Sums and Differences
198_0201_C05L01_103031.indd 199
199
E
exercises.
3/18/10 4:43 PM
Estimating provides a “reasonableness” check to an answer, and this can be used to
help students spot errors in computation. Estimates in this lesson are based on two
methods, rounding and compatible numbers. It should be noted that when the
directions instruct students to which place value to round, their estimates should all be
the same. Alternately, when using compatible numbers to estimate, their answers may
or may not be the same. In this case, students should pick numbers that are close to
the numbers in the problem.
Additional Answer
12. Sample answer: Use estimation when you do not need an exact answer. An
example is calculating the amount of tip to leave. You do not need to know the
exact cent.
199
indicates a multi-step problem
AL
If
students have trouble estimating sums
and differences . . .
Then
1
2
AL
Reteach Worksheet
Personal Tutor Have students use
Personal Tutor to reteach the concept.
IWB
3 Use Base-Ten Blocks Have students work in
pairs or small groups with base-ten blocks to
model addition or subtraction after they have
rounded or found compatible numbers. One
student models the problem using compatible
numbers. The other student models the same
problem using rounding. Encourage students to
compare and discuss the differences between
the two ways to model the same numbers.
EXTRA
%
#E
4) C
!# TI
2 AC
PR
0
Begins on page EP2.
Estimate
E
ti t each
h sum or difference.
diff
See Examples
l 1–3 13–27. Sample answers are given.
13.
$3.85 4 - 2 = $2
- $2.17
−−−−−
14.
9.5 10 - 7 = 3
7.1
−−−−
15.
7.6 8 + 2 = 10
+
1.9
−−−−
16.
$8.58 9 - 3 = $6
- $3.11
−−−−−
17.
7.7 8 - 6 = 2
6.3
−−−−
18.
52.85 53 - 10 = 43
9.09
−−−−−
19. 150.9 + 310.6
150 + 310 = 460
20. 19.8 + 9.93
20 + 10 = 30
21. 24.86 - 12.49
25 - 12 = 13
22. 4.087 - 1.692
4-2=2
23. 3.872 + 12.49
4 + 12 = 16
24. 9.86 - 8.7
10 - 9 = 1
25. $42.01 - $5.92
$42 - $6 = $36
26. 791.3 + 38.6
790 + 40 = 830
27. 321.75 - 16.65
320 - 20 = 300
28. The graphic shows the average speeds of
two airplanes in miles per hour. About
how much faster is the Foxbat than the
Hawkeye? Show your work. Sample
answer: 2,000 - 400 or about 1,600 mph
29. Sophia has $20. She buys a hair band for
$3.99, gum for $1.29, and a brush for $6.75.
Not including tax, estimate how much
change she should receive. Show your work.
Sample answer: 4 + 1 + 7 = 12 and 20 - 12 = 8; about $8
375.52
1,864.29
3 PRACTICE
Level
Assignment
AL
Approaching Level
13–27 odd, 28, 30–37
OL
On Level
14–28 even, 29–37
BL
Beyond Level
14–28 even, 29–37
complete the Higher Order Thinking problems. Encourage
students to make up examples or use models to help them
explore the effects of rounding all addends down.
E
E
Follow-up
• How is estimating with decimals similar to
estimating with whole numbers? Sample answer:
Estimating with both decimals and whole numbers may
involve rounding, and the same rules of rounding apply
to both decimals and whole numbers.
200
30. FIND THE ERROR Kim is estimating 549.16 + 110.48
by rounding to the nearest hundred. Help find and
correct his mistake. Sample answer: Kim rounded 549.16 to
600 instead of 500. 500 + 100 = 600
549.16
+
110.48
−−−−−−−
→
→
600
+
100
−−−−−
700
E WRITE MATH Suppose you round all addends down. Will the
estimate be greater than or less than the actual sum? Explain.
Sample answer: less than; since each rounded addend is less than
the actual addend, the estimate is less than the actual sum.
31.
0198_0201_C05L01_101808.indd 200
!
COMMON ERROR!
Students often are not sure to which place to round. Point out
that rounding to the nearest one will produce a better estimate
than rounding to the nearest ten.
12/7/09 1:03
4 ASSESS
Test Practice
32. The table shows the lengths of four
trails at a horseback riding camp.
Which is the best estimate for the
total length of all the trails? B
Trail
Length
(mi)
A. 8 mi
B. 12 mi
33.
A
B
C
D
2.6
1.8
4.2
3.3
34. Mr. Dixon bought a plasma
television that was on sale for
$1,989.99. The regular price was
$2,499.89. Which is the best
estimate of the amount of money
Mr. Dixon saved by buying the
television on sale? F
C. 14 mi
F. $500
H. $3,000
D. 15 mi
G. $1,000
I. $4,000
SHORT RESPONSE Aluminum
and tin are both metals. The standard
atomic weight for aluminum is 26.98.
The standard atomic weight for tin is
118.71. Estimate the difference
between the standard atomic weights
of these two metals. 92
Write the following on the board:
Morning temperature: 55.4° F
Noon temperature: 73.8° F
Afternoon temperature: 89.5° F
• Estimate the difference between the high
temperature and the low temperature. Explain how
you made your estimate. 30°F; Round 55.4 to 60 and
89.5 to 90, then subtract 90 - 60.
35. Lorena and her cousin are fishing at
the lake. They caught two largemouth bass. One fish weighs
71.27 ounces, and the other fish
weighs 38.86 ounces. Which is the
best estimate of the total weight of
the two fish? B
A. 10 ounces
C. 500 ounces
B. 110 ounces
D. 1,000 ounces
• Estimate the difference between the high and low
temperatures by rounding to the nearest whole
number. Explain how you estimated. 35°F;
55.4 rounds down to the nearest whole number.
89.5 rounds up to the nearest whole number.
90 - 55 = 35
Estimating
Another way to estimate sums and differences is to use truncation.
To truncate a number, you “cut off” the digits after a specific place
value instead of rounding.
✔ 0506.1.3 Explore different
methods of estimation including
rounding and truncating.
• What strategy would provide a more accurate
estimate than rounding to the nearest ten? Sample
answer: Rounding to the nearest whole number (35°F)
is closer to the original number than rounding to the
nearest ten (30°F). The closer the estimate is to
the original number, the more accurate the estimate
will be.
Estimate 789.4432 + 31.7835 by truncating to the tens place.
789.4432
+
33.7835
−−−−−−−
780
+
30
−−−−
810
with estimating sums and differences?
Remove all digits after the tens place
and replace non-decimal digits with zeros.
So, 789.4432 + 31.7835 is about 810.
If Yes
AL
AL
Estimate by truncating to the place value indicated.
36. 42.99943 + 18.33920; ones 60
AL
Differentiated Instruction Option 1
(p. 195c)
(p. 195c)
37. 139.48293 - 29.13003; tens 110
If No
201
OL
OL
BL
198_0201_C05L01_103031.indd 201
Enrich Worksheet
(p. 195c)
2/26/10 10:39 AM
Interactive Whiteboard Outline four 10 × 10 grids on the whiteboard.
Have students take turns coloring in any number of squares. Define what
represents a 1; for example, either an entire 10 × 10 grid can represent 1 or
each small square of a grid can represent 1. Name a place value and have the
class say the rounded number.
Tell students that truncating does not use rounding
based on the value of the digits in a particular
place value.
• Work the Example as a class.
• Assign the exercises.
Have students explain how
rounding whole numbers and decimals
yesterday’s lesson on round
helped them with today’s lesson on estimating sums and
differences.
201
Multi-Part
Lesson
1
PART
PART
C
A
B
C
Multi-Part
Lesson
E
1
PART
A
B
C
Problem-Solving Investigation
Problem-Solving
Investigation
Main Idea I will learn to determine if a problem needs an estimate or an exact answer.
Objective
Determine whether a problem needs an estimate or an
exact answer.
MADISON: My family drove to my
grandparents’ house. We drove 58.6 miles
in the first hour, 67.2 miles in the second
d
hour, and 60.5 miles in the third hour. We
followed the same route to return home.
Resources
Leveled Worksheets
YOUR MISSION: Find about how far Madison’s
family traveled.
Get ConnectED
Understand
and decimals. GLE 0506.1.2 Apply and adapt a variety of
and reasonableness of the solution.
What facts do you know?
• The family drove 58.6 miles, 67.2 miles, and 60.5 miles.
What do you need to find?
• How far Madison’s family traveled altogether.
1 INTRODUCE
Plan
Solve
• Have students work in pairs to write a real-world
problem that can be solved by finding an estimate.
• Have students trade papers to solve and discuss their
solutions.
• As a class, talk about the words, phrases, or other
hints in the problems that indicate that the problem
can be solved by using an estimate rather than an
exact answer.
Check
Understand
Using the questions, review what
students know and need to find.
Plan Have them discuss their strategy.
Solve Guide students to find an estimate to solve
the problem.
• About how far was it to Madison’s grandparents?
Explain. 190 miles; add up the rounded distances
driven each hour.
• What word told you to round? about
• If it is 190 miles to her grandparents, how far is
it back to Madison’s house? 190 miles
Check
Have students look back at the problem to make
sure that the answer fits the facts.
202
Hour One
Hour Two
Hour Three
58.6
67.2
+ 60.5
______
60
70
+
60
_____
190
The one-way trip was about 190 miles. The return trip was another
190 miles. Madison’s family traveled about 190 + 190, or 380 miles.
The trip was a total of 6 hours and they drove about 60 miles
each hour. Find 60 + 60 + 60 + 60 + 60 + 60. Since the sum
is 360, 380 miles is reasonable. GLE 0506.2.5 Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and
decimals. GLE 0506.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including estimation,
2 TEACH
Have students read the problem on the student page.
Guide them through the problem-solving steps.
Since you only need to find about how far they traveled, you can
estimate the number of miles traveled each hour. Add the
estimated miles. Then double that amount for the trip back home.
2
0202_0203_C05PSI_103031.indd 202
!
COMMON ERROR!
Students may forget to include the distance of the trip back
home. Encourage them to draw a map to help them remember.
Additional Answer
11. Sample answer: Using estimation saves time because an exact answer is not
needed. Since your answer is not exact, you might have underestimated or
overestimated, which could be troublesome. For example, underestimating the
cost of car repairs would result in higher repair costs than expected.
2/26/10 10:39 A
indicates multi-step problem
EXTRA
%
#E
4) C
!# TI
2 AC
0R
P
Begins on page EP2.
• Use estimation.
• Use the four-step plan.
For each problem, determine whether you
need an estimate or an exact answer.
Then solve.
5. Students at a high school filled out a
survey. The results showed that out of
640 students, 331 speak more than
one language. How many students
speak only one language?
exact answer; 309 students
students have trouble deciding whether to
estimate or compute an exact answer . . .
Then
1
AL
Reteach Worksheet
2 Use Key Words Help students identify key
words that indicate that an estimate is appropriate.
7. A library wants to buy a new painting
2. Measurement A gardener has
that costs $989.99. So far, the library
35 feet of fencing to enclose the
has collected $311.25 in donations.
garden shown. About how much
About how much more money does
fencing will be left over after the garden
the library need to buy the painting?
is enclosed? estimate; 5 ft
estimate; $700
8. The fisherman with the longest fish
wins a fishing competition. About how
much longer is the first place fish than
the third place fish? estimate; 10 cm
4. Four friends split the cost of two
pizzas. If the total cost of the pizzas
was $27.80, about how much will
each friend have to pay? estimate; $7
If
6. Evita has 9 quarters, 7 dimes, and
5 nickels. Does she have enough
money to buy the box of crayons
shown? exact answer; no
1. A restaurant can make 95 dinners each
night. The restaurant has been sold out
for 7 nights in a row. How many dinners
were sold during this week?
exact answer; 665 dinners
3. A family is renting a cabin for $59.95 a
day for 5 days. About how much will
they pay for the cabin? estimate; $300
AL
Place
Fish Length (cm)
1st
2nd
3rd
68.7
59.8
58.2
WRITE MATH Explain an advantage
and a disadvantage of using estimation
to solve a problem. See margin.
To assess partial mastery of SPI 0506.1.2, see your Tennessee Assessment Book.
202_0203_C05PSI_103031.indd 203
Multi-Part Lesson 1 What are some ways that decimal estimation is used
in real-world situations? Sample answer: Gas prices are calculated to the
thousandths but estimated to the hundredths. Daily weather temperatures are
rounded to the nearest whole number. Distances to and from work or school
are estimated to the nearest mile.
3 PRACTICE
Exercises 1–10 provide opportunities for students to
decide whether a problem requires an estimate or an
exact answer.
10. On Friday, a museum had 185 visitors.
On Saturday there were twice as many
visitors as Friday. On Sunday, 50 fewer
people visited than Saturday. How
many people visited the museum
during these three days?
exact answer; 875 people
E
• Have them list these words on an index card
to use as a study aid.
Using the Exercises
9. Tomás orders a meal that costs $7.89.
Lisa’s meal costs $9.05. About how
much is the combined cost of their
meals? estimate; $17
11.
• What key words tell you to find an estimate?
Sample answers: about, approximately, around
203
2/26/10 10:39 AM
Exercise 10 Students should list the number of visitors for
each day first, then find the total.
4 ASSESS
Write this problem on the board. Have students solve.
Duena’s older brother is in high school. Last week he
spent 2 hours and 20 minutes, 2 hours and 6 minutes,
2 hours and 12 minutes, 1 hour and 50 minutes, and
2 hours and 10 minutes on homework each night.
About how long did he spend on homework last week?
Explain how you found your answer. 10 hours; Sample
answer: Round each day’s hours to 2 hours; 5 × 2 = 10.
with whether a problem needs an
estimate or an exact answer?
If Yes
AL
If No
OL
Enrich Worksheet
BL
BL
Lesson 1C Estimate Sums and Differences
(p. 195d)
203
Multi-Part
Lesson
2
Add Decimals
Planner
PART
A
PART
Add Decimals Using
Base-Ten Blocks
B
Title/Objective
Add Decimals
Using Models
C
Add Decimals
D
Addition Properties
Standards
PART
A
B
Add Decimals Using
Base-Ten Blocks
l
(pp. 204–205)
Models
d l
Add Decimals Using
Explore adding decimals using
base-ten blocks.
Explore using decimal models to add
decimals.
GLE 0506.2.5
GLE 0506.2.5
place-value chart
grid paper, colored pencils
(pp. 206–207)
Vocabulary
E
Essential Questions
How is adding decimals like adding whole
numbers? How is it different? Sample answer:
Adding decimals is like adding whole numbers
because you add using place value. It is
different because the answers must have the
decimal point placed correctly and the answer
represents part of a whole.
Materials/
Manipulatives
base-ten blocks
Resources
✔ 0506.1.9
Get ConnecttE
ED
D
Get ConnecttE
ED
D
Explore Worksheet
Explore Worksheet
Lesson Animations
Lesson Animations
Students practice modeling decimal addition
with base-ten blocks and then on grid paper.
Students then learn to use the standard
addition algorithm to add decimals. Remind
students that the place values of the addends
must be lined up in order to add properly.
Explain that lining up the decimal points is a
quick and easy way to make sure that the
place values of the addends are lined up
correctly.
Blended Approach
Refer to the Blending
Math Connects and
IMPACT Mathematics
guide for detailed
lesson plans.
IWB
Whiteboard ready.
Suggested Pacing
Multi-Part Lessons
1
(11 Days)
2
PART
A
B
C
Days
1
1
1
A
B
1
3
C
D
1
1
A
B
1
Assess
C
D
SGR
PCT
1
1
1
1
Add Decimals
PART
PART
C
Add Decimals
(pp. 208–211)
Notes
D
Addition Properties
(pp. 212–215)
Add decimals through thousandths.
Use Associative, Commutative, and
Identity Properties to add whole
numbers and decimals mentally.
GLE 0506.2.5
GLE 0506.2.5
Title/Objective
Standards
Vocabulary
empty milk carton, empty orange juice
carton, empty cereal box, a bunch of
bananas, play money, grid paper
Get ConnecttED
ED
index cards
Get ConnecttED
ED
Leveled Worksheets
Leveled Worksheets
Lesson Animations
Lesson Animations
Problem of the Day
Problem of the Day
Self-Check Quiz
Self-Check Quiz
Personal Tutor
Personal Tutor
Materials/
Manipulatives
Resources
✔ 0506.1.9
IMPACT Mathematics: D-1
Blended Approach
Game Time
Find the Least Sum (p. 216)
Mid-Chapter
Mid
Ch t Ch
Checkk ((p. 217)
Add Decimals
204b
Approaching Level
On Level
AL
Option 1
Use with 2A
OL
Option 1
Use with 2C
Hands-On Activity
Materials: base-ten blocks
Hands-On Activity
Materials: index cards
• Say a decimal number aloud.
Have students model the number
with base-ten blocks.
• Make sets of three index cards so that there is one card per
student. In each set, there should be two cards that each
display one decimal addend of a number sentence written in
black and one card that displays the sum written in red.
• Have students break the blocks into two decimal addends.
• Have students say the two decimal numbers they have
modeled in an addition sentence, using the original number
as the sum.
• As students become more proficient at breaking a decimal
number into two parts, provide students with parameters such
as having no tenths in one of the numbers.
Option 2
• Provide each student with a decimal number and grid paper.
• Have students use the grid paper to model their numbers.
• Use the numbers that the students have modeled to write
addition problems on the board.
• Have students take turns posting their models below the
appropriate numbers.
• Finally, have each student model the solution to each problem
on grid paper and write the numeric answer.
• Review the correct answers as a class, allowing student
volunteers to post their solution models and numbers.
Other Options
Get ConnectED
• Without talking, students must circulate around the room and
find the other two students that complete the addition
sentence.
• The groups of three silently sit down together.
• When all students have found their partners, have each group
write their number sentence on the board.
Use with 2B
Hands-On Activity
Materials: grid paper
TE
• Distribute the cards.
Manipulatives, eGames: Number Voyage
Option 2
Hands-On Activity
• Prepare a set of 36 index cards by writing 12 numerical
examples of each of the Commutative Property, the
Associative Property, and the Identity Property on individual
index cards.
• Give each pair of students a set of the 36 prepared index
cards. Each card should show an example of the Commutative
Property, the Associative Property, or the Identity Property.
• Students play this game like a
memory game. In this version,
two cards that show examples
of the same property will be
considered a match.
• The student with the most
matches wins.
0 + 15.97 = 15.97 + 0
2.35 + 4.17 = 4.17 + 2.35
19.8 + 17.1 = 17.1 + 19.8
Get ConnectED
(12 + 4) + 27 =
12 + (4 + 27)
Other Options
TE
204c
Use with 2D
Manipulatives, eGames: Number Voyage
Add Decimals
Beyond Level
BL
Option 1
Use with 2C
Hands-On Activity
Materials: 1” squares with digits 0–9, sheets with 3 addition and
subtraction fill-in-the-blank problems
• Give groups of students a set of digit
squares and a sheet of paper with the
three fill-in-the-blank problems.
• Instruct students that they can
use each digit only once per sheet.
1. 1.
2. 4.
3.
6
7
5+
0
7-
5
1
.4
3
= 7.18
9
= 6.3
• This activity works best if problems
are written so that each blank is
a 1” square. Groups can then move
the digits around until all problems are correct.
This strategy helps English Learners learn and use the language
required to add decimals.
Find Core Vocabulary and Common Use Verbs in the
online EL strategies to help students grasp the math skills;
use Language Alerts at point of use in the Teacher Edition.
Beginning
Phonemics Pronounce the /ths/ sound that occurs at the end of
decimal place names.
AL
.38 = 2.69
.25 + 0.0
ELL
4
• Write a five-digit number with two decimal places. Point to the
digit in the hundreds place. Say “hundreds” chorally. Continue
with decimals, emphasizing the /ths/ sound in the decimal
places.
• Have students place their fingers against their mouths to feel
the /ths/ sound. Extend the activity with other numbers.
Option 2
Use with 2D
Hands-On Activity
Materials: play money:
dollar bills, dimes, and pennies
OL Intermediate
Scaffold Distinguish between decimal place names and
whole-number place names.
• In small groups, have
one student gather several
items from around the classroom to set up in a pretend store.
• Write a five-digit number with two decimal places. Have
students chorally identify the place values of each digit.
• The store clerk will price the items, using compatible numbers
such as $4.73, $2.17, $0.49, and $3.81.
• The rest of the students in the group have $10.00 in play
money to spend at the store.
• Student shoppers will add the total cost for the items they
would like to purchase, keeping the total under $10.00.
• The store clerk will add the cost of the items purchased by
each student, take the play money from the shopper, and
provide the correct change.
• Shoppers should check to make sure that the clerk has added
and subtracted correctly and provided them with the correct
change.
• Students may switch rolls and play again with new items or
new prices.
Other Options
TE
Get ConnectED
Lesson Animations, eGames: Number Voyage
• In multilingual groups, one student says a whole or decimal
number. The next student holds up a ths card if the number is
a decimal. The activity continues around the group.
Advanced
Academic Vocabulary Students use the terms tenths and
hundredths in complete sentences.
BL
• Students use a number cube to generate numbers with two
decimal places and write the number on cards.
• Students switch numbers with a partner and use complete
sentences to identify the digits in the tenths and hundredths
places. Pairs present their work to the group, allowing the
group to check and discuss answers.
Extend
Have pairs make a place value
chart using the number 215.49.
Have pairs use their knowledge
of whole-number place values to
determine the place value to the
right of the digit 9 (thousandths).
Repeat for all numbers.
Add Decimals
204d
Multi-Part
Lesson
PART
2
Multi-Part
Lesson
Add Decimals
A
B
C
D
E
2
MP-Title
M
P-TDecimals
itle
Add
A
PART
PART
C
D
Add Decimals Using
Base-Ten Blocks
A
Add Decimals Using
Base-Ten Blocks
B
Main Idea
I will explore adding
decimals using baseten blocks.
Objective
Find 1.3 + 0.5.
F
Materials
Step 1
base-ten blocks
Explore adding decimals using base-ten blocks.
Model 1.3 and 0.5.
Ones
Tenths
Hundredths
Resources
Materials: place-value chart
Workmat 6:
place-value chart
%FDJNBMT
POFT
IVOESFET
Explore Worksheet
UFOT
0OFT
IVOESFEUIT
Hands-On Activity Tools and Resources (pp. 67 and 90)
UFOUIT
Get ConnectED
and decimals. SPI 0506.2.5 Solve addition and subtraction
problems involving both fractions and decimals. Also
addresses GLE 0506.1.4.
1 INTRODUCE
Introduce the Concept
Review decimal place value to the hundredths place.
• How are the place values to the right of the decimal
similar to the place values to the left of the
decimal? Sample answer: Both are ordered from
ten(th)s, hundred(th)s, and thousand(th)s.
• How are they different? Sample answer: There is no
decimal place value called oneths.
• Compare the hundreds place with the tens place.
Sample answer: The hundreds place is ten times greater
than the tens place.
• Compare the hundredths place with the tenths
place. Sample answer: The hundredths place is ten
times less than, or 1/10 the value, of the tenths place.
2 TEACH
Activity 1 Have students explore why tenths are
represented by rods in relationship to the ones being
represented by flats. If a flat represents one whole,
one tenth of that is a rod. So, one tenth is represented
by a rod.
• Which block would you use to represent the
hundredths place? Why? a unit; Sample answer: The
hundredths place is ten times smaller than the tenths
place. One tenth of a rod is a unit.
204
Step 2
Get ConnectED
Combine the base-ten blocks. Three tenths added
to 5 tenths is equal to 8 tenths.
Ones
GLE 0506.2.5
SPI 0506.2.5 Solve addition
and subtraction problems
involving both fractions and
decimals. Also addresses
GLE 0506.1.4.
Tenths
Hundredths
So, 1.3 + 0.5 = 1.8.
✔ 0506.2.3 Use visual models,
benchmarks, and equivalent forms
to add and subtract commonly
used fractions and decimals.
2
0204_0205_C05L02_103031.indd 204
ELL
Activating Prior Knowledge: Money and Decimals Students may need
help understanding decimals out of context. Connect their prior
understanding of money using both play bills and coins to scaffold the
introductory
t oducto y lesson.
esso
2/26/10 10:40 A
Activity 2 Discuss how many hundredths equals one
tenth and how many tenths equals one whole.
Find 1.42 + 0.87.
F
Step 1
Step 2
Model 1.42 and 0.87.
Ones
Tenths
Hundredths
• How is regrouping when adding decimals similar
to regrouping when adding whole numbers?
Sample answer: When the blocks in a place value are
equal to or greater than one unit of the next higher
place, you can carry that one over.
3 ASSESS
Combine the base-ten blocks.
Ones
Tenths
Hundredths
Assign the Practice and Apply It Exercises to assess
whether students understand adding decimals by using
base-ten blocks.
From Concrete to Abstract Exercise 7 bridges the gap
between concrete and abstract learning by having students
verbally express the regrouping process.
Step 3
Regroup.
Since there are 12 tenths, you can
regroup as 1 whole and 2 tenths.
Ones
Tenths
Hundredths
Extending the Concept Look at the sum in Activity 2.
Think about the base-ten blocks. How could you represent
that number on grid paper? Sample answer: Look at the
squares on the base-ten blocks that equal 2.29. Shade an
equal number of squares on the grid paper.
For more practice of the concepts presented in this Explore
lesson, see
Explore Worksheet.
So, 1.42 + 0.87 = 2.29.
and Apply It
Add. Use base-ten blocks. See students’ work for models.
1. 0.3 + 0.4 0.7
2. 2.4 + 0.5 2.9
3. 1.5 + 0.3 1.8
4. 3.7 + 1.5 5.2
5. 2.83 + 0.36 3.19
6. 3.1 + 1.34 4.44
7.
E TALK MATH Explain when you should regroup when adding
decimals with base-ten blocks. Sample answer: If you have more than 9 tenths or
hundredths.
204_0205_C05L02_101808.indd 205
Lesson 2A Add Decimals 205
12/7/09 1:08 PM
Lesson 2A Add Decimals
205
Multi-Part
Lesson
PART
2
Multi-Part
Lesson
Add Decimals
A
B
C
D
E
2
MP-Title
-TDecimals
itle
Add
PART
A
PART
Objective
Explore using decimal models to add decimals.
C
Main Idea
I will explore using
decimal models to
add decimals.
Materials
You can use grid paper to add decimals.
Find 1.2 + 0.7.
grid paper
Step 1
Resources
colored pencils
EXP
- Co
• Show students a 10-by-10 grid.
• Explain that the whole grid represents one whole.
What does each of the 100 smaller squares represent?
1 hundredth
• How would you represent one tenth on this grid?
Explain. Sample answer: Shade one column of the
larger square because there are 10 equal columns in
the grid.
dp
enc
Model 0.7.
To show 0.7,
7
shade _ of the
10
second grid using
a different color.
il
Get ConnectED
GLE 0506.2.5
GLE 0506.1.4.
0.2
Step 3
Add the decimals.
1
⎫
⎬
⎭
1 INTRODUCE
Step 2
1
⎫
⎬
⎭
lore
⎫
⎬
⎭
Get ConnectED
⎫
⎬
⎭
Explore Worksheet
Model 1.2.
To show 1.2,
shade one whole
10-by-10 grid
2
and _ of a
10
second grid.
Materials: grid paper, colored pencils
Hands-On Activity Tools and Resources (pp. 131–133)
D
Add Decimals
Using Models
B
Add Decimals Using Models
B
0.2 + 0.7
Count the total number of shaded squares.
Write the decimal that represents the number
of shaded squares.
So, 1.2 + 0.7 = 1.9.
2
2 TEACH
Activity 1 Before beginning this activity, help students
outline three 10-by-10 grids on grid paper.
Have them use one color to shade 1.2 using the first two
grids and a different color to shade 0.7 on the third grid.
Have them count the total number of shaded squares to
find the sum.
• How many hundredths did you shade?
190 hundredths
206
0206_0207_C05L02_103031.indd 206
2/26/10 10:40 A
Activity 2
Use Models to Add Decimals
• Verify that students understand the reasoning behind
using 10-by-10 grids.
Find 1.08 + 0.45.
F
Step 1
Model 1.08.
• What does a 10-by-10 grid represent? one whole
To show 1.08, shade one
whole 10-by-10 grid
8
and _ of a second grid.
• What does each column in a 10-by-10 grid
represent? one tenth
100
Step 2
• What does each square in a 10-by-10 grid
represent? one hundredth
⎫
⎬
⎭
1
0.08
Model 0.45.
• Remind students that it does not matter which
45 squares are shaded to represent the second decimal.
There will still be a total of 53 shaded squares in the
second grid.
45
To show 0.45, shade _
100
of the second grid using
a different color.
⎫
⎬
1
⎭
⎫
⎬
⎭
Step 3
0.08 + 0.45
Add the decimals.
3 ASSESS
Count the total number of shaded squares. Write the
decimal that represents the number of shaded squares.
• Explain the similarities and differences in using
models to add 1.08 + 0.45 and 108 + 45. Sample
answer: The same number of squares in the same
number of grids will be shaded to represent the sum of
either expression. The difference is that each square of
the grid is equal to one when modeling whole numbers
but equal to one hundredth when modeling decimals.
So, 1.08 + 0.45 = 1.53.
and Apply It
Add. Use decimal models. 1–9. See Answer Appendix for models.
1. 2.46 + 1.13 3.59
2. 2.05 + 1.87 3.92
3. 2.91 + 1.8 4.71
4. 1.34 + 1.15 2.49
5. 0.51 + 0.63 1.14
6. 1.74 + 0.36 2.1
7. 2.05 + 1.12 3.17
8. 2.93 + 2.74 5.67
student comprehension of the concept presented in
the Activities.
From Concrete to Abstract Use Exercise 10 to bridge the
idea between adding decimals with models and adding
decimals without models.
9. The length of a nickel is 2.1 centimeters. What is the length of
two nickels laying side by side? 4.2 cm
10.
Extending the Concept Have students find the sum of 0.3
and 0.41 without using models.
E
WRITE MATH Explain how to add decimals with decimal models.
Explain where to place the decimal point in the sum.
Sample answer: shade each decimal on as many hundredths grids as needed.
Then count the shaded squares. The decimal is placed between the ones and tenths.
Lesson 2B Add Decimals
206_0207_C05L02_101808.indd 207
207
lesson, see
Explore Worksheet.
11/17/09 2:12 PM
Tips for New Teachers
Students may have difficulty visualizing the whole number of the sum when addition of the
decimal values results in a regrouping to the ones place. Encourage students to shade the
two decimal values within the same grid. Students should shade an additional grid only
when the first one is completely shaded. Starting another grid only after the first one is
completely shaded allows students to more easily see the value of the whole number in
the sum.
Lesson 2B Add Decimals
207
Multi-Part
Lesson
2
PART
PART
C
Multi-Part
Lesson
Add Decimals
A
B
C
D
E
Add Decimals
Objective
2
PART
Add Decimals
A
Main Idea
I will add decimals
through thousandths.
Get ConnectED
Add decimals through thousandths.
Resources
Materials: empty milk carton, empty orange juice carton,
empty cereal box, a bunch of bananas, play money,
grid paper
GLE 0506.2.5
GLE 0506.1.7.
Hands-On Activity Tools and Resources (pp. 120–121,
131–133)
Leveled Worksheet
Get ConnectED
B
C
D
E
Add Decimals
To add decimals, line up the decimal points, add as with whole
numbers, and bring the decimal point straight down in the sum.
Just as with whole numbers, you add digits in the same
place-value position.
I CREAM In Australia,
ICE
each person eats an average
e
of 44.2 pints of ice cream
per year. In the United States,
the average is 33.1 pints.
How much ice cream is
eaten annually, on average,
by each person in these two
countries combined?
Find 44.2 + 33.1.
Estimate 44 + 33 = 77
Step 1
Line up the
decimal points.
44.2
+
33.1
−−−−−
1 INTRODUCE
44.2
+
33.1
−−−−−
77 3
Sometimes the last digits of the numbers in an addition problem
do not have the same place value. When this happens, it is
helpful to write zeros before you add.
• How can you find the exact cost? Add up the cost of
the four items.
0208_0211_C05L02_103031.indd 208
Activity Choice 2: Act It Out
Provide each small group with an assortment of coin and
bill denominations. As you read each scenario, students
make a collection with the correct amount of money.
Allow time between scenarios for students to exchange
coin and bill combinations as necessary.
• You earn $3.50 for feeding the neighbors’ fish while
they are away on vacation.
• You find $1.19 beneath the couch cushions.
• When you clean your room, you find $0.84.
• You find $0.06 stuck in your piggy bank.
• How much money do you have altogether? $7.87
208
44.2
+
33.1
−−−−−
77.3
Check 77.3 is almost equal to (≈) 77.
The answer is reasonable. • Ask students if they think that you can buy all four
items with $10.
• Your mom sends you to the store and says that you
can keep the change: $2.28.
Step 3
Bring the decimal
point straight down
in the sum.
So, 77.3 pints of ice cream are eaten on average per person
each year in Australia and the United States combined.
• Bring in empty cartons of milk, orange juice, cereal, and
a bunch of bananas. List the prices on the board:
milk: $3.29; juice: $2.50; bananas: $0.89; cereal: $3.85.
• Since the total is more than $10, how can you
determine how much more money is needed?
subtract, $10.53 - $10 = $0.53
Step 2
Add as with
whole numbers.
Have students write in their Math Journals an explanation of the
difference between a decimal number and a decimal point.
2/26/10 10:52 A
2 TEACH
Add Decimals
Find 19.6 + 4.31.
Estimate 20 + 4 = 24
Line up the decimal points.
Write a 0 so that both
numbers have the same
place value.
19.60
+
4.31
−−−−−
Step 2 Add as with whole
numbers, from right to left.
Rename if necessary.
19.60
+
4.31
−−−−−
2 3 91
Step 3
19.60
+
4.31
−−−−−
23.91
Step 1
Equivalent Decimals
0.6 and 0.60
are equivalent.
Write the grocery items’ costs on the board: gallon of
milk: $3.29; half gallon of juice: $2.50; a bunch of bananas:
$0.89; cereal: $3.85.
• How much will the milk and cereal cost? $7.14
1
Bring the decimal point
straight down in the sum.
• How much will 3 half gallons of juice cost? $7.50
• How much more does the milk cost than the
juice? $0.79
• How much does it cost to buy 2 bunches of bananas,
one box of cereal, and a gallon of milk? $8.92
If you pay for these items with a ten-dollar bill,
how much change will you get back? $1.08
The sum is 23.91. Since 23.91 is close to the estimate, the
answer is reasonable.
Model Adding Decimals
BOOKS Brett’s social studies
book weighs 5.34 pounds.
His science book weighs
4.78 pounds. Suppose Brett
only has these books in his
bookbag. How much weight
is he carrying, not including
the weight of his bookbag?
Step 1
The members of the Crawford household consume
39.2 gallons of milk per year. The Ramirez
family consumes 54.6 gallons of milk per year.
How many gallons of milk do the two families
consume in all? 93.8 gallons
Find 52.1 + 9.31. 61.41
Make a diagram.
Bernice has grown 8.89 centimeters since last
year. Tyrone has grown 5.72 centimeters. How
many centimeters have Bernice and Tyrone
grown altogether? 14.61 centimeters
?
Step 2
weight of the
social studies book
weight of the
science book
5.34
4.78
To find the total weight, add.
1 1
5. 34
+
4.78
−−−−−
10.12
So, Brett is carrying 10.12 pounds in books.
Lesson 2C Add Decimals 209
E
208_0211_C05L02_101808.indd 209
12/7/09 1:14 PM
Decimal points are lined up when decimals are added or subtracted vertically (which is
not the case for multiplication). This ensures that digits with the same place value are
combined or separated.
For addition and subtraction of so-called “ragged decimals” that
have unequal numbers of decimal places, extra zeros are added as placeholders.
63.4
63.400
For example, -11.265 becomes -11.265.
Note that the zero placeholders do not change the value of the minuend, but help with
the alignment of the columns and regrouping. To subtract, the 4 tenths must be
renamed as “3 tenths plus 9 hundredths plus 10 thousandths” so that the hundredths
and thousandths place subtractions can be carried out.
exercises.
AL
If
students have difficulty aligning the numbers
correctly when adding decimals . . .
Then
1
2
AL
Reteach Worksheet
IWB Personal Tutor Have students use
Personal Tutor to reteach the concept.
3 Have students use grid paper to aid with
alignment when adding decimals. They should
use one square for the decimal point and for
each of the digits in the numbers.
Lesson 2C Add Decimals
209
3 PRACTICE
Level
Assignment
AL
Approaching Level
13–25 odd, 26–29
OL
On Level
14–24 even, 25–29
BL
Beyond Level
14–20 even, 21–29
complete the Higher Order Thinking problems. Suggest
that students round each of the numbers down and
estimate the sum. Then ask them if their estimate is an
under-estimate or an over-estimate.
Add. See Examples 1–3
Add
1 3
1.
6.32 7.78
+
1.46
−−−−−
2.
3.
0.89 0.92
+
0.03
−−−−−
4.
0.54 8.34
+
7.8
−−−−−
5. 25 + 8.46 33.46
6. 6.57 + 1.2 7.77
7. 19.21 + 11.03 30.24
8. 3.008 + 1.64 4.648
9. 8.9 + 0.15 9.05
10. 42.2 + 7.169 49.369
11. Horacio bought a logic puzzle and batteries from a
toy store. Use the table at the right to find the total
cost of the two items, not including tax. $25.34
12.
Item
Cost ($)
logic puzzle
batteries
carrying case
14.95
10.39
12.73
E TALK MATH Explain how writing zeros might be
helpful when adding decimals. Sample answer:
writing zeros helps to line up decimal points.
indicates a multi-step problem
EXTRA
E
Rewatch “Filling a Phone.”
14.8 25.06
+
10.26
−−−−−−
%
#E
4) C
!# TI
2 AC
0R
P
Begins on page EP2.
Add. See Examples
Add
l 1–3
13.
35.08 46.98
+
11.9
−−−−−
16. 5.603 + 1.22 6.823
14.
0.8 1.02
+ 0.22
_______
17. 26.768 + 2.991 29.759
19. An athlete training for the Olympics
swims each lap of a four-lap race in
the following times: 54.73, 54.56,
54.32, and 54.54 seconds. What is
the total time it takes her to swim
the four laps? 218.15 s
21. Terrance is biking a trail. He bikes
12.6 miles and takes a break. Then he
bikes 10.7 miles. How many miles has
Terrance biked in all? 23.3 mi
15.
9.14 11.215
+ 2.075
________
18. 12.03 + 0.145 12.175
20. Grady wants to buy a basketball video
game that costs $59.95, including tax.
He has $45.50 in cash and a gift
certificate for $15.25. Is that enough to
buy the video game? Explain.
See margin.
22. A large bag of sand weighs
48.5 pounds. A small bag of sand
weighs 24.6 pounds. If Mrs. Waggoner
buys a large bag and a small bag, how
many pounds of sand did she
purchase? 73.1 pounds
0208_0211_C05L02_103031.indd 210
Additional Answer
20. Yes. Sample answer: $45.50 + $15.25 = $60.75 and $60.75 > $59.95.
E
TALK MATH Have students discuss what they
know about gigabytes. Have them compare the values of
1.5 gigabytes and 1.35 gigabytes before attempting to
solve the problem.
!
COMMON ERROR!
Students may right align decimal numbers as they do whole
numbers. Students may find it helpful to first align the decimal
points and then go back and fill in the digits in the appropriate
places. Remind students that empty places may be filled in
with zeros.
210
2/26/10 10:52 A
4 ASSESS
23. Bo feeds his dog 7.5 pounds of food in a week. He feeds his cat
3.75 pounds of food in a week. How many pounds of food do his
pets eat in a week? 11.25 pounds
24. BAR DIAGRAM Lakshmi wants to start saving
coins in a piggy bank. Her mother gave her
three quarters and two pennies on Monday
and two dimes and one nickel on Tuesday.
How much money has Lakshmi’s mother
given her? $1.02
Write 3.94 and 14.2 on the board.
• What is the sum of the two numbers? 18.14
?
Monday
Tuesday
• What are some important rules to remember when
adding decimals? Sample answer: Line the numbers
up according to the decimal, not the last digit.
25. BAR DIAGRAM Marcus entered a race that involves swimming
and running. He will need to swim 0.72 mile and run 1.65 miles.
How far will Marcus travel in all during the race? Draw and label a
diagram. Then solve. See margin for diagram. 2.37 miles
✔ 0506.1.9 Use age-appropriate
books, stories, and videos to
Use the information to solve the problem.
• Why can you add a zero to 14.2 without changing
its value? Sample answer: Adding a zero to the end of
a number after the decimal point does not change the
value of the number.
with adding decimals?
If Yes
AL
If No
OL
Enrich Worksheet
OL
BL
BL
(p. 204c)
(p. 204d)
26. Does Desiree have enough space on her cell phone for the rest of
her music? Explain. Yes. 1.35 + 0.12 = 1.47. 1.47 < 1.5.
Ask students to find the
A
sum: 82.05 + 29.139. Ask them to show all their work
andd to explain
l eachh step they
h used. 111.189
27. OPEN ENDED Write two different pairs of decimals whose sums
are 8.69. One pair should involve regrouping. See margin.
28. NUMBER SENSE Explain how you know that the sum of 2.4, 3.6,
and 5.1 is greater than 10. See margin.
29.
E WRITE MATH Write a real-world word problem that can be
solved by adding 34.99 and 5.79. Describe what the solution
means. Sample answer: Sarah has $34.99 in her purse. She puts in
another $5.79. How much money is in her purse now?
Word Processing Have students write decimal
Lesson 2C Add Decimals 211
208_0211_C05L02_103031.indd 211
addition problems for each other using a word
processing program.
3/10/10 10:40 AM
Additional Answers
25.
2.37
Swim
Run
0.72
1.65
27. Sample answer: 4.29 + 4.4 and 5.8 + 2.89
28. Sample answer: When you just add the whole numbers, the sum is 10. The sum
of the decimals will be added on, which makes the sum greater than 10.
Lesson 2C Add Decimals
211
Multi-Part
Lesson
2
PART
PART
D
Multi-Part
Lesson
Add Decimals
A
B
C
D
E
Addition Properties
Objective
Use Associative, Commutative, and Identity Properties to
add whole numbers and decimals mentally.
Resources
Leveled Worksheets
Get ConnectED
2
PART
Add Decimals
A
Main Idea
I will use Associative,
Commutative, and
Identity Properties to
add whole numbers
and decimals mentally.
B
C
D
E
Addition Properties
You can use properties of addition to simplify adding and to
find sums of whole numbers and decimals mentally.
Addition Properties
Get ConnectED
GLE 0506.2.5
decimals.
problems involving both fractions and decimals.
Commutative Property
The order in which numbers are
added does not change the sum.
Associative Property
The way in which numbers are
grouped does not change the sum.
Identity Property
The sum of any number and
0 equals the number.
Identify Properties
Identify the addition property shown.
17 + (3 + 24) = (17 + 3) + 24
1 INTRODUCE
The numbers to be added are grouped in a different way.
This shows the Associative Property of Addition.
• Copy the following 10 numbers onto large index
cards (one number per card):
3, 4, 5, 7, 8, 9, 12, 16, 21, and 25.
ANIMALS Hama recorded the number
of birds he saw. Use properties of
addition to mentally find the total
number of birds.
• Hand them out to 10 students. Ask them to tape the
cards to the board one at a time. The order should be
random.
You can easily add 5 and 15. So, change the
order and group those numbers together.
• Ask students to add up the 10 numbers without using a
pencil or paper. While a few students may be able to
do this, it will be quite difficult for most.
• Ask for ideas on how to make this easier to do. Discuss
rearranging the numbers. Then move them into the
following order:
12 + 8 + 16 + 4 + 3 + 7 + 21 + 9 + 25 + 5
J
5 + 27 + 15 =
=
=
=
5 + 15 + 27
(5 + 15) + 27
20 + 27
47
Add mentally. 5 + 15 = 20
Add mentally. 20 + 27 = 47
• Now find the sum. 110
0212_0215_C05L02_103031.indd 212
Activity Choice 2: Game
• Make pairs of index cards whose sum is a multiple
of 10. One addend should be written on each card. For
example, 18 on one card and 22 on another.
• Give one card to each student.
• Say, “Green light.” Students silently find the other card
that makes a sum of a multiple of 10.
• Say, “Red light.” Partners say the sum to each other.
• What makes these compatible numbers? Sample
answer: The sum of the ones place is always 10.
Have students write in their Math Journals an example of the
Commutative and the Associative Properties of Addition.
212
2/26/10 10:51 A
Use Properties to Add Decimals
Use properties of addition to find 0.8 + 5.6 + 0.4 mentally.
Since 0.6 + 0.4 = 1, group 5.6 and 0.4 together.
Decimals that can be
grouped to form a
whole number are
compatible numbers.
5.6 + 0.4 = 6
0.8 + 5.6 + 0.4 = 0.8 + (5.6 + 0.4)
= 0.8 + 6.0
= 6.8
5.6 + 0.4 = 6.0
0.8 + 6.0 = 6.8
• Why would you add in this order?
Each small sum is 10.
• Does changing the order in which you add change
the sum? no
Add Decimals
• While some students will quickly accept and understand
this, you may want to find the sum both ways to show
the more hesitant learners.
Use properties of addition to find 1.8 + 2.6 mentally.
(1 + 0.8) + (2 + 0.6)
1 + 2 + 0.8 + 0.6
(1 + 2) + (0.8 + 0.6)
3 + 1.4
4.4
Write the digits 1–9 on the board.
• How could you group these numbers to make the
sum easier to find? Sample answer:
(1 + 9) + (2 + 8) + (3 + 7) + (4 + 6) + 5
You can also regroup whole numbers and decimals to make
adding easier.
1.8 + 2.6 =
=
=
=
=
2 TEACH
• Which property tells you that we can add numbers
in any order? Commutative Property
Add.
Add.
Identify the addition property shown.
14 + (26 + 5) = (14 + 26) + 5 Associative
Property of Addition
Identify the addition property used to rewrite each problem.
problem
See Example 1
1. (11 + 37) + 3 = 11 + (37 + 3)
Associative
2. 0.1 + 8 + 1.9 = 0.1 + 1.9 + 8
Commutative
Use properties of addition to find each sum mentally.
Show your steps and identify the properties that you used.
Aisling counted the cars. Use the properties of
addition to mentally find the total number of
cars she counted. 41 cars
3–5. Sample answers are
given. See margin for steps.
See Examples 2–4
3. 9 + 27 + 1 37
4. 3.9 + 0.5 + 2.5 6.9
5. 69 + 22 91
Cars
6. Danielle writes the following on the board. What addition property
is shown? Identity
0 + 6.75 = 6.75
7.
E TALK MATH Describe how properties of addition help to add
numbers mentally. See margin.
13
Gray
21
Red
7
Use properties of addition to find 1.7 + 0.6 +
0.3 mentally. 2.6
Lesson 2D Add Decimals 213
212_0215_C05L02_101808.indd 213
White
Use properties of addition to find 2.4 + 1.7
mentally. 4.1
12/7/09 1:36 PM
Additional Answers
3. 9 + 27 + 1 = 9 + 1 + 27
= (9 + 1) + 27 Associative Property
= 10 + 27
Add 9 and 1 mentally.
= 37
4. 3.9 + 0.5 + 2.5 = 3.9 + (0.5 + 2.5) Associative Property
= 3.9 + 3.0
Add 0.5 and 2.5 mentally.
= 6.9
5. 69 + 22 = (60 + 9) + (20 + 2) 69 = 60 + 9 and 22 = 20 + 2
= 60 + 20 + 9 + 2
= (60 + 20) + (9 + 2)
= 80 + 11
Add inside the parentheses mentally.
= 91
E
exercises.
7. Sample answer: It helps to have numbers that are easy to add grouped together.
Lesson 2D Add Decimals
213
AL
If
students have trouble remembering
addition properties . . .
Then
1
AL
Reteach Worksheet
2 Use Flash Cards Have students make flash
cards with the name of the property on one side
and an example on the other. Below each
example, have students write hints they can use
to remember the property.
EXTRA
%
#E
4) C
!# TI
2 AC
0R
P
Begins on page EP2.
Identify
Id
tif the
th addition
dditi
property
t used
d to
t rewrite
it each
h problem.
bl
See Example 1
8. 20 + 6 = 6 + 20 Commutative
10. 49 + (51 + 21) = (49 + 51) + 21
Associative
9. 19.5 + 0 = 19.5 Identity
11. 13 + 11 + 87 = 13 + 87 + 11
Commutative
Use properties of addition to find each sum mentally. Show your
steps and identify the properties that you used. See Examples 2–4
12. 15 + 8 + 25 48
13. 7.7 + 4.3 + 11 23
14. 37 + 26 + 53 116
15. 10.9 + 3 + 0.1 14
16. 63 + 35 98
17. 57 + 48 105
12–17. Sample answers are given. See Answer Appendix for steps.
Algebra For Exercises 18 and 19, find the value that makes each
sentence true.
18. 27 + (37 + 13) = 13 + (27 + ) 37
3 PRACTICE
Level
Assignment
AL
Approaching Level
8–10, 12, 14, 21, 23–36
OL
On Level
8–14, 18–20, 22–36
BL
Beyond Level
9–21 odd, 23–36
complete the Higher Order Thinking problems. Suggest
that students write a word problem that uses compatible
numbers that can be grouped for easier mental calculation.
E
!
COMMON ERROR!
Students often confuse the Associative and the
Commutative Property. Point out that if the order of
the addends has been changed, the Commutative
Property has been used.
Additional Answers
23. Sample answer: I spent $7.75 on a book, $13.55 on
a CD, $3.25 on a magazine, and $15.45 on a DVD.
How much did I spend in all? (7.75 + 3.25) +
(15.45 + 13.55); $40
25. Sample answer: Putting a math book and then a
science book into a backpack is commutative,
because the end results are the same. Preparing a
cake is not commutative because you mix first and
then bake, not bake then mix.
214
19. (8 + 1.6) + 0.4 = 0.4 + ( + 1.6) 8
20. The table shows the cost of a cheerleading
uniform. Use properties of addition to
find the total cost of the uniform mentally.
Show your steps and identify the
properties that you used.
20–21. See Answer Appendix.
21. In one week, a classroom collected 43, 58, 62, 57, and 42 cans.
Find the total number of cans the classroom collected using
mental math. Explain how you solved it.
22. Casey spent $2.50 on a snack, $1.24 on gum, $3.76 on a comic
book, and $5.50 on lunch. Use mental math to find the total
amount that he spent. $13
23. OPEN ENDED Write a word problem that can be solved using the
Associative Property of Addition. Explain your answer. See margin.
24. NUMBER SENSE Without solving, would 0.4 + (2 + 0.6) be less
than, greater than, or equal to 3? Explain.
Sample answer: equal to; 0.4 + 0.6 = 1 and 1 + 2 = 3.
WRITE MATH Jogging 2 miles and then walking 1 mile is
25. E
the same as walking 1 mile and then jogging 2. This is a
commutative action. Give another example of a commutative action.
Then give an example of an action that is not commutative. Explain. See margin.
0212_0215_C05L02_101808.indd 214
Knowing and understanding the basic properties of operations helps students develop
operation sense.
• The Commutative Property of Addition says you can add in any order, so,
a + b = b + a.
• The Associative Property says you can change the grouping of the addends when
you add, so, (a + b) + c = a + (b + c).
• The Identity Property says that the sum of any number and 0 is the number, so,
a + 0 = a.
These properties are very useful to students as they add whole numbers and decimals
mentally. Students should be aware that subtraction is not commutative,
e.g., 8 - 5 ≠ 5 - 8. However, there are rules that do apply to subtraction. For
example, when you subtract 0 from a number, the result is the number (a - 0 = a),
and when you subtract a number from itself, the result is 0 (a - a = 0).
11/17/09 2:23
4 ASSESS
Test Practice
26.
SHORT RESPONSE Fina went to
the grocery store and bought eggs,
milk, butter, and sugar. What is the
total cost of her purchase? $6
$2.25
$1.65
28. Round 563.829 to the nearest
hundredth. H
Find the following sum mentally:
25 + 9 + 15
Then show your steps and identify the properties that
you used.
25 + 9 + 15 = 9 + 25 + 15
= 9 + (25 + 15) Associative Property
= 9 + 40
Add 25 and 15 mentally
= 49
Add 40 and 9 mentally
F. 563.81
G. 563.828
H. 563.83
I. 600
$1.12
$0.9
8
27. Sancho and Luther ran a relay race.
Sancho ran his part of the race in
6.85 seconds. Luther ran his part of
the race in 6.14 seconds. Which
is the best estimate for their
combined time? C
29. Abby is gluing together two pieces of
wood so that their length equals the
length of the board below. Which
two lengths should she use? D
with using addition properties to add
whole numbers and decimals mentally?
2.84 m
A. 10 seconds
B. 11 seconds
A. 1.84 meters and 2.84 meters
C. 13 seconds
B. 2.5 meters and 0.3 meter
D. 15 seconds
C. 1.8 meters and 1.4 meters
If Yes
AL
If No
OL
Enrich Worksheet
OL
D. 1.04 meters and 1.8 meters
BL
BL
(p. 204c)
(p. 204d)
Add. (Lesson 2C)
30. 5.08 + 13.7 18.78
31. 12.01 + 0.23 12.24
32. 24.8 + 16.095 40.895
33. Students at a middle school filled out a survey.
The survey showed that out of the 748 students
that are going on a summer vacation, half of
them are going to the beach. Find how many
students are going to the beach. Is your solution
an exact answer or an estimation? Explain.
(Lesson 1C) 374 students; exact answer; the question asks
for an exact number of students.
Round each decimal to the underlined place. (Lesson 1A)
34. 14.73 14.7
35. 7.638 7.64
36. 839.64 840
Lesson 2D Add Decimals 215
212_0215_C05L02_103031.indd 215
Tell students that the
nextt llesson iis on subtracting
bt ti ddecimals. Ask them to
write how they think today’s lesson on the addition
properties will help them with tomorrow’s lesson.
Review and assess mastery of skills and concepts from the
previous lessons in the chapter.
2/26/10 10:51 AM
Multi-Part Lesson 2 How can using the Commutative and Associative Properties
of Addition help you add compatible numbers? Sample answer: The Commutative
Property allows the order of the addends to be changed so that compatible
numbers are consecutive. The Associative Property allows the grouping of the
addends to be changed so that compatible numbers are grouped together.
Lesson 2D Add Decimals
215
Find The Least Sum
Adding Decimals
Find the Least Sum
Materials 10 index cards, paper, pencils
You will need:
10 index cards, paper
Adding Decimals
Introduce the game to your students to play as a class, in
small groups, or at a learning station to review concepts
introduced in this chapter.
Get Ready!
Players: 2 to 4 players
Get Set!
Instructions
Write a different digit from
0 to 9 on each index card.
• Students play in teams of 2 to 4 people. They write a
different digit on each index card, using the digits
0 through 9. They shuffle the cards and place them in a
pile facedown on the table.
Place the cards in a pile
facedown.
Each player takes a turn
choosing a card.
Each time a card is chosen,
each player writes the digit
from the card on one of the
boxes. The goal is to make
up the least sum. You may
not move digits after you
have placed them in a box.
• Play continues until boxes on the game boards are full.
Students add up their decimals. The player with the
least sum wins.
When all the boxes are full,
find the sum of your
decimals.
The player with the least
sum is the winner.
BL
• For another game focusing on the same mathematical
concept, see
Game Time.
.
Go!
• Students take turns choosing cards. Each time a card is
chosen, each player writes the digit on the card in one
of the boxes on his or her game board. Students try to
make up the least sum of all six boxes once the boxes
are full. They may not move the digits after they have
placed them in their boxes.
• Have students make the game using three addends and
replacing the cards back into the deck once they have
been written into the boxes, in order to re-use the cards
until boxes are full.
+
Draw six boxes on a piece
of paper with decimal points
as shown.
• Students each make a game board, drawing six boxes
on a piece of paper, with decimal points in each box
as shown.
Extend the Game
.
Play again!
0216_C05GT_101808.indd 216
11/17/09 2:25
Differentiated Practice
Use these leveled suggestions to differentiate the game for all learners.
Level
Assignment
AL
Approaching Level
Students create game boards with only four
boxes.
OL
On Level
Have students play the game with the rules
as written.
For extra practice of basic facts the students have learned, see
216
Fast Facts.
Mid-Chapter
Check
Round each decimal to the place
indicated. (Lesson 1A)
2. 4.328; tenths 4.3
3. 0.016; hundredths 0.02
4. MULTIPLE CHOICE At sea level, the
speed of sound is 340.29 meters per
second. What is the speed to the
nearest tenth? (Lesson 1A) C
C. 340.3
B. 340.2
D. 341
11. MULTIPLE CHOICE Tammy made a
bracelet using red, white, and blue
string. The red string is 2.4 centimeters
long, the white string is 2.1 centimeters
long, and the blue string is
2.6 centimeters long. What is the total
length of the three strings? (Lesson 2C) F
1. 11.8; ones 12
A. 340
Mid-Chapter
Check
19. Sample answer: align the addends
on the decimal point. Write a zero
on the end of 4.2. 4.20
+ 2.14
−−−−
6.34
F. 7.1 cm
H. 5.5 cm
G. 6.1 cm
I.
Use the Mid-Chapter check to assess students’ progress in
the first half of the chapter.
Customize and create multiple
versions of your Mid-Chapter Check and the test
answer keys.
4.27 cm
Add. (Lesson 2C)
Dinah Zike’s
Foldables®
12. 3.15 + 1.20 4.35
13. 68.9 + 7.1 76
5. Measurement Estimate
the amount of liquid
in the sports drink
bottle to the nearest
whole number.
(Lesson 1A) 6 L
Use these lesson suggestions to incorporate the Foldables
during the chapter.
14. 4.678 + 1.709 6.387
15. 25.39 + 18.687 44.077
Multi-Part Lesson 1 Under the left flap of the Foldable,
students provide examples of estimating sums and
differences of decimals.
16. What is the combined cost of the
sweatshirt and hat below? $44.89
Estimate each sum or difference. (Lesson 1B)
7.
8.9
15.9
+ 6.2
- 12.1
−−−−
−−−−−
9 + 6 = 15
16 - 12 = 4
8. 37.1 + 1,215
9. 60.3 - 18.55
60 - 20 = 40
40 + 1,220 = 1,260
10. Measurement About how much
greater is the side of the square than
the side of the triangle? Show how you
estimated. (Lesson 1C)
Multi-Part Lesson 2 Under the center flap of the
Foldable, students provide examples of adding decimals,
and how the commutative and associative properties can
be applied.
6.
18.45 cm
21.72 cm
.15
$25
.74
$19
Identify the addition property used to
rewrite each problem. (Lesson 2C)
17. 23.7 + 4.9 = 4.9 + 23.7 Commutative
18. (87 + 22) + 6 = 87 + (22 + 6)
Associative
WRITE MATH Explain how you
19. E
would find the sum of 4.2 and 2.14.
(Lesson 2C)
Sample answer: 22 - 18 = 4; about 4 cm
Mid-Chapter Check
217_C05MCC_101808.indd 217
217
11/17/09 2:27 PM
Data-Driven Decision Making
Based on the results of the Mid-Chapter Check, use the following resources to review concepts that continue to give students problems.
Exercises
Tennessee
Standards
What’s the Math?
Error Analysis
1–5
GLE 0506.2.5
Round decimal numbers.
Did not understand decimal place value.
Did not know the rules for rounding.
6–10
GLE 0506.1.2
Estimate decimal sums and differences.
Did not know the rules for rounding.
11–16
GLE 0506.2.5
Add decimal numbers.
Did not know how to add decimal numbers.
17–19
GLE 0506.1.2
Identify addition properties and
explain problem-solving processes.
Did not understand how to apply the
Commutative and/or Associative Properties
of Addition.
Resources for Review
Chapter Resource Masters
Get ConnectED
Lesson Animations • Personal Tutor
• Self-Check Quiz
Mid-Chapter Check
217
Multi-Part
Lesson
3
Subtract Decimals
Planner
PART
A
PART
Base-Ten Blocks
B
Title/Objective
PART
A
Subtract Decimals
Using
i Base-Ten Blocks
B
Subtract Decimals
Using
i Models
d l (pp. 220–221)
(pp. 218–219)
Subtract Decimals
Using Models
C
Subtract Decimals
D
Work Backward
E
Essential Question
Why is adding decimals helpful when checking
exercises that subtract decimals? Sample
answer: Addition is the opposite of subtraction.
You can check the exact answer of the
subtraction exercise by using addition.
Students build upon their work with decimal
models and decimal addition by learning to
subtract decimals. Remind students that, as
with decimal addition, it is crucial to correctly
line up the place values when subtracting.
Explain that the subtraction algorithm used for
decimals is the same as that used for whole
numbers.
Standards
Explore subtracting decimals using
base-ten blocks.
Explore using models to represent
subtraction of decimals.
GLE 0506.2.5
GLE 0506.2.5
place-value
l
l chart
h
grid
id paper
base-ten blocks
colored pencils
Vocabulary
Materials/
Manipulatives
Resources
✔ 0506.1.9
Get ConnecttED
Get ConnecttED
Explore Worksheet
Explore Worksheet
Lesson Animations
Lesson Animations
Blended Approach
Refer to the Blending
Math Connects and
IMPACT Mathematics
guide for detailed
lesson plans.
IWB
Whiteboard ready.
Suggested Pacing
Multi-Part Lessons
1
(11 Days)
2
PART
A
B
C
Days
1
1
1
A
B
1
3
C
D
1
1
A
B
1
Assess
C
D
SGR
PCT
1
1
1
1
Subtract Decimals
PART
PART
C
Subtract Decimals
(pp. 222–225)
Notes
D
Work Backward
Title/Objective
(pp. 226–227)
Subtract decimals.
Solve non-routine problems by using
the work backwardd strategy.
GLE 0506.2.5
GLE 0506.1.2
Standards
Vocabulary
ddouble
bl 9 ddominos
i
Get ConnecttED
Materials/
Manipulatives
Get ConnecttED
Leveled Worksheets
Leveled Worksheets
Lesson Animations
Lesson Animations
Problem of the Day
Problem of the Day
Self-Check Quiz
Personal Tutor
Personal Tutor
RWPS: A Growing Nation
Resources
✔ 0506.1.9
Blended Approach
Problem-Solving in Social Studies
The Core Facts About Apples (p. 228)
Chapter Study Guide and
Review (p. 230)
Practice Chapter Test (p. 235)
Test Practice (p. 236)
Subtract Decimals
218b
Approaching Level
On Level
AL
Option 1
Use with 3B
OL
Option 1
Use with 3C
Hands-On Activity
Materials: grid paper
Hands-On Activity
Materials: take-out menus from local restaurants, play money
• Each student draws a model of a decimal less than 10 that
includes two decimal places on a piece of grid paper.
• Give each student $25.00 in play money.
• Students work in pairs and use their models to form a
subtraction problem. Students work together to draw another
model for the difference between the first two models.
• Have students share their subtraction model and solution.
Use with 3C
Hands-On Activity
Materials: cards numbered 0–9
• Each group of four students should
have a subtraction mat, like the
one shown.
Subtraction Mat
-
• The player places the card on an empty space on the mat. The
player scores points equal to the number on the card. The
player’s turn is over.
• Play continues until the mat is filled with number cards. Once
the mat is filled, the students should then find the difference.
• If the top number is smaller than the bottom number, the next
player says, “Mix it up,” rearranges the cards, and scores
10 points.
• Players who find the correct answer add the points they
earned that round to their previous total. Players who find an
incorrect answer forfeit the points they earned that round,
scoring 0 for that round.
• All cards are shuffled, and play continues. The first player to
score 50 points wins.
Other Options
Personal Tutor, Lesson Animations,
Virtual Manipulatives,
• When students have spent all they can, allow them to share
what items they bought, how much each item cost, and what
subtotals they found after subtracting each item.
Option 2
.
• The first player may select one card from another player or
draw a card from their pile.
218c
• Challenge students to buy as many different items as possible.
.
• Shuffle and give each player two
cards facedown. Place the remaining
cards facedown in the center of the table as a draw pile.
Get ConnectED
• Students should record each new difference as they continue
to select items and subtract the costs.
• Challenge students to spend as much of the $25.00 as possible.
Option 2
TE
• Students should select one item at a time from the menu and
subtract the cost from the amount of money they have to spend.
Use with 3D
Materials: art supplies
• Ask students to write and illustrate
two problems that can be solved by
working backward. To help them get
started, ask students to think of a
solution, and then define the
starting point.
August 18, 2006,
was a Friday. What
day of the week was
August 1, 2006?
• Use the finished products as classroom posters or examples.
Option 3
Use with 3A
Materials: shopping ads, base-ten blocks
• Have students gather base-ten blocks to represent $45.78.
• Next, students will use local shopping ads to find items that
have pricing listed that they would like to purchase.
• Have students model subtracting the cost of each item from
the base-ten blocks. They can subtract each item from the
original amount, if they want to only purchase one item, or they
can subtract successively as they find items they want to buy.
Other Options
TE
Get ConnectED
Personal Tutor, Lesson Animations,
Virtual Manipulatives,
Subtract Decimals
Beyond Level
BL
Option 1
Use with 3A
Hands-On Activity
Materials: play money
Use the work backward strategy or any other strategy to solve
the problem.
Bryce went to the mall. While he was
there, he ate lunch, saw a movie,
and bought a book and a pair of
shoes. All four items cost 4 times as
much money as Bryce has left. He has $17.38 left. He spent half
of the money he took to the mall on shoes. The book cost $30
less than the shoes. The lunch cost $10.00 less than the book.
What was the cost of each of the four items? shoes: $43.45;
book: $13.45; lunch: $3.45; movie: $9.17
ELL
This strategy helps English Learners learn and use the language
required to subtract decimals.
Find Core Vocabulary and Common Use Verbs in the
online EL strategies to help students grasp the math skills;
use Language Alerts at point of use in the Teacher Edition.
Beginning
Word Recognition Distinguish between different and
difference.
AL
• Hold up two different items, and have the class chorally say
“different.” Emphasize the /t/ sound.
• Write a simple subtraction problem on the board, point to the
answer, and have students say “difference.” Emphasize the
/s/ sound. Repeat the process with other examples.
Intermediate
Memory Devices Remember place values.
OL
Option 2
Use with 3D
Materials: chart paper, markers, pencils, paper
• Write the problem below on the chart paper:
• Write and read aloud similar-looking
decimals with different values. (0.7, 0.07,
0.007, etc.).
• Say, “The letter L can help them
remember that the farther Left the number, the Larger it is.”
Repect for other decimal sets. Have students vocalize the
decimals and tell which is larger. Reread them, starting from
top down, then bottom up.
Advanced
Testing Language Students identify language that indicates
subtraction in word problems.
BL
• Ask the students to solve the problem and show their work.
• Upon solving the problem, students share their strategy with
the others in the group. Solicit different methods of solving
this problem.
Other Options
Get ConnectED
Lesson Animations,
eGames: Number Voyager
• Have a student read a problem chorally and write the list of
words and phrases that signify subtraction. Discuss the
language used to signify subtraction in word problems.
• Have multilingual pairs read word problems from a book or a
test and highlight the words or phrases that signify
subtraction. Students take notes recording term and practice
spelling and recognizing them.
Extend
Have multilingual pairs create a subtraction word problem. Then
have pairs switch papers. Have the pair’s native English speakers
read the problem aloud before partners work together to solve
the problems. Pairs work together to vocalize, correct, and
discuss the solution process in English.
Subtract Decimals
218d
Multi-Part
Lesson
PART
3
Subtract Decimals
A
B
C
D
F
Multi-Part
Lesson
3
Subtract Decimals
A
PART
PART
Objective
Explore subtracting decimals using base-ten blocks.
C
D
E
Subtract Decimals
Using Base-Ten Blocks
A
Base-Ten Blocks
B
Main Idea
I will explore
subtracting decimals
using base-ten blocks.
Materials
Find 1.8 - 0.4.
F
Step 1
base-ten blocks
Model 1.8.
Ones
Tenths
Hundredths
Resources
Materials: place-value chart
Workmat:
place-value chart
Step 2
IVOESFEUIT
%FDJNBMT
POFT
IVOESFET
Explore Worksheet
0OFT
UFOUIT
Hands-On Activity Tools and Resources (pp. 67 and 90)
UFOT
Take 0.4 away. Four tenths taken away from
eight tenths is equal to four tenths.
Ones
Tenths
Hundredths
Get ConnectED
1 INTRODUCE
• Have students model 357 - 286 by using base-ten blocks.
• How is modeling 3.57 - 2.86 with base-ten blocks
the same? How is it different? Sample answer: The
process is the same. The difference is that the units
represent the hundredths place and the rods represent
the tenths place. The flats would represent the ones place.
GLE 0506.2.5
GLE 0506.1.4.
Step 3
Count the remaining base-ten blocks.
Ones
Tenths
Hundredths
So, 1.8 - 0.4 = 1.4.
ELL
Activating Prior Knowledge: Lining Up Decimals
Students may need help connecting the math form
of subtracting decimals they learned in their native
culture to the method instructed. Allow EL groups to
sentences to scaffold the EL
ppresent their problem
p
forms for English speakers.
2 TEACH
Activity 1 It is important that students take away from
the correct place value. Although mathematically correct,
taking away four tenths from the ones place rather than
the tenths place is visually misrepresentative of the
difference.
• How do you know which place value to subtract?
Sample answer: Find the place value of the number
being subtracted, and take that many blocks away.
218
Get ConnectED
0218_0219_C05L03_103031.indd 218
2/26/10 10:52 A
Activity 2 Show students how to borrow by regrouping
the ones to tenths. Students can see that they now have
12 tenths (rods) from which to subtract 7 tenths.
Find 2.25 - 0.75.
F
Step 1
Model 2.25.
Step 2
Subtract 0.75.
To take away 0.75, you
take away 7 tenths and
5 hundredths. But you
cannot subtract 7 tenths
from 2 tenths. So, regroup
the ones block as 10 tenths.
Then subtract.
Step 3
Count the remaining
base-ten blocks.
Ones
Tenths
Hundredths
Ones
Tenths
Hundredths
Ones
Tenths
Hundredths
From Concrete to Abstract Exercise 7 bridges the gap
between concrete and abstract learning by having students
assess the similarities and differences between subtracting
whole numbers and decimals.
Extending the Concept How do you think you could
represent the subtraction in Activity 2 on 10-by-10 grids?
Sample answer: Shade the total number of squares in the
first number, and then cross out the total number of
squares in the second number. The squares that are left
represent the difference.
and Apply It
lesson, see
Explore Worksheet.
Use base-ten blocks to subtract. See students’ work for models.
1. 0.8 - 0.3 0.5
2. 2.8 - 0.7 2.1
3. 1.43 - 0.31 1.12
4. 2.17 - 1.9 0.27
5. 1.3 - 0.28 1.02
6. 3.52 - 1.39 2.13
E TALK MATH Compare and contrast subtracting decimals
using base-ten blocks and subtracting whole numbers with
base-ten blocks. Sample answer: You need to regroup for each. The
place value positions are different for decimals.
Lesson 3A Subtract Decimals
218_0219_C05L03_101808.indd 219
3 PRACTICE
whether students understand using base-ten blocks to
model decimal subtraction.
So, 2.25 - 0.75 = 1.5.
7.
• How could you use this method to subtract
2.2 - 0.75? Sample answer: Place a zero at the end of
2.2 as a place holder. Trade 1 tenth for 10 hundredths,
and take 5 away. Trade 1 one for 10 tenths, and take
7 away. Because there are no ones to take away, there
is 1 left in the answer.
219
11/17/09 2:31 PM
Lesson 3A Subtract Decimals
219
Multi-Part
Lesson
PART
3
Subtract Decimals
A
B
C
D
F
Multi-Part
Lesson
3
PART
Subtract Decimals
A
PART
Objective
Explore using models to represent subtraction of decimals.
Main Idea
I will explore using
models to represent
subtraction of decimals.
D
E
You can use grid paper to subtract decimals.
Materials
grid paper
Find 2.4 - 1.07.
F
Step 1
Resources
Materials: grid paper, colored pencils
C
Subtract Decimals
Using Models
B
Models
B
Model 2.4.
To show 2.4, shade 2 whole grids and
4
_
of a third grid.
colored pencils
10
Hands-On Activity Tools and Resources (pp. 131–133)
Explore Worksheet
Get ConnectED
2
0.4
Get ConnectED
GLE 0506.2.5
GLE 0506.1.4.
• How do you think you could model subtraction on a
grid? Sample answer: First, shade in grids to model the
larger number. Then, cross out sections of the grids to
represent subtraction.
Step 2
Subtract 1.07.
To subtract 1.07, cross out 1 whole grid and
7
_
of the third grid.
100
Step 3
⎫
⎬
⎭
• Have students explain how to model decimal addition
by using grids.
e
⎫
⎬
⎭
• Show students a 10-by-10 grid.
dp
⎫
⎬
⎭
1 INTRODUCE
lore
⎫
⎬
⎭
EXP
- Co
2-1
0.4 - 0.07
Count the remaining shaded squares.
Write the decimal that represents the number of
remaining shaded squares.
So, 2.4 - 1.07 = 1.33.
2 TEACH
0220_0221_C05L03_103031.indd 220
Activity 1 Help students outline three 10-by-10 grids.
Point out that this time, they are going to subtract two
decimal numbers by crossing out the number of squares
that represent the second number from the shaded
squares that represent the first minuend. Discuss why
three squares are needed.
Have students shade 2.4 in the three squares in a light
color. Then have them cross out 1.07 of the squares using
a darker color. Point out that it does not matter how they
cross out the squares, there will be one 10-by-10 grid and
33 small squares left.
220
2/26/10 10:52 A
Activity 2
Use Decimal Models
Find 1.66 - 0.84.
F
• How many 10-by-10 grids will you need? 2
Step 1
Model 1.66.
• How many whole grids will you shade? 1
To show 1.66,
shade one whole
• How many squares of the second grid will you
shade? 66; 6 rows of 10 and 6 more smaller squares
66
grid and _ of a
second grid.
• How many squares will you cross out? 84; 8 rows of
10 and 4 more smaller squares
Subtract 0.84.
• What is the difference of 1.66 and 0.84? 0.82
100
Step 2
To subtract 0.84,
cross out
4 hundredths and
8 tenths.
Step 3
3 PRACTICE
Assign the Think About It Exercise to assess student
comprehension of the concept presented in the Activities.
Count the remaining shaded squares.
Write the decimal that represents the number of
remaining shaded squares.
Use the Practice and Apply It Exercises to assess whether
students understand how to use models to represent
decimal subtraction.
So, 1.66 - 0.84 = 0.82.
From Concrete to Abstract Use Exercise 10 to bridge the
idea between adding and subtracting decimals with models.
About It
1. Explain how using models to find 2.4 - 1.07 is similar to using
models to find 240 - 107. See margin.
Extending the Concept Have students find the difference
of 0.41 and 0.3 without using models. 0.11
and Apply It
lesson, see
Explore Worksheet.
Subtract. Use decimal models. 2–9. See Answer Appendix for models.
2. 0.93 - 0.7 0.23
3. 2.53 - 1.41 1.12
4. 0.9 - 0.3 0.6
5. 4.94 - 0.4 4.54
6. 3.55 - 0.1 3.45
7. 4.4 - 0.9 3.5
8. 3.8 - 2.3 1.5
9. 2.13 - 1.7 0.43
10.
Additional Answer
1. Sample answer: When using models to find the
difference between 2.4 and 1.07 you model and take
away the same number of squares as finding the
difference between 240 and 107 using models.
E WRITE MATH Explain how adding decimals with models is
different from subtracting decimals with models. Sample answer:
subtracting decimals using models requires taking blocks away.
220_0221_C05L03_101808.indd 221
Lesson 3B Subtract Decimals 221
11/17/09 2:33 PM
Lesson 3B Subtract Decimals
221
Multi-Part
Lesson
3
PART
PART
C
Subtract Decimals
A
B
C
D
Multi-Part
Lesson
3
PART
Subtract Decimals
Subtract Decimals
A
Main Idea
I will subtract decimals.
Get ConnectED
Objective
Subtract decimals.
GLE 0506.2.5
GLE 0506.1.7.
Resources
Materials: double-9 dominos
Leveled Worksheet
Get ConnectED
B
C
D
E
Subtract Decimals
To subtract decimals, line up the decimal points. Then subtract
digits in the same place-value position.
BONES The table
B
shows
the average
s
length of the three
longest bones in the
human body. How
much longer is the
average femur than
the average tibia?
Longest Bones in the Human Body
Bone
Length (in.)
Femur (upper leg)
19.8
Tibia (inner lower leg)
16.9
Fibula (outer lower leg)
15.9
Estimate 19.8 - 16.9 ≈ 20 - 17 or 3
818
1\9.\8
- 16.9
2.9
Subtract as with whole numbers.
So, the average femur is 2.9 inches longer than
the average tibia.
1 INTRODUCE
Check for Reasonableness 2.9 ≈ 3 Activity Choice 1: Hands-On
• Have students place a set of dominos facedown in the
center of the table.
Subtract Decimals
Find 0.84 - 0.56.
• Each student draws two dominos. The dots represent a
two-digit number.
714
0.8\4\
- 0.56
0.28
• Have students subtract the value of the smaller domino
from the value of the larger domino.
• If a decimal point is placed between the two sets of
dots, what is the difference?
Subtract as with whole numbers.
So, 0.84 - 0.56 = 0.28.
Check by Adding Subtraction and addition are inverse operations.
Use addition to check your answer.
Activity Choice 2: Eating Out
0.28 + 0.56 = 0.84 • Write the menu on the board.
Menu
Veggie Burger
$0.89
Turkey Burger
$1.09
Fruit Cocktail
$0.99 small
$1.19 large
Drinks
$0.75 small
$0.95 large
0222_0225_C05L03_103031.indd 222
• Each group of three students has a total of $10.00.
• Have students decide which items each person will
purchase for lunch while remaining under budget.
Have students use a dictionary to define the word reasonable in
their Math Journal. Then have them explain how the definition
applies to using estimation to check the reasonableness of
an answer.
222
2/26/10 10:51 A
Sometimes the last digits of the numbers in a subtraction problem
do not have the same place value. Write zeros where they are
needed before you subtract.
• What does it mean when a whole number has a
decimal point followed by digits? Sample answer:
There is a part of one more whole.
Write Zeros
Find 6 - 4.78. Estimate 6 - 4.78 ≈ 6 - 5 or 1
6.00
- 4.78
1.22
2 TEACH
Place a decimal and zeros so that both numbers
have the same place value.
• What would happen if there were no decimal
numbers? Sample answer: Something that cost $1.85
would have to be rounded up to $2.00.
So, 6 - 4.78 = 1.22.
Check for Reasonableness 1.22 ≈ 1 Subtract Decimals
The table shows three shot put distances. How
much longer is the longest shot put distance
than the shortest shot put distance? 3.19 feet
M
MONEY
Stephen’s father gave him $10 to buy lunch at the
cconcession stand. If his lunch cost $7.74, how much change
should Stephen give his father?
$10
One Way:
Cost of the food
Amount of
change
$7.74
?
Shot Put Records
Find $10.00 - $7.74.
09 9 1 0
\1 \0.0\\0
- 7.74
2.26
Another Way:
Distance
Tyrone
16.06 feet
Marcus
13.24 feet
Steven
12.87 feet
Find 0.64 - 0.28. 0.36
So, Stephen should give his father $2.26.
Check by Adding $2.26 + $7.74 = $10.00 To solve problems
more easily,
sometimes you can
use the properties to
rewrite numbers.
Athete
Find 7 - 3.19. 3.81
Janice has $20 to buy a new outfit. The outfit
costs $18.37. How much change will Janice
receive? $1.63
Rewrite the subtraction problem to make it
easier to solve. Then subtract.
$10.00 - $7.74
Think $9.99 - $7.74 = $2.25. Then add back $0.01.
So, $10.00 - $7.74 = $2.26
Lesson 3C Subtract Decimals
222_0225_C05L03_101808.indd 223
!
223
12/7/09 1:56 PM
AL
COMMON ERROR!
Students may automatically right-align decimal numbers without
considering the place value of the digits. Encourage students to
write zeros behind each decimal number first so that all the
numbers extend to the same place value. In this way, when
students align the right-most digit, this will always correctly align
the decimal point too.
If
students have difficulty with subtracting
decimals . . .
Then
1
AL
Reteach Worksheet
2 Use Kinesthetic Activities Hand out random
slips of paper that have a place value from ten
to hundredths and other slips of paper with a
digit 0 through 9 written on them. Have students
arrange themselves into decimal numbers based
on their place value and then find the difference
between the two groups.
223
3 PRACTICE
Level
Assignment
AL
Approaching Level
9–19 odd, 20–33
OL
On Level
10–20 even, 21–33
Beyond Level
10–18 even, 19–33
BL
Subtract. See Examples 1–4
Subtract
1 4
1. 5.5 - 3.2 2.3
2. 72.4 - 12.5 59.9
3. 29.34 - 9 20.34
4. 0.40 - 0.20 0.2
5. 9.67 - 2.35 7.32
6. 36 - 7.3 28.7
7. Use the table to find out how many more people there
are per square mile in Iowa than in Colorado. 10.9 people
8.
E TALK MATH Is it possible to have an answer with a
number in the thousandths place when subtracting
money? Explain. Sample answer: No. Since the smallest unit
of money is the cent, there is no thousandths place.
Population Density
People Per
State
Square Mile
Colorado
41.5
lowa
52.4
EXTRA
%
#E
4) C
!# TI
2 AC
0R
P
Begins on page EP2.
complete the Higher Order Thinking problems. Encourage
students to explain how placing a decimal point and
adding zeros at the end of a whole number does not
change its value.
E
Subtract.
S
bt t See Examples
l 1–4
9. 5.6 - 3.5 2.1
10. 19.86 - 4.94 14.92
11. 97 - 16.98 80.02
12. 42.28 - 1.52 40.76
13. 8 - 5.78 2.22
14. 15 - 6.24 8.76
15. 82 - 67.18 14.82
16. 58.67 - 28.72 29.95
17. 14.39 - 12.16 2.23
18. The table shows the top three finishers in barrel racing
at the Livestock Show and Rodeo. What is the time
difference between first place and second place? 0.13 s
19. BAR DIAGRAM You decide to buy a hat for $10.95 and
a T-shirt for $14.20. How much change will you receive
if you pay with a $50 bill? $24.85
Barrel Racing Results
Rider
Time (s)
Denise
15.87
Angela
16.00
Liz
16.03
Use the information to solve the problem.
Rewatch “Filling a Phone.”
20. How many more gigabytes of space does Desiree’s new
phone have than her old phone? 0.75 gigabyte
✔ 0506.1.9 Use age-appropriate
books, stories, and videos to
0222_0225_C05L03_103031.indd 224
E
WRITE MATH Have students write their own
graphic novel in which they add and subtract decimals.
Tips for New Teachers
Allow students to take turns teaching decimal addition and
subtraction to the class. Learning is often clarified and
internalized when understanding is verbally expressed as
organized thought.
224
2/26/10 10:51 A
4 ASSESS
21. NUMBER SENSE Without solving, would the difference of
4.23 - 2.75 be less than or equal to 2? Explain. Sample answer:
less than; 2.75 is about 3 and 4 - 3 = 1.
WRITE MATH Explain how you would find the difference
22. E
of 3 and 2.89. Sample answer: Write zeros so that both numbers have the same place
value. Line up the decimal points, then subtract as with whole numbers.
• What are some important things to remember
about subtracting decimals? Sample answer: Line up
the decimals.
• How can estimating the difference help you when
subtracting decimals? Sample answer: Estimating the
difference can show what the exact answer should be
close to.
Test Practice
23. Alvin had $15.00 to spend at the
sports card store. Baseball cards cost
$1.75 per pack, and hockey cards cost
$0.99 per pack. If Alvin buys 6 packs
of baseball cards for $10.50, how can
he determine how much money he
has left to spend on hockey cards? A
24.
A. Subtract $10.50 from $15.00.
B. Add $1.75 and $0.99.
C. Subtract $0.99 from $1.75.
SHORT RESPONSE The table
lists the average number of people
per square mile for several states.
Population per
square mile
State
Florida
296.4
Indiana
169.5
Kentucky
101.7
North Carolina
165.2
with subtracting decimals?
If Yes
How many more people per square
mile are in Florida than in Kentucky?
194.7 people per sq mile
D. Add $0.99 and $10.50.
AL
AL
If No
OL
OL
BL
Enrich Worksheet
(p. 218c)
(p. 218c)
Use properties of addition to find each sum mentally. Show
your steps and identify the properties that you used. (Lesson 2D) 25–27. See margin.
25. 12 + 65 + 5
26. 39 + 17 + 1
27. 2.6 + 1.3 + 1.7
Subtract 0.47 from 6. Explain your
strategy. 5.53; Answers will vary.
Add. (Lesson 2C)
28.
0.5
+ 1.1
−−−−
1.6
29.
0.95
+ 0.34
−−−−−
1.29
Estimate. (Lesson 1B)
30. 4.231 + 3.98
31. 3.945 + 1.92 + 3.55
4+4=8
4 + 2 + 4 = 10
32. Round 28.561 to the nearest tenth. (Lesson 1A) 28.6
Review and assess mastery of skills and concepts from the
previous lessons in the chapter.
33. A cougar has a mass of 102.948 kilograms. Round the
mass to the nearest tenth of a kilogram. (Lesson 1A) 102.9 kg
222_0225_C05L03_103031.indd 225
225
2/26/10 10:51 AM
Additional Answers
25. 82; 12 + 65 + 5 = 12 + (65 + 5) Associative
Property for Addition; = 12 + 70 Add 65 and 5
mentally; = 82 Add 12 and 70 mentally
26. 57; 39 + 17 + 1 = 39 + 1 + 17 Commutative
Property for Addition; = 40 + 17 Add 39 and 1
mentally; = 57 Add 40 and 17 mentally
Multi-Part Lesson 3 Why is it helpful to place a zero in the hundredths place
of the number 7.4 before subtracting 3.85? Sample answer: Placing a zero in
the hundredths place reminds you to “borrow” from the 4 in the tenths place
before subtracting. This will help you to subtract accurately.
27. 5.6; 2.6 + 1.3 + 1.7 = 2.6 + (1.3 + 1.7)
Associative Property for Addition; = 2.6 + 3.0 Add
1.3 and 1.7 mentally; = 5.6 Add 2.6 and 3.0
mentally
225
3
Multi-Part
Lesson
PART
PART
D
Multi-Part
Lesson
Subtract Decimals
A
B
C
D
3
Subtract Decimals
PART
A
B
C
D
Problem-Solving
Strategy: Work Backward
Work Backward
Main Idea I will solve non-routine problems by using the work backward strategy.
The Nature Club raised $125.25 to buy
and install nesting boxes for birds at a
wildlife site. Each box costs $5. It costs
$75.25 to rent a bus so the members
can travel to the site. How many boxes
can the club buy?
Objective
Solve non-routine problems using the work backward
strategy.
Understand
Resources
Leveled Worksheet
• $125.25 is available to buy and install the nesting boxes.
Get ConnectED
• Each box costs $5.
• The bus costs $75.25.
and decimals. GLE 0506.1.2 Apply and adapt a variety of
• How many boxes can the club buy?
Plan
1 INTRODUCE
Activity Choice 1: Review
Solve
• Present students with the following problem:
Then undo the multiplication of the cost of the boxes. To undo, divide by
the cost for each box.
$50 ÷ $5 = 10
• What strategy would you use to solve this problem?
guess and check
So, ten boxes can be bought.
Check
• How old are the girls now? Jennika is 8; Akili is 4.
Activity Choice 2: RWPS Reader
• Allow students to extend their knowledge by
investigating the advantages and disadvantages of
different modes of transportation.
2 TEACH
Have students read the problem on the student page.
Guide them through the problem-solving steps.
Understand
Using the questions, review what
students know and need to find.
Plan
Have them discuss their strategy.
226
Since, 10 × $5 = $50 and $50 + $75.25 = $125.25, the answer is correct. GLE 0506.2.5 Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and
decimals. GLE 0506.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including estimation,
• Read A Growing Nation as a class.
• Have students solve the problems using the four-step
plan. Then ask them to share which strategy they used
to solve problems.
First, undo the addition of the cost of the bus by subtracting the
cost of the bus.
$125.25 - $75.25 = $50
Today Jennika is twice as old as her cousin Akili. In five
years, the sum of their ages will be 22. How old are
Jennika and Akili now?
• Use the information in the Real-World Problem Solving
Readers Teacher Guide to preview, read, and respond
to the book.
You can work backward to find the number of boxes that can be bought.
Start with $125.25, the amount the Nature Club has raised. Then subtract
the costs. Recall that subtraction “undoes” addition and that division
“undoes” multiplication.
2
0226_0227_C05PSS_103031.indd 226
AL
2/26/10 11:06 A
If
Then
students have trouble understanding how to work
backward to solve a problem . . .
1 AL Reteach Worksheet
2 Use a Strategy Have students use additional problem-solving
strategies to help them solve the problem, such as the use the
four-step plan or the guess, check, and revise strategy.
Solve
Guide students to work backward.
• How much is left after paying for the bus?
Explain. $50; subtract 125.25 - 75.25.
1–4. See margin.
Refer to the problem on the previous page.
1. Explain how using the work backward
strategy helped you find the number of
nesting boxes the club could buy.
3. What is the best way to check your
solution when using the work
backward strategy?
2. Suppose the club had $152 to spend.
How many boxes could the club buy?
Would there be any money left?
4. Explain when you would use the work
backward strategy to solve a problem.
EXTRA
• What operation will help figure out how many $5
boxes can be bought with $50? division
%
#E
4) C
!# TI
2 AC
0R
P
Check
Have students look back at the problem.
• Should 10 boxes cost $50? Explain. Yes; they cost
$5 each and $5 × 10 = $50.
Begins on page EP2.
Solve. Use the work backward strategy.
5. Students sold raffle tickets to raise
money for a field trip. The first
20 tickets sold cost $4 each. To sell
more tickets, they lowered the price to
$2 each. If they raise $216, how many
tickets did they sell in all? 88 tickets
6. Allie collected 15 more cans of food
than Peyton. Ling collected 8 more
than Allie. Ling collected 72 cans of
food. How many cans of food did
Peyton collect? 49 cans
7. Jeanette’s sister charges $5.50 per hour
before midnight for babysitting and
$8 per hour after midnight. She
finished babysitting at 2:00 A.M. and
earned $38. At what time did she
begin babysitting? 8:00 P.M.
8. Seth bought a movie ticket, popcorn,
and a drink. After the movie, he played
4 video games that each cost the same.
He spent a total of $19. How much did
it cost to play each video game? $1
Popcorn $4
Drink
$3
Ticket
$8
9. Russell has two times as many dimes
as quarters. The number of nickels is
shown below. He has 3 more quarters
than nickels. How much money does
Russell have in all? $2.85
3 PRACTICE
Using the Exercises
Use the Extend Exercises to analyze and discuss the
problem-solving strategy.
Exercises 5–9 provide students with practice using the
work backward strategy.
10. Chet has $4 in change after buying a
bike and a helmet. How much money
did Chet have originally? $124
Exercise 12 Help the students to explain their operation
selection(s) using proper mathematical language.
$89.25
4 ASSESS
$30.75
11. Rosita is 3 years older than Ramiro.
Ramiro is 2 years older than Francesca.
Francesca is 8 years younger than
Pablo. If Pablo is 21 years old, how old
is Rosita? 18 years old
12.
E
WRITE MATH Suppose Carla scored
7 more goals than Papina and Stu
scored 2 more than Carla. If Stu scored
15 goals, what operation(s) can you
use to find the number of goals Papina
scored? Solve, then explain your
selection(s). See margin.
To assess partial mastery of SPI 0506.1.2 and SPI 0506.2.5, see your Tennessee Assessment Book.
226_0227_C05PSS_103031.indd 227
227
Have students use the work backward strategy to solve the
following problem:
Soto collects rocks. While on his summer vacation he lost
5 rocks that he took to show his cousin, but later that
week he found 12 new rocks to add to his collection.
He now has 28 rocks. How many rocks did he have before
his summer vacation? 21 rocks
Explain the order of the steps you took to find the
solution.
Sample answer: I started with 28 rocks and subtracted 12.
Then I added five to find the answer of 21 rocks.
2/26/10 11:40 AM
Additional Answers
1. Sample answer: You knew the cost of each nesting box, the cost of the bus, and
the total amount of money the club had to spend, so by working backwards you
could find the total number of nesting boxes the club could buy.
with using the work backward strategy?
2. 15 boxes; Yes. There is $1.75 left.
If Yes
AL
3. Sample answer: Start with the answer that you found and then work the problem
forward to see if you arrive at the number you were given in the problem.
If No
OL
Enrich Worksheet
4. Sample answer: When you are given a solution and some steps taken to arrive at
the solution and you are asked to find an earlier amount.
12. Subtraction; 6; The word more implies addition, so to undo addition use
subtraction.
OL
BL
BL
(p. 218c)
(p. 218d)
Lesson 3D Subtract Decimals
227
Objective
Interpret information and data from social studies to solve
problems.
Resources
Get ConnectED
and decimals. GLE 0506.1.7 Recognize the historical
development of mathematics, mathematics in context, and the
connections between mathematics and the real world.
✔ 0506.1.9 Use age-appropriate books, stories, and videos to
Activate Prior Knowledge
Before you turn students’ attention to the pages, ask them
to discuss apples.
• What kinds of apples have you eaten? Sample
Answers: Red Delicious, Macintosh, Granny Smith
Baseball, hot dogs, and apple pie are American
favorites. There are about 8,000
0 apple orchards in
the United States, producing more
ore than 100 different
pple crops in the
kinds of apples. The value of apple
United States is about $1.8 billion.
ion. Farmers harvest
enough for each person in the United States to have
79 apples. That would make a lot of apple pies!
• Where are apples grown? in an orchard, on trees
• What kinds of foods are made with apples? Sample
answer: applesauce, pies, fruit salad
Use the Student Page
Ask students to read the information on the student page
and answer these questions.
• How many pounds of apples can one tree produce?
840 pounds
• What is the difference between the apple crops of
the two states that produced the least amount
of apples? 0.09 million
One apple
e
0
tree can fill 20
xe
es
42-pound boxes
s.
with apples.
0228_0229_C05CC_101808.indd 228
Fun Facts
• Apples are grown in all 50 states; 36 states grow apples
commercially.
• Apples are fat, sodium, and cholesterol free.
• The science of apple growing is called pomology.
• Apples are the second most valuable fruit grown in the United
States. Oranges are the first.
228
11/17/09 3:15
Assign the exercises. Encourage students to choose a
problem-solving strategy before beginning each exercise.
California
0.41
States
Michigan
New York
Pennsylvania
Virginia
1.15
0.43
Exercise 6 Remind students that they can also use
addition properties when finding an exact sum.
0.32
Washington
0
1.00
Exercise 3 Remind students that they do not need to
use the long version of millions in order to answer this
question.
0.82
2.00
3.00
5.60
4.00
5.00
E
6.00
WRITE MATH Have students create a word
problem that uses the information found in the text and
in the graph.
Pounds (millions)
Extend the Activity
Use the information on the previous page and the graph above to solve
each problem.
228_0229_C05CC_101808.indd 229
Which state produced the least
amount of apples? How many
pounds of apples did this state
produce? Round to the nearest
tenth. Virginia, 0.3 million
Which state’s apple crop was
closest to 1 million pounds?
New York
How many more millions of pounds
of apples were produced in
Washington than Virginia?
5.28 million
What is the difference in apple
production between the top two
states? 4.45 million
BL
Have students find the total number of apples produced
by all six top apple-producing states.
Use rounding to estimate the total
amount of apples produced in
Michigan, California, and
Pennsylvania.
Sample answer: 1.6 million
Find the exact sum of the apples
produced in Michigan, California,
and Pennsylvania. Compare this
number to your answer to
Exercise 5. 1.66; 1.66 > 1.6 million
Two pounds of apples make one
pie. If you want to make 6 pies, how
many pounds of apples should
you pick? 12 pounds
Problem Solving in Social Studies
229
12/7/09 2:00 PM
Problem Solving in Social Studies
229
Chapter Study
Guide and Review
Chapter Study
Guide and Review
The
BIG Idea
Be sure the following Big
Ideas are noted in your
Foldable.
As a class, revist this chapter’s Big Idea.
How do I add and subtract decimals
accurately?
Vocabulary
decimal
Vocabulary Check
Sample answer: In order to add and subtract accurately, it
is important to align the place value, using the decimal
point as an anchor.
Choose the correct term or number
to complete each sentence.
Estima
Est
imate
te
Sum
Suums and
nd
Ad
Difffer
ferences
fe
es Dec d
imals Su
De btra
cim ct
als
1. When you round a number, you
find its (approximate, exact) value.
Key Concepts with
Use these lesson suggestions to incorporate the Foldable
during the chapter. Students can then use their Foldables
to review for the test.
Multi-Part Lesson 3 Under the right flap of the Foldable,
students demonstrate their ability to subtract decimals.
Key Vocabulary
Review chapter vocabulary using one of the following
options.
• Visual Vocabulary Cards
Key Concepts
Estimation (Lesson 1)
• When you round a number, you find its
approximate value to a specified place
value.
6.79 rounded to the nearest tenth is 6.8.
• You can use rounding to estimate sums
and differences.
40 Round each addend to
+
40 the nearest ten.
−−−−
80 The sum is about 80.
42.6
+
38.5
−−−−−
• eGlossary
•
Vocabulary Test
Add and Subtract Decimals (Lessons 2 and 3)
Vocabulary Check
If students have difficulty answering the Exercises, remind
them they can use the Key Vocabulary terms listed on the
student page. You may also direct them to the lesson in
which each term is taught.
• To add or subtract decimals, estimate first.
Line up the decimal points. Add or subtract
digits in each place-value position.
2.46
+
1.73
−−−−−
4.19
36.19
2.07
−−−−−
34.12
2. A (whole number, decimal) is a
number that has digits in the
tenths place, hundredths place,
and beyond.
3. The difference between 10.8 and
2.05 is (8.3, 8.75).
4. To find a number that is close to
the exact answer, you can
(estimate, add).
5. A reasonable estimate for
6.19 + 2.85 is (9, 90).
6. The (Associative, Commutative)
Property states that you can add
numbers in any order.
7. The (Identity, Associative) property
of addition states that the sum of
any number and zero equals that
number.
0230_0235_C05SGR_101808.indd 230
Chapter Project
Food Drive In pairs, small groups, or as a class have students discuss the results of
their completed chapter project. Assess their work using the Project Rubric found
in the
Chapter Resource Masters.
230
12/7/09 2:02
Multi-Part Lesson Review
Lesson 1
Round Decimals
(Lesson 1A)
Round each number to the place
indicated.
EXAMPLE 1
Round 47.12 to the underlined digit.
8. 8.4; ones 8
The digit in the place to be rounded is 7.
The digit to the right of 7 is 1. Since 1 < 5,
round down.
9. 675.5; hundreds 700
47.12
10. 3.26; tenths 3.3
11. 0.92; tenths 0.9
47
Round 0.865 to the underlined digit.
The digit in the place to be rounded is 8.
The digit to the right of 8 is 6. Since 6 > 5,
round up.
13. 75.235; hundredths 75.24
14. Measurement A person set a
world record by eating 14 hard boiled
eggs in 14.42 seconds. Round this
time to the nearest tenth of a
second. 14.4 s
15–20. Sample answers given.
15. 9.1 + 1.4
9 + 1 = 10
16. 5.73 - 4.29
6-4=2
17. 26.09 - 5.8
26 - 6 = 20
18. 3.95 + 11.76
4 + 12 = 16
19. 80.8 - 3.92
81 - 4 = 77
20. 3.162 + 0.624
3+1=4
0.865
Have students complete the Multi-Part Lesson Review.
Then you can use ExamView® Assessment Suite to
customize another review worksheet that practices all the
objectives of this chapter or only the objectives on which
your students need more help.
Intervention If the given examples are not sufficient to
review the topics covered by the questions, remind
students to:
• Use the multi-part lesson titles above each set of
exercises to review that topic in the Student Edition.
EXAMPLE 2
12. 13.61; ones 14
•
Get ConnectED
Review Personal Tutors
Reflecting on the Chapter
0.9
Provide this study tip for your students.
Aligning Decimal Numbers
(Lesson 1B)
21. Sherita had $78.51 in her bank at
home. She adds $3.67 in change.
About how much does she have now?
Show your work. Sample answer:
79 + 4 = $83
230_0235_C05SGR_103031.indd 231
Multi-Part Lesson Review
Remind students to line up the decimals
in each number before adding or
subtracting. Students may want to add
zeros at the end of some numbers to
create the same place value for all the
numbers. This may help students
accurately complete the computation.
EXAMPLE 3
Estimate 9.45 + 5.85 using rounding.
Round 9.45 to 9.
Round 5.85 to 6.
9.45
+
5.85
−−−−−
9
+
6
−−−
15
The sum is about 15.
Chapter Study Guide and Review
231
2/26/10 11:06 AM
231
Chapter Study
Chapter
Study G
Guide
uide a
and
nd R
Review
eview
Lesson 1
(continued)
Problem-Solving Investigation: Estimate or an Exact Answer
For each problem, determine whether
you need an estimate or an exact
answer. Then solve.
22. A total of 8 fifth-grade teachers
donated $15 each to the school’s
band. How much money did they
donate in all? exact answer; $120
23. A group of 5 friends are sharing the
cost of renting a boat for one day. If
the boat costs $144.95, about how
much will they each pay for the boat?
estimate; $30
24. The local bakery makes 85 pies each
day. The bakery has sold all of the pies
for 9 days in a row. About how many
pies were sold during these 9 days?
estimate; 850 pies
Lesson 2
(Lesson 1C)
EXAMPLE 4
Nina’s breakfast cost $2.64. She gave
the cashier $5. How much change
should Nina receive?
You need to find an exact answer.
Subtract $2.64 from $5.
5.00
2.64
−−−−−
2.36
Nina’s change is $2.36.
Add Decimals
Add Decimals
(Lesson 2C)
Add.
26.
0.64 27.
8.63
4.8
+
5.7
+
0.52
+
0.19
−−−−
−−−−−
−−−−−
10.5
1.16
8.82
28. 0.625 + 4.8
29. 7.013 + 2.21
9.223
5.425
30. The average female heart weighs
9.3 ounces. The average male heart
weighs 1.8 ounces more. What is the
average weight of a male heart?
11.1 oz
31. Measurement The female Dwarf
Goby is the smallest marine fish. Its
average length is 0.35 inch. How long
are 2 female Dwarf Goby fish? 0.7 in.
25.
EXAMPLE 5
Find 8.3 + 10.75.
Estimate 8 + 11 = 19
Line up the
Write a zero. Add as with
decimal points.
whole numbers.
8.3
+
10.75
−−−−−−
8.30
+
10.75
−−−−−−
8.30
+
10.75
−−−−−−
19.05
The sum is 19.05. Since this is close to the
estimate, the answer is reasonable.
0230_0235_C05SGR_101808.indd 232
232
11/17/09 3:19
Lesson 2
Add Decimals
Addition Properties
(continued)
(Lesson 2D)
rewrite each problem.
32. 7 + 65 + 13 = 7 + 13 + 65
Commutative
33. (4 + 0.7) + 0.3 = 4 + (0.7 + 0.3)
Associative
34. 328 + 0 = 328 Identity
Use properties of addition to find each
sum mentally. Show your steps and
identify the properties that you used.
35. 46 + 4 + 31 36. 8.7 + 4 + 0.3
35, 36. See margin.
37. Use the Associative Property to group
the numbers in the table and find the
total amount of money the sports
teams raised.
Lesson 3
Additional Answers
35. 46 + 4 + 31 = (46 + 4) + 31 Associative Property
Sports Team
Donations ($)
Soccer
Football
Tennis
3,500
4,250
2,750
EXAMPLE 6
rewrite the problem below.
= 81
36. 8.7 + 4 + 0.3 = 8.7 + 0.3 + 4
28 + 5 + 62 = 28 + 62 + 5
The order of the numbers changed. This is
the Commutative Property.
EXAMPLE 7
= (8.7 + 0.3) + 4 Associative Property
=9+4
= 13
Use properties of addition to find
1.4 + 9.7 + 8.6 mentally.
1.4 + 9.7 + 8.6
= 1.4 + 8.6 + 9.7 Commutative Property
= (1.4 + 8.6) + 9.7 Associative Property
= 10 + 9.7
Add 1.4 and 8.6.
= 19.7
Add mentally.
37. (2,750 + 4,250) + 3,500; $10,500
Subtract Decimals
Subtract Decimals
(Lesson 3C)
Subtract.
EXAMPLE 8
39.
0.44 40.
2.63
5.2
0.36
3.8
0.15
−−−−
−−−−−
−−−−−
1.4
0.08
2.48
41. 3.25 - 1.7 1.5542. 8.01 - 2.519 5.491
Estimate 18 - 12 = 6
38.
43. 0.8 - 0.39 0.4144. 65.2 - 9.51 55.69
45. Measurement The head and body
of a pygmy mouse lemur measures
2.4 inches and its tail measures
5.3 inches. How much longer is the
animal’s tail than head and body? 2.9 in.
230_0235_C05SGR_103031.indd 233
= 50 + 31
Find 18.34 - 12.1.
Line up the
decimal points.
18.34
12.1
−−−−−−
Write a
zero.
18.34
12.10
−−−−−−
Subtract as with
whole numbers.
18.34
12.10
−−−−−−
6.24
The difference is 6.24.
Check 6.24 ≈ 6 Chapter Study Guide and Review
233
2/26/10 11:06 AM
233
Lesson 3
Subtract Decimals
(continued)
Problem-Solving Strategy: Work Backward
Solve. Use the work backward strategy.
46. The science club raised money to
clean the beach. They spent $29.75
on trash bags and $74.75 on
waterproof boots. They still have $47
left. How much did they raise? $151.50
47. Mr. Charles cut fresh roses from his
garden and gave 10 roses to his
neighbor. Then he gave half of what
was left to his niece. He kept the
remaining 14 roses. How many roses
did he cut? 38 roses
(Lesson 3D)
EXAMPLE 9
The swim team spent $385.25 to travel
to a meet. The bus cost $145.25. Each
person had to pay $30 for the hotel.
How many people went on the trip?
Understand
• The swim team spent a total
of $385.25.
• The bus cost $145.25.
• The hotel was $30 per person.
• The number of people that went
on the trip.
Plan
48. A number is divided by 6. 8.5 is
added to the quotient. Then 3.2 is
subtracted from the sum. The result
is 7.3. What is the number? 12
49. Mr. Evans bought the items listed. He
had $5 left over. About how much did
Mr. Evans have to start with?
Work backward.
Solve
Subtract to undo the cost of the bus.
$385.25 - $145.25 = $240
Divide to find the number of people.
$240 ÷ $30 = 8
So, 8 people went on the trip.
Items Purchased
toothpaste
soap
$3.84
$2.21
mints
$0.88
Sample answer: $12; $4 + $2 + $1 = $7 and
$7 + $5 = $12.
Check
Solve the problem working forward.
8 × $30 = $240,
$240 + $145.25 = $385.25 234 Add and Subtract Decimals
0230_0235_C05SGR_103031.indd 234
234
2/26/10 11:06 A
Practice
Chapter Test
Practice
Chapter Test
2. 12.034; hundredths 12.03
3. 6.93; ones 7
4. 3.041; tenths 3.0
5. MULTIPLE CHOICE One mile is equal
to 1.609 kilometers. Round this to the
nearest hundredth. B
C. 1.60 kilometers
B. 1.61 kilometers D. 1 kilometer
6. 65.3 - 8.1 57
Use these alternate leveled chapter tests to differentiate
assessment for the specific needs of your students.
19, use the table that shows the typical
lengths of a Rusty-spotted Cat.
1. 7.85; tenths 7.9
A. 2 kilometers
Summative Assessment
Measurement For Exercises 18 and
Round each number to the place
indicated.
7. 42.9 + 6.02 49
Measure
Least
Length (in.)
Greatest
Length (in.)
body
tail
13.7
5.9
18.8
9.8
18. What is the difference between the
greatest and least lengths for the cat’s
body? 5.1 in.
19. How long is a Rusty-spotted Cat if it
has the greatest lengths for its body
and tail? 28.6 in.
Use properties of addition to find each
sum mentally.
20. 38 + 19 + 1 58
21. 0.3 + 1.2 + 0.7
2.2
8. 9.16 + 2.04 11
9. 73.8 - 59.74 10
22. 75 + 27 + 25 127 23. 1.6 + 33 + 11.4
46
10. Measurement The table shows the
24. The fee to join the community baseball
heights of mountains. How much taller
league is $34.25. However, if you are a
is Mt. McKinley than Mt. Saint Elias?
returning member to the league, you
770.7 yd
receive a discount of $12.50 off the
Mountain
Height (yd)
regular price. What is the cost in dollars
Mt. McKinley
6,773.3
for a returning member? $21.75
6,002.6
Mt. Saint Elias
11. A helicopter flight to and from the rain
forest costs $499.50. Supplies cost
$75.48 for each day. How much would
it cost for a scientist to study in the rain
forest for two days? $650.46
25.
Add or subtract.
12. 3.87 + 12.5 16.37 13. 43.8 - 7.51
14. 15.2 + 7.69 22.89 15. 239.6 - 0.85
16. 3.47 + 1.95 5.42 17. 260.3 - 71.8
13. 36.29 15. 238.75 17. 188.5
Baseball
League
Price
New
Member
$34.25
Returning
Member
AL
BL
E WRITE MATH A speed skater’s time
in an event was 40.33 seconds. The
same skater was 1.08 seconds faster
the next time she skated in the
event. What was her time in the
second race? Explain. See Answer
Appendix.
230_0235_C05SGR_103031.indd 235
Form
AL
Multiple Choice
1A
AL
Multiple Choice
1B
OL
Multiple Choice/Free
Response
2A
OL
Multiple Choice/Free
Response
2B
BL
Free Response
3A
BL
Free Response
3B
Additional Chapter Resource Masters
OL
Practice Chapter Test
Chapter Tests
Type
Level
OL
Vocabulary Test
OL
Extended Response Test
OL
Oral Assessment
= approaching grade level
= on grade level
= beyond grade level
Customize and create multiple
versions of your Chapter Test and the test answer keys.
235
2/26/10 11:06 AM
Data-Driven Decision Making
Based on the results of the Chapter Test, use the following to review concepts that continue to present students with problems.
Exercises
Tennessee
Standards
What’s the Math?
Error Analysis
Resources for Review
1–5
GLE 0506.1.2
Round decimal numbers.
Did not understand the rules for rounding.
Chapter Resource Masters
6–9
GLE 0506.2.5
Estimate sums or differences of decimal
numbers.
Did not understand the rules for rounding or
the concept of compatible numbers.
Get ConnectED
10–19
GLE 0506.1.2
Add and subtract decimals.
Did not understand the algorithm for adding
and subtracting decimal numbers.
20–23
GLE 0506.2.5
Add decimal and whole numbers
mentally, using the properties of addition.
Did not understand the Commutative,
Associative, and Identity Properties of Addition.
Add and subtract decimal numbers in
problem situations.
Does not understand the algorithm for
subtracting decimal numbers.
24–25
GLE 0506.1.2
Lesson Animations • Personal Tutor
• Self-Check Quiz
235
Test Practice
Test Practice
1 INTRODUCE
Remind students to read the test questions carefully. The
instructions in the example say to estimate the number of
hours worked. Students should not find the exact number
of hours, but rather use rounding to estimate the total
number of hours worked.
2 TEACH
Before beginning the practice test, give students an
opportunity to solve the Additional Example.
The table shows the number of hours José worked last summer
at his part-time job. Estimate the total number of hours worked.
Month
Hours
May
78.50
June
83.25
July
81.50
August
79.75
A. 280 h
C. 320 h
B. 300 h
D. 360 h
Read the Test Item
You need to estimate the sum.
Solve the Test Item
Round the number of hours worked each month then add.
The table shows the amount of money raised by
each class at the book fair. Estimate the total
amount of money raised by all four classes by
rounding each amount to the greatest place
value. B
Class
Amount
3rd grade
$52.42
4th
grade
$48.27
5th grade
$54.08
6th grade
$50.23
A. $190.00
C. $204.00
B. $200.00
D. $205.00
78.50 80 83.25 80
81.50 80 79.75 80
80 + 80 + 80 + 80 = 320
The answer is C.
Read each question. Then fill in the correct answer on the answer
sheet provided by your teacher or on a separate sheet of paper.
1. The times of four runners in a relay
race are shown in the table. Estimate
the total time of the team. D
2. Which is the best estimate for the total
cost of a hamburger, a bag of chips,
and a drink? F
Runner
1
2
3
4
F. $2.50
Time(s)
14.9
15.1
14.8
15.3
G. $2.75
Cafeteria Prices ($)
Hamburger
$1.19
A. 40 s
C. 50 s
H. $3.00
Chips
$0.49
B. 45 s
D. 60 s
I. $3.25
Drink
$0.79
0236_0237_C05STP_103031.indd 236
3 ASSESS
• Use these pages as practice and cumulative review. The
questions are written in the same style as those found
on standardized tests.
• You can use these pages to benchmark student
progress, or as an alternate homework assignment.
236
3/10/10 12:07
3. Refer to the table that shows the prices
of several items. How much more does
a box of crayons cost than a pen? D
7.
Bookstore Prices
5.
$0.79
notebook
$0.49
A
34.5
box of crayons
$3.69
B
40.6
C
39.2
C. $2.80
B. $2.50
D. $2.90
Runner
I. 40
/Volumes/121/GO00398/GO00398_Math_Connects_CRM_NA_G5%0/XXXXXXXXXXXXX_SE/Appli...
Name _____________________________ Date ________________
Student Recording Sheet
8. Bruce received $50 for his birthday. He
wants to buy the items listed below. All
prices include tax. How much will
Bruce have left over after paying for
these items? B
A. $5.98
C. $7.22
B. $6.31
D. $8.56
Item
Cost
Video game
$24.89
CD
$11.18
1.
A
B
C
D
6.
2.
F
G
H
I
7.
3.
A
B
C
D
4.
8.
F
G
H
I
.
A
B
C
D
9.
5.
77
Grade 5 • Add and Subtract Decimals
Poster
$7.62
Additional Practice
6. Rachel has a collection
of 128 shells. If she
has 4 shelves to
equally display her
collection, how many shells
should she have on each shelf?? G
G. 32
055_078_C05_101837.indd Page 77 11/24/09 3:34:14 PM s-013
Read each question. Then fill in the correct answer.
SHORT RESPONSE A football team
scored 27 points in a game. These
points were either 3-point field goals or
7-point touchdowns. How many field
goals and touchdowns did the team
score? 2 field goals and 3 touchdowns, or
9 field goals, 0 touchdowns
H. 35
Student Recording Sheet
Time (seconds)
Use this recording sheet with the Test Practice pages located at the
end of the chapter in the Student Edition.
GRIDDED RESPONSE In one year
Brian plays a total of 372 hours of
video games. How many hours of video
games does Brian play in one month? 31
F. 24
Have students simulate taking a standardized test by
recording their answers on a practice recording sheet.
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4.
pen
A. $2
Answer Sheet Practice
GRIDDED RESPONSE The table
shows the times of 3 runners. How
much faster is Runner A than
Runner C in seconds? 4.7
9.
SHORT RESPONSE Explain if an
estimate or an exact answer is needed
for the problem below. Then solve.
Mr. Brooks pays $70 to buy five jerseys
that cost $12 each. How much change
should Mr. Brooks receive? exact; $10
•
Standardized Test Practice
•
Get ConnectED
•
Find additional test practice.
Create practice worksheets or
tests that align to your state’s
standards.
NEED EXTRA HELP?
If You Missed Question . . .
Go to Chapter-Lesson . . .
236_0237_C05STP_103031.indd 237
For help with . . .
1
2
3
4
5
6
7
8
9
5-1B
5-1B
5-3C
4-2B
3-1E
3-2D
5-3C
5-3C
5-1C
SPI 1.2 SPI 1.2 SPI 2.5 SPI 2.4 GLE 1.2 SPI 2.4 SPI 2.5 SPI 2.5 GLE 1.2
Test Practice 237
2/26/10 11:06 AM
Test Practice
237
Chapter Answer Appendix
Multi-Part Lesson
2
PART B
9.
PAGE 207
1.
2.
PART D
PAGE 214
12. 15 + 8 + 25 = 15 + 25 + 8
= (15 + 25) + 8 Associative Property
3.
= 40 + 8
= 48
13. 7.7 + 4.3 + 11 = (7.7 + 4.3) + 11
4.
= 12 + 11
= 23
14. 37 + 26 + 53 = 37 + 53 + 26
5.
= (37 + 53) + 26
= 90 + 26
= 116
15. 10.9 + 3 + 0.1 = 10.9 + 0.1 + 3
6.
= (10.9 + 0.1) + 3
= 11 + 3
= 14
16. 63 + 35 = (60 + 3) + (30 + 5)
63 = 60 + 3 and
35 = 30 + 5 = 60 + 30 + 3 + 5
= (60 + 30) + (3 + 5)
7.
= 90 + 8
= 98
17. 57 + 48 = (50 + 7) + (40 + 8)
57 = 50 + 7 and
48 = 40 + 8 = 50 + 40 + 7 + 8
= (50 + 40) + (7 + 8)
8.
= 90 + 15
= 105
20. 65 + 18 + 35 = 65 + 35 + 18
= (65 + 35) + 18
= 100 + 18
= 118
The total cost is $118.
21. 262 cans; Sample answer: (43 + 57) + (58 + 42) + 62 =
100 + 100 + 62 = 262
PART B
9.
3
PAGE 221
2.
3.
PAGE 235
25. 39.25 s; Subtract 0.08 from 1.08 and 40.33. Then
40.25 - 1 = 39.25.
4.
5.
6.
7.
8.
237b
Multi-Part Lesson
Photo Credits:
Unless otherwise credited, all currency courtesy of the US Mint; 192c 192f Richard
Hutchings/Digital Light Source; 195c The McGraw-Hill Companies; 195d (tr)Mark
Steinmetz/The McGraw-Hill Companies, (cl)Richard Hutchings/Digital Light Source;
204d (br)Ed-Imaging, (others)Michael Houghton/StudiOhio; 218d (tl)Ken Cavanagh/
The McGraw-Hill Companies, (cr)Ingram Publishing/AGE Fotostock.
Copyright © 2012 by the McGraw-Hill Companies, Inc. All rights reserved. Permission is granted
to reproduce the Chapter Resource Masters material on pages 1-78 on the condition that such
material be reproduced only for classroom use; be provided to students, teachers, and families
without charge; and be used solely in conjunction with Tennessee Math Connects. Any other
reproduction, for use or sale, is prohibited without prior written permission of the publisher. No
additional parts of this publication may be reproduced or distributed in any form or by any means,
or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill
Companies, Inc., including, but not limited to, network storage or transmission, or broadcast for
distance learning.
Send all inquiries to:
Macmillan/McGraw-Hill
8787 Orion Place
Columbus, OH 43240-4027
ISBN: 978-0-02-103111-5 (Teacher Edition)
MHID: 0-02-103111-8 (Teacher Edition)
ISBN: 978-0-02-103031-6 (Student Edition)
MHID: 0-02-103031-6 (Student Edition)
Printed in the United States of America.
1 2 3 4 5 6 7 8 9 10 RMN 19 18 17 16 15 14 13 12 11 10
Tennessee Math Connects, Grade 5

Chapter 5 - Macmillan/McGraw-Hill

Transcription

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