GRADES 5-8 CD-404213 Practice Assessment Learning Stations Review
Table of Contents 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 ii
Introduction to the Teacher 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. 1
Reading and Writing Decimals in Tenths 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 Place Value Ones Decimal Point Tenths 0. 1 2. 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. 0.1 If a whole is divided into 10 equal parts, each part is 1 tenth. 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 have two whole dollars and 55 equal parts of another dollar. 3 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
Name: Reading and Writing Decimals in Tenths 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 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. 4
Reading and Writing Decimals in Hundredths 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 0.01 If a whole is divided 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 and fifty-three hundredths. Place Value Ones Decimal Point Tenths Hundredths 0. 0 1 2. 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 Form 4.32 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. 5
Name: Reading and Writing Decimals in Hundredths 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 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? 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. 6
Reading and Writing Decimals in Thousandths 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 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 thousands hundreds tens units decimal point tenths hundredths thousandths 0. 0 0 1 2 2. 0 4 9 6 0 8. 3 6 0 Reading and Writing Decimals 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 0.001 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 to make one pound. 7
Name: Reading and Writing Decimals in Thousandths 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 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. millions hundred thousands ten thousands thousands hundreds tens units decimal point tenths hundredths 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? 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. 8
Place Value Through Thousandths 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. Place Value Example millions hundred thousands ten thousands thousands hundreds tens units decimal point tenths hundredths thousandths 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. 9
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 7. 8. 9. millions hundred thousands ten thousands thousands hundreds tens units decimal point tenths hundredths thousandths 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? 10
Comparing 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 Example Which is greater, 0.68 or 0.679? When comparing two decimals, it is helpful to write one below the other. ones and tenths hundredths thousandths 0. 6 8 0 0. 6 7 9 0.68 is greater than 0.679. 0.68 > 0.679 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. 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. 11
Name: Practice: Comparing Decimals Directions: Write an equal decimal for each decimal given. Date: Comparing Decimals 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? 12
Answer Keys 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 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. 395,000.14 10. 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. 0.2 13. 98.68 14. 222.37 15. 638.01 16. 53.15 17. 657.70 18. 9.28 Answer Keys 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 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 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. 400.04 17. 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 61