5
G
R
D
- 8 ES
CD-404213
Practice
A
• Assessment • Learning Stations • Review
Table of Contents
All About Decimals
Table of Contents
Introduction to the Teacher ......................................................................................................... 1
Common Core State Standards Matrix ...................................................................................... 2
Meaning of Decimals
Reading and Writing Decimals in Tenths ............................................................................ 3
Reading and Writing Decimals in Hundredths .................................................................... 5
Reading and Writing Decimals in Thousandths .................................................................. 7
Place Value Through Thousandths ..................................................................................... 9
Comparing Decimals ........................................................................................................ 11
Ordering Decimals ............................................................................................................ 13
Rounding Decimals........................................................................................................... 15
Unit Assessment ............................................................................................................... 17
Adding and Subtracting Decimals
Adding Decimals ............................................................................................................... 19
Subtracting Decimals ........................................................................................................ 21
Unit Assessment ............................................................................................................... 23
Multiplying Decimals
Counting Decimal Places.................................................................................................. 25
Multiplying a Decimal by a Whole Number ....................................................................... 27
Multiplying a Decimal by a Decimal .................................................................................. 29
Multiplying Decimals—Zero in the Product ....................................................................... 31
Multiplying Decimals by 10, 100, or 1,000 ........................................................................ 33
Unit Assessment ............................................................................................................... 35
Dividing Decimals
Dividing a Decimal by a Whole Number ........................................................................... 37
Dividing by a Decimal ....................................................................................................... 39
Dividing Decimals—Rounding Quotients .......................................................................... 41
Dividing Decimals by 10, 100, or 1,000 ............................................................................ 43
Converting Decimals to Fractions ..................................................................................... 45
Converting Fractions to Decimal ....................................................................................... 47
Converting Percents to Decimals...................................................................................... 49
Unit Assessment ............................................................................................................... 51
Learning Stations Center-Based Activities ............................................................................. 53
Daily Math Review ..................................................................................................................... 58
Glossary of Terms ..................................................................................................................... 60
Answer Keys .............................................................................................................................. 61
404213-EB ©Mark Twain Media, Inc., Publishers
ii
Introduction to the Teacher
All About Decimals
Introduction to the Teacher
Decimals are an integral part of performing higher math skills. What is learned at one grade
level is built upon at the next grade level. The Common Core State Standards for Mathematics
suggests part of the instructional time for grades five through seven should focus on decimals. In
the eighth grade, students should be able to apply previous understanding of decimals to solve
problems involving mathematical expressions, equations, and statistics and probability.
All About Decimals: Math for CCSS targets the basic concepts needed to build a solid foundation for understanding and performing decimal operations involving higher math. The structure
of the content and presentation of concepts and skills in this book supports the Common Core
State Standards for Mathematics.
This book is divided into four units. The units cover decimal concepts and the basic operations of adding, subtracting, multiplying, and dividing decimals. Units are divided into several
lessons. Each lesson covers one concept. The format of this book is designed to facilitate lesson
planning.
•
Lesson Introduction is designed as a teacher-guided introduction of the lesson’s concepts
and skills. Each page includes the lesson objective, vocabulary and definitions, overview
of skills and concepts to be taught, example problems with clear and concise explanations,
sample problems to try with the students, and a real-world connection for the skill.
•
Practice is a set of exercises involving concepts and skills presented in the Lesson
Introduction.
•
Assessment is an evaluation of what the student has learned in each Unit. Each assessment is presented in standardized-test format.
•
Learning Stations Activity is a set of activities that allow students to apply the concepts
they have learned about decimals.
•
Glossary of Terms is an organized list of the vocabulary presented in the book.
•
Daily Math Review are sets of problems that can be used to review concepts and skills
involving decimals.
All About Decimals: Math for CCSS offers teachers a wide variety of instructional options to
meet the diverse learning styles of middle-school students. The book can be used to introduce, review, or reinforce decimal skills and concepts needed by middle-school students. The lessons can
be used for whole-group or small-group instruction, independent practice, or homework. Lessons
can be used to supplement or enhance the regular classroom curriculum or with Title I instruction.
Downloadable versions of the Lesson Introduction pages can be found at www.carsondellosa.
com. Search for product number CD-404213 On the All About Decimals: Math for CCSS product
page, click on the Resources or Downloads tab. Click on the file and download the pages for free.
These can be easily used with a classroom whiteboard, projection device, or computer.
404213-EB ©Mark Twain Media, Inc., Publishers
1
Reading and Writing Decimals in Tenths
All About Decimals
Lesson Introduction: Reading and Writing Decimals in Tenths
Common Core State Standard
• Math.Content.5.NBT.A.1, A.3
• Math.Content.8.NS.A.1
Objective
• Identify parts of a decimal.
• Read and write decimals to tenths.
• Read and write decimals in standard, word,
and expanded form.
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Vocabulary
decimal, decimal point, decomposition, expanded form, standard form, tenths, word form
Overview
A decimal is a number that expresses a whole divided into equal parts. A whole divided into
ten equal parts is divided into tenths. A decimal point is a dot placed after the figure representing
units in a decimal fraction.
Meaning of Decimals
Examples
0.1
2.4
The decimal point is read
as and in numbers greater than 1.0. The decimal
for the example to the left
would be read as two and
four-tenths
If a whole is divided
into 10 equal parts,
each part is 1 tenth.
Place Value
Examples
Ones
0
2
Decimal Point
.
.
Tenths
1
4
Writing Decimals
A decimal can be written in standard form, word form, or expanded form. A decimal written
in standard form is written as a number. When a decimal is written in standard form, a decimal
point separates the whole number part of the decimal from the part that is less than 1. Read
the number from left to right. Read as a whole number, followed by the last digit’s place value. A
decimal written in word form is written as words. Insert a hyphen between the numerator and the
denominator, unless the numerator or denominator is already a hyphenated number. A decimal
written in expanded form is a way to break the number down (decomposition) into several more
easily managed numbers.
Examples
Standard Form
3.1
Word Form
three and one-tenth
Problems to Try
a. Write the standard form of four-tenths.
Answer: 0.4
Expanded Form
3 + 0.1
b. Write the word form of 5.9.
Answer: five and nine-tenths
Real-World Connection
You use decimals every time you use money. The amount of money $2.55 means you have
two whole dollars and 55 equal parts of another dollar.
404213-EB ©Mark Twain Media, Inc., Publishers
3
Reading and Writing Decimals in Tenths
All About Decimals
Name:
Date:
Practice: Reading and Writing Decimals in Tenths
Directions: Write each decimal represented by the pictures.
1.
2.
3.
Directions: Write the following decimals in the table.
Ones
Decimal Point
4. five and three-tenths
5. seven-tenths
6. four and eight-tenths
7. What is the standard form of one and four-tenths?
8. What is the standard form of nine and two-tenths?
9. What is the word form of 0.4?
10. Write the expanded form of 5.9.
Apply
11. Kathy walked eight-tenths of a mile. Write the decimal.
12. Alex and Dawn hiked 5.5 miles on the park trail. Write the decimal in
words.
404213-EB ©Mark Twain Media, Inc., Publishers
4
Tenths
Reading and Writing Decimals in Hundredths
All About Decimals
Lesson Introduction: Reading and Writing Decimals in
Hundredths
Common Core State Standard
• Math.Content.5.NBT.A.1, A.3
• Math.Content.8.NS.A.1
Objective
• Identify parts of a decimal.
• Read and write decimals to hundredths.
• Read and write decimals in standard, word,
and expanded form.
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Vocabulary
decimal, decimal point, decomposition, expanded form, hundredths, standard form, word form
Overview
A decimal is a number that expresses a whole divided into equal parts. A whole divided
into one hundred equal parts is divided into hundredths. A decimal point is a dot placed after the
figure representing units in a decimal fraction.
Meaning of Decimals
Examples
0.01
If a whole is
divided into
100 equal
parts, each
part is
1 hundredth.
The decimal point is read
as and in numbers greater
than 1.0. The decimal for
the example to the left
would be read as two and
fifty-three hundredths.
2.53
Place Value
Examples
Ones
0
2
Decimal Point
.
.
Tenths
0
5
Hundredths
1
3
Writing Decimals
A decimal can be written in standard form, word form, or expanded form. A decimal written
in standard form is written as a number. When a decimal is written in standard form, a decimal
point separates the whole number part of the decimal from the part that is less than 1. Read
the number from left to right. Read as a whole number, followed by the last digit’s place value. A
decimal written in word form is written as words. A decimal written in expanded form is a way to
break the number down (decomposition) into several more easily managed numbers.
Examples
Standard Form
4.32
Word Form
Four and thirty-two hundredths
Problems to Try
a. Write the word form of 6.61.
Answer: six and sixty-one hundredths
Expanded Form
4 + 0.3 + 0.02
b.
1 tenth =
Answer: 10
hundredths
Real-World Connection
You use decimals every time you use money. There are 100 pennies in a dollar. One penny
is one-hundredth of a dollar or $0.01.
404213-EB ©Mark Twain Media, Inc., Publishers
5
Reading and Writing Decimals in Hundredths
All About Decimals
Name:
Date:
Practice: Reading and Writing Decimals in Hundredths
Directions: Write each decimal represented by the pictures.
1.
2.
3.
Directions: Write the following decimals in the table.
4.
forty-four hundredths
Tens
Ones
5. twenty-five and eighteen-hundredths
Decimal Point
Tenths
6. four-hundredths
Hundredths
7. What is the standard form of two and eight-hundredths?
8. What is the standard form of thirteen and twenty-six hundredths?
9. What is the word form of 3.04?
10. Write the expanded form of 82.19.
Apply
11. A candy bar cost 88¢. Write the decimal.
12. Jerry spent $15.97 at the convenience store. Write the decimal in words.
404213-EB ©Mark Twain Media, Inc., Publishers
6
Reading and Writing Decimals in Thousandths
All About Decimals
Lesson Introduction: Reading and Writing Decimals in
Thousandths
Common Core State Standard
• Math.Content.5.NBT.A.1, A.3
• Math.Content.8.NS.A.1
Objective
• Identify parts of a decimal.
• Read and write decimals to thousandths.
• Read and write decimals in standard, word,
and expanded form.
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Vocabulary
decimal, decimal point, decomposition, expanded form, standard form, thousandths, word
form
thousands
hundreds
tens
units
• decimal point
tenths
hundredths
thousandths
Overview
A decimal is a number that expresses a whole divided into equal parts. A whole divided into
one thousand equal parts is divided into thousandths. A decimal point is a dot placed after the
figure representing units in a decimal fraction. The decimal point is read as and in numbers greater
than 1.0.
Writing Decimals
Place Value
A decimal can be written in standard form, word
form, or expanded form. A decimal written in standard form is written as a number. When a decimal
Examples
is written in standard form, a decimal point separates the whole number part of the decimal from the
part that is less than 1. Read the number from left to
right. Read as a whole number, followed by the last
digit’s place value. A decimal written in word form
0 . 0 0 1
is written as words. A decimal written in expanded
2 2 . 0 4 9
form is a way to break the number down (decompo6 0 8 . 3 6 0
sition) into several more easily managed numbers.
Reading and Writing Decimals
Examples
Standard Form
0.001
22.049
508.360
Problems to Try
a. Write the word form of 0.020.
Answer: twenty-thousandths
Word Form
one thousandth
twenty-two and forty-nine thousandths
five hundred eight and three hundred sixty thousandths
Expanded Form
500 + 8 + 0.300 + 0.060
b.
c.
1=
0.053 =
thousandths
Answer: 1,000
thousandths Answer: 53
Real-World Connection
A grain of rice weighs approximately 0.028 grams. It takes about 22,700 grains of rice to
make one pound.
404213-EB ©Mark Twain Media, Inc., Publishers
7
Reading and Writing Decimals in Thousandths
All About Decimals
Name:
Date:
Practice: Reading and Writing Decimals in Thousandths
Directions: Write how many thousandths are indicated by the number below.
1. 0.007 =
thousandths
2. 0.563 =
thousandths
3. 0.966 =
thousandths
4. 0.829 =
thousandths
millions
hundred thousands
ten thousands
thousands
hundreds
tens
units
• decimal point
tenths
hundredths
thousandths
Directions: Write the following decimals in the table.
5. seventy-nine and eighty-five
hundredths
6. eight thousand, five hundred
twenty-three and seven-tenths
7. seven million, six hundred
fifteen and nine hundred
forty-six thousandths
5.
6.
7.
8. What is the standard form of six and twenty-eight thousandths?
9. What is the standard form of seven million three and thirty-four hundredths?
10. What is the word form of 73.045?
11. Write the expanded form of 33,645.098.
Apply
12. The odometer reads 5,922.4. What number is in the tenths place?
13. Joe’s calculator reads 16.002. Write the decimal in words.
404213-EB ©Mark Twain Media, Inc., Publishers
8
Place Value Through Thousandths
All About Decimals
Lesson Introduction: Place Value Through Thousandths
Common Core State Standard
• Fifth Grade: 5.NBT.A.1, A.3
• Eighth Grade: 8.NS.1
Objective
• Identify the place value for any digit in
a decimal through thousandths.
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Vocabulary
decimal, hundredths, place value, tenths, thousandths
Overview
A decimal is a number that expresses a whole divided into equal parts. A whole divided
into ten equal parts is divided into tenths. A whole divided into one hundred equal parts is divided
into hundredths. A whole divided into one thousand equal parts is divided into thousandths. A
decimal point is a dot placed after the figure representing units in a decimal fraction. In a number,
place value is the value given to the place in which a digit appears.
Example
millions
hundred thousands
ten thousands
thousands
hundreds
tens
units
• decimal point
tenths
hundredths
thousandths
Place Value
2 4 5
1 6 3 8
.
7
The 4 means 4 tens.
9 2
The 7 means 7 tenths.
1,638,245.792
One million, six hundred thirty-eight thousand, two hundred forty-five
and seven hundred ninety-two thousandths
Problems to Try
a. Which number has a 6 in the tenths place?
Answer: 45.60
26.53
366.06
Real-World Connection
Swim times are recorded in decimals. Michael Phelps swam
in four Olympic Games, broke 39 world records, and won 19 gold
medals. He set the world record for the 100 m butterfly swim race. His
time was 50.58 seconds.
404213-EB ©Mark Twain Media, Inc., Publishers
9
45.60
Place Value Through Thousandths
All About Decimals
Name:
Date:
Practice: Place Value Through Thousandths
Directions: Tell what the 5 means in each number.
1. 4,783,614.57
2. 861.534
3. 647,501.937
4. 95,271.33
5. 8,577,899.311
6. 3,261.005
millions
hundred thousands
ten thousands
thousands
hundreds
tens
units
• decimal point
tenths
hundredths
thousandths
Directions: Write the following decimals in the table.
7. six million, fifty-two thousand, four
hundred one and three-thousandths
8. five thousand, eleven and eight-tenths
9. three hundred ninety-five thousand and
fourteen-hundredths
7.
8.
9.
10. Circle the decimal with 9 in the hundreds place.
11. Circle the decimal with 8 in the thousandths place.
965.55
303.90
83,953.004
6.739
8,711.20
Directions: Tell what the 7 means in each number.
12. 3.627
13. 721.102
Apply
14. Gasoline is $3.89 per gallon. What number is in the tenths place?
15. Mary’s answer is 473.078. What number is in the thousandths place?
404213-EB ©Mark Twain Media, Inc., Publishers
10
921.738
Comparing Decimals
All About Decimals
Lesson Introduction: Comparing Decimals
Common Core State Standard
• Math.Content.5.NBT.A.1, A.3
• Math.Content.6.NS.C.7
• Math.Content.8.NS.A.1
Objective
• Write equal decimals through thousandths.
• Compare decimals through thousandths.
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Vocabulary
decimal, decimal point, <, >, =
Overview
A decimal is a number that expresses a whole divided into equal parts. A decimal point
is a dot placed after the figure representing units in a decimal fraction. When comparing decimals,
use the symbols <, >, and =. The symbol > means greater than, < means less than, and = means
equal to.
Comparing Decimals
Example
0.6
0.60
0 .
0 .
6
6
thousandths
hundredths
tenths
When comparing two
decimals, it is helpful
to write one below the
other.
and
Which is greater, 0.68 or 0.679?
ones
Example
=
It is easier to compare two decimals
when you have the same number of
decimal digits, so an extra zero can
be written to the right of the digit 8
in the decimal 0.68. Adding a zero
to the end of the decimal does not
change its value.
8 0
7 9
0.68 is greater than 0.679.
0.68 > 0.679
Problems to Try
a.
Write an equal decimal in thousandths for 0.45.
Answer: 0.450
b.
Compare 9.21
Answer: >
9.201
Real-World Connection
You use decimals when you compare and shop the sales at your local grocery stores.
404213-EB ©Mark Twain Media, Inc., Publishers
11
Comparing Decimals
All About Decimals
Name:
Date:
Practice: Comparing Decimals
Directions: Write an equal decimal for each decimal given.
1. 0.5 in hundredths
2. 4.86 in thousandths
3. 0.80 in tenths
4. 0.3 in thousandths
5. 2.710 in hundredths
6. 0. 400 in tenths
7. 9.6 in thousandths
8. 8.610 in hundredths
9. 0.2 in thousandths
10. 0.9 in hundredths
Directions: Compare the decimals using <, >, =.
11. 1.3
1.20
12. 1.56
13. 17.4
7.4
14. 6.2
6.20
15. 0.5
0.416
16. 15.6
5.6
17. 6.731
6.73
18. 82.050
19. 0.742
0.741
20. 0.9
1.562
82.05
0.812
Apply
21. Kimberly spent $4.95 for a burger and fries. Her friend, Joy, spent $4.98
for a hot dog and soda. Who spent more?
22. While shopping for his parents at the grocery store, Larry bought three packages of chicken.
The first package weighed 1.25 pounds, the second package weighed 1.05 pounds, and the
third package weighed 1.2 pounds. Which package weighed more?
404213-EB ©Mark Twain Media, Inc., Publishers
12
Answer Keys
All About Decimals
Answer Keys
19. 1; Accidents Increased One Per Week on New
Bypass
20. 88.5%
MEANING OF DECIMALS
Reading and Writing Decimals in Tenths (p. 4)
1. 0.4
2. 3.1
3. 2
4. 5.3
5. 0.7
6. 4.8
7. 1.4
8. 9.2
9. four-tenths
10. 5 + 0.9 11. 0.8
12. five and five-tenths
Unit Assessment: Meaning of Decimals (p. 17–18)
1. b
2. b
3. a
4. c
5. b
6. d
7. d
8. a
9. a 10. b 11. c 12. d
Reading and Writing Decimals in Hundredths (p. 6)
1. 0.92
2. 0.80
3. 3.04
4. 0.44
5. 25.18
6. 0.04
7. 2.08
8. 13.26
9. three and four-hundredths
10. 80 + 2 + 0.1 + 0.09
11. 0.88
12. fifteen and ninety-seven hundredths
ADDING AND SUBTRACTING DECIMALS
Adding Decimals (p. 20)
1. 105.2
2. 39.84
3. 82.33
4. 61.62
5. 801.159
6. 36.950
7. 34.227
8. 433.58
9. Mike; 307.1494
10. 8.42 miles
Reading and Writing Decimals in Thousandths (p. 8)
1. 7
2. 563
3. 966
4. 829
5. 79.85
6. 8,523.7 7. 7,000,615.946
8. 6.028
9. 7,000,003.34
10. seventy-three and forty-five thousandths
11. 30,000 + 3,000 + 600 + 40 + 5 + 0.09 + 0.008 =
12. 4
13. sixteen and two-thousandths
Subtracting Decimals (p. 22)
1. 1.967
2. 78.478
4. 186.22
5. 39.565
7. 82.91
8. 55.68
10. $52.47
Unit Assessment: Adding and Subtracting
Decimals (p. 23–24)
1. b
2. c
3. a
4. d
5. d
6. a
7. c
8. a
9. b 10. b 11. c 12. d
Place Value Through Thousandths (p. 10)
1. tenths
2. tenths
3. hundreds
4. thousands 5. hundred thousands
6. thousandths
7. 6,052,401.003
8. 5,011.8
9. 395,000.14
10. 965.55
11. 921.738
12. thousandths
13. hundreds
14. 8
15. 8
MULTIPLYING DECIMALS
Counting Decimal Places (p. 26)
1. 3
2. 2
3. 0
4. 3
5.
7. 5
8. 1
9. 5 10. 3 11.
13. 2 14. 0 15. 807.005
16.
17. 8.0357
18. 0.865337 19.
20. 487.6
21. 78.0422
22.
Comparing Decimals (p. 12)
1. 0.50
2. 4.860
3. 0.8
4. 0.300
5. 2.71
6. 0.4
7. 9.600
8. 8.61
9. 0.200 10. 0.90
11. >
12. <
13. >
14. =
15. >
16. >
17. >
18. =
19. >
20. >
21. Joy; $4.98
22. Package 1; 1.25 lbs.
3
6. 4
5 12. 4
400.04
0.00294
9.0004
Multiplying a Decimal by a Whole Number (p. 28)
1. 2.4
2. 0.76
3. 43.4
4. 169.8
5. 4.023
6. 204.16 7. 66.294 8. 0.3714
9. 189.84 ounces
10. $1.78
Multiplying a Decimal by a Decimal (p. 30)
1. 5.32
2. 466.752 3. 2.7272 4. 66.429
5. 29.785 6. 2.1144 7. 1.584
8. 0.0882
9. $318.00
10. $16,536.00
Ordering Decimals (p. 14)
1. A 6.3, B 6.6, C 7.1, D 7.7
2. A 0.25, B 0.27, C 0.32, D 0.38
3. 2.09, 2.8, 3.0
4. 0.72, 0.79, 0.84
5. 9.3, 9.56, 9.9
6. 9.07, 9.215, 9.7
7. 2.001, 2.01, 2.101
8. 1.3, 1.4, 1.7
9. Art Club: $201.40
10. Monday
11. White bass
12. Striped bass
Multiplying Decimals—Zero in the Product (p. 32)
1. 0.00468
2. 0.088
3. 0.049
4. 0.02996
5. 0.00105
6. 0.00056
7. 0.0621
8. 0.0084
9. $0.07
10. $0.0388 or $0.04
Rounding Decimals (p. 16)
1. 18
2. 913
3. 85
4. 77
5. 22
6. 442
7. 56.3
8. 743.1
9. 3.9
10. 49.8
11. 0.1
12. 0.2
13. 98.68 14. 222.37 15. 638.01 16. 53.15
17. 657.70 18. 9.28
404213-EB ©Mark Twain Media, Inc., Publishers
3. 1.37
6. 16.66
9. 4.23 meters
Multiplying by 10, 100, or 1,000 (p. 34)
1. 6
2. 3,590
3. 571,800
4. 2,780
5. 9
6. 52.51
7. 0.08
8. 662,100
9. $12.50 10. 16 mm
61