Practice Assessment Learning Stations Review › ... › 404213_sb.pdfAll About Decimals: Math for CCSS targets the basic concepts needed to build a solid foun-dation for understanding

All About Decimals: Math for CCSS focuses on basic instruction in adding, subtracting, multiplying, and dividing decimals. The book is arranged in a systematic way with each lesson focusing on one new skill or concept that builds on those learned previously. Lesson introduction pages are designed as teacher-guided introductions of the lesson’s concepts and skills. They include the standards, vocabulary, examples, and real-world connections associated with the lesson. Student practice pages feature exercises that allow students to practice and apply the concepts learned.

4 Unit assessments are presented in standardized test format.

4 Includes a decimals learning station activity, daily math review problems, glossary, and answer key.

4 Downloadable versions of the Lesson Introduction pages are available for use with whiteboards, projection devices, and individual computers.

4 Correlated to Common Core State, National, and Provincial standards. Visit www.carsondellosa.com for correlations.

CD-404213

Mark Twain Media/Carson-Dellosa Publishing LLC

P.O. Box 35665

Greensboro, NC 27425

www.carsondellosa.com

Printed in the U.S.A.

ISBN 978-1-62223-462-2

GRADES5- 8

CD-404213

CD

-404213

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Practice • Assessment • Learning Stations • Review

All About Decimals

ii404213-EB ©Mark Twain Media, Inc., Publishers

Table of Contents

Introduction to the Teacher ......................................................................................................... 1Common 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 ............................................................................. 53Daily Math Review ..................................................................................................................... 58Glossary of Terms ..................................................................................................................... 60Answer Keys .............................................................................................................................. 61

Table of Contents

All About Decimals

1404213-EB ©Mark Twain Media, Inc., Publishers

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 foun-dation 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 op-erations 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 assess-ment 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, re-view, 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 instruc-tion.

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.

Introduction to the Teacher

All About Decimals


Lesson Introduction: Reading and Writing Decimals in Tenths

Common Core State Standard Objective • Math.Content.5.NBT.A.1, A.3 • Identify parts of a decimal. • Math.Content.8.NS.A.1 • Read and write decimals to tenths.

• Read and write decimals in standard, word, and expanded form.

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

Place Value Ones Decimal Point Tenths

0 . 12 . 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.

Standard Form Word Form Expanded Form 3.1 three and one-tenth 3 + 0.1

Problems to Try a. Write the standard form of four-tenths. b. Write the word form of 5.9.

Answer: 0.4 Answer: five and nine-tenths

Real-World Connection You use decimals every time you use money. The amount of money $2.55 means you havetwo whole dollars and 55 equal parts of another dollar.

Examples

Examples

Reading and Writing Decimals in Tenths

© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

If a whole is dividedinto 10 equal parts,each part is 1 tenth.

0.1

2.4The decimal point is read as and in numbers great-er than 1.0. The decimal for the example to the left would be read as two andfour-tenths

3.1

Problems to Try

Examples

All About Decimals


Name: Date:

Reading and Writing Decimals in Tenths

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 Tenths

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.

All About Decimals


Lesson Introduction: Reading and Writing Decimals in Hundredths

Common Core State Standard Objective • Math.Content.5.NBT.A.1, A.3 • Identify parts of a decimal. • Math.Content.8.NS.A.1 • Read and write decimals to hundredths.


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

Place Value

Ones Decimal Point Tenths Hundredths0 . 0 12 . 5 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.

Standard Form Word Form Expanded Form4.32 Four and thirty-two hundredths 4 + 0.3 + 0.02

Problems to Try a. Write the word form of 6.61. b.

Answer: six and sixty-one hundredths 1 tenth = hundredths Answer: 10

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.

Examples

Examples

Reading and Writing Decimals in Hundredths


0.01

If a whole isdivided into 100 equal parts, each part is 1 hundredth. 2.53

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 andfifty-three hundredths.

Examples

All About Decimals


Name: Date:

Reading and Writing Decimals in Hundredths

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 5. twenty-five and eighteen-hundredths 6. four-hundredths

Tens Ones Decimal Point Tenths Hundredths

7. What is the standard form of two and eight-hundredths?

8. What is the standard form of thirteen and twenty-six hundredths?


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.

All About Decimals


Lesson Introduction: Reading and Writing Decimals in Thousandths

Common Core State Standard Objective• Math.Content.5.NBT.A.1, A.3 • Identify parts of a decimal.• Math.Content.8.NS.A.1 • Read and write decimals to thousandths.


Vocabulary decimal, decimal point, decomposition, expanded form, standard form, thousandths, word form

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.

Place Value

Reading and Writing Decimals

Standard Form Word Form0.001 one thousandth

22.049 twenty-two and forty-nine thousandths 508.360 five hundred eight and three hundred sixty thousandths

Expanded Form 500 + 8 + 0.300 + 0.060

Problems to Try a. Write the word form of 0.020. b. 1 = thousandths Answer: 1,000

Answer: twenty-thousandths c. 0.053 = thousandths Answer: 53 Real-World Connection A grain of rice weighs approximately 0.028 grams. It takes about 22,700 grains of rice tomake one pound.

Examples

Examples

Reading and Writing Decimals in Thousandths


Writing DecimalsA decimal can be written in standard form, word form, or expanded form. A decimal written in stan-dard form is written as a number. When a decimal is written in standard form, a decimal point sepa-rates 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 formis written as words. A decimal written in expanded form is a way to break the number down (decompo-sition) into several more easily managed numbers.

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All About Decimals


Name: Date:

Reading and Writing Decimals in Thousandths

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 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

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?


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.

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All About Decimals


Lesson Introduction: Place Value Through Thousandths

Common Core State Standard Objective • Fifth Grade: 5.NBT.A.1, A.3 • Identify the place value for any digit in • Eighth Grade: 8.NS.1 a decimal through thousandths.

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.

Place Value

1 6 3 8 2 4 5 . 7 9 2

The 4 means 4 tens. 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? 26.53 366.06 45.60

Answer: 45.60 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.

Example

Place Value Through Thousandths


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All About Decimals


Name: Date:

Place Value Through Thousandths

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

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

10. Circle the decimal with 9 in the hundreds place. 965.55 303.90 6.739

11. Circle the decimal with 8 in the thousandths place. 83,953.004 8,711.20 921.738

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?

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All About Decimals


Lesson Introduction: Comparing Decimals

Common Core State Standard Objective • Math.Content.5.NBT.A.1, A.3 • Write equal decimals through thousandths. • Math.Content.6.NS.C.7 • Compare decimals through thousandths. • Math.Content.8.NS.A.1

Vocabulary decimal, decimal point, <, >, =

Overview A decimal is a number that expresses a whole divided into equal parts. A decimal pointis 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

0.6 = 0.60

Which is greater, 0.68 or 0.679?

0.68 is greater than 0.679.0.68 > 0.679

Problems to Try

a. Write an equal decimal in thousandths for 0.45. b. Compare 9.21 9.201 Answer: 0.450 Answer: >

Real-World Connection You use decimals when you compare and shop the sales at your local grocery stores.

Example

WhichExample

Comparing Decimals


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.

When comparing two decimals, it is helpful to write one below the other.

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All About Decimals


Name: Date:

Comparing Decimals

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 1.562

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 82.05

19. 0.742 0.741 20. 0.9 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?

All About Decimals


Answer Keys

Answer Keys

MEANING OF DECIMALSReading 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

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

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

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. 395,000.1410. 965.55 11. 921.738 12. thousandths 13. hundreds 14. 8 15. 8

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.

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

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. 0.213. 98.68 14. 222.37 15. 638.01 16. 53.15 17. 657.70 18. 9.28

19. 1; Accidents Increased One Per Week on New Bypass 20. 88.5%

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

ADDING AND SUBTRACTING DECIMALSAdding 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

Subtracting Decimals (p. 22) 1. 1.967 2. 78.478 3. 1.37 4. 186.22 5. 39.565 6. 16.66 7. 82.91 8. 55.68 9. 4.23 meters 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

MULTIPLYING DECIMALS Counting Decimal Places (p. 26) 1. 3 2. 2 3. 0 4. 3 5. 3 6. 4 7. 5 8. 1 9. 5 10. 3 11. 5 12. 4 13. 2 14. 0 15. 807.005 16. 400.0417. 8.0357 18. 0.865337 19. 0.00294 20. 487.6 21. 78.0422 22. 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 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

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

Documents

Practice Assessment Learning Stations Review › ... › 404213_sb.pdfAll About Decimals: Math for CCSS targets the basic concepts needed to build a solid foun-dation for understanding