Math Worksheets

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Chapter File Folders Teacher Tools Assessment Guide English Language Learner Handbook Math Center Cards Problem of the Day Quit Success on Standardized Tests Print This Page Name Explore How Big Is a Million? Print This 1–1 Page P PRACTICE Solve. 1. How many 10-by-10 grids would 2. you need to make a thousand cube? How many thousand cubes would you need to make a million? 3. How many hundreds are in 1,000? 4. How many hundreds are in 10,000? 5. How many thousands are in 1,000? 6. How many thousands are in 10,000? 7. How many thousands are in 100,000? © McGraw-Hill School Division 8. How many thousands are in 1,000,000? 9. How many ten thousands are in 10,000? 10. How many ten thousands are in 100,000? 11. How many ten thousands are in 1,000,000? 12. How many hundred thousands are in 100,000? 13. How many hundred thousands are in 1,000,000? Use with Grade 4, Chapter 1, Lesson 1, pages 2–3. (1) NS 1.1 Print This Page Name Print This 1–1 Page Explore How Big Is a Million? R RETEACH You can show numbers in different ways. You can think of 1,000 in the following ways: 1 thousand 10 hundreds 100 tens 1,000 ones 1 thousand 10 hundreds 1. What number is shown below? Complete. Name each number in different ways. © McGraw-Hill School Division 2. 10,000 3. 100,000 4. 1,000,000 ten thousand hundred thousand million thousands ten thousands hundred thousands hundreds thousands ten thousands tens hundreds thousands ones tens hundreds ones tens ones Use with Grade 4, Chapter 1, Lesson 1, pages 2–3. (2) NS 1.1 Print This Page Name Explore How Big Is a Million? Print This 1–1 Page E ENRICH A Million Pizzas Skye just opened Skye’s Pizzas. Her dream is to sell one million pizzas. She wants to see how long it will take. Answer these questions to help her find out. 1. Skye says, “If I sell 100 pizzas every day, I can sell 1,000,000 pizzas in days!” She frowns. “That’s a long time.” 2. Suddenly Skye snaps her fingers. “I know! I’ll open more stores! If I have 10 stores and each store sells 100 pizzas every day, it will only take days to sell 1,000,000 pizzas!” 3. “Wait a minute!” she exclaims. “What if I have 100 stores and each store sells 1,000 pizzas every day? How long will it take to sell 1,000,000 pizzas?” “Why don’t you try to sell 1,000,000 pizzas in just 1 day?” Skye’s friend Emma asks. “Hmmm,” Skye murmurs. “How many stores would I need? How many pizzas would each store need to sell?” 4. Decide how many stores Skye would need and how many pizzas © McGraw-Hill School Division each store would need to sell in 1 day. 5. What if you were Skye? What would be your plan? Tell about your plan. Use with Grade 4, Chapter 1, Lesson 1, pages 2–3. (3) NS 1.1 Print This Page Name Print This 1–2 Page Place Value Through Millions P PRACTICE Write the word name and the expanded form for each number. 1. 1,420,316 2. 2,672,400 3. 12,060,072 4. 785,004,012 Write the value of each underlined digit. 5. 842,753 6. 6,782,141 7. 153,428,090 8. 715,124,068 Write each number in standard form. 9. one million, two hundred thousand, five 10. thirty-eight million, four hundred thousand, eight © McGraw-Hill School Division 11. five hundred eighty million, sixty-two thousand, seventeen 12. two hundred fifty-four million, seven thousand, five Algebra & Functions Write the missing number. 13. 42,865  40,000   800  60  5 14. 168,943  100,000  60,000  8,000  15. 888,888  800,000  Use with Grade 4, Chapter 1, Lesson 2, pages 4–7. (4)  40  3  8,000  800  80  8 NS 1.1 Print This Page Name Print This 1–2 Page Place Value Through Millions R RETEACH Numbers in the millions have three periods. Each period is separated by a comma. Millions Thousands Ones Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones 7 0 1 2 2 1 3 5 4 Expanded form: 700,000,000  1,000,000  200,000  20,000  1,000  300  50  4 Standard form: 701,221,354 Word name: seven hundred one million, two hundred twenty-one thousand, three hundred fifty-four Complete. 1. 824,124 = + 20,000 + 4,000 + 2. 7,624,139 = 7,000,000 + 3. 42,521,012 = © McGraw-Hill School Division Standard Form + 20,000 + + 2,000,000 + 500,000 + Expanded Form 4. 3,000,000  200,000  500  20 5. 2,000,000  400,000  50,000  7,000  800  20  1 6. 30,000,000  7,000,000  800,000  50,000  2,000  4 7. 40,000,000  9,000,000  300,000  50,000  2,000  6 Use with Grade 4, Chapter 1, Lesson 2, pages 4–7. (5) + + + + + + + 10 + Word Name NS 1.1 Print This Page Name Print This 1–2 Page Place Value Through Millions E ENRICH And the Number Is . . . Use the digits below only once in each exercise. 1 2 3 4 5 6 7 8 9 1. What is the greatest number with 4 in the hundred millions place? , , 2. What is the greatest number with 5 in the hundred thousands place? , , 3. What is the least number with 6 in the millions place? , , 4. What is the least number with 3 in the ten thousands place? , , 5. What is the greatest number with 8 in the thousands place? , , 6. What is the greatest number with 1 in the ten millions place? , , 7. What is the least number with 9 in the millions place and 2 in the ten thousands place? , , © McGraw-Hill School Division 8. What is the greatest number with 7 in the hundred thousands place and 1 in the thousands place? , , 9. How did you use place value to help you make the greatest possible number? the least possible number? Use with Grade 4, Chapter 1, Lesson 2, pages 4–7. (6) NS 1.1 Print This Page Name Print This 1–3 Page Compare and Order Numbers and Money P PRACTICE Compare. Write >, <, or =. 1. 3,874 4. 14,624 7. $101.42 3,862 1,462 $126.41 2. 5,741 5,862 3. $78.24 $77.24 5. 42,542 41,617 6. 32,145 32,264 8. 25,632 25,632 9. 89,000 87,999 10. 150,420 100,042 11. 434,121 432,154 12. 187,654 197,541 13. 782,421 782,342 14. 642,134 642,134 15. 874,158 972,421 Order from greatest to least. 16. 3,421; 3,641; 3,481; 3,562 17. $216.49; $218.42; $206.49 18. 72,642; 71,848; 70,621 19. 748,629; 747,832; 748,532 Order from least to greatest. 20. $64.21; $68.78; $87.68; $65.43 21. 25,421; 24,462; 24,416 © McGraw-Hill School Division 22. 324,621; 324,742; 325,697 23. 524,607; 525,712; 524,872 Problem Solving 24. Sean has 1,575 bird stamps and Li has 25. Sean’s stamp album cost $12.75 and 2,075 bird stamps. Cindy has a Li’s album cost $18.50. Cindy’s album number of stamps between Sean’s and cost the most. Is it $18.75 or $11.75? Li’s numbers. Is it 1,075 or 1,755? Explain. Explain. Use with Grade 4, Chapter 1, Lesson 3, pages 8–11. (7) NS 1.2 Print This Page Name Print This 1–3 Page Compare and Order Numbers and Money R RETEACH You can use a place-value chart to compare numbers. Start at the left. Look for the first place where the digits are different. Compare 4,872 and 4,892. Thousands Hundreds Tens Ones 4 8 7 2 4 8 9 2 same number of thousands same number of hundreds 4,892 has more tens than 4,872. So, 4,892 4,872. Compare $306.97 and $319.23. Hundred Dollars Ten Dollars One Dollars Cents 3 0 6 97 3 1 9 23 same number of hundred dollars $319.23 has more ten dollars than $306.97. So, $319.23 $306.97. Use the place-value chart to compare the numbers. Write , , or . 1. Compare 3,234 and 3,216. © McGraw-Hill School Division Thousands Hundreds 3,234 Tens 3,216 Ones Compare. Write , , or . 2. 8,504 8,515 3. $25.16 4. 5,558 5,585 5. 6,117 6. $324.89 8. 56,619 10. 502,300 $314.89 56,916 510,239 Use with Grade 4, Chapter 1, Lesson 3, pages 8–11. (8) 7. 50,281 $21.12 6,117 51,002 9. $285.45 $293.45 11. 832,077 822,077 NS 1.2 Print This Page Name Compare and Order Numbers and Money Print This 1–3 Page E ENRICH Greater Numbers Look at the value that each letter represents. Then order the letters from least to greatest values in the boxes below. A. There are 9,123 public libraries in the United States. B. There were 54,773 poodles registered by the American Kennel Club, Inc. C. There were 54,470 beagles registered by the American Kennel Club, Inc. D. The area of Mexico is 761,604 square miles. E. In the year ending December 31, 1997, there were 4,819 Maine coon cats registered in the United States. F. The area of the United States is 3,618,770 square miles. G. In the 1864 United States Presidential election, Abraham Lincoln received 2,216,067 votes. © McGraw-Hill School Division H. In the 1868 United States Presidential election, Ulysses S. Grant received 3,015,071 votes. I. The area of Japan is 145,856 square miles. Use with Grade 4, Chapter 1, Lesson 3, pages 8–11. (9) NS 1.2 Print This Page Name Print This 1–4 Page Problem Solving: Reading for Math P PRACTICE Reading Skill Using the Four-Step Process Read the problem. Then read each step in the problem-solving process. Write a number next to each step to show the order in which the steps are done. Write a 1 for the first step, and so on. 1. A male elk weighs 600 pounds. A male moose weighs 1,000 pounds. A male caribou weighs 300 pounds. What is the order of the three animals from greatest to least weight? Check your answer. Identify what you need to find. You need to find the order of the male elk, the male moose, and the male caribou from greatest to least weight. Read the problem. Identify what you know: A male elk weighs 600 pounds. A male moose weighs 1,000 pounds. A male caribou weighs 300 pounds. Make a plan for solving the problem. Order the animals by comparing their weights two at a time. List the animals from greatest to least weight. Follow your plan to solve the problem. What is the order of the three animals from greatest to least weight? 2. A mink can be 20 inches long. A wolverine can be 36 inches long. A black-footed ferret can be 18 inches long. Which animal can grow to the greatest length? © McGraw-Hill School Division Identify what you know. A mink can be 20 inches long. A wolverine can be 36 inches long. A black-footed ferret can be 18 inches long. Check your answer. Make a plan for solving the problem. Order the animals by comparing their lengths two at a time. List the animals from least to greatest length. Identify what you need to find: Which animal can grow to the greatest length? Follow your plan to solve the problem. Read the problem. Which animal can grow to the greatest length? Use with Grade 4, Chapter 1, Lesson 4, pages 12–13. (10) MR 1.1, 1.2, 2.3, 2.4, 3.2 Print This Page Name Print This 1–4 Page Problem Solving: Reading for Math P Using the Four-Step Process PRACTICE Math Skills Test Prep Choose the correct answer. A bottle-nosed dolphin can weigh up to 440 pounds. A common dolphin can weigh up to 165 pounds. Which kind of dolphin can be heavier? 1. Which of these statements is true? A A bottle-nosed dolphin cannot be as heavy as a common dolphin. B A common dolphin can weigh 615 pounds. C A bottle-nosed dolphin can weigh 440 pounds. 2. Which plan will help you solve the problem? F Add 440 and 165. G Compare 440 and 165. H Subtract 165 from 440. On Friday, 660 people went to Ocean World Animal Park. On Saturday, 1,096 people went to Ocean World. On Sunday, 998 people went to Ocean World. On which day did the most people go to Ocean World? 3. Which plan can you use to solve this 4. On which day did the most people problem? go to Ocean World? A Compare 660; 1,096; and 998. B Add 660 and 1,096. C Add 1,096 and 998. F Friday G Saturday H Sunday © McGraw-Hill School Division Lassie’s Dog Walking Service walks 68 dogs per week. Doggie Express walks 57 dogs per week. Top Dog Company walks 101 dogs per week. List the dog walking services in order from least dogs walked per week to most dogs walked per week. 5. Which statement is true? A Lassie’s Dog Walking Service walks the most dogs per week. B Doggie Express walks 57 dogs per week. C Top Dog Company walks 68 dogs per week Use with Grade 4, Chapter 1, Lesson 4, pages 12–13. (11) 6. Which plan can you use to solve the problem? F Compare the numbers of dogs walked two at a time. G Find the difference between the number of dogs walked by Top Dog Company and the number walked by Lassie’s. H Find the total number of dogs walked by the three services. MR 1.1, 1.2, 2.3, 2.4, 3.2 Print This Page Name Problem Solving: Reading for Math Using the Four-Step Process Print This 1–4 Page P PRACTICE Math Skills Test Prep Choose the correct answer. Ocean World Animal Park needs 750 customers each day to make money. On Monday, Ocean World had 803 customers. On Tuesday, Ocean World had 691 customers. On Wednesday, Ocean World had 911 customers. On which day or days did Ocean World make money? 7. Which plan will help you solve the problem? A Compare the daily customer totals two at a time. B Compare each daily customer total to 750. C Order the daily customer totals from greatest to least. Solve. 9. A marlin can move at a speed of 50 miles per hour. A striped dolphin can move 19 miles per hour. A killer whale can move 55 miles per hour. List the animals in order from slowest to fastest. © McGraw-Hill School Division 11. A poll shows that 311 students have dogs, 424 students have cats, 96 students have birds, and 38 students have a different pet. Which kind of pet is owned by the most students? 13. Dylan spots 48 birds. Nicole spots 51 birds. Who spots fewer birds? Use with Grade 4, Chapter 1, Lesson 4, pages 12–13. (12) 8. On which day or days did Ocean World make money? F Tuesday only G Wednesday only H Monday and Wednesday only 10. Brandon, Timothy, and Norah have pet care services. Last year, Brandon earned $712, Timothy earned $1,110, and Norah earned $650. List the people in order from greatest amount earned to least amount earned. 12. The pet shelter has 324 dogs in April, 411 dogs in May, and 399 dogs in June. List the months in order from least number of dogs to greatest number of dogs. 14. In 1997, about 36,000,000 people went to aquariums and about 86,000,000 people went to zoos. Did more people go to aquariums or to zoos? MR 1.1, 1.2, 2.3, 2.4, 3.2 Print This Page Name Print This 1–5 Page Round Numbers and Money P PRACTICE Round to the given place. 1. 923 to the nearest 2. $0.93 to the nearest ten 3. $6.49 to the nearest ten cents 4. $57.52 to the nearest dollar dollar 5. 862 to the nearest 6. $46.47 to the nearest hundred 7. 4,357 to the nearest dollar 8. $73.96 to the nearest thousand 9. 8,553 to the nearest ten cents hundred 10. 380,256 to the nearest 11. 61,479 to the nearest 12. 1,555 to the nearest hundred thousand ten thousand 13. $34.06 to the nearest ten cents hundred 14. 7,502,475 to the 15. 2,653,789 to the nearest million nearest hundred thousand Algebra & Functions Find the rule. Complete the table. 16. © McGraw-Hill School Division Rule: Input 57,124 Output 60,000 64,142 91,722 234,162 478,234 Problem Solving 17.The radio announcer said that there were 1,532 bluebird sightings on the island. To the nearest hundred, how many sightings were there? Use with Grade 4, Chapter 1, Lesson 5, pages 14–17. (13) 18.Joe’s class bought a bird feeder for $38.75. To the nearest dollar, what was the cost? NS 1.3 Print This Page Name Print This 1–5 Page Round Numbers and Money R RETEACH You can use a number line to help you round. 40,000 41,000 42,000 43,000 44,000 45,000 46,000 47,000 48,000 49,000 50,000 Round 46,208 to the nearest ten thousand. Think: 46,000 is closer to 50,000 than 40,000. So, 46,208 rounds up to 50,000. $6.00 $6.10 $6.20 $6.50 $6.60 $6.30 $6.40 $6.70 $6.80 $6.90 $7.00 Round $6.38 to the nearest dollar. Think: $6.30 is closer to $6.00 than $7.00. So, $6.38 rounds down to $6.00. Round to the nearest ten thousand. 1. 42,496 2. 49,009 3. 43,875 4. 45,800 5. 42,900 6. 47,250 7. 44,987 8. 41,875 9. 45,203 © McGraw-Hill School Division Round to the nearest million. 10. 7,450,000 11. 7,550,000 12. 7,832,010 13. 7,289,999 14. 7,362,800 15. 7,512,300 Round to the nearest dollar. 16. $12.60 17. $12.45 18. $12.13 19. $12.93 20. $12.53 21. $12.39 22. $12.25 23. $12.62 24. $12.59 Use with Grade 4, Chapter 1, Lesson 5, pages 14–17. (14) NS 1.3 Print This Page Name Round Numbers and Money Print This 1–5 Page E ENRICH Mystery Numbers 1. If you round me to the nearest hundred, you get 400. If you round me to the nearest ten, you get 430. The sum of my digits is 8. What number am I? 2. If you round me to the nearest thousand, you get 3,000. If you round me to the nearest hundred, you get 2,600. Three of my digits are the same. The sum of my digits is 17. What number am I? 3. If you round me to the nearest thousand, you get 4,000. The sum of my digits is 10. If you read me forward or backward, I am the same. What number am I? 4. If you round me to the nearest ten thousand, you get 50,000. My first two digits add up to 10. The digit in my hundreds place is one more than 2. My last three digits add up to 8, and round (to the nearest hundred) to 400. © McGraw-Hill School Division What number am I? 5. The sum of my seven digits is 60. Six of the digits are the same. Rounding me to the nearest ten, hundred, thousand, ten thousand, or million will give you the same number. What number am I? 6. If you round me to the nearest 100,000, you get 600,000. Each of my six digits is the same. What number am I? Use with Grade 4, Chapter 1, Lesson 5, pages 14–17. (15) NS 1.3 Print This Page Name Print This 1–6 Page Problem Solving: Strategy P PRACTICE Make a Table Make a table. Use data from the table to solve problems 1 and 2. Elliot—dog Marion—cat Tina—hamster Paula—fish Sam—cat What is your favorite kind of pet? Howard—dog Jane—bird Noriko—bird Teri—cat Yolanda—dog Sarah—cat Barry—cat Bruce—dog Juan—dog Mike—cat Rebecca—bird Melanie—cat Traci—dog Noreen—fish Sylvia—cat 1. Which pet had the most votes? 2. Which pet had the least votes? 3. Mark cuts out letters to make a sign. 4. Which letter does Mark need to The sign says, "Get Pet Kittens for Free." How many different kinds of letters does Mark need to make? Mixed Strategy Review Solve. Use any strategy. 5. A pet store sold 137 bags of dog food called The Vet’s Choice. It sold 249 bags of a dog food called Fido’s Friend. How many more bags of Fido’s Friend than The Vet’s Choice were sold? make the most of? How many of these letters does Mark have to make? 6. In 1999, The Pet Palace made about $100,000. In 2000, The Pet Palace increased this amount by $10,000. How much did The Pet Palace make in 2000? © McGraw-Hill School Division Strategy: Strategy: 7. Science Adult sun bears usually weigh from 60 to 100 pounds. Adult grizzly bears weigh from 350 to 500 pounds. Adult Asiatic black bears weigh about 250 pounds. Which bear weighs the least? 8. Create a problem you would make a table to solve. Share it with others. Strategy: Use with Grade 4, Chapter 1, Lesson 6, pages 20–21. (16) NS 1.2; SDP 1.3; MR 1.1, 2.3, 3.2 Print This Page Name Print This 1–6 Page Problem Solving: Strategy R RETEACH Make a Table Page 21, Problem 2 Which type of fish has the greatest number of varieties? Different Varieties of Tetras, Goldfish, and Angelfish tetras—black neon tetra goldfish—black moor angelfish—gold angel tetras—lemon tetra goldfish—fan tail goldfish tetras—white skirt tetras—silver dollar angelfish—marble angel goldfish—lionhead tetras—black neon tetras angelfish—silver angel Step 1 Read Be sure you understand the problem. Read carefully. What do you know? • There are different varieties of , and , . What do you need to find? • You need to know how many different varieties of , , and there are. Step 2 Plan ■ © McGraw-Hill School Division ■ ■ ■ ■ ■ ■ ■ ■ ■ Make a Table or List Write a Number Sentence Work Backward Act it Out Find a Pattern Make a Graph Guess and Check Logical Reasoning Solve a Simpler Problem Draw a Picture Make a plan. Choose a strategy. A table can help you organize what you know. Make a table to solve the problem. Use with Grade 4, Chapter 1, Lesson 6, pages 20–21. (17) NS 1.2; SDP 1.3; MR 1.1, 2.3, 3.2 Print This Page Name Print This 1–6 Page R Problem Solving: Strategy RETEACH Make a Table Step 3 Solve Carry out your plan. Make a table to solve. Tally the number of for each fish. Write a number for each set of tallies. Compare the numbers. Complete the table. Type of Fish Tally of Different Varieties Number Tetras Goldfish 3 Angelfish There are different kinds of tetras. There are different kinds of goldfish. There are different kinds of angelfish. There are more varieties of two kinds of fish. Step 4 © McGraw-Hill School Division Look Back than either of the other Is the solution reasonable? Reread the problem. Does your answer match the data given in the problem? Practice 1. Jack lists the fish in his aquarium. He has a fan tail goldfish, a lionhead goldfish, a gold angel angelfish, a lemon tetra, and a black neon tetra. Of which type of fish does Jack have the least? Use with Grade 4, Chapter 1, Lesson 6, pages 20–21. (18) 2. Alex, Brian, and Yumi each like one kind of dog. The dog is either a terrier, a retriever, or a poodle. Alex does not like retrievers. Brian does not like poodles or retrievers. Who likes poodles? NS 1.2; SDP 1.3; MR 1.1, 2.3, 3.2 Print This Page Name Print This 1–7 Page Count Money and Make Change P PRACTICE Write the amount of money shown. 1. 2. 3. 8 8 SCHOOL MONEY 8 8 8 8 SCHOOL MONEY 8 8 Tell which coins and bills make the amount. 4. $0.89 5. $3.62 6. $7.67 8. Price: $2.45 9. Price: $7.81 Find the amount of change. 7. Price: $0.59 Amount given: $1.00 10. Price: $0.86 © McGraw-Hill School Division Amount given: $5.00 Amount given: $5.00 11. Price: $3.09 Amount given: $10.00 12. Price: $9.25 Amount given: $10.00 Amount given: $10.00 Problem Solving 13. Andy gives the cashier $5.00 to pay for a $3.75 calendar. How much change does he receive? Use with Grade 4, Chapter 1, Lesson 7, pages 22–23. (19) 14. Lowanda receives 1 quarter, 2 dimes, and 1 nickel in change. How much money is that? NS 1.0; MR 2.4 Print This Page Name Print This 1–7 Page Count Money and Make Change R RETEACH To make change, start with the cost. Then count up to the amount given to you. Use the fewest number of bills and coins possible. You sell a pen for $2.49. Someone gives you $5.00 for the pen. $2.49 Cost $2.50 $2.75 $3.00 $4.00 $5.00 Count the bills and coins to find the change: $2.51. Count up. Find the amount of change. 1. Amount given: $6.00 $5.34 Cost Amount of change: © McGraw-Hill School Division 2. Amount given: $10.00 8 8 SCHOOL MONEY 8 8 $3.79 Cost Amount of change: Use with Grade 4, Chapter 1, Lesson 7, pages 22–23. (20) NS 1.0; MR 2.4 Print This Page Name Print This 1–7 Page Count Money and Make Change E ENRICH Money Detective Use the clues to find which coins and bills are inside each bank. 1. 2. $0.47 $0.58 Clue: 6 coins 3. Clue: 13 coins 4. $0.73 $0.81 Clue: 10 coins 5. Clue: 8 coins 6. $1.00 $7.45 © McGraw-Hill School Division Clue: 19 coins, but only two kinds 7. Clue: 3 bills, 3 coins 8. $15.55 Clue: 2 bills, 3 coins Use with Grade 4, Chapter 1, Lesson 7, pages 22–23. (21) $23.00 Clue: 5 bills, 3 coins NS 1.0; MR 2.4 Print This Page Name Print This 1–8 Page Negative Numbers P PRACTICE Write a positive or negative number to represent each situation. 1. Lose $4 2. Deposit $50 3. 300 feet above sea level 4. 12F below zero 5. Gain 3 pounds 6. Go 3 floors down 7. Take 8 steps back 8. Earn $25 9. 52F 10. Lose 10 pounds Compare. Write  or . You may use a number line to help. 11. 0 15.  4 19. 1 23. 27.  5  4 © McGraw-Hill School Division 31. 11 35.  6 9 12. 2  3 7 16. 0  12 20. 6   2  8 24. 8 12  24 13 11 32. 0 8   1 36. 2 17. 10  28. 17 13. 10  2 14.  0 18.  22. 7 4 3 21. 12 25. 29. 33. 37. 12  5 3 0 26.   30. 0 11 15 9  15 9  34. 13  4 38. 4 3   6 6   10   12 9  11 3  7 Problem Solving 39. Manuel deposited a check for $25 in his savings account. Then he withdrew $30. Write a number to represent each situation. Use with Grade 4, Chapter 1, Lesson 8, pages 24–25. (22) 40. An airplane descended 1,000 feet. Ten minutes later, it climbed 9,500 feet. Write a number to represent each situation. NS 1.8 Print This Page Name Print This 1–8 Page Negative Numbers R RETEACH You can use a number line to understand and compare positive and negative numbers.  6   5 4 negative numbers positive numbers less than zero greater than zero   3  1 2  1 0  2   3 4   5 6 Numbers to the right are greater than numbers to the left.  2 is to the right of 2, so 2  2.   0 is to the right of 4, so 0  4.  3 is to the right of 6, so 3  6. Complete. 1. 2. 3. 4. © McGraw-Hill School Division 5. 6.  5 is to the right of 3, so 5   3.  of 1, so 1   of 6, so 5   of 1, so 4   of 6, so 6   of 4, so 2 1 is to the 5 is to the 4 is to the 6 is to the 2 is to the 1. 6. 1. 6.  4. Compare. Write  or . You may use a number line to help. 7. 11. 15. 19.     14 14 12 21     6 7 8. 12. 15 16. 7 20.       13 31 25 5 10  8 12  2 Use with Grade 4, Chapter 1, Lesson 8, pages 24–25. (23) 9. 13. 17. 21.         9 8 2 9 15 2 12 8 10. 14.   20 18   20 20   22. 0  18. 4 4 10 NS 1.8 Print This Page Name Print This 1–8 Page Negative Numbers E ENRICH Are You Positive or Negative? Play with a partner. You will need 10 blank cards for each player. • Each player writes five different negative and five different positive integers, one on each card. They should use the integers from 10 to 10. Each player mixes up their cards and spreads them out face down. • To play, each player touches one of these cards. One player announces “Mine is greater than (or ‘less than’ or ‘equal to’) yours.” Both players turn over their card. If the statement was correct, that player gets both cards. If not, they go to the original player.  9 • Repeat touching cards and taking turns making the statements. When all cards are collected, the player with the most cards wins.  7 8  © McGraw-Hill School Division 2 0  1 6 3 5  Use with Grade 4, Chapter 1, Lesson 8, pages 24–25. (24) 4 NS 1.8 Print This Page Name Problem Solving: Application Print This Page 1–9 Part A WORKSHEET Decision Making Applying Place Value Record your data. Answers may vary. Store Cost of 20 Pounds of Dog Food Cost of Gas for Trip to Store Pet Supply Animal World Pet’s Place © McGraw-Hill School Division Discount Pet Food Your Decision What is your recommendation for Stacia? Explain. Use with Grade 4, Chapter 1, Lesson 9, pages 26–27. (25) NS 1.2; MR 1.1, 2.3 Print This Page Name Print This Page 1–9 Part B WORKSHEET Problem Solving: Application Math & Science How do you compare with your partner? Record your data. Data for Student 1 Data for Student 2 Are the two sets of data the same or close to being the same? 1. Your favorite number 2. Number of hours you sleep each night 3. Number of push-ups you can do in 30 seconds 4. Number of objects in your desk right now 5. Number of cups of water you drank yesterday 6. Number of cats and dogs you know © McGraw-Hill School Division 7. Length of your arm from shoulder to wrist 8. How long you can stand on one foot 9. Number of times you breathe in one minute 10. Your age Use with Grade 4, Chapter 1, Lesson 9, pages 28–29. (26) NS 1.2; MR 1.1, 2.3, 3.3 Print This Page Name Problem Solving: Application How do you compare with your partner? Print This Page 1–9 Part B WORKSHEET Math & Science 1. How many times were you and your partner the same? different? 2. Explain how you decided whether you and your partner were the same. Did the numbers have to be exactly alike? Why or why not? 3. In which areas did you vary the most from your partner? © McGraw-Hill School Division 4. In which areas did you vary the least from your partner? 5. Why is it good to have variation in nature? Use with Grade 4, Chapter 1, Lesson 9, pages 28–29. (27) NS 1.2; MR 1.1, 2.3, 3.3 Print This Page Name Print This 2–1 Page Use Properties of Addition P PRACTICE Complete the set of related number sentences. 1. 5 , 3, 8 2. 6, 8, 14 5n8 68n n38 85n 8n5 8  n  14 4. 3, 7, 10 3. 6, 9, 15 n  6  15 6  n  15 15  n  6 15  6  n 14  6  n 14  n  8 5. 22, 5, 27 6. 34, 4, 38 3  n  10 22  n  27 34  n  38 37n 5  22  n 4  n  38 n37 10  n  3 n  22  5 27  5  n 38  n  34 n  4  34 Find the sum or difference. Write the related number sentences. 7. 2  9  8. 35  4  9. 54  0  Write the related number sentences for the set of numbers. © McGraw-Hill School Division 10. 4, 5, 9 11. 11, 24, 35 Problem Solving 13. Ken has 6 coins in his collection. Barb has 5 more coins than Ken. How many coins does Barb have? Use with Grade 4, Chapter 2, Lesson 1, pages 44–45. (28) 12. 0, 46, 46 14. Meg has 13 coins in her collection. Then she gives 7 coins to her cousin. How many coins does Meg have now? NS 3.1; AF 1.1 Print This Page Name Print This 2–1 Page Use Properties of Addition R RETEACH Every number sentence in a set of related number sentences uses the same numbers. The model below shows a set of related number sentences. 538 358 } Commutative Property: 5  3  8 is the same as 3  5  8. 835 853 You can also use the properties and the idea of related sentences with greater numbers. Look at each model. Write the related number sentences. 1. 2. Find the sum. Write the related number sentences. © McGraw-Hill School Division 3. 8  3  n 4. 2  7  n 5. 18  0  n Write the related number sentences for the set of numbers. 6. 26, 17, 43 7. 0, 56, 56 Use with Grade 4, Chapter 2, Lesson 1, pages 44–45. (29) 8. 9, 45, 54 NS 3.1; AF 1.1 Print This Page Name Print This 2–1 Page Use Properties of Addition E ENRICH Properties and Rules Complete each number sentence. Then write the property or rule you used. 1. MNM N 2. A  3. CDC D 4. HH 5. 6. © McGraw-Hill School Division BB JJ Z0 7. QQP 8. 0W Write the related number sentences. 9. ANB Use with Grade 4, Chapter 2, Lesson 1, pages 44–45. (30) 10. DEF NS 3.1; AF 1.1 Print This Page Name Print This 2–2 Page Addition Patterns P PRACTICE Complete the pattern. 1. 8  8  n 2. 7  6  n 80  80  n 70  60  n 800  800  n 700  600  n 8,000  8,000  n 7,000  6,000  n 80,000  80,000  n 70,000  60,000  n 800,000  800,000  n 700,000  600,000  n 3. 5  9  n 4. 8  9  n 50  90  n 80  90  n 500  900  n 800  900  n 5,000  9,000  n 8,000  9,000  n 50,000  90,000  n 80,000  90,000  n 500,000  900,000  n 800,000  900,000  n Add mentally. 5. 500  400  6. 3,000  9,000  7. 30,000  80,000  8. 700  800  9. 600  500  © McGraw-Hill School Division 11. 100,000  900,000  10. 70,000  30,000  12. 800,000  500,000  Problem Solving 13. A music store made $50,000 selling CDs and tapes in December. In January, the store made $30,000. How much did the store make in all? Use with Grade 4, Chapter 2, Lesson 2, pages 46–47. (31) 14. The Green Hornets sold 800,000 copies of their first CD. They sold 500,000 copies of their second CD. How many CDs did the Green Hornets sell in all? NS 3.1; MR 1.1 Print This Page Name Print This 2–2 Page Addition Patterns R RETEACH You can use addition facts and patterns to add multiples of ten mentally. Add the front digits. Then write a zero to match each place value. 5  7  12 5 7 12 5,000  7,000  12,000 5,000  7,000 12,000 50  70  120 50  70 120 50,000  70,000  120,000 50,000  70,000 120,000 500  700  1,200 500  700 1,200 500,000  700,000  1,200,000 500,000  700,000 1,200,000 Complete the pattern. © McGraw-Hill School Division 1. 3  8  n 2. 5  9  n 30  80  n 50  90  n 300  800  n 500  900  n 3,000  8,000  n 5,000  9,000  n 30,000  80,000  n 50,000  90,000  n 300,000  800,000  n 500,000  900,000  n Add mentally. 3. 800  600  4. 9,000  7,000  5. 80,000  80,000  6. 5,000  4,000  7. 900  500  8. 700,000  600,000  9. 800,000  700,000  11. 300  700  Use with Grade 4, Chapter 2, Lesson 2, pages 46–47. (32) 10. 60,000  50,000  12. 80,000  90,000  NS 3.1; MR 1.1 Print This Page Name Print This 2–2 Page Addition Patterns E ENRICH Pascal’s Triangle The triangle below is called Pascal’s Triangle. Each row begins and ends with the number 1. Every other number is the sum of the two numbers above it. Complete this Pascal’s Triangle. Row 1 1 Row 2 1 Row 3 1 Row 4 1 Row 5 Row 7 2 3 1 Row 6 1 1 3 1 6 1 1 1 1 1 Now complete this Pascal’s Triangle. Each row begins and ends with 200. Row 1 200 Row 2 200 © McGraw-Hill School Division Row 3 200 Row 4 200 Row 5 200 Row 6 Row 7 200 200 Use with Grade 4, Chapter 2, Lesson 2, pages 46–47. (33) 200 400 600 200 600 1,200 200 200 200 200 NS 3.1; MR 1.1 Print This Page Name Print This 2–3 Page Add Whole Numbers and Money P PRACTICE © McGraw-Hill School Division Find each sum. 1. 688  207 2. 574  434 3. 757  529 4. $8.72  1.38 5. $2.98  0.59 6. 989  624 7. 8,489  2,467 8. $3,824  962 9. 5,174  327 10. $12.57  7.43 11. 6,672  878 12. $78.29  45.32 13. 12,345  67,890 14. 43,802  7,526 15. 24,316  893 16. 183,462  570,184 17. $3,421.78  1,657.18 18. 204,177  678,687 19. 741,243  85,278 20. $427,535  6,280 21. $7.77  $6.66  22. 5,872  754  23. 3,489  87  741  24. $256.82  $357.47  $83.95  25. 42,608  7,709  3,047  26. 782,070  879,162  115,603  Problem Solving 27. At the Lakeside School, 522 students ride the bus and 714 students walk or are driven to school. How many students attend Lakeside School? Use with Grade 4, Chapter 2, Lesson 3, pages 48–51. (34) 28. Last week, $325 worth of play tickets and $729 worth of carnival tickets were sold. How much money was collected altogether? NS 3.1 Print This Page Name Print This 2–3 Page Add Whole Numbers and Money Add 587  269. Step 1 Add the ones. Regroup if necessary. H T Step 2 Add the tens. Regroup if necessary. O H T 1 1 5 2 8 6 5 1 5 2 8 6 7 9 6 R RETEACH Step 3 Add the hundreds. Regroup if necessary. O H T O 1 1 7 9 5 2 8 6 7 9 6 8 5 6 7 ones  9 ones  16 ones 1 ten  8 tens  6 tens 1 hundred  5 hundreds   15 tens 2 hundreds  8 hundreds 16 ones  1 ten 6 ones 15 tens  1 hundred 5 tens © McGraw-Hill School Division Find each sum. 1. 413  228 2. 336  574 3. $4.80  2.57 4. 327  425 5. $828  16 6. 187  219 7. 534  394 8. $9.34  3.68 9. 692  810 10. $7.99  7.99 11. 1,245  3,717 12. $31.15  85.29 13. 6,289  764 14. 8,147  3,988 15. 5,326  383 16. 71,128  3,511 17. 87,421 2,032  5,857 18. 25,784 4,408  64,726 19. 399,625 99,990  437,487 20. $62.41 7.38  1.21 Use with Grade 4, Chapter 2, Lesson 3, pages 48–51. (35) NS 3.1 Print This Page Name Print This 2–3 Page Add Whole Numbers and Money E ENRICH Hindu Addition The Hindu people of ancient India added numbers from the left and moved to the right. Here is an example of Hindu addition. Add the hundreds. 589  782 12 Next add the tens. 8  8  16. Regroup to the hundreds place. Last, add the ones. Regroup to the tens place. The sum is 1,371. 589  782 126 3 589  782 1261 37 © McGraw-Hill School Division Use the Hindu method of addition to find the sum. Show your work. 1. 56  35 2. 96  87 3. 538  247 4. 322  489 5. 289  556 6. $9.63  8.75 7. 238  849 8. 766  984 9. $1.87  7.58 10. 11. 385  496 12. 874  496 $6.11  9.97 Compare the Hindu method of addition to the method of addition you use. Which method do you like best? Explain. Use with Grade 4, Chapter 2, Lesson 3, pages 48–51. (36) NS 3.1 Print This Page Name Print This 2–4 Page Use Mental Math to Add P PRACTICE Add mentally. 1. 32  45  2. 21  64  3. 35  13  4. $39  $24  5. 48  31  6. 298  311  7. 595  409  8. 255  344  9. 238  495  10. 730  214  11. 891  108  12. $256  $222  13. 4,524  3,173  14. 8,999  1,333  15. 2,295  2,124  16. 1,487  1,511  Algebra & Functions Find each missing number. 17. 36  a  86 19. $498  21. c  $698 e  657  957 23. $725  k  $1,125 © McGraw-Hill School Division 25. 1,650  n  3,300 18. b  61  81 20. d  298  598 22. $63  h  $243 24. m  837  1,137 26. r  $750  $1,500 Problem Solving 27. There are 38 dogs and 24 cats at the pet show. How many cats and dogs are there in all? Use with Grade 4, Chapter 2, Lesson 4, pages 52–53. (37) 28. The pet show committee spends $316 on dog treats and $299 on cat treats. How much does the committee spend on treats? NS 3.1; AF 1.1 Print This Page Name Print This 2–4 Page Use Mental Math to Add R RETEACH You can use these two strategies to add mentally. Compensation Use compensation when a number is close to a ten or a hundred. 197 → 200  254 →  251 451 Add 3 to make 200: 197  3  200. Subtract 3 from the other number: 254  3  251. Zig-zag Use the zig-zag method to add 356  627. Take apart 627. 627  600  20  7 Then add each place separately. 356  627 356  600 956 956  20 976 976  7 983 © McGraw-Hill School Division Add mentally. 1. 62  39  2. 54  17  3. 202  248  4. $316  $455  5. $625  $330  6. 437  128  7. 499  252  8. 697  140  9. $29  $56  10. $62  $78  11. $268  $441  12. 298  465  13. 752  247 14. 365  113  15. 599  109  16. 232  657  17. 253  35  18. 849  52  19. 425  222  20. 723  245  21. 3,398  1,343  22. 2,377  196  23. $6,512  $950  24. 1,783  5,097  Use with Grade 4, Chapter 2, Lesson 4, pages 52–53. (38) NS 3.1; AF 1.1 Print This Page Name Print This 2–4 Page Use Mental Math to Add E ENRICH Countdown! Move from left to right. Add each pair of numbers mentally. Shade any box that is the sum of the previous two boxes. Example: In row 1, add 19 and 53. The sum is 72. Shade the box with 72 in it. Add 53 and 72. If the sum is 125, then shade the box with 125 in it. 19 53 72 125 197 232 429 661 1,090 1,000 3,090 4,090 195 302 402 67 469 12 480 115 595 110 805 915 17 21 37 58 95 22 127 149 270 199 39 238 34 51 99 154 253 307 560 857 1,317 174 399 573 79 15 94 109 203 311 514 825 1,339 2,064 2,213 4,277 1. Look at the shaded boxes. What number do the boxes form? 2. Which method did you use to add pairs of numbers mentally when: the sum of the digits was less than 9? one number was close to 10, 100, or 1,000? © McGraw-Hill School Division the sum of the digits was greater than 9? How is mental math different from estimation? Use with Grade 4, Chapter 2, Lesson 4, pages 52–53. (39) NS 3.1; AF 1.1 Print This Page Name Print This 2–5 Page Estimate Sums P PRACTICE Estimate each sum. Show your work 1. 478  597 2. $8.65  $7.15 3. $0.32  $0.65 4. 4,990  405 5. 2,188  5,621 6. 47,522  3,721 7. 863,122  254,087 Add. Estimate to check that each answer is reasonable. 8. 621  308  9. 2,188  5,621  10. $4.20  $8.12  11. 601,128  328,125  Compare. Write  or  to make a true sentence. 12. 176  335 14. 500 251  127 16. 1,348  2,489 © McGraw-Hill School Division 18. 9,000 13. 243  50 400 15. 900 5,000 4,487  5,672 20. 22,152  28,174 60,000 300 895  68 17. 4,725  321 19. 8,000 3,923  289 6,081  950 21. 49,912  2,839 5,000 Problem Solving 22. Julio wants to buy drawing paper for $8.50 and brushes for $19.95. About how much will he spend? Use with Grade 4, Chapter 2, Lesson 5, pages 54–55. (40) 23. The fourth-grade students make 268 posters about bicycle safety. The fifth-grade students make 229. About how many posters do the students make altogether? NS 2.1; 3.1; MR 2.1, 2.5 Print This Page Name Print This 2–5 Page Estimate Sums R RETEACH To estimate a sum, you can round each number. Then add the rounded numbers. Estimate 252  49. Round each number to the nearest ten. Add. Estimate $5.95  $7.25. 252  49 250  50 Round each $5.95  $7.25 ↓ ↓ number to the nearest dollar. $6.00  $7.00 250  50  300 Add. ↓ ↓ So, 252  49 is about 300. $6.00  $7.00  $13.00 So, $5.95  $7.25 is about $13.00. To which place will you round each number? Circle the digits in that place. Then estimate each sum. Show how you rounded. 1. $7.89  $5.29 2. $0.32  $0.48 3. 6,714  8,217 4. 27,822  2,321 5. 5,214  642 6. 38,629  5,927 Estimate each sum. © McGraw-Hill School Division 7. 469  563 8. $9.08  $12.75 9. 143  431 10. 5,723  3,501 11. 1,827  764 12. 2,357  8,605 13. $38,956  $7,653 14. $46.90  $327.54 15. 896,455  11,321 16. 477,995  865,311 Use with Grade 4, Chapter 2, Lesson 5, pages 54–55. (41) NS 2.1, 3.1; MR 2.1, 2.5 Print This Page Name Print This 2–5 Page Estimate Sums E ENRICH Star Estimates There are five paths. Each path has six numbers. Round each number to the nearest hundred. Then estimate the sum of the rounded numbers on each path of the star. Write your estimate in the box at the end of each path. 3. 30,800 23,724 5,627 3,846 1. Start 225 5. 45,672 152 172 429 47,600 874 44,100 810 126,582 714 © McGraw-Hill School Division 381 825 524 418,670 174 41,321 432 2. 129,600 Use with Grade 4, Chapter 2, Lesson 5, pages 54–55. (42) 645 4. 447,700 NS 2.1, 3.1; MR 2.1, 2.5 Print This Page Name Print This 2–6 Page Problem Solving: Reading for Math P PRACTICE Reading Skill Estimate or Exact Answer Solve. Explain why you gave an estimate or an exact answer. 1. James, Max, and Melba collect baseball cards. James has 870 cards, Max has 569 cards, and Melba has 812 cards. Do the three friends have more than 2,000 baseball cards? 2. Nicki has a collection of 79 shells and 64 rocks. How many items are in her collection? 3. Kelly has a coin collection. Her quarters are worth $104.50. Her dimes are worth $75.10. Her nickels are worth $27.75. What is the total value of Kelly’s coin collection? 4. The Comic Book Show sells 474 tickets on Friday and 396 tickets on Saturday. About how many tickets does the Comic Book Show sell? © McGraw-Hill School Division 5. Eldon has 98 rock CDs, 121 classical CDs, and 25 folk music CDs. How many CDs does Eldon have? 6. Molly has 221 stamps from the United States and 395 stamps from other countries. About how many stamps does Molly have? Use with Grade 4, Chapter 2, Lesson 6, pages 56–57. (43) MR 1.1, 2.1, 2.3, 2.4, 2.5, 3.1, 3.2 Print This Page Name Print This 2–6 Page Problem Solving: Reading for Math P Estimate or Exact Answer PRACTICE Math Skills Test Prep Choose the correct answer. Jenny has a collection of 249 football cards. Ken has a collection of 329 football cards. Are there more than 500 cards in these two collections altogether? 1. Which of the following statements is 2. Which number sentence will help true? you solve the problem? A Jenny has more cards than Ken. F 249  329  500 B Ken has more than 500 cards. G 329  249  500 C Jenny has 249 cards. H 500  249  500 Paco has 129 toy cars. His brother has 167 toy cars. How many toy cars do they have in all? 3. Which plan can you use to solve the 4. How many toy cars do they have problem? in all? A Estimate the sum of 129 and 167. F 300 B Add 129 and 167. G 296 C Compare 129 and 167. H 200 © McGraw-Hill School Division Hiroshi has 429 football cards, 278 baseball cards, and 97 hockey cards. Does Hiroshi have more than 1,000 cards in all? 5. Which of the following statements is true? A Hiroshi has 278 baseball cards. B Hiroshi has 429 cards in all. C Hiroshi has 97 football cards. 6. What do you have to do to solve this problem? F Find the exact sum for 429  278  97. G Estimate to tell if 429  278 is greater than 1,000. H Estimate to tell if 429  278  97 is greater than 1,000. Use with Grade 4, Chapter 2, Lesson 6, pages 56–57. (44) MR 1.1, 2.1, 2.3, 2.4, 2.5, 3.1, 3.2 Print This Page Name Print This 2–6 Page Problem Solving: Reading for Math P Estimate or Exact Answer PRACTICE Math Skills Test Prep Choose the correct answer. On Friday, 529 people see the museum’s collection of antique dolls. On Saturday, 994 people see the collection. On Sunday, 812 people see the collection. How many people came to see the antique doll show during the three days? 7. Which plan can you use to solve the problem? A Estimate the sum of 529, 994, and 812. 8. How many people came to see the antique doll show during the three days? F 2,335 B Add 529, 994, and 812. G 2,300 C Order 529, 994 and 812 from least to greatest. H 1,523 Solve. 9. Chelsea has 635 postcards from the United States, 291 postcards from Canada, and 456 postcards from Europe and Asia. Does she have more than 2,000 postcards? © McGraw-Hill School Division 11. Miles has 75 old movie posters, 63 concert posters, and 54 posters from plays. How many posters does Miles have? 13. Nina has 379 stamps from the United States and 458 stamps from other countries. How many stamps does she have? Use with Grade 4, Chapter 2, Lesson 6, pages 56–57. (45) 10. Gus has 65 autographs from sports players, 97 autographs from actors and actresses, and 27 autographs from singers. About how many autographs does he have? 12. Evan has 4,212 cards. His sister has 5,349 cards. If they put their cards together, will they have more than 9,000 cards? 14. Morris has a collection of 44 quarters, 92 dimes, and 89 pennies. About how many coins does he have? MR 1.1, 2.1, 2.3, 2.4, 2.5, 3.1, 3.2 Print This Page Name Print This 2–7 Page Subtraction Patterns P PRACTICE Complete the pattern. 1. 12  8  n 2. 16  7  n 120  80  n 160  70  n 1,200  800  n 1,600  700  n 12,000  8,000  n 16,000  7,000  n 120,000  80,000  n 160,000  70,000  n 1,200,000  800,000  n 1,600,000  700,000  n 3. 11  5  n 4. 15  8  n 110  50  n 150  80  n 1,100  500  n 1,500  800  n 11,000  5,000  n 15,000  8,000  n 110,000  50,000  n 150,000  80,000  n 1,100,000  500,000  n 1,500,000  800,000  n Subtract mentally. 5. 1,200  600  6. $8,000  $3,000  7. 600,000  500,000  8. 70,000  50,000  9. $13,000  $9,000  © McGraw-Hill School Division 11. 140,000  50,000  10. 160,000  80,000  12. 1,200,000  600,000  Problem Solving 13. A video store rented 900,000 videos last year. This year the store rented 1,500,000 videos. How many more videos did it rent this year? Use with Grade 4, Chapter 2, Lesson 7, pages 60–61. (46) 14. The price for a house is $120,000. Ms. Smith decides to make an offer that is $30,000 less than the price. How much does Ms. Smith offer for the house? NS 3.1; MR 1.1 Print This Page Name Print This 2–7 Page Subtraction Patterns R RETEACH You can use subtraction facts and patterns to subtract multiples of ten mentally. Subtract the front digits. Then write a zero to match each place value. 12  7  5 12  7 5 12,000  7,000  5,000 12,000  7,000 5,000 120  70  50 120  70 50 120,000  70,000  50,000 120,000  70,000 50,000 1,200  700  500 1,200  700 500 1,200,000  700,000  500,000 1,200,000  700,000 500,000 Complete the pattern. © McGraw-Hill School Division 1. 11  8  n 2. 14  5  n 110  80  n 140  50  n 1,100  800  n 1,400  500  n 11,000 – 80,000 = n 14,000  5,000  n 110,000  800,000  n 140,000  50,000  n 1,100,000  8,000,000  n 1,400,000  500,000  n Subtract mentally. 3. 1,400  600  4. $16,000  $7,000  5. 160,000  80,000  6. 1,200  500  7. $1,500  $700  8. 110,000  50,000  9. 14,000  8,000  11. 1,800,000  900,000  Use with Grade 4, Chapter 2, Lesson 7, pages 60–61. (47) 10. $1,700,000  $900,000  12. 120,000  40,000  NS 3.1; MR 1.1 Print This Page Name Print This 2–7 Page Subtraction Patterns E ENRICH Subtraction Squares (Diffy) Each subtraction square is made up of eight numbers. To find the missing numbers, subtract the two corner numbers in each square and write the difference in between the numbers. Find the missing numbers. Subtract until you reach the center of the square. 70 150 10 30 20 60 10 80 20 40 0 0 0 0 20 0 0 20 30 30 0 0 0 0 © McGraw-Hill School Division 20 90 20 10 20 10 40 50 2. What happens in the center of the squares? 3. What do you think will happen if you choose four other corner numbers for the largest square? Try it and check your prediction! Use with Grade 4, Chapter 2, Lesson 7, pages 60–61. (48) NS 3.1; MR 1.1 Print This Page Name Print This 2–8 Page Explore Subtracting Whole Numbers P PRACTICE Subtract. 1. Use models to subtract 525  272.   Subtract the ones. 5 2 2 7 5 2 Subtract the tens. Regroup 1 hundred as 10 tens. 5 2 2 7 5 2 Subtract the hundreds. 5 2 2 7 5 2 © McGraw-Hill School Division Subtract. 2. 187  95 3. 612  74 4. 356  127 5. 923  707 6. 319  79 7. 711  380 8. 425  258 9. 857  79 10. 562  348 11. 227  138 12. 684  327  13. 573  495  14. 813  75  15. 263  88  Use with Grade 4, Chapter 2, Lesson 8, pages 62–63. (49) NS 3.1 Print This Page Name Print This 2–8 Page Explore Subtracting Whole Numbers R RETEACH Use models to subtract 322  145. Step 1 Model the greater number. You need to subtract 145, or 1 hundred 4 tens 5 ones. 322 145 1 12 Step 2 Subtract the ones. Regroup a ten for 10 ones, if necessary. Subtract 5 ones. Step 3 Subtract the tens. Regroup a hundred for 10 tens, if necessary. 3 2/ 2/ 145 7 2 11 12 3/ 2/ 2/ 145 77 Subtract 4 tens. Step 4 Subtract the hundreds. 2 11 12 3/ 2/ 2/ 145 177 Subtract 1 hundred. © McGraw-Hill School Division Subtract. Use or draw models to help you subtract. 1. 724  318 2. 916  108 3. 568  59 4. 428  247 5. 353  182 6. 964  281 7. 735  586 8. 327  299 9. 863  575 10. 651  93 11. 274  126  Use with Grade 4, Chapter 2, Lesson 8, pages 62–63. (50) 12. 745  67  NS 3.1 Print This Page Name Print This 2–8 Page Explore Subtracting Whole Numbers E ENRICH Crack the Code Find each difference. Match the code number beside each problem with the correct code letter. Problems Code Numbers 1. $3.63  $1.77 6 761  S 2. $4.25  $2.86 4 88  A 3. 181  92 9 $1.39  U 4. 573  397 13 176  T 5. 426  326 14 304  C 6. 880  119 5 $1.59  N 7. 625  317 2 89  V 12 $1.86  E 8. 682 594 9. 170  98 308  M 7 10. 590  399 15 11. 731  427 11 77  N 3 191  O 16 47  A 14. 464  387 8 138  A 15. 222  175 1 72  O 16. 832  694 10 $1.16  O 12. $9.05 $7.89 13. $6.52  $4.93 © McGraw-Hill School Division Code Letters 100  I Use this code to solve the riddle. Write the correct letter above each number. Riddle: What animal is gray and has a trunk? 1 2 3 4 5 6 7 Use with Grade 4, Chapter 2, Lesson 8, pages 62–63. (51) 8 9 10 11 12 13 14 15 16 NS 3.1 Print This Page Name Print This 2–9 Page Subtract Whole Numbers and Money P PRACTICE © McGraw-Hill School Division Subtract. Check by adding. 1. 757  28 2. $582  492 3. 693  516 4. 851  569 5. $2.48  1.95 6. 2,345  1,658 7. $67.89  18.95 8. $11,321  979 9. 4,672  873 10. 3,523  2,846 11. $33,572  13,689 12. 74,125  65,239 13. 49,785  8,998 14. 98,142  617 15. $224.39  15.87 16. $4,561.71  291.68 17. 389,243  136,354 18. $672,145  98,276 19. 914,617  117,814 20. $7,211.53  5,926.84 21. 827  468  22. $9.12  $7.58  23. 42,625  9,846  24. 65,932  46,464  25. $311.42  $4.65  26. $578,423  $89,743  27. 982,561  678,984  28. $2,176.53  $1,993.76  Problem Solving 29. A toy factory made 32,154 board 30. A store earned $12,415 selling games on Monday. On Tuesday it made 31,687 board games. How many more board games did the factory make on Monday? puzzles this week. Last week it earned $9,326 selling puzzles. How much more did the store earn this week? Use with Grade 4, Chapter 2, Lesson 9, pages 64–65. (52) NS 3.1 Print This Page Name Print This 2–9 Page Subtract Whole Numbers and Money R RETEACH Subtract 7,617  5,789. Step 1 Subtract the ones. Regroup if necessary. TH 7 5 H 6 7 T O 0 17 1/ 8 7 / 9 Step 2 Subtract the tens. Regroup if necessary. TH 7 5 H T O 5 10 0/ 17 6/ 7 1/ 8 7 / 9 2 8 8 Step 4 Subtract the thousands. Step 3 Subtract the hundreds. Regroup if necessary. TH H T O 15 5/ 10 0/ 17 6 7 / 9 7/ 5 6/ 7 1/ 8 7 / 9 8 1 8 2 8 TH H T O 15 5/ 10 0/ 17 6 7/ 5 6/ 7 1/ 8 8 2 Use the same steps to subtract money. © McGraw-Hill School Division Subtract. Check by adding. 1. 577  385 2. 872  465 3. $6.21  4.43 4. 3,457  965 6. 4,872  3,785 7. 7,501  6,874 8. 8,142  6,527 9. 12,435  8,679 11. 24,652  9,788 12. $56,716  39,897 13. 347,072  59,687 Use with Grade 4, Chapter 2, Lesson 9, pages 64–65. (53) 14. 5. 10. $2.49  0.98 $6,423  2,496 743,219 $6,192.48 15.  1,671.39  19,733 NS 3.1 Print This Page Name Subtract Whole Numbers and Money Print This 2–9 Page E ENRICH Sumerian Numbers The Sumerians were an ancient civilization. Sumerians were one of the first people to develop a written number system and compute with it. They had five number symbols. The chart shows the value of each symbol. 1 10 60 600 3,600 The symbols were combined to represent numbers. Example: 3,600  600  60  10  10  4,280 Solve the Sumerian subtraction problems. Translate the Sumerian symbols to the numbers in our system and subtract. Then write the difference using Sumerian symbols. 1. 133  125 2. 1,263  © McGraw-Hill School Division  1,821  1,205 7,280   626 637 8 4. 3. 5. 3,750  616 Use with Grade 4, Chapter 2, Lesson 9, pages 64–65. (54)  3,650 100  4,861 2,419 6.  1,242  922 320 NS 3.1 Print This Page Name Print This 2–10 Page Regroup Across Zeros P PRACTICE © McGraw-Hill School Division Subtract. Check by adding. 1. 804  565 2. 701  387 3. $500  244 4. 600  58 5. 300  108 6. 3,000  2,987 7. 9,000  5,431 8. 4,050  2,542 9. 2,000  784 10. 8,000  2,450 11. $15,000  7,641 12. 70,700  8,633 13. 50,000  25,625 14. 80,000  35,189 15. 30,000  7,984 16. 600,003  25,178 17. $900,000  321,229 18. 400,707  39,698 19. 210,303  101,506 20. 575,000  89,342 21. 602  423  22. 800  68  23. 3,400  1,762  24. 6,000  672  25. $20,800  $13,972  26. 70,000  52,087  27. 160,000  149,999  28. 307,000  198,621  Problem Solving 29. Crystal Lake School held a dance 30. At the festival, 39,251 people festival. There were 3,000 dancers at the festival. Of those dancers, 2,682 did not win prizes. How many dancers did win prizes? watched the dancers. Another 700,000 people watched the festival on television. How many more people watched the festival on television? Use with Grade 4, Chapter 2, Lesson 10, pages 66–67. (55) NS 3.1 Print This Page Name Print This 2–10 Page Regroup Across Zeros R RETEACH Subtract 500  185. Step 1 No ones. No tens. Regroup the hundreds. H T 4 5/ 10 0 / 5 / 1 0/ 8 O 0 5 5 hundreds  4 hundreds 10 tens There are not enough ones to subtract 9 ones. Step 3 Subtract the ones, the tens, and then the hundreds. Step 2 Regroup the tens. H T O H T O 4 9 10 / 10 4 9 10 / 10 5 / 1 0/ 8 0/ 5 5 / 1 0/ 8 0/ 5 3 1 5 10 tens  9 tens 10 ones 10 ones  5 ones  5 ones 9 tens  8 tens  1 ten 4 hundreds  1 hundred  3 hundreds © McGraw-Hill School Division Subtract. Check by adding. 304  150 1. 602  314 2. 700  203 3. $900  306 4. 800  523 6. $4,000  1,527 7. 2,005  1,083 8. 3,000  2,225 9. 5,000  259 10. 6,000  1,326 $40,050  32,037 15. 45,000  2,374 11. 68,000  11,770 12. 80,000 13. 74,800  5,287  27,862 14. 5. 16. 300,077  124,364  17. $200,008  $187,053  18. 107,006  84,119  19. 906,004  205,457  20. 60,000  29,730  21. $500,600  $50,250  Use with Grade 4, Chapter 2, Lesson 10, pages 66–67. (56) NS 3.1 Print This Page Name Print This 2–10 Page Regroup Across Zeros E ENRICH Missing Digits Find the missing digits. 1. 8  0 7 1 3 4. 0  1 7. 10. 6,  3, 7  2 © McGraw-Hill School Division 13. 7 16. 2. 8 9 5. 4 , 2 0 7 , 7 3 9 0 8 6 8.  2 2 9 8 9  3 0 8 6 1 6 6, 7 3 1  17. 5 2 0 0  2 3 3 Use with Grade 4, Chapter 2, Lesson 10, pages 66–67. (57) 3 6 1  4, 12. 3 5, 6. 1 5 2 8 7 9. 7 9  2 3. 3 , 7 0 2 7 6 3 14. 7 5 8 2,  1, 11. 4 5  2 0 3 2 4 7 0 6 5,  2, 9 0 8  3 6 5 7 7 9 15. 6 5,  3, 5 2, 2 7,  3, 3 0 5 8 4 5 0 8 8 3 3 0 8 0 5 , 2 1 5 , 0  4, 8 7 8 , 1 18. 7 ,  , 2 5, 7 1 4 1 3 4 6 NS 3.1 Print This Page Name Print This 2–11 Page Problem Solving: Strategy P PRACTICE Write a Number Sentence Write a number sentence to solve. 1. Meg buys candle-making supplies for $37. She has $25 left. How much money did Meg have before she bought the supplies? 3. Eric sells a painting for $125. He sells a sculpture for $390. How much money does Eric earn in all? 2. Sally has finished 86 squares in her quilt. The quilt will have 100 squares. How many squares does Sally still have to make? 4. Noah has saved $42. How much more money does he need to buy a rare coin for $90? Mixed Strategy Review Solve. Use any strategy. 5. Howard has 75 shells. On a trip, he collects another 16 shells. How many shells does he have now? 6. Tom makes letters for a sign that says “Arts and Crafts Fair.” Which letter does Mark need to make the most of? Strategy: Strategy: © McGraw-Hill School Division 7. Social Studies During the 1800s, sailors made carvings called scrimshaw on whale teeth, whalebone, and tortoise shells. Suppose a sailor made a carving in 1805. A collector buys the carving in 2000. How many years old is the carving? 8. Create a problem which you could write a number sentence to solve. Share it with others. Strategy: Use with Grade 4, Chapter 2, Lesson 11, pages 68–69. (58) NS 3.1; AF 1.1, 2.1; MR 1.1 Print This Page Name Print This 2–11 Page Problem Solving: Strategy R RETEACH Write a Number Sentence Page 69, Problem 2 Ms. Green had 29 buttons to sew on dolls. She has 14 buttons left. How many buttons has she already sewn on? Step 1 Read Be sure you understand the problem. Read carefully. What do you know? • Ms. Green had • She has buttons to sew on dolls. buttons left. What do you need to find? • You need to find how many . Step 2 Plan ■ ■ ■ ■ ■ © McGraw-Hill School Division ■ ■ ■ ■ ■ Make a Table or List Write a Number Sentence Work Backward Act It Out Find a Pattern Make a Graph Guess and Check Logical Reasoning Solve a Simpler Problem Draw a Picture Make a plan. Choose a strategy. You can write a number sentence to solve the problem. Since you know the original total and the number left, you can write a subtraction sentence. Use with Grade 4, Chapter 2, Lesson 11, pages 68–69. (59) NS 3.1; AF 1.1, 2.1; MR 1.1 Print This Page Name Print This 2–11 Page Problem Solving: Strategy R RETEACH Write a Number Sentence Step 3 Solve Carry out your plan. • You know Ms. Green had • You know she has buttons to sew on dolls. buttons left. Write a subtration sentence to represent the situation. 29  n  14 number of buttons buttons left buttons she had already sewn on Then use a related sentence to solve.  number of buttons she had  buttons left She has already sewn on Step 4 Look Back buttons already sewn on buttons. Is the solution reasonable? Reread the problem. Does your answer make sense? Did you answer the question? Yes Yes No No How can you check your answer? © McGraw-Hill School Division What other stategies could you use to solve the problem? Practice 1. Keshawn spends $45 on glass and copper molding. He pays with a hundred-dollar bill. How much change does Keshawn get back? Use with Grade 4, Chapter 2, Lesson 11, pages 68–69. (60) 2. Melanie sells a model sailing ship and a model airplane for a total of $40.95. She receives $23.49 for the ship. How much money does Melanie receive for the airplane? NS 3.1; AF 1.1, 2.1; MR 1.1 Print This Page Name Print This 2–12 Page Subtract Using Mental Math P PRACTICE Subtract mentally. 1. 46  7  2. 81  36  3. 53  19  4. 99  19  5. $78  $49  6. 92  28  7. 74  38  8. 95  37 9. 64  37  10. 687  48  11. $273  $58  12. 394  86  13. $704  $589  14. 745  597  15. 782  203  16. 613  309  17. 555  299  18. 998  145  19. 578  465  Algebra & Functions Find each missing number. 20. 648  22. a  548 21. b  60  340 c  412  388 23. d  235  665 24. 950  © McGraw-Hill School Division 26. e  400 25. 823  h  123 k  599  301 27. 450  m  100 28. 775  n  200 29. r  300  1,456 Problem Solving 30. Josh buys a wooden horse for $4.89. He gives the cashier $5.00. How much change should Josh receive? Use with Grade 4, Chapter 2, Lesson 12, pages 70–71. (61) 31. A bicycle shop has 309 water-bottle holders in stock. Ashley buys 259 water-bottle holders from the shop. How many water-bottle holders does the store have left? NS 3.1; AF 2.1 Print This Page Name Print This 2–12 Page Subtract Using Mental Math R RETEACH You can use these two strategies to subtract mentally. Compensation Use compensation when one number is close to a ten or a hundred. Add or subtract the same number from both numbers. 95  28 97 → →  30 Add 2 to 28 to make 30: 28  2  30. Add 2 to the other number: 95  2  97. 67 103  45 → 100 →  42 Subtract 3 from 103 to make 100: 103  3  100. Subtract 3 from 45: 45  3  42. 58 Zig-zag Use the zig-zag method to subtract 95  28. Take apart 28. 28  20  8 Then subtract each place separately. 95  28 95  20 75 75  8 67 © McGraw-Hill School Division Subtract mentally. 1. 26  7  2. 84  32  3. 79  31  4. $58  $17  5. 94  38  6. 86  24  7. 196  49  9. 395  91  8. $253  $42 10. 888  277  11. 245  197  12. $428  $117  13. 482  204  14. 613  307  15. 354  99  16. $755  $402  17. 519  404  18. 505  301  19. $535  $122  20. 350  198  21. 657  312 22. 648  305 Use with Grade 4, Chapter 2, Lesson 12, pages 70–71. (62) NS 3.1; AF 2.1 Print This Page Name Print This 2–12 Page Subtract Using Mental Math E ENRICH Crossnumber Puzzle Subtract mentally to complete the crossnumber puzzle. A 4 8 E 2 G 9 B 2 © McGraw-Hill School Division 9 5 2 4 F 5 8 6 5 L 2 4 6 I M 8 3 J 4 2 7 5 O 4 1 3 H 5 8 D 3 1 7 K N C 3 7 Across Down A. 596  111 A. 626  197 C. 879  65 B. 360  308 E. 281  28 D. 237 105 G. 192  95 F. 591  76 H. 383  99 I. 950  113 K. 1,253599 J. 765  723 M. 194  162 K. 686  28 N. 448  203 L. 635  179 O. 662  25 N. 228  199 Look at N. Down. What method did you use to subtract mentally? Use with Grade 4, Chapter 2, Lesson 12, pages 70–71. (63) NS 3.1; AF 2.1 Print This Page Name Print This 2–13 Page Estimate Differences P PRACTICE Estimate each difference. Show your work. 1. 467  215 2. 2,835  1,487 3. $13.95  $7.25 4. 65,074  15,472 5. 174,921  18,421 Subtract. Estimate to check that each answer is reasonable. 6. 835  487 $81.79  31.55 7. 8. 6,984  322 11. $0.88  $0.35  9. 242,003  49,887 10. 654,026  529,620 12. 787,008  117,584  Compare. Write  or  to make a true sentence. 13. 4,173  2,589 15. $300.00 2,000 $367.20  $59.45 17. 15,425  3,535 © McGraw-Hill School Division 19. 42,345  16,174 10,000 20,000 14. 8,329  957 16. 600 7,000 938  452 18. 8,053  7,645 20. 48,592  961 1,000 4,000 Problem Solving 21. There were 787,897 copies of the Science Monthly sold last year. This year, 914,632 copies were sold. About how many more were sold this year? Use with Grade 4, Chapter 2, Lesson 13, pages 72–73. (64) 22. The Hoop Store spends $129.99 for an ad in the Science Monthly. The store spends $19.29 for an ad in the Allentown News. About how much more does the store spend on advertising in the Science Monthly than in the Allentown News? NS 2.1, 3.1; MR 2.1, 2.5 Print This Page Name Print This 2–13 Page Estimate Differences R RETEACH To estimate a difference, you can round each number. Then subtract the rounded numbers. Estimate $6.98  $4.59. Estimate 486  27. Round each number to the nearest ten. Subtract. 490  30 Round each number $6.98  $4.59 ↓ ↓ to the nearest dollar $7.00  $5.00 490  30  460 Subtract. 486  27 ↓ ↓ So, 486  27 is about 460. $7.00  $5.00  $2.00 So, $6.98  $4.59 is about $2.00. To which place will you round each number? Circle the digits in that place. Then estimate each difference. Show how you rounded. 1. $14.95  $8.35 2. $0.78  $0.29 3. 7,842  799 4. $589.10  $85.25 5. 53,425  20,741 6. 425,697  289,721 © McGraw-Hill School Division Estimate each difference. 7. 529  158 8. $683  $475 9. 947  349 10. 5,522  1,378 11. $12.48  $3.98 12. 3,241  678 13. 52,745  47,523 14. 72,393  8,088 15. 232,500  83,900 16. 809,765  528,750 Use with Grade 4, Chapter 2, Lesson 13, pages 72–73. (65) NS 2.1, 3.1; MR 2.1, 2.5 Print This Page Name Print This 2–13 Page Estimate Differences E ENRICH A-Mazing Differences Estimate each difference. Circle the correct answer. Use your answers to find the path through the maze. 1. 961  472 2. 874  215 3. 4,971  2,364 4. 729 346 A. 400 A. 500 A. 3,000 A. 300 B. 500 B. 600 B. 2,000 B. 400 C. 600 C. 700 C. 1,000 C. 500 5. 526  481 6. $8.16  $1.92 7. $72.59  $24.71 8. 9,742  6,381 A. 0 A. $5.00 A. $30.00 A. 2,000 B. 100 B. $6.00 B. $40.00 B. 3,000 C. 200 C. $7.00 C. $50.00 C. 4,000 9. 5,692  3,766 10. 42,874  16,422 11. 69,124  31,346 12. 892,617 85,600 A. 40,000 A. 700,000 B. 2,000 B. 30,000 B. 30,000 B. 800,000 C. 3,000 C. 40,000 C. 20,000 C. 900,000 7C 6B 6A 6C 7B 4C B sh 12 C 11 A 11 C Fi 12 B ni 12 3B A 11 B 8B 3A 3C 2C 2A 10 10 A 1B 2B © McGraw-Hill School Division 1C 4A 10 C 8C 4B 1A 5C 9B 5A 7A 8A 5B t ar St 7A A. 20,000 9C A. 1,000 Use with Grade 4, Chapter 2, Lesson 13, pages 72–73. (66) NS 2.1, 3.1; MR 2.1, 2.5 Print This Page Name Problem Solving: Application Applying Addition and Subtraction Print This Page 2–14 Part A WORKSHEET Decision Making Record your data. © McGraw-Hill School Division Burgers-to-Go Ruby’s Healthy Diner Carnival Lunch Menu Your Decision Where do you think The Outdoor Club should eat? Explain. Use with Grade 4, Chapter 2, Lesson 14, pages 74–75. (67) MR 1.1; NS 3.1 Print This Page Name Problem Solving: Application Which materials block a magnet? Print This Page 2–14 Part B WORKSHEET Math & Science Record your data. Material used as blocker Number of paper clips Find the difference. that the magnet can hold (Number of paper clips a when this material is magnet can hold with used as a blocker no blocker) minus (Number of paper clips a magnet can hold when this material is used as a blocker) Magnet only © McGraw-Hill School Division Magnet with paper Magnet with foil Magnet with tape Use with Grade 4, Chapter 2, Lesson 14, pages 76–77. (68) NS 1.2, 3.1; MR 1.1, 3.1 Print This Page Name Print This Page 2–14 Part B WORKSHEET Problem Solving: Application Math & Science Which materials block a magnet? 1. What is the difference between the number of paper clips a magnet can hold with no blocker and the number of paper clips a magnet can hold with each of the different blockers you used? 2. Put the three materials in order from best blocker to worst. 3. Explain the results of your activity in terms of shielding. 4. What are some other materials that you think would be good © McGraw-Hill School Division blockers? Explain. 5. What are some other materials that you think would be bad blockers? Explain. Use with Grade 4, Chapter 2, Lesson 14, pages 76–77. (69) NS 1.2, 3.1; MR 1.1, 3.1 Print This Page Name Print This 3–1 Page Tell Time P PRACTICE Write the time in two ways. 1. 2. 3. 9 48 Choose the most reasonable units of time. Write seconds, minutes, or hours. 4. Debbie spends 20 at the dentist. 5. You are in school for about 6 . 6. Jerry walks to the store in 15 . 7. Ben swims underwater for 30 . Tell how much time. 8. 120 minutes = 1 10. 2 hour = © McGraw-Hill School Division 12. hours 9. minutes seconds = 3 minutes 11. 15 minutes = minutes = 2 12 hours 13. hour minutes = 1 41 hours Algebra & Functions Describe and complete the conversion patterns. 14. 15. Minutes 60 120 Hours 1 2 Minutes 1 2 Seconds 60 120 Use with Grade 4, Chapter 3, Lesson 1, pages 92–95. (70) 180 240 300 3 4 5 MR 1.1, 2.3 Print This Page Name Print This 3–1 Page Tell Time R RETEACH You can read time in different ways. 5 40 Read: five-forty Read: forty minutes after five Read: twenty minutes before six or twenty minutes to six Write: 5:40 Write the time in as many different ways as you can. 1. 2. 3. 4. 5. 6. © McGraw-Hill School Division 4 15 7. 3 20 8. Use with Grade 4, Chapter 3, Lesson 1, pages 92–95. (71) 2 50 9. MR 1.1, 2.3 Print This Page Name Print This 3–1 Page Tell Time E ENRICH Patterns in Time The times shown on the clocks are in a pattern. What time would the next clock show? What is the pattern? 1. 11 12 1 2 10 3 9 4 8 7 6 5 Time: 2. 5 :45 Time: 3. 11 12 1 2 10 3 9 4 8 7 6 5 Time: © McGraw-Hill School Division 4. 3 :10 Time: 5. 11 12 1 2 10 3 9 4 8 7 6 5 Time: 11 12 1 2 10 3 9 4 8 7 6 5 11 12 1 2 10 3 9 4 8 7 6 5 Pattern: Increase by 5 :30 hour. 5 :15 Pattern: Decrease by 11 12 1 2 10 3 9 4 8 7 6 5 Pattern: Increase by 3 :00 Pattern: Decrease by 11 12 1 2 10 3 9 4 8 7 6 5 Pattern: Increase by Use with Grade 4, Chapter 3, Lesson 1, pages 92–95. (72) hour. 11 12 1 2 10 3 9 4 8 7 6 5 hour. 2 :50 hour. 11 12 1 2 10 3 9 4 8 7 6 5 hour. MR 1.1, 2.3 Print This Page Name Print This 3–2 Page Elapsed Time P PRACTICE How much time has passed? 1. Begin: 12:00 P.M. 2. Begin: 1:15 A.M. 3. Begin: 11:05 P.M. End: 2:20 P.M. End: 1:50 A.M. End: 1:00 A.M. 4. Begin: 2:25 A.M. 5. Begin: 3:40 P.M. End: 5:40 A.M. 7. Begin: 8:10 P.M. 6. Begin: 5:45 A.M. End: 12:00 A.M. End: 12:15 P.M. 8. Begin: 9:30 A.M. 9. Begin: 10:35 P.M. End: 2:10 P.M. End: 8:00 A.M. End: 1:55 A.M. What time will it be in 1 hour 20 minutes? 10. 11. 12. 8 50 © McGraw-Hill School Division Algebra & Functions Write the missing numbers. 13. 5:16 A.M. is minutes after 5:00 A.M. 14. 2:45 P.M. is minutes before 3:00 P.M. 15. 7:22 P.M. is hours 16. 9:58 A.M. is minutes before minutes after 7:00 P.M. A.M. Problem Solving 17. Lisa leaves her house at 8:45 A.M. She gets to karate class 35 minutes later. At what time does Lisa get to karate class? Use with Grade 4, Chapter 3, Lesson 2, pages 96–97. (73) 18. The Big Beach bus leaves the city at 6:40 P.M. The bus arrives at the beach at 8:25 P.M. How long is the trip to the beach? MR 1.1, 2.3 Print This Page Name Print This 3–2 Page Elapsed Time R RETEACH Elapsed time is the amount of time that passes from the start to the end of an action. Follow these steps to find how much time has elapsed from 8:20 A.M. to 11:35 A.M. First count the number of hours. Then count the number of minutes. From 8:20 to 11:20 is 3 hours. From 11:20 to 11:35 is 15 minutes. So, 3 hours 15 minutes have passed. How much time has passed? 1. Begin End 3. Begin End 2. Begin End 4. Begin End © McGraw-Hill School Division 12 15 5. Begin End 6 00 6. Begin 10 30 Use with Grade 4, Chapter 3, Lesson 2, pages 96–97. (74) 3 15 End 2 15 2 35 MR 1.1, 2.3 Print This Page Name Print This 3–2 Page Elapsed Time E ENRICH Flying Time Use the time zone map to answer each question. Show your answer in local time. Remember to include the time zone; for example, 7:00 A.M. Central Time. Pacific Time Mountain Time Central Time Eastern Time 11 12 1 2 10 3 9 4 8 7 6 5 11 12 1 2 10 3 9 4 8 7 6 5 11 12 1 2 10 3 9 4 8 7 6 5 11 12 1 2 10 3 9 4 8 7 6 5 Seattle New York City Los Angeles Phoenix Atlanta Dallas Miami 1. It takes about 5 hours to fly from Los Angeles to New York City. If a plane leaves Los Angeles at 8:00 A.M., at what time will it arrive in New York City? 2. It takes 4 hours 30 minutes for a plane to fly from Atlanta to Phoenix. If a plane departs from Atlanta at 10:00 A.M., at what time will it arrive in Phoenix? 3. A plane flew from Seattle to Atlanta. It arrived in Atlanta at 1:05 A.M. The flight lasted for 5 hours 40 minutes. At what time did it depart from Seattle? 4. The flight between Dallas and Miami takes 2 hours 41 minutes. © McGraw-Hill School Division Complete the flight schedule below. Depart Dallas Arrive Miami Depart Miami 7:00 A.M. CT 2:30 P.M. ET 9:10 A.M. CT 4:45 P.M. ET 11:20 A.M. CT 6:57 P.M. ET Arrive Dallas 5. How did you adjust for the time zones in your answers? Use with Grade 4, Chapter 3, Lesson 2, pages 96–97. (75) MR 1.1, 2.3 Print This Page Name Print This 3–3 Page Calendar P PRACTICE Use the calendars for July and August for exercises 1–8. July 2000 S M T W August 2000 T F S S M 1 T 1 W T F S 2 3 4 5 Nick arrives! 2 3 4 5 6 7 8 6 7 8 9 10 11 12 15 16 17 18 19 25 26 Independence Day! 9 10 11 12 13 14 15 13 14 16 17 18 19 20 21 22 20 21 22 23 24 23 24 25 26 27 28 29 27 28 29 30 31 30 31 1. What is the date of the fourth Thursday in July? 3. Cindy will return from vacation on © McGraw-Hill School Division the Monday after Nick arrives. On which date will Cindy return? 5. Justin is moving to a new town on August 1. The movers are coming 4 days before that. On which date will the movers arrive? Football practice begins! 2. On which day of the week is Independence Day? 4. If soccer camp runs from July 7 through the following Saturday, how long is soccer camp? 6. Jason has a violin lesson every Wednesday. How many lessons will he have in July and August? 8. Pat saw the dentist on July 25. He has 7. Nick will leave on August 30. For how many weeks will he visit? Use with Grade 4, Chapter 3, Lesson 3, pages 98–99. (76) another appointment 10 days later. On which date is Pat’s appointment? MR 1.1, 2.3 Print This Page Name Print This 3–3 Page Calendar R RETEACH You can use a calendar to find elapsed time. Suppose today is May 8. How many days is it until Mother’s Day? Count on from May 8 to May 14. It is 6 days from May 8 to May 14. May 2000 S June 2000 M T W T F S S M T 1 2 3 4 5 6 7 8 9 10 11 12 13 4 5 6 14 15 16 17 18 19 20 11 12 13 Mother’s Day 21 W T F S 1 2 3 7 8 9 10 14 15 16 17 Flag Day 22 23 24 25 26 27 18 19 20 21 22 23 24 26 27 28 29 30 31 Father’s Day 28 29 30 31 25 Use the calendars above for exercises 1–8. 1. How long is it from Flag Day to Father’s Day? 3. Sports camp runs from June 19 through © McGraw-Hill School Division June 30. How long is camp? 5. On which day of the week is Flag Day? 2. How long is it from Mother’s Day to the following Sunday? 4. How many weeks are there from May 1 to June 5? 6. Memorial Day is celebrated on the last Monday in May. Which date is that? 7. Dave will return from vacation on the Monday after Flag Day. On which date will he return? Use with Grade 4, Chapter 3, Lesson 3, pages 98–99. (77) 8. The last day of school is June 7. Tom’s birthday is 5 days before that. When is Tom’s birthday? MR 1.1, 2.3 Print This Page Name Print This 3–3 Page Calendar E ENRICH Calendar Calculations Use the calendar to solve the problems. January February March April May June S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S 1 1 1 2 3 4 5 1 2 3 4 1 2 3 4 5 6 1 2 3 2 3 4 5 6 7 8 6 7 8 9 10 11 12 5 6 7 8 9 10 11 2 3 4 5 6 7 8 7 8 9 10 11 12 13 4 5 6 7 8 9 10 9 10 11 12 13 14 15 13 14 15 16 17 18 19 12 13 14 15 16 17 18 9 10 11 12 13 14 15 14 15 16 17 18 19 20 11 12 13 14 15 16 17 16 17 18 19 20 21 22 20 21 22 23 24 25 26 19 20 21 22 23 24 25 16 17 18 19 20 21 22 21 22 23 24 25 26 27 18 19 20 21 22 23 24 23 24 25 26 27 28 29 27 28 29 23 24 25 26 27 28 29 28 29 30 31 26 27 28 29 30 31 25 26 27 28 29 30 30 31 30 July August September October November S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S 1 1 2 3 4 5 1 2 1 2 3 4 5 6 7 1 2 3 4 2 3 4 5 6 7 8 6 7 8 9 10 11 12 3 4 5 6 7 8 9 8 9 10 11 12 13 14 5 6 7 8 9 10 11 9 10 11 12 13 14 15 13 14 15 16 17 18 19 10 11 12 13 14 15 16 15 16 17 18 19 20 21 12 13 14 15 16 17 18 16 17 18 19 20 21 22 20 21 22 23 24 25 26 17 18 19 20 21 22 23 22 23 24 25 26 27 28 19 20 21 22 23 24 25 23 24 25 26 27 28 29 27 28 29 30 31 24 25 26 27 28 29 30 29 30 31 26 27 28 29 30 30 31 1. Jamie will start basketball practice on the first Monday in September. She plans to buy sneakers at least two weeks before practice begins. On which date will basketball practice begin? Which is the latest date on which she can buy her sneakers? © McGraw-Hill School Division 3. George's team has its first game on May 15. They plan to spend four Saturdays practicing. Then they will spend a week practicing every day after school. Which is the latest date on which they should start practicing? Use with Grade 4, Chapter 3, Lesson 3, pages 98–99. (78) December S M T W T F S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 2. John plans to go on a skiing trip the third Friday in December. He must buy his ticket 14 days in advance of the flight. He wants to make the plane reservations 4 weeks before buying the ticket. Which is the latest date on which he should make his plane reservations? 4. Holly wants to run her best race the second Saturday in June. To train, she wants to do speed workouts for 5 weeks. Before she begins speed training, she must do endurance runs for 4 weeks. Which is the latest date on which she should begin training? MR 1.1, 2.3 Print This Page Name Print This 3–4 Page Line Plots P PRACTICE 1. Complete the tally table and line plot for the following data. Number of Miles Run Each Day by the Members of the Fleet-Footed Club 3 2 5 4 6 3 1 5 4 3 2 6 4 3 5 3 2 2 1 5 4 3 6 3 2 5 3 1 4 2 5 6 2 3 2 Number of Miles Run Each Day by the Members of the Fleet-Footed Club Number of Miles Tally Number of Miles Run Each Day by Members of The Fleet-Footed Club Total 1 2 3 4 5 6 1 2 3 4 5 6 Use the line plot to answer the questions. 2. How many miles did the greatest number of students run? 3. How many members ran 6 miles a day? 4. How many members ran 4 miles or more a day? 5. How many more members ran 4 miles a day than ran 1 mile a day? © McGraw-Hill School Division 6. How many members are in the club? Use the data below to make a tally table and line plot on a separate sheet of paper. Ages of Fleet-Footed Club Members 8 11 12 9 13 14 12 11 8 12 10 12 11 9 13 12 11 9 12 14 11 12 13 10 9 12 10 13 9 12 11 14 10 9 13 7. What statement can you make about the data in your line plot? Use with Grade 4, Chapter 3, Lesson 4, pages 100–101. (79) SDP 1.1 Print This Page Name Print This 3–4 Page Line Plots R RETEACH Marcia counted the number of letters in each word in a story. The data is shown below. 3 3 5 3 2 6 5 3 3 Number of Letters in Words in a Story 6 4 2 1 5 6 3 5 2 8 4 5 3 3 5 1 4 4 5 7 2 You can organize the data in a tally table. To compare the data, you can make a line plot. Example: For the first number, 3, make a tally mark in the table. Cross out the 3 in the data above. Then record and cross out the remaining 3s. In the line plot, use an X to stand for each word in the story. Complete the tally table and the line plot. Number of Letters in Words in a Story Number of Letters in Words Tally 1 Total Number of Words Number of Letters in Words in a Story 2 words had 7 words had 1 letter. 5 letters. ↓ ↓ X 2 X 2 3 X 8 X ↓ X X X X X 6 X X X 7 1 5 6 4 5 © McGraw-Hill School Division 3 words had 6 letters. 2 3 4 7 8 8 Use the line plot. How many words had: 1. 3 letters? 2. 2 letters? 4. more than 3 letters? 3. 8 letters? 5. less than 3 letters? 6. How many letters did the greatest number of words have? Use with Grade 4, Chapter 3, Lesson 4, pages 100–101. (80) SDP 1.1 Print This Page Name Print This 3–4 Page Line Plots E ENRICH Mystery Plot Use the clues below to complete the line plot. Number of Books Read in September by Students in Fourth Grade 5 6 7 Clues • There are 4 students who read 5 books a month and 3 times as many who read 7 books a month. © McGraw-Hill School Division • The number of students who read 6 books a month is 7 less than the number of students who read 7 books a month. • The number of students who read 10 books a month is half the number who read 7 books a month. 8 9 10 • The number of students who read 8 books a month is 2 less than the number of students who read 6 and 9 books a month combined. • The number of students who read 9 books a month is twice as many as the number of the students who read 6 books a month. Use the line plot to answer the questions. 1. How many students were surveyed? 2. How many books were read by the greatest number of students each month? About how many was that a week? 3. How many books were read by the least number of students? Use with Grade 4, Chapter 3, Lesson 4, pages 100–101. (81) SDP 1.1 Print This Page Name Print This 3–5 Page Range, Median and Mode P PRACTICE The third-grade class at Blue Hill School collects and recycles aluminum cans. The line plot shows how many cans the students collected in March. Use data from the line plot for exercises 1–3. 1. Find the range, median, and mode from the line plot. Number of Aluminum Cans Collected in March Range: Median: Mode: 2. What does the mode tell you about this data? X X 3. What does the median tell you about X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 24 25 26 27 28 29 30 31 32 this data? Complete the table. © McGraw-Hill School Division Data Order Data from Least to Greatest Range Median Mode 4. 6, 8, 8, 9, 5, 4, 8, 7, 5 5. 30, 35, 29, 42, 35, 35, 40 6. 30, 19, 21, 17, 25, 23, 25 7. 20, 80, 40, 50, 90, 60, 50 8. 78, 85, 100, 100, 95, 92, 88 9. $9, $13, $23, $15, $13 Use with Grade 4, Chapter 3, Lesson 5, pages 102–103. (82) SDP 1.1, 1.2 Print This Page Name Print This 3–5 Page Range, Median and Mode R RETEACH You can analyze data using the range, median, and mode. Use the line plot to help you find the range, median, and mode. Time It Takes to Get to School X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 0 5 10 15 20 25 Minutes Range: the difference between the greatest and least numbers Range: 25  5  20 Median: the middle number when the data is arranged in order from least to greatest The data in the line plot is arranged in order. There are 29 Xs, so the middle X is the 15th X. The 15th X in the line plot is above 10, so the median is 10. Mode: the number that occurs most often The greatest number of Xs is above 10, so 10 is the mode. Order the data from least to greatest. Then find the range, median, and mode. 1. Data: 6, 4, 3, 3, 0, 5, 8 List in order from least to greatest: , , , , , , Range: – 0 = Median: Mode: 2. Data: 83, 96, 72, 91, 83 © McGraw-Hill School Division List in order from least to greatest: Range: 96 – , , , , , , , = Median: Mode: 3. Data: 56, 88, 100, 34, 96, 56, 92 List in order from least to greatest: , , , Range: Median: Mode: Use with Grade 4, Chapter 3, Lesson 5, pages 102–103. (83) SDP 1.1, 1.2 Print This Page Name Print This 3–5 Page Range, Median, and Mode E ENRICH The Case of the Missing Math Tests Ms. Lee's math class is divided into three groups. Each group found the range, median, and mode of the group's scores. Use the data for each group to find the missing scores. 1. 2. © McGraw-Hill School Division 3. Group 1’s Test Scores Students’ Scores for Group 1 Range 18 Megan 80 Joe 90 Median 88 Stephanie 92 Chris 76 Mode 94 Gregory 84 Alison 94 Brian 86 Nancy Group 2’s Test Scores Students’ Scores for Group 2 Range 18 Jason Ann 88 Median 91 Steven 82 Karen 94 Mode 94 Melissa 94 Leroy 90 Serena 98 Carl 80 Group 3’s Test Scores Students’ Scores for Group 3 Range 16 Sam Jamal 92 Median 92 Beth 92 Sally 96 Mode 92 Susan 88 Bill 82 Mario 86 Rita 92 4. Explain how you found each missing test score. Use with Grade 4, Chapter 3, Lesson 5, pages 102–103. (84) SDP 1.1,1.2 Print This Page Name Problem Solving: Reading for Math Identify Extra and Missing Information Print This 3–6 Page P PRACTICE Reading Skill Circle the question that you need to answer. Cross out any extra information. Then solve or tell what information you need to solve the problem. 1. Fiona is taking a train from Boston to Providence on May 6th. The train arrives in Providence at 3:54 P.M. How long is the train trip? 3. Marion and her daughter fly from Atlanta to Dallas. The round-trip fare for Marion is $349. The fare for Marion’s daughter is the same. This fare costs $50 more than the fare the last time Marion flew. What was the round-trip fare the last time Marion flew? © McGraw-Hill School Division 5. Kendra wants to fly from Atlanta to Philadelphia. Flight 17 leaves Atlanta at 11:39 A.M. and arrives in Philadelphia at 1:43 P.M. Flight 20 leaves Atlanta at 8:40 P.M. and arrives in Philadelphia at 10:54 P.M. A coach ticket on Flight 17 is $109. This is $20 more than a ticket on Flight 20. Which flight is shorter? How much shorter is it? Use with Grade 4, Chapter 3, Lesson 6, pages 104–105. (85) 2. On Tuesday, September 7, Noah bought a ticket for a flight that leaves on September 20th. The ticket cost $329. On what day of the week is Noah’s flight? 4. A train leaves Washington, D.C., at 5:45 A.M. and arrives in Philadelphia at 8:00 A.M. A train from New York City arrives in Washington, D.C., at 8:10 A.M. Which train ride takes more time? 6. A round-trip coach ticket on Flight 54 from New York City to San Francisco costs $399. A round-trip first-class ticket on Flight 54 costs $1,609. A round-trip coach ticket on Flight 98 from New York City to San Francisco costs $438. How much more expensive is a round-trip coach ticket on Flight 98 than on Flight 54? MR 1.1, 2.3, 2.4, 3.1, 3.2, 3.3 Print This Page Name Problem Solving: Reading for Math Identify Extra and Missing Information Print This 3–6 Page P PRACTICE Math Skills Test Prep © McGraw-Hill School Division Choose the correct answer. Flight 81 leaves Salt Lake City at 2:55 P.M. and arrives in Phoenix at 4:30 P.M. Flight 62 from Salt Lake City, which is sold out, arrives in Phoenix at 3:45 P.M. Which flight is faster? 1. Which of the following statements 2. What important information is is false? missing? A Flight 81 takes less than 2 hours. F the time that Flight 81 leaves Salt Lake City B Flight 62 arrives in Phoenix after Flight 81 does. G the time that Flight 81 arrives in Phoenix C Flight 62 is sold out. H the time that Flight 62 leaves Salt D Flight 81 arrives in Phoenix before Lake City 5:00 P.M. J the time that Flight 62 arrives in Salt Lake City An express train leaves Grand Terminal at 5:05 P.M. The train arrives at the first stop at 5:21 P.M., the second stop at 5:46 P.M., and the last stop at 6:04 P.M. How long is the train ride? 3. Which extra information is not 4. How long is the train ride? needed to solve the problem? F 16 minutes A the time the train leaves Grand G 41 minutes Terminal H 59 minutes B the time the train arrives at the J 61 minutes second stop C the time the train arrives at the last stop D none of the above A train leaves Chicago at 4:20 P.M. on Wednesday, November 24. It arrives in Houston at 11:50 A.M. the next day. How long does the train ride take? 5. Which extra information is not 6. How long does the train ride take? needed to solve the problem? F 4 hours 30 minutes A the time the train leaves Chicago G 7 hours 30 minutes B the time the train arrives in H 8 hours 30 minutes Sacramento J 19 hours 30 minutes C the date the train leaves D none of the above Use with Grade 4, Chapter 3, Lesson 6, pages 104–105. (86) MR 1.1, 2.3, 2.4, 3.1, 3.2, 3.3 Print This Page Name Problem Solving: Reading for Math Print This 3–6 Page P Identify Extra and Missing Information PRACTICE Math Skills Test Prep Choose the correct answer. Ty wants to take a nonstop flight that leaves Miami at 7:25 A.M. and arrives in Cincinnati at 9:55 A.M., but the flight is sold out. Instead, he takes a 9:00 A.M. flight from Miami to Atlanta. Then Ty takes a flight from Atlanta to Cincinnati. That flight leaves Atlanta at 12:00 noon. How much later does Ty arrive in Cincinnati than he would have if he had taken a nonstop flight? 7. Which of the following statements is false? A Ty catches a 12:00 noon flight. B Ty catches a 9:00 A.M. flight. C The nonstop flight takes less than 3 hours. D Ty’s trip to Cincinnati takes 3 hours. 8. What information do you still need to solve the problem? F the time the 12:00 noon flight from Atlanta arrives in Cincinnati G the time the 9:00 A.M. flight from Miami arrives in Atlanta H the time the 7:25 A.M. flight from Miami arrives in Cincinnati J the time the 7:25 A.M. flight from Miami arrives in Atlanta Solve. Identify extra or missing information in each problem. 9. A round-trip first-class ticket from St. © McGraw-Hill School Division Louis to San Diego costs $1,600. A round-trip coach ticket costs $359. The Howards buy 3 tickets. How much do they spend? 11. A bus leaves the terminal at 6:10 P.M. It makes its first stop at 6:30 P.M. and its second stop at 6:55 P.M. When will the bus arrive at its third stop? Use with Grade 4, Chapter 3, Lesson 6, pages 104–105. (87) 10. A train leaves Rocky Mount, NC, at 1:16 P.M. The train arrives in Petersburg, VA, at 2:45 P.M. and in Richmond, VA, at 3:22 P.M. How long is the trip from Rocky Mount to Richmond? 12. Samantha takes a train to New York City. She catches the train at 7:25 A.M. The train stops in Newark at 7:41 A.M. The train arrives in New York at 7:59 A.M. How much time does Samantha’s ride take? MR 1.1, 2.3, 2.4, 3.1, 3.2, 3.3 Print This Page Name Print This 3–7 Page Problem Solving: Strategy P PRACTICE Work Backward Work backward to solve. 1. Bill wants to arrive 15 minutes early for a movie that starts at 7:45 P.M. It will take him about 20 minutes to walk to the theater. When should Bill leave home? 3. Nick spent $21.50 on a theater ticket and $12.50 on a meal. He has $14.25 left. How much money did Nick start with? 2. It takes Sandy 35 minutes to walk from school to the mall. She spends 45 minutes at the mall. Sandy leaves the mall at 4:20 P.M. When did she leave school? 4. Sally spends $16.50 on gas, $2.25 on tolls, and $2.75 on a snack. She has $32.10. How much money did she start with? Mixed Strategy Review Solve. Use any strategy. 5. Barry makes letters for a sign that reads “Free Field Trip Sign-Up Sheet.” Which letter does Mark need to make the most of? 6. Mr. Carlson has $424. He spends $29 on gasoline. How much money does Mr. Carlson have left? Strategy: © McGraw-Hill School Division Strategy: 7. Health Walking a mile burns about 110 calories. About how many calories would you burn if you walked 2 miles? 8. Create a problem which can be solved by working backward. Share it with others. Strategy: Use with Grade 4, Chapter 3, Lesson 7, pages 108–109. (88) MR 1.1, 2.3, 2.4, 3.1, 3.2, 3.3 Print This Page Name Print This 3–7 Page Problem Solving: Strategy R RETEACH Work Backward Page 109, Problem 1 Mindy wants to eat before the 7:40 P.M. show. She needs about 45 minutes to order and eat her dinner. What is the latest time she can order? Step 1 Read Be sure you understand the problem. Read carefully. What do you know? • Mindy needs about eat her dinner. minutes to order and • She wants to eat before . What do you need to find? • You need to find the latest time that Mindy . Step 2 Plan ■ ■ ■ © McGraw-Hill School Division ■ ■ ■ ■ ■ ■ ■ Make a Table or List Write a Number Sentence Work Backward Act it Out Find a Pattern Make a Graph Guess and Check Logical Reasoning Solve Simpler Problem Draw a Picture Make a plan. Choose a strategy. You can work backward to solve the problem. Start at the time of the show. Then work backward to find the time that Mindy needs to order. Use with Grade 4, Chapter 3, Lesson 7, pages 108–109. (89) MR 1.1, 2.3, 2.4, 3.1, 3.2, 3.3 Print This Page Name Print This 3–7 Page Problem Solving: Strategy R RETEACH Work Backward Step 3 Solve Carry out your plan. • Mindy needs about eat her dinner. minutes to order and • She wants to finish eating by . Start at 7:40 P.M. Think: Mindy wants to finish eating by 7:40 P.M. She needs to order 45 minutes before that time. Move backward 45 minutes. The latest time that Mindy can order is Step 4 Look Back . Is the solution reasonable? Reread the problem. Work forward to check your answer. Start with your answer. Move forward 45 minutes. Did you end at 7:40 P.M.? © McGraw-Hill School Division What other strategies could you use to solve the problem? Practice 1. Laurel wants to watch a show that begins at 8:30 A.M. Before she can watch TV, she has to practice piano for 1 hour 15 minutes. At what time does Laurel have to start practicing? Use with Grade 4, Chapter 3, Lesson 7, pages 108–109. (90) 2. Paul plays basketball for 30 minutes and Frisbee for 15 minutes. Then he walks home.The walk takes 20 minutes. If Paul gets home at 2:30 P.M., at what time did he start playing basketball? MR 1.1, 2.3, 2.4, 3.1, 3.2, 3.3 Print This Page Name Print This 3–8 Page Explore Pictographs P PRACTICE 1. Complete the table. Then use the table to complete the pictograph. Which Modern Invention Do You Like the Most? Invention Tally Total Computer Which Modern Invention Do You Like the Most? Computer CD Player CD Player Car Car Television Television Key: Each stands for people Use the pictograph for exercises 2–5. 2. Which item do people like the most? 3. How many more people like their computers than their televisions? 4. How many people were surveyed? © McGraw-Hill School Division 5. What key would you use if 80 people were surveyed? Explain. Use the table to make a pictograph on a separate piece of paper. Then answer each question. 6. Favorite Lunches Lunch 7. How many more students like pizza more than spaghetti? Tally Pizza Hamburgers 8. How many students took part in the survey? Spaghetti Chicken Use with Grade 4, Chapter 3, Lesson 8, pages 110–111. (91) SDP 1.1, 1.3 Print This Page Name Print This 3–8 Page Explore Pictographs R Evan and Jenny surveyed students to find out whether their favorite color is red, blue, or yellow. This is the data they collected. Favorite Colors Red 10 Blue 11 Yellow 6 Here is how to make a pictograph of the data. Step 1: Write a title. List the categories. Step 2: Choose a picture to show the data. You can use 1 picture to represent 2 students. So, half of a picture will represent 1 student. Use the picture to make a key. RETEACH Favorite Colors Red Blue Yellow Key: Each Step 3: Use the key to draw pictures to show Key: Each the data for each category. stands for 2 students. stands for 1 student. Use the data in the table to complete the pictograph. Answer the questions to help you. 1. How many people chose oranges? How many faces will you draw? 2. How many people chose apples? How many faces will you draw? © McGraw-Hill School Division Favorite Fruit Fruit Tally Favorite Fruit Total Apples 9 Pears 5 Oranges 10 Plums 4 Apples Pears Oranges Plums Key: Each Key: Each Use with Grade 4, Chapter 3, Lesson 1, pages 110–111. (92) stands for 2 people. stands for 1 person. SDP 1.1, 1.3 Print This Page Name Explore Pictographs Print This 3–8 Page E ENRICH Stamp Collecting Use the clues below to complete the pictograph. Sarah’s Stamp Collection Stamps of famous people Stamps of famous landmarks Stamps of famous events Stamps of birds Stamps from other countries Stamps of flowers © McGraw-Hill School Division Key: Each stands for 2 stamps. Clues • Sarah has 5 fewer stamps from other countries than stamps of famous people. • Sarah has twice as many stamps of famous events as stamps from other countries. • Sarah has 3 more stamps of famous landmarks than stamps from other countries. • Sarah has 1 more than twice as many bird stamps as stamps of famous events. • If Sarah had 6 more flower stamps, she would have an amount equal to the number of bird stamps. Would you use 1 stamp to stand for 8 stamps in the key? Why or why not? Use with Grade 4, Chapter 3, Lesson 8, pages 110–111. (93) SDP 1.1, 1.3 Print This Page Name Print This 3–9 Page Bar Graphs P PRACTICE Complete the table below. Then use it to complete the bar graph and answer exercises 1–4. Favorite Types of Music Adults Type of Music Tally Marks Teenagers Total Tally Marks Total Country Classical Jazz Rap Rock and roll Favorite Types of Music Number of People 16 14 12 10 8 6 4 2 0 Country Classical Jazz © McGraw-Hill School Division Adults Rap Rock and Roll Teenagers 1. How many teenagers chose rock and roll? 2. Which type of music was chosen about the same number of times by adults and teenagers? 3. Which type of music do adults like the most? 4. Did more adults or teenagers choose jazz as their favorite music? Use with Grade 4, Chapter 3, Lesson 9, pages 112–115. (94) SDP 1.1, 1.3 Print This Page Name Print This 3–9 Page Bar Graphs R RETEACH You can use single-bar graphs or double-bar graphs to show data. A single-bar graph presents one set of data. A double-bar graph presents two sets of data. When you create a double-bar graph, you need to make a key to represent each set of data. Write a title, headings for the vertical and horizontal sides, and select a scale just as you would for a single-bar graph. Remember to include different headings for both sets of data. Use the graphs to answer the questions. 1. What is the favorite Number of People vacation spot? How many people chose it? 2. Did more people choose France, Hawaii, or Greece as their favorite vacation spot? Hawaii 4. Which vacation spot shows the greatest difference between boys and girls? Number of People © McGraw-Hill School Division 3. How many more boys than girls chose Hawaii as their favorite vacation spot? Favorite Vacation Spots 20 18 16 14 12 10 8 6 4 2 0 Greece Florida France Australia Favorite Vacation Spots 10 9 8 7 6 5 4 3 2 1 0 Hawaii Greece Boys Use with Grade 4, Chapter 3, Lesson 9, pages 112–115. (95) Florida France Australia Girls SDP 1.1, 1.3 Print This Page Name Print This 3–9 Page Bar Graphs E ENRICH Misleading Graphs The bar graph shows the earnings of Bayside Auto Plaza and Auto World. 1. The bar for Auto World is twice as high as the bar for Bayside Auto Plaza. Does this mean that Auto World earns twice as much as Bayside Auto Plaza? 2. What is the actual difference in the Earnings of Car Sales $150,000 $140,000 $130,000 earnings of the two stores? $120,000 3. Is the graph misleading? Explain. 0 130,000 150,000 Bayside Auto Plaza Auto World Month 40 Oct.– Dec. 0 July– Sept. 20 April– June 10 0 60 Jan.– March 20 Number of Cars Sold 30 Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec. Number of Cars Sold © McGraw-Hill School Division A car salesperson made Graphs A and B to show the number of cars she sold in one year. Car Sales—Graph A Car Sales—Graph B 100 50 80 40 Months 4. Do both bar graphs show the same data? 5. Which graph do you think the salesperson showed her boss? Tell why. Use with Grade 4, Chapter 3, Lesson 9, pages 112–115. (96) SDP 1.1, 1.3 Print This Page Name Print This 3–10 Page Coordinate Graphing P PRACTICE Give the ordered pair for each place on the grid. 1. mall 2. library 3. park 4. school 5. video arcade Name the place at each location. 12 11 school 10 post office 9 library 8 bank 7 park 6 5 mall fire station 4 3 video arcade 2 pool 1 0 0 1 2 3 4 5 6 7 8 9 10 1112 6. (9, 1) 7. (1, 9) 8. (4, 5) 9. (3, 8) Give the ordered pair for each place on the grid. 10. jail 11. movie theater 12. police station 13. grocery store © McGraw-Hill School Division Name the place at each location. 12 city hall 11 police station 10 jail 9 court house 8 pet store 7 6 movie theater 5 grocery store 4 3 2 soccer field 1 0 0 1 2 3 4 5 6 7 8 9 10 1112 14. (7, 2) 15. (8, 11) 16. (8, 9) 17. (4, 8) 18. A drive-in diner is being built 19. A parking garage is being built 3 blocks down from the pet store. What ordered pair names this location? Use with Grade 4, Chapter 3, Lesson 10, pages 116–117. (97) between the city hall and the court house. What ordered pair names the garage’s location? MG 2.1, 2.2, 2.3 Print This Page Name Print This 3–10 Page Coordinate Graphing The grid shows the location of rides at an amusement park. R RETEACH 10 9 Where is the Space Ride located? Start at 0. Go right 1, and then go up 2. You can write the location of the Space Ride as the ordered pair (1, 2). 8 Ferris Wheel Carousel Sky Ride 7 In an ordered pair, the first number tells you how far to go to the right. The second number tells you how far to go up. Paddle Boats Swings 6 Tidal Force 5 Log Ride 4 3 Try this. Go right 5, Go up 1. Scrambler Shells 2 (5, 1) ← ordered pair Roller Coaster Space Ride Tea Cups 1 Which ride do you find? 0 0 1 2 3 4 5 6 7 8 9 10 Complete. Use the grid above. 1. Start at 0. Go right 8, then up 3. The ordered pair is (8, ). The ordered pair is ( What is here? © McGraw-Hill School Division , 4). What is here? 3. Start at 0. Go right 2, then up 8. The ordered pair is 2. Start at 0. Go right 4, then up 4. . What is here? 4. Start at 0. Go right 6, then up 7. The ordered pair is . What is here? Use the grid above to tell which is at each location. 5. (5, 8) 6. (2, 3) 7. (4, 6) 8. (1, 6) 9. (6, 4) 10. (8, 8) Use with Grade 4, Chapter 3, Lesson 10, pages 116–117. (98) MG 2.1, 2.2, 2.3 Print This Page Name Print This 3–10 Page Coordinate Graphing E ENRICH Find the Hidden Picture Locate each ordered pair on the grid below. Label it with the exercise number. Then connect the dots in order. 1. (17, 3) 2. (11, 7) 3. (10, 0) 4. (9, 7) 5. (3, 3) 6. (7, 9) 7. (0, 10) 8. (7, 11) 10. (9, 13) 11. (10, 20) 12. (11, 13) 14. (13, 11) 15. (20, 10) 16. (13, 9) 9. (3, 17) 13. (17, 17) 20 19 18 17 16 15 14 13 12 11 10 9 © McGraw-Hill School Division 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Use with Grade 4, Chapter 3, Lesson 10, pages 116–117. (99) MG 2.1, 2.2, 2.3 Print This Page Name Print This 3–11 Page Explore Line Graphs P PRACTICE Use the table to complete the line graph. Toy Sales at Toy City Amount July $1,700 August $1,000 September $1,700 October $2,500 November $2,700 December $3,200 Amount Month Toys Sold at Toy City $3,200 $3,000 $2,800 $2,600 $2,400 $2,200 $2,000 $1,800 $1,600 $1,400 $1,200 $1,000 0 July Aug. Sept. Oct. Nov. Dec. Month Use the line graph to answer the questions. 1. In which month was the greatest 2. © McGraw-Hill School Division dollar amount of toys sold at Toy City? 3. During which month did sales the same? 4. decrease? 5. What is the difference in sales between the highest and lowest In which two months were sales During which month did sales increase the most? 6. In how many months did Toy City sell more than $1,600 worth of toys? points on the graph Use with Grade 4, Chapter 3, Lesson 11, pages 118–119. (100) SDP 1.1,1.3 Print This Page Name Print This 3–11 Page Explore Line Graphs R RETEACH A line graph shows change over a period of time. The table below shows the number of ice-cream cones sold over a year at the Ice-Cream Cottage. You can also show this information in a line graph. Ice-Cream Cone Sales Month Number July 800 August 900 September 700 October 650 November 350 December 100 Number of Cones Sold Ice-Cream Cones Sold 900 800 700 600 500 400 300 200 100 0 Show the data from the table in the line graph. July Aug. Sept. Oct. Nov. Dec. Month • In October, 650 cones were sold. Draw a dot across from 650 on the graph’s scale (650 is half way between 600 and 700). © McGraw-Hill School Division • Draw a dot for each of the other month’s number of sales. Use the line graph to answer the questions. 1. In which month was the greatest number of ice-cream cones sold? 3. How many more ice-cream cones were sold in July than in December? Use with Grade 4, Chapter 3, Lesson 11, pages 118–119. (101) 2. How many ice-cream cones were sold in July? 4. Between which two months did the greatest decrease in sales take place? SDP 1.1, 1.3 Print This Page Name Print This 3–11 Page Explore Line Graphs E ENRICH Population Trends Use the clues to complete the line graph. Clues • Foxwood had 200 more people in 1930 than it did in 1920. • The population was the same in 1940 as it was in 1930. • In 1950, the number of people increased by 200. • There were 1,600 people living in Foxwood in 1960. • The number of people decreased by 200 in 1970 and 100 in 1980. • The population in 1990 was 200 more than in 1980. Number of People Population Changes in Foxwood 2,200 2,100 2,000 1,900 1,800 1,700 1,600 1,500 1,400 1,300 1,200 1,100 0 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Year © McGraw-Hill School Division Write the years during which each event most likely happened. Event Years For the first time in 30 years, the population began growing again. between and A computer factory opened. People moved to Foxwood for jobs. between and The town's toy factory closed. Many people lost their jobs. between and Use with Grade 4, Chapter 3, Lesson 11, pages 118–119. (102) SDP 1.1, 1.3 Print This Page Name Print This Page 3–12 Part A WORKSHEET Problem Solving: Application Decision Making Applying Time and Data Show how the Sequoia Nature Club can spend its time. Make a schedule. Activity Starting Time of Activity Ending Time of Activity © McGraw-Hill School Division Your Decision Which activities did you choose for the Sequoia Nature Club? Explain your choices. Use with Grade 4, Chapter 3, Lesson 12, pages 120–121. (103) MR 1.1, 2.3, 2.4, 2.6, 3.1 Print This Page Name Problem Solving: Application Print This Page 3–12 Part B WORKSHEET Math & Science Does practice make perfect? Record your data. Attempt Time Needed to Complete the Puzzle 1 2 3 4 5 6 7 8 © McGraw-Hill School Division 9 10 1. Describe what happened to the time you needed as you repeated the puzzle over and over. Use with Grade 4, Chapter 3, Lesson 12, pages 122–123. (104) NS 1.2; SDP 1.1, 1.3; MR 2.3, 3.2 Print This Page Name Print This Page 3–12 Part B WORKSHEET Problem Solving: Application Math & Science Does practice make perfect? 2. How many times did you have to work the puzzle until you mastered it? 3. What happened to your time after you mastered the puzzle? 4. Make a line graph, comparing puzzle number and time. © McGraw-Hill School Division What happened to the line on the graph after you mastered the puzzle? 5. Explain how you used your short- and long-term memory to learn the puzzle. Use with Grade 4, Chapter 3, Lesson 12, pages 122–123. (105) NS 1.2; SDP 1.1, 1.3; MR 2.3, 3.2 Print This Page Name Print This 4–1 Page The Meaning of Multiplication P PRACTICE Write a multiplication sentence for each model. 1. 2. 3. 4. Find each product. 5. 6 6 6. 7 7 7. 3 5 8. 7 3 9. 6 0 10. 7 5 11. 5 8 12. 8 7 13. 4 6 14. 9 5 15. 6 8 16. 4 8 17. 8  8  18. 2  6  19. 9  6  20. 9  8  21. 3  3  22. 6  7  23. 2  3  24. 6  9  25. 8  6  26. 3  6  27. 1  9  28. 9  3  © McGraw-Hill School Division Algebra & Functions Find the missing number. 29. 2  (n  5)  30 30. (j  7)  4  56 31. (2  v)  6  48 32. (3  r)  8  72 Problem Solving 33. Jason practices his violin 2 hours every day. How many hours does he practice in 7 days? Use with Grade 4, Chapter 4, Lesson 1, pages 138–139. (106) 34. Sheila arranges her pennies in 9 rows with 6 pennies in each row. How many pennies does Sheila have? AF 1.1 Print This Page Name Print This 4–1 Page The Meaning of Multiplication R RETEACH The numbers you multiply are the factors. The answer is the product. First factor: number of rows 5 Second factor: number in each row 6 6 ←factor 6  6  6  6  6  30 You can write 5  6  30 or  5 ←factor ↑ ↑ ↑ 30 ←product factor factor product Complete the table. Number of Rows Number in Number Multiplication Each Row in All Sentence 1. 2. 3. © McGraw-Hill School Division Find each product. 4. 4 3 5. 7 3 6. 6 4 7. 5 0 8. 3 5 9. 6 5 10. 2  5  11. 5  3  12. 9  3  13. 5  5  14. 4  7  15. 8  3  16. 5  9  17. 6  2  Use with Grade 4, Chapter 4, Lesson 1, pages 138–139. (107) AF 1.1 Print This Page Name Print This 4–1 Page The Meaning of Multiplication E ENRICH Factors, Products, and Rectangles To show all the facts with a product of 6, draw as many rectangles as you can that contain 6 squares. Count the number of squares in each column and row. List the numbers you count. Those are the factors. The factors of 6 are 1, 2, 3, and 6. 616 166 326 236 Draw as many rectangles as you can to show different facts for each product. Then list the factors. 2. 18 3. 20 4. 24 © McGraw-Hill School Division 1. 12 Use with Grade 4, Chapter 4, Lesson 1, pages 138–139. (108) AF 1.1 Print This Page Name Print This 4–2 Page Properties of Multiplication P PRACTICE Find the product. Then use the Commutative Property to write a different multiplication sentence. 1. 9  8  2. 8  7  3. 5  2  4. 9  4  5. 3  4  6. 9  2  7. 6  9  8. 2  3  9. 7  4  10. 3  9  11. 9  7  12. 5  8  13. 5  0  14. 1  8  15. 4  5  © McGraw-Hill School Division Write  or  to make a true sentence. 16. 6 6  36 17. 8 19 18. 3 9  27 19. 7 7  14 20. 9 09 21. 9 9  81 22. 4 39 3 23. 8 75 3 24. 6 4  12 25. 9 26 3 26. 6 79 4 27. 4 48 2 8 Problem Solving 28. Joe plants pine seedlings in 7 rows. He puts 6 seedlings in each row. How many seedlings does Joe plant? Use with Grade 4, Chapter 4, Lesson 2, pages 140–141. (109) 29. Tanya has 9 pencils in each package. She has 6 packages. How many pencils does Tanya have in all? AF 1.1; MR 1.1 Print This Page Name Print This 4–2 Page Properties of Multiplication R RETEACH Commutative Property The order of the factors does not change the answer. 428 248 Identity Property The product of 1 and any number is that number. Zero Property The product of any number and zero is zero. 313 Think: 4 rows of 0 counters. 400 166 Think: 0 rows of 7 counters. 070 Find each product. Then use the Commutative Property to write another sentence. 1. 3  9  © McGraw-Hill School Division 9 4. 2  8  2. 5  7   27 5 5. 1  4  3. 4  6  6  6. 0  5  Multiply. Tell which property you used. 7. 1  8  8. 0  7  9. 5  1  10. 6  0  11. 0  4  12. 1  9  Use with Grade 4, Chapter 4, Lesson 2, pages 140–141. (110) AF 1.1; MR 1.1 Print This Page Name Print This 4–2 Page Properties of Multiplication E ENRICH Crack the Code! What number does each symbol in the table below stand for? Use the Commutative, Identity, and Zero properties of multiplication to help you find out. Write the number next to the symbol in the code key.       6 2. 6  7 8 5  0 6    7.  10 4. 6  5. 9  6. 9   9. If you know that  8  05 8.  10    26 90 5   1. 6  3. © McGraw-Hill School Division    4  6 , what other multiplication fact do you know? Use with Grade 4, Chapter 4, Lesson 2, pages 140–141. (111) AF 1.1; MR 1.1 Print This Page Name Print This 4–3 Page Multiply by 2, 3, 4, and 6 P PRACTICE Write the multiplication sentence. 1. 2. Multiply. 3. 7  4  4. 1  6  5. 8  2  6. 3  3  7. 9  6  8. 5  4  9. 0  6  10. 5  3  11. 5  2  12. 6  4  13. 9  4  14. 6  3  15. 2  4  16. 8  3  17. 4  2  18. 6  7  19. 4 3 20. 5 6 21. 2 2 22. 3 6 23. 4 8 24. 9 6 25. 4 4 26. 2 3 27. 2 0 28. 7 6 29. 6 2 30. 1 6 31. 4 6 32. 6 8 33. 2 5 34. 6 6 35. 3 9 36. 4 7 © McGraw-Hill School Division Algebra & Functions Find the answer. 37. If   3, then how much is    ? 38. If   6, then how much is     ? 39. If   4, then how much is     ? Problem Solving 40. Cars are parked in 2 rows. There are 8 cars in each row. How many cars are parked? Use with Grade 4, Chapter 4, Lesson 3, pages 142–145. (112) 41. Four parents are needed on each of 9 committees. How many parents are needed? NS 4.1 Print This Page Name Print This 4–3 Page Multiply by 2, 3, 4, and 6 R RETEACH You can skip count to multiply by 2 and 3. Find 2  8. Think: Skip count by 2s eight times. 2 4 6 8 10 12 14 16         These are multiples of 2. 2  8  16 Find 7  3. Think: Skip count by 3s seven times. 3 6 9 12 15 18       21  These are multiples of 3. 7  3  21 You can double a fact you know to multiply by 4 and 6. Double a fact to multiply by 4. Double a fact to multiply by 6. 4  5  (2  5)  (2  5) ↓ ↓ 10  10  20 ••••• ••••• •••••  ••••• •••••  ••••• ••••• ••••• 6  5  (3  5)  (3  5) ↓ ↓ 15  15  30 ••••• ••••• ••••• ••••• •••••  ••••• •••••  ••••• ••••• ••••• ••••• ••••• © McGraw-Hill School Division Skip count to find the answer. Use the models above to help you. 1. 2  7  2. 6  2  3. 2  8  4. 9  2  5. 6  3  6. 3  8  7. 9  3  8. 3  7  Double a fact to find the answer. You can use counters to help you. 9. 6  8  (3  8)  (3   11. 7  6  (7  )  (7   ) 10. 4  7  (2   )  (2   )  Use with Grade 4, Chapter 4, Lesson 3, pages 142–145. (113) 12. 8  4  (8  )  (8   )  )  NS 4.1 Print This Page Name Print This 4–3 Page Multiply by 2, 3, 4, and 6 E ENRICH Triangle Math In each triangle, the number on the bottom left is the product of the middle left and the top number. The number on the bottom right is the product of the middle right and the top number. Complete the triangles. The top number must be a 2, 3, 4, or 6. 1. 2. 3. 2 1 6 12 5. 9 6. 7 9. 13. 1 3 12 16 21 5 5 15 27 28 9 20 36 16. 2 6 7 24 4 15. 4 8 12. 4 4 24 9 48 14. 3 7 3 8 36 10 3 6 8 6 6 12 8. 11. 2 3 32 6 2 16 10. 18 8 4 8 14 9 5 1 7. 7 30 4 18 2 5 42 3 3 18 6 © McGraw-Hill School Division 6 3 6 2 4. 4 24 9 54 2 4 3 6 17. Explain how you found the answer to the triangle in exercise 3. Use with Grade 4, Chapter 4, Lesson 3, pages 142–145. (114) NS 4.1 Print This Page Name Print This 4–4 Page Multiply by 5 and 10 P PRACTICE © McGraw-Hill School Division Multiply. 1. 5  4  2. 5  8  3. 6  10  4. 1  5  5. 0  5  6. 3  10  7. 7  5  8. 4  10  9. 3  5  10. 6  5  11. 5  10  12. 1  10  13. 2  5  14. 4  5  15. 9  5  16. 8  10  17. 9  10  18. 2  10  19. 8  5  20. 5  5  21. 10  6  22. 0  10  23. 5  2  24. 7  10  25. 5 6 26. 10  3 27. 5 3 28. 10  8 29. 5 2 30. 10  5 31. 10  9 32. 5 1 33. 5 5 34. 10  6 35. 10  4 36. 5 4 37. 10  7 38. 5 8 39. 5 0 40. 10  0 41. 10  2 42. 5 7 43. 10  1 44. 5 9 45. 6 5 46. 9 5 47. 8 5 48. 3 5 Tell whether the number is a multiple of 2, 5, or 10. 49. 18 50. 30 51. 35 52. 40 Problem Solving 53. Gene has 5 boxes of crayons with 10 crayons in each box. How many crayons does Gene have? Use with Grade 4, Chapter 4, Lesson 4, pages 146–147. (115) 54. Jan places 5 rows of 8 stars in a rectangle to make a design. How many stars does she use? NS 3.2 Print This Page Name Print This 4–4 Page Multiply by 5 and 10 R RETEACH You can skip count using nickels to multiply by 5. Find 7  5 Think: Skip count by 5s four times. five 5 ten 10 fifteen 15 twenty 20 twenty-five 25 thirty 30 thirty-five 35 7  5  35 You can skip count using dimes to multiply by ten. Find 8  10. Think: Skip count by 10s three times. ten 10 twenty 20 thirty 30 forty 40 fifty 50 sixty 60 seventy 70 eighty 80 8  10  80 Skip count to find the answer. 1. 2. 65 5  10  © McGraw-Hill School Division Multiply. You can use nickels and dimes to help you. 3. 4  5  4. 3  10  5. 5  10  7. 9  5  8. 6  10  9. 7  5  11. 2  5  12. 2  10  15. 10  8 16. 5 8 17. 10  5 6. 6  5  10. 7  10  13. 1  10  18. Use with Grade 4, Chapter 4, Lesson 4, pages 146–147. (116) 10  9 19. 14. 5  5  5 9 20. 10  4 NS 3.2 Print This Page Name Print This 4–4 Page Multiply by 5 and 10 E ENRICH True Sums Write multiplication sentences to make each sum true. Each multiplication sentence must have a 5 or a 10 as one of its factors. Product 1. 2  5 10 4 2. 10  20 20 40 5 1 2 Sum 5 10  5. 5  3 15 10 100 8 6 10 5 85 8. 9 10  5 8 Sum © McGraw-Hill School Division 5 10 9 6. 4 10  5 9 Product 9. 5  45 80 11. 4  5 10 10 Sum 5 1 10 5 50 55 Sum Product 40 50 90 20 90 110 Sum Product 30 45 75 30 80 125 Sum Product 10. 3  Product Product 35 50 70 40 110 Sum Sum 110 Sum Product 7 10 8 10 5 Product 115 Sum 7. 5  3. 7  10 10 20 Product 4. Product Product 12. 5 10  Sum 5 6 25 60 85 Sum Can you follow the rules and find other numbers that will give a true sum for exercises 1 and 4? Use with Grade 4, Chapter 4, Lesson 4, pages 146–147. (117) NS 3.2 Print This Page Name Print This 4–5 Page Multiply by 7, 8, and 9 P PRACTICE Multiply. 1. 5  7  2. 9  7  3. 1  8  4. 9  9  5. 3  8  6. 8  7  7. 4  9  8. 2  8  9. 3  7  10. 6  9  11. 7  8  12. 7  7  13. 5  8  14. 2  9  15. 0  7  16. 1  9  17. 6  8  18. 4  7  19. 8  9  20. 4  8  21. 5 9 22. 7 2 23. 9 8 24. 9 3 25. 8 0 26. 7 9 27. 8 8 28. 2 8 29. 7 1 30. 6 7 31. 9 1 32. 9 6 33. 8 4 34. 9 2 35. 7 3 36. 8 3 37. 7 5 38. 8 6 Algebra & Functions Find the rule. Then complete the table. 39. Rule: 0 1 2 3 0 9 18 27 0 1 2 3 0 8 16 24 4 5 6 4 5 6 © McGraw-Hill School Division 40. Rule: Problem Solving 41. Nathan puts 6 cards on each of 8 pages in an album. How many cards does he put in the album? Use with Grade 4, Chapter 4, Lesson 5, pages 148–149. (118) 42. A marching band has 5 rows with 9 students in each row. How many students are in the marching band? NS 3.2, 4.1 Print This Page Name Print This 4–5 Page Multiply by 7, 8, and 9 R RETEACH You can use known facts to multiply by 7, 8, and 9. Add to a known fact to multiply by 7. Subtract from a known fact to multiply by 9. Double a fact to multiply by 8. Find 7  6. Find 6  9. Find 8  7. Double 4  7. (4  7)  (4  7) Think: Think: ↓ 35  7 is the same as 7  6. 60  6 is the same as 6  9. ↓ 28  28  56 You know 7  5  35. You know 6  10  60. 35  7  42 60  6  54 7  6  42 6  9  54 8  7  56 © McGraw-Hill School Division Multiply. 1. 7  5  2. 8  6  3. 9  8  4. 8  8  5. 9  7  6. 7  7  7. 9  9  8. 7  9  9. 8  10  10. 3  8  11. 7  4  12. 9  2  13. 5 9 14. 8 9 15. 4 7 16. 19. 10  9 20. 4 6 21. 5 8 22. Use with Grade 4, Chapter 4, Lesson 5, pages 148–149. (119) 3 9 4 9 17. 6 7 18. 4 8 23. 10  7 24. 9 8 NS 3.2, 4.1 Print This Page Name Print This 4–5 Page Multiply by 7, 8, and 9 E ENRICH Multiplication Game Play with a partner. Cut out the game markers. One player puts the glove on START. The other puts the baseball on START. You will need: Two sets of number cards. Each set contains number cards from 0 through 10. Label one set A and the other set B. Take turns. • Pick a card from A and a card from B. Find the product of the two numbers. • Have your partner check the product. If the product is correct, move forward two spaces. If the product is wrong, move back one space. The first player to get to the field wins. Eq uip Bo me x nt Ball is Lost in Woods. Go to equipment box. Ball bounced in puddle. Go back to Start. Woods Tripped over feet. Go back 3 spaces. © McGraw-Hill School Division glo Dro v p Go e in ped 3s b m pa ack ud. ce s. Puddle Field Markers Start Use with Grade 4, Chapter 4, Lesson 5, pages 148–149. (120) NS 3.2, 4.1 Print This Page Name Problem Solving: Reading for Math Print This 4–6 Page P PRACTICE Reading Skill Choose an Operation Solve. Tell how you chose the operation. 1. Georgia puts coins in an album. There are 8 pages in the album. Each page has slots for 8 coins. How many coins can Georgia put in the album? 2. Dina has 37 international dolls. Maxine has 26 international dolls. Who has more dolls? How many more does she have? 3. Ben buys 9 packs of dinosaur stickers. There are 6 stickers in each pack. How many stickers does Ben buy? 4. Melanie has a collection of 242 stamps. At a stamp convention, she buys 19 more stamps. How many stamps does Melanie have now? 5. James collects model cars. He has 48 model cars. On his birthday, © McGraw-Hill School Division James gets 7 more cars. How many model cars does James have in all? 6. Wendy has 10 flower stickers. She gives away 7 flower stickers. How many flower stickers does Wendy have left? Use with Grade 4, Chapter 4, Lesson 6, pages 150–151. (121) MR 1.1, 2.3, 2.4, 3.2 Print This Page Name Problem Solving: Reading for Math Choose an Operation Print This 4–6 Page P PRACTICE Math Skills Test Prep Choose the correct answer. Juan buys 6 packs of stickers. Each pack has 4 stickers. How many stickers does Juan buy in all? 1. Which of the following statements 2. Which of the following can you use is true? to solve the problem? A B C D F G H J Juan has 4 packs of stickers. Juan has 10 stickers. Juan has 24 packs of stickers. Juan has 24 stickers. 64 64 64 64 Warren has 9 silver dollars. At a coin show, he buys 3 silver dollars. How many silver dollars does Warren have now? © McGraw-Hill School Division 3. What do you have to do to solve 4. How many silver dollars does this problem? Warren have? A find how many silver dollars are left B find the total of 2 unequal groups of silver dollars C find the total of 3 equal groups of silver dollars D find how many silver dollars there are when you split 9 into 3 equal groups F G H J 3 silver dollars 6 silver dollars 12 silver dollars 27 silver dollars Nadia collects souvenir flags. She puts the flags in her bookcase in 3 rows. There are 7 flags in each row. How many flags does Nadia have? 5. What do you have to do to solve this problem? A find the total of 2 unequal groups of flags B find the total of 2 equal groups of flags C find the total of 3 equal groups of flags D find how many flags are left Use with Grade 4, Chapter 4, Lesson 6, pages 150–151. (122) 6. How many flags are there? F G H J 21 flags 10 flags 4 flags 3 flags MR 1.1, 2.3, 2.4, 3.2 Print This Page Name Problem Solving: Reading for Math Choose an Operation Print This 4–6 Page P PRACTICE Math Skills Test Prep Choose the correct answer. Selena has 42 movie posters. Her brother has 26 movie posters. How many movie posters do they have in all? 7. What operation could you use to 8. How many movie posters do Selena solve this problem? and her brother have in all? A addition F 16 B subtraction G 26 C multiplication H 68 D division J 78 Solve. 9. Lois sells 10 rock-star posters. She gets $8 for each poster. How much money does Lois receive? 11. Janell has 472 baseball cards. Lou © McGraw-Hill School Division has 397 baseball cards. How many more baseball cards does Janell have than Lou? 13. Brian displays his trophies in his bedroom. He puts his trophies in 3 rows. There are 6 trophies in each row. How many trophies does Brian have? Use with Grade 4, Chapter 4, Lesson 6, pages 150–151. (123) 10. Morris has 16 kites. He buys 4 more kites. How many kites does Morris have now? 12. Kevin buys 7 packs of football cards. There are 4 football cards in each pack. How many football cards does Kevin buy? 14. Barbara puts photos of France in a photo album. The photo album can hold 94 photos. Barbara has 78 photos. How many more photos can she put in the album? MR 1.1, 2.3, 2.4, 3.2 Print This Page Name Print This 4–7 Page Multiplication Table and Patterns P PRACTICE Complete the table.  0 0 0 1 0 1 2 1 2 2 2 4 3 3 3 4 5 6 7 4 9 10 11 12 21 8 27 36 20 5 15 30 6 40 50 60 36 7 12 8 9 4 8 66 7 72 77 8 16 32 96 9 54 108 10 11 22 12 24 55 88 99 84 121 132 120 144 Use the table to multiply. 1. 9  8  © McGraw-Hill School Division 5. 12  8 2. 3  12  6. 12  12 7. 12  7 11. What is the pattern of odd and even numbers in the 3 row or 3 column? 3. 11  11  8. 10  10 9. 4. 4  12  11  7 10. 12  9 12. What is the pattern of odd and even numbers in the 4 row or 4 column? Compare. Write , , or . 13. 6  3 33 14. 15  7 16. 9  7 6  11 17. 9  7 Use with Grade 4, Chapter 4, Lesson 7, pages 152–153. (124) 27 44 15. 4  8 18. 12  4 25  4 23 NS 4.1, 4.2, MR 1.1 Print This Page Name Print This 4–7 Page Multiplication Table and Patterns R RETEACH To find 8  9, draw arrows to show where the 8 row and the 9 column meet in the table. The 8 row and the 9 column meet at 72. So, 8  9  72.  0 1 2 3 4 5 6 7 8 9 10 11 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 10 11 12 2 0 2 4 6 8 10 12 14 16 18 20 22 24 3 0 3 6 9 12 15 18 21 24 27 30 33 36 4 0 4 8 12 16 20 24 28 32 36 40 44 48 5 0 5 10 15 20 25 30 35 40 45 50 55 60 6 0 6 12 18 24 30 36 42 48 54 60 66 72 7 0 7 14 21 28 35 42 49 56 63 70 77 84 8 0 8 16 24 32 40 48 56 64 72 80 88 96 9 0 9 18 27 36 45 54 63 72 81 90 99 108 10 0 10 20 30 40 50 60 70 80 90 100 110 120 11 0 11 22 33 44 55 66 77 88 99 110 121 132 12 0 12 24 36 48 60 72 84 96 108 120 132 144 © McGraw-Hill School Division Multiply. You can use the multiplication table to help you. 1. 6  8  2. 8  12  3. 8  4  4. 7  7  5. 10  5  6. 9  11  7. 7  4  8. 3  8  9. 4  9  11. 9  9  12. 6  7  10. 7  12  13. 9  12 14. 8 7 15. 8  11 16. 9 8 17. 12  10 18. 11  7 19. 11  12 20. 8 8 21. 9 7 22. 12  12 23. 11  3 24. 11  11 Use with Grade 4, Chapter 4, Lesson 7, pages 152–153. (125) NS 4.1, 4.2; MR 1.1 Print This Page Name Print This 4–7 Page Multiplication Table and Patterns E ENRICH Twisted Tables Complete each multiplication table. Fill in the missing factors. 1. 3. 5. 2.   10 15 20 42 14 28 12 18 24 18 6 12 14 21 28 30 10 20 4.   36 42 54 24 12 28 0 8 6 7 9 4 24 56 0 16 12 14 18 8 3 7 0 2 30 35 45 20 9 21 0 6 63 42 21 6.   72 28 24 27 © McGraw-Hill School Division 7 7. 6 72 6 18 2 0 8.  56 28 16 40  15 35 18 16 24 9 0 36 18 21 6 Use with Grade 4, Chapter 4, Lesson 7, pages 152–153. (126) 42 NS 4.1, 4.2; MR 1.1 Print This Page Name Print This 4–8 Page Multiply Three Numbers P PRACTICE Multiply. 1. (2  5)  4  2. 3  (2  8)  3. (4  2)  3  4. 6  (3  2)  5. 4  (4  2)  6. 7  (2  5)  7. (5  2)  4  8. (2  2)  2  9. (9  3)  0  10. (8  2)  3  11. 7  (3  3)  12. (6  2)  2  13. 2  (7  2)  14. (8  4)  2  15. (9  2)  4  16. 5  (3  3)  17. 4  (8  1)  18. 7  (2  3)  19. 9  (2  3)  20. (8  1)  9  21. 5  (3  2)  22. (8  3)  0  23. 9  (3  3)  24. (7  2)  4  25. 2  (4  3)  26. (3  3)  3  27. (7  2)  2  Complete the multiplication sentence. 28. 5  4  5 © McGraw-Hill School Division 30. (9  3)  32.  27  (3  5)  9  5 29. (  8)  7  0 31. 5  6  5  (3  ) 33. 4  4  2  (2  )  (4  2) Problem Solving 34. The school gives each basketball player 2 shirts. Each shirt costs $8. What is the total cost of shirts for 6 players? Use with Grade 4, Chapter 4, Lesson 8, pages 156–157. (127) 35. In a baseball game of 9 innings, each of the 2 teams gets 3 outs per inning. How many outs are there in a game? AF 1.3 Print This Page Name Print This 4–8 Page Multiply Three Numbers R RETEACH Find: (3  5)  2 Think: 3  2 is a known fact. (5  3)  2 Use the Commutative Property to change the order. 5  (3  2) Use the Associative Property to regroup the numbers. 56 Multiply inside the parentheses first. Think: 3 twos 5  6  30 Multiply again. Think: 5 sixes Multiply. 1. (2  5)  4 (5  )4 5(  © McGraw-Hill School Division 5 2. 3  (4  3) 3( ) (   3. (2  6)  3 ) (6  )3 )4 6(  4 6 4. 2  (2  3)  5. (2  4)  3  6. (5  2)  3  7. (7  1)  3  8. (4  8)  1  9. 3  (3  2)  10. (5  4)  2  11. 9  (2  3)  12. (3  3)  3  13. (8  2)  4  14. 3  (3  5)  15. (9  2)  2  16. (9  6)  1  17. (2  7)  3  18. 5  (4  3)  Use with Grade 4, Chapter 4, Lesson 8, pages 156–157. (128) ) AF 1.3 Print This Page Name Print This 4–8 Page Multiply Three Numbers E ENRICH The Search for 48 © McGraw-Hill School Division Circle each combination of numbers that has a product of 48. You can multiply up to four numbers. Look across, up, down, and diagonally. Can you find all 26 combinations? 4 3 4 2 3 7 8 4 9 2 2 4 6 4 5 2 3 2 4 8 8 6 6 6 7 6 6 3 7 4 9 4 3 4 2 2 2 2 8 3 2 9 Choose one of these numbers: 24, 36, 64, or 72. Make your own number search and give it to a friend to solve. Be sure to keep a copy with the solution! Use with Grade 4, Chapter 4, Lesson 8, pages 156–157. (129) AF 1.3 Print This Page Name Print This 4–9 Page Relate Multiplication and Division Facts P PRACTICE Write a related multiplication fact and complete the division sentence. 1. 18  9 9 2. 15  3  18 3 18  9  3. 16  4  15 4  16 15  3  16  4  4. 6  2  5. 18  2  6. 15  5  7. 8  4  8. 27  3  9. 14  2  10. 28  7  11. 18  3  12. 63  7  13. 48  6  14. 35  7  15. 42  7  Divide. 7 16. 3 21 9 21. 5 45 7 © McGraw-Hill School Division 26. 8 56 9 31. 7 63 3 17. 7 21 8 22. 7 56 5 27. 9 45 9 32. 6 54 8 18. 2 16 3 23. 8 24 9 28. 9 81 6 33. 4 24 6 19. 3 18 6 24. 9 54 4 29. 9 36 9 34. 4 36 5 20. 5 25 3 25. 3 9 8 30. 8 64 7 35. 9 63 Problem Solving 36. It takes 4 horses to pull a coach. How 37. Groups of 6 visitors can take tours of many coaches can 20 horses pull? an old western town. How many groups can 24 people make? Use with Grade 4, Chapter 4, Lesson 9, pages 160–161. (130) NS 3.2; MR 1.1 Print This Page Name Print This 4–9 Page Relate Multiplication and Division Facts Find 15  5. R RETEACH Think: How many groups of 5 are in 15? 5  ?  15 → 5  3  15 There are 3 groups of 5 in 15. So, 15  5  3. Write a related multiplication fact and complete the division sentence. 1. 18  6 6 2. 16  8  18 18  6  4. 20  5 © McGraw-Hill School Division 20  5  7. 30  5 30  5  8 3. 12  3  16 16  8  5. 21  7 21  7  8. 27  9 27  9  Use with Grade 4, Chapter 4, Lesson 9, pages 160–161. (131) 4  12 12  3  6. 24  6 24  6  9. 28  4 28  4  NS 3.2; MR 1.1 Print This Page Name Print This 4–9 Page Relate Multiplication and Division Facts E ENRICH Word Puzzle Use the letters in the table below to complete the word puzzle. Words have to connect as they do in a crossword puzzle. Letter Values Letter Value Letter Value A 10  3  ? L 45  5  ? B 25  5  ? N 49? D 12  6  ? O 30  3  ? E 36? S 55? F 45? T 67? G 36  4  ? U 42  7  ? J 10  4  ? Y 54  6  ? Rules • Use each letter in the table only once. © McGraw-Hill School Division • You cannot move the vowels in the puzzle. • Try to get the highest score you can. To find your score, complete the multiplication or division to find the value of each letter you used. For example, if you placed the letter B in the top left square, you would get 5 for that square (25  5  5). Then add to find the value of each word. Finally, add the values of all four words. J O E T G U A N Use with Grade 4, Chapter 4, Lesson 9, pages 160–161. (132) NS 3.2; MR 1.1 Print This Page Name Print This 4–10 Page Problem Solving: Strategy P PRACTICE Act It Out Use act it out to solve. 1. The Rare Book Club invites its 25 members to a dinner. Square tables seat 4 people and round tables seat 5 people. If the club wants full tables, which tables should the club use? How many of these tables will be needed? 3. Courtney is making a display of 42 shells. She arranges the shells in rows of 6. How many rows does Courtney make? © McGraw-Hill School Division Mixed Strategy Review Solve. Use any strategy. 5. Yoki has 20 posters of science-fiction movies. She puts an equal number of these posters on each of 4 walls. How many posters does Yoki put on each wall? Strategy: 7. Dinner starts at 6:00 P.M. It will take Robert 45 minutes to get there. On his way, he wants to stop at the library for 30 minutes. What time does Robert need to leave to get to the dinner on time? 2. Len delivers 16 bottles of juice and soda. A small box will hold 6 bottles and a large box will hold 8 bottles. Which box should Len use if he wants to put an equal number of bottles in each box? How many boxes will he need? 4. The Sailing Club puts 12 of its 48 trophies in a large display case. There are 6 smaller cases. How can the club arrange the rest of the trophies so that each smaller case has an equal number of trophies? 6. Art For posters, Nancy has a piece of poster paper that is 9 feet by 2 feet. She cuts 3-foot by 1-foot rectangles from it. How many posters does she make? Strategy: 8. Create a problem which you could act out to solve. Share it with others. Strategy: Use with Grade 4, Chapter 4, Lesson 10, pages 162–163. (133) NS 3.2; MR 1.1 Print This Page Name Print This 4–10 Page Problem Solving: Strategy R RETEACH Act It Out Page 163, Problem 2 For placemats, Meg is going to cut 2-foot by 1-foot rectangles from a piece of fabric with a starry background. The fabric is 4 feet wide and 3 feet long. How many placemats can she cut from one piece of fabric? Step 1 Read Be sure you understand the problem. Read carefully. What do you know? • The placemats are by . • Meg is going to cut the placemats from a piece of fabric that is by . What do you need to find? • You need to find how many . Step 2 Plan ■ ■ © McGraw-Hill School Division ■ ■ ■ ■ ■ ■ ■ ■ Make a Table or List Write a Number Sentence Work Backward Act it Out Find a Pattern Make a Graph Guess and Check Logical Reasoning Solve a Simpler Problem Draw a Picture Make a plan. Choose a strategy. To solve the problem, you can act it out using models. Draw a rectangle that represents the piece of fabric. A rectangle that is 4 feet by 3 feet would be very large, so draw a rectangle that is 4 centimeters by 3 centimeters to represent the piece of fabric. Make rectangles that represent the placemats. Since the placemats are 2 feet by 1 foot, cut out rectangles that are 2 centimeters by 1 centimeter. Use with Grade 4, Chapter 4, Lesson 10, pages 162–163. (134) NS 3.2; MR 1.1 Print This Page Name Print This 4–10 Page Problem Solving: Strategy R RETEACH Act It Out Step 3 Solve Carry out your plan. Fill the large rectangle with small rectangles. The large rectangle represents . Each small rectangle represents Meg can cut Step 4 Look Back . placemats from the piece of fabric. Is the solution reasonable? Reread the problem. Does your answer make sense? Did you answer the question? Yes Yes No No © McGraw-Hill School Division What other stategies could you use to solve the problem? Practice 1. Randy wants to cut name tags from a piece of poster paper. The poster paper is 18 inches by 24 inches. Each name tag will be 3 inches by 4 inches. How many name tags can Randy cut from the piece of poster paper? Use with Grade 4, Chapter 4, Lesson 10, pages 162–163. (135) 2. Ted has 54 model train cars. He has large boxes that will each hold 8 train cars. He has small boxes that will each hold 6 train cars. Which type of box should Ted use if he wants to put an equal number of cars in each box? How many of those boxes will he need? NS 3.2; MR 1.1 Print This Page Name Print This 4–11 Page Divide by 2 Through 12 P PRACTICE Divide. 1. 12  2  2. 24  3  3. 32  4  4. 35  5  5. 54  6  6. 56  7  7. 64  8  8. 81  9  9. 40  8  10. 48  6  11. 49  7  12. 27  3  13. 30  5  14. 36  4  15. 72  9  16. 90  10  17. 121  11  18. 144  12  9 6 19. 2 18 6 20. 3 18 9 21. 4 24 7 24. 7 63 7 25. 6 42 6 29. 12 72 26. 9 63 7 8 30. 11 77 31. 10 80 2 2 22. 7 14 23. 8 16 9 9 27. 5 45 28. 8 72 9 9 32. 11 99 33. 12 108 Algebra & Functions Find the rule. Then complete the table. 34. © McGraw-Hill School Division 35. Rule: 0 9 0 1 2 3 4 5 6 2 3 4 5 6 Rule: 0 7 0 1 Problem Solving 36. There are 42 tomato plants in rows of 6 plants in each row. How many rows of tomato plants are there? Use with Grade 4, Chapter 4, Lesson 11, pages 164–167. (136) 37. There are 45 tomatoes on 5 tomato plants. Each tomato plant has the same number of tomatoes. How many tomatoes are on each plant? NS 3.2; MR 1.1, 2.4, 3.2 Print This Page Name Print This 4–11 Page Divide by 2 Through 12 Find 48  6. R RETEACH Think: How many groups of 6 are in 48? 6  ?  48 → 6  8  48 There are 8 groups of 6 in 48. So, 48  6  8. Complete the division sentence. 1. 2. 30  5  3. 24  8  16  4  Divide. Draw models if you wish. 4. 12  2  5. 21  3  6. 20  5  7. 14  7  8. 24  6  9. 16  2  10. 32  8  11. 18  3  9 © McGraw-Hill School Division 13. 2 18 3 16. 5 15 3 19. 10 30 9 22. 6 54 9 25. 9 81 9 14. 4 36 6 17. 7 42 3 20. 11 33 8 23. 5 40 2 26. 12 24 Use with Grade 4, Chapter 4, Lesson 11, pages 164–167. (137) 12. 28  4  12 15. 3 36 5 18. 9 45 3 21. 12 36 8 24. 10 80 9 27. 11 99 NS 3.2; MR 1.1, 2.4, 3.2 Print This Page Name Print This 4–11 Page Divide by 2 Through 12 E ENRICH Win the Division Play this division football game with a partner. You’ll need a number cube and 2 two-color counters to use as game pieces. Rules • Place your game pieces at the START positions on the 50-yard line. Each player can only move in the direction of the arrow. • Take turns rolling the number cubes. Add the number cubes to get a divisor. • If the number in the circle on the next 10-yard line can be evenly divided by the divisor, move to that circle. • Keep rolling the number cubes until one of you scores a touchdown. 16 42 TOUCHDOWN! G 28 10 15 20 36 30 12 40 Start Start © McGraw-Hill School Division 24 40 18 30 30 20 54 10 10 TOUCHDOWN! 50 G 35 Use with Grade 4, Chapter 4, Lesson 11, pages 164–167. (138) NS 3.2; MR 1.1, 2.4, 3.2 Print This Page Name Print This 4–12 Page Fact Families P PRACTICE Complete each fact family. 1. 4  8  2. 9  5  q 3. 8  9  a m 8  r  32 5  b  45 8  n  72 32  8  s 45  5  c 72  8  o 32  t  8 45  d  5 72  p  8 Find the missing factor. 4. 5  k  30 30  5  k 5. 7. 9  8. 9  w  54 54  9  w h  7  56 56  7  h y  63 63  9  y 6. 9  g  72 72  9  g 9. d  8  48 48  8  d © McGraw-Hill School Division Write a multiplication and division fact family for each group of numbers. 10. 8, 5, 40 11. 3, 9, 27 12. 6, 7, 42 13. 9, 8, 72 14. 5, 7, 35 15. 4, 5, 20 16. 6, 9, 54 17. 5, 9, 45 Divide. What patterns do you see? 18. 4  4  88 99 66 19. 0  7  08 01 05 Use with Grade 4, Chapter 4, Lesson 12, pages 168–171. (139) NS 3.2; AF 1.1; MR 1.1 Print This Page Name Print This 4–12 Page Fact Families R RETEACH Multiplication and division sentences that are related make up a fact family. Every sentence in a fact family uses the same numbers. Fact Family 3  4  12 4  3  12 12  3  4 12  4  3 Fact Family 5  2  10 2  5  10 10  5  2 10  2  5 Complete each fact family. 1. 2. 3  5  15 5 9   15  5  15    4   [9]  Write the fact family for each set of numbers. © McGraw-Hill School Division 3. 4, 6, 24 4. 3, 7, 21 5. 35, 7, 5 6. 54, 6, 9 Find the missing numbers. 7. 5  n  30 30  5  n n 8. n  7  56 56  7  n n Use with Grade 4, Chapter 4, Lesson 12, pages 168–171. (140) 9. n  8  64 64  8  n n 10. 3  n  27 27  3  n n NS 3.2; AF 1.1; MR 1.1 Print This Page Name Print This 4–12 Page Fact Families E ENRICH Chain Reaction © McGraw-Hill School Division Write the missing numbers to complete each chain. 4 24 1. 24  6  6 2. 98 72  12  3. 8 6  48  4   4. 66  11  5. 5  12  60  6. 81 9 93 7. 45  9  5 6  6 1 6 12 8 3 4  30  6  5 10 69 9  45  5  Use with Grade 4, Chapter 4, Lesson 12, pages 168–171. (141) 0 0 48 6 8 5 9 45 6 54 3 3 40 5 9 9 9 9 81 3 27 NS 3.2; AF 1.1; MR 1.1 Print This Page Name Problem Solving: Application Applying Multiplication and Division Print This Page 4–13 Part A WORKSHEET Decision Making Record your data. Storage Unit Capacity: Number of trophies or medals per unit Number of Units Used Total Cost Shelf © McGraw-Hill School Division Frame (small or large) Your Decision What is your recommendation for Lily? Explain. Use with Grade 4, Chapter 4, Lesson 13, pages 174–175. (142) NS 3.1, 3.3; MR 1.1, 1.2 Print This Page Name Print This Page 4–13 Part B WORKSHEET Problem Solving: Application Ramp races: How does height affect distance? Math & Science Record your data. Ramp height Distance traveled Use division. How many times farther did the crayon travel on this ramp than it did on the 1-book ramp? Round to the nearest whole number. 1 book 2 books © McGraw-Hill School Division 3 books 4 books 5 books Use with Grade 4, Chapter 4, Lesson 13, pages 176–177. (143) NS 3.4; MR 1.1, 2.3 Print This Page Name Problem Solving: Application Print This Page 4–13 Part B WORKSHEET Math & Science Ramp races: How does height affect distance? 1. On which ramp did the crayon travel the farthest? On which ramp did the crayon travel the shortest distance? 2. Use division to calculate how many times farther the crayon traveled for the 2-, 3-, 4-, and 5-book ramps than it did for the 1-book ramp. Do your calculations in the table and then list your answers here. Round to the nearest whole number. 3. Do you see a pattern? Describe it. 4. If the pattern continues, how far will a crayon travel if released from a © McGraw-Hill School Division 10-book ramp? a 20-book ramp? Explain how you made these estimates. 5. Explain the activity in terms of speed. Use with Grade 4, Chapter 4, Lesson 13, pages 176–177. (144) NS 3.4; MR 1.1, 2.3 Print This Page Name Print This 5–1 Page Patterns of Multiplication P PRACTICE Complete. 1. 3  2  a 3  b  60 c  200  600 3  2,000  d a b c d 2. 5  8  e f g h e 5  c  400 g  800  4,000 5  8,000  h Multiply. Use mental math. 3. 80 6 4. 70 8 8. 400  5 9. 800  6 5. 10. 40 5 6. 700  9 11. 60 7 7. 2,000  4 12. 90 6 3,000  6 13. 90  5  14. 4  90  15. 5  600  16. 700  8  17. 9  600  18. 700  4  19. 2,000  8  20. 5,000  7  21. 8  4,000  Find each missing number. 22. a  5  300 © McGraw-Hill School Division a 25. 3  23. b  4  320 24. 2  a a  900 a 26. 6  c  180 c b  3,600 b 27. c  8  72,000 c Problem Solving 28. Stamps are sold in rolls of 100. How many stamps are in 9 rolls? Use with Grade 4, Chapter 5, Lesson 1, pages 192–193. (145) 29. A ream of paper is 500 sheets of paper. How many sheets are in 7 reams? NS 3.2 Print This Page Name Print This 5–1 Page Patterns of Multiplication R RETEACH Using basic facts and patterns can help you multiply mentally. 2  4 ones  8 ones 248 2  4 tens  8 tens 2  40  80 2  4 hundreds  8 hundreds 2  400  800 Complete the pattern. 1. 3  3  2. 6  3  3. 4  5  3  30  6  30  4  50  3  300  6  300  4  500  3  3,000  6  3,000  4  5,000  © McGraw-Hill School Division Multiply. Use mental math. 4. 70 8 9. 200  8 5. 10. 90 4 500  7 6. 11. 70 4 3,000  8 7. 12. 60 7 8. 7,000  3 13. 800  9 6,000  8 14. 9  60  15. 6  50  16. 8  200  17. 8  800  18. 6  800  19. 5  900  20. 6  600  21. 8  400  22. 9  700  23. 4  600  24. 8  5,000  25. 3  4,000  26. 7  2,000  27. 5  6,000  28. 4  4,000  Use with Grade 4, Chapter 5, Lesson 1, pages 192–193. (146) NS 3.2 Print This Page Name Print This 5–1 Page Patterns of Multiplication E ENRICH History Riddles Find each missing number. Then find the letter in the table that matches that number. Solve the riddles. Write the letter in the blank above the same exercise number.  5  100 1. 2. 60   24,000 3. 7   350 4. 4   2,000 5.  9  1,800 6.  8  400 7. 7   21,000 8.  5  1,000 9.  6  3,000 11. 7   1,400 12.  6  1,200 15. 6  10. 3   1,200 13.  6  240 14. 6   480 16.  3  600 17. 9   18,000 18. 19. 6   2,400  7  2,100 22. 20 30 40 50 80 E N B A M 20.  3,000  5  100  8  4,000 21. 9   180  4,800 24. 7   210 23. 6  200 300 400 500 800 2,000 3,000 4,000 5,000 8,000 T S H O I F W U K Y © McGraw-Hill School Division What did Paul Revere say at the end of his ride? 7. 2. 9. 3. Where was the Declaration of Independence signed? 6. 11. 12. 10. 1. 13. 15. 5. 8. 4. 14. When Columbus discovered America, where did he first stand? 20. 24. 19. 23. 22. Use with Grade 4, Chapter 5, Lesson 1, pages 192–193. (147) 17. 18. 21. 16. NS 3.2 Print This Page Name Print This 5–2 Page Explore Multiplying 2-Digit Numbers by1-Digit Numbers P PRACTICE 1. Multiply 4  15. Draw squares to multiply. © McGraw-Hill School Division Find each product. 2. 62 2 3. 38 4 4. 91 3 5. 46 5 6. 78 6 7. 98 5 8. 76 6 9. 24 9 10. 56 7 11. 48 8 12. 66 6 13. 77 7 14. 94 3 15. 59 4 16. 44 9 17. 24 7 18. 19 8 19. 67 5 20. 84 4 21. 76 7 22. 5  26  23. 37  8  24. 45  6  25. 38  4  26. 7  22  27. 9  49  28. 8  67  29. 35  4  30. 99  3  Problem Solving 31. Katy arranges oranges in 5 layers in a crate. Each layer has 24 oranges. How many oranges does she put in the crate? Use with Grade 4, Chapter 5, Lesson 2, pages 194–195. (148) 32. Band members march in 24 rows. There are 8 members in each row. How many members are in the band? NS 3.2 Print This Page Name Print This 5–2 Page Explore Multiplying 2-Digit Numbers by 1-Digit Numbers R RETEACH Find 5  21. You can draw an array to multiply. Find the total number of dots. 5  21  105 5 dots 21 dots Draw an array to multiply. 1. 4  18  2. 5  24  5 dots 4 dots 24 dots 18 dots © McGraw-Hill School Division Find each product. 3. 19 6 4. 24 5 5. 25 8 6. 13 9 7. 12 9 8. 46 3 9. 37 4 10. 58 5 11. 28  7 12. 23  6 13. 33 4 14. 21 5 15. 18 3 16. 30 6 17. 18 9 18. 4  17  19. 22  6  20. 7  14  21. 20  6  22. 5  31  23. 26  4  24. 3  13  25. 4  50  26. 5  15  Use with Grade 4, Chapter 5, Lesson 2, pages 194–195. (149) NS 3.2 Print This Page Name Print This 5–2 Page Explore Multiplying 2-Digit Numbers by1-Digit Numbers E ENRICH The Abacus The abacus is a computing tool that is thousands of years old. To multiply 3  32 using a Russian abacus, first multiply 2 ones by 3. Move 6 beads to the bottom of the ones column to show 3  2  6. H T Next, multiply 3 tens by 3. Move 9 beads to the bottom of the tens column to show 3  3 tens  9 tens. O H T O Count the beads in each column. There are 9 tens 6 ones, so 3  32  96. Use the abacus to find each product. Show the answer by drawing the beads you moved down. Cross out the beads you moved down from the top. 1. 4  22  © McGraw-Hill School Division H 2. 2  34  T O 4. 5  43  H H 3. 3  31  T O 5. 4  212  T O H Use with Grade 4, Chapter 5, Lesson 2, pages 194–195. (150) T H T O 6. 3  304  O H T O NS 3.2 Print This Page Name Print This 5–3 Page Multiply 2-Digit Numbers by 1-Digit Numbers P PRACTICE © McGraw-Hill School Division Multiply. 1. 73 3 2. 44 5 3. 31 7 4. 68 8 5. 32 9 6. 65 5 7. 33 6 8. 96 3 9. 88 4 10. 74 5 11. 85 4 12. 77 6 13. 97 2 14. 66 8 15. 94 3 16. 44 4 17. 77 7 18. 18 9 19. 38 8 20. 99 6 21. 55  5  22. 75  6  23. 8  47  24. 6  39  25. 2  98  26. 84  6  27. 4  52  28. 63  7  29. 29  9  30. Multiply 63 by 8. 31. Multiply 78 by 4. 32. Multiply 37 by 6. 33. Multiply 45 by 5. 34. Multiply 56 by 7. 35. Multiply 82 by 3. Problem Solving 36. A rectangle is 5 tiles wide by 13 tiles high. How many tiles are in the rectangle? Use with Grade 4, Chapter 5, Lesson 3, pages 196–199. (151) 37. Books are stacked in 3 stacks with 17 books in each stack. How many books are in the stacks? NS 3.2, 3.3 Print This Page Name Print This 5–3 Page Multiply 2-Digit Numbers by 1-Digit Numbers R RETEACH You can multiply using models or pencil and paper. Find 4  26. Show 4 groups of 26. You can record this way: 26 4 24 Step 1 Multiply the ones. 4  6 ones  24 ones 26 4 24  80 Step 2 Multiply the tens. 4  2 tens  8 tens 26 4 24  80 104 Step 3 Add. © McGraw-Hill School Division Complete to find the product. You may use models to help you. 1. 23 5 2. 44 3 3. 31 8 4. 52 7 5. 45 9 6. 45 5 7. 64 6 8. 78 3 9. 86 4 10. 92 5 11. 9  52  12. 72  7  13. 68  3  14. 5  83  15. 2  88  16. 48  6  Use with Grade 4, Chapter 5, Lesson 3, pages 196–199. (152) NS 3.2, 3.3 Print This Page Name Print This 5–3 Page Multiply 2-Digit Numbers by 1-Digit Numbers E ENRICH Lattice Multiplication You can use lattice multiplication to multiply. Multiply 7  48. Multiply 7  8. Write 56 in the first box. Write 48 over the top boxes. Write 7 on the right. 4 8 4 Multiply 7  4. Write 28 in the second box. Add on the diagonals. Start at the right. Regroup as you would in any addition problem. 4 8 8 2 5 3 7 7 48 7  7 336 6 5 8 6 3 6 Use lattice multiplication to find the products. 1. 2  27  2. 5  34  2 7 3 1 © McGraw-Hill School Division 4 5 4 2 5 2 5 7 7 0 5 6 6 8 5 4 Use with Grade 4, Chapter 5, Lesson 3, pages 196–199. (153) 2 6 2 0 2 4 4 4 6. 7  79  3 7 2 8 0 2 0 6 5 4 9 1 4 5. 8  63  3 2 1 4 4. 8  37  2 3. 4  56  4 4 8 5 4 9 6 9 5 3 7 3 NS 3.2, 3.3 Print This Page Name Print This 5–4 Page Estimate Products P PRACTICE Estimate each product. 1. 5  21  2. 3  39  3. 7  $46  4. 85  6  5. 17  9  6. 81  3  7. 2  $298  8. 4  305  9. 478  6  10. 5  784  11. 612  9  12. 6  556  13. 2  1,987  14. 3  $2,126  15. 7  1,905  16. 8  3,495  17. 4,723  4  18. 5  $7,118  19. 41  6 20. 28  7 21. 96  2 22. 17 8 23. 31 9 24. 255  4 25. 488  3 26. 563  5 27. 2,307  5 28. 7,596  6 Algebra & Functions 29. 2  36 1  49 30. 96  3 32. 97  1 89  2 33. 6  105 4  209 34. 396  4 106  9 6  523 36. 3  666 2  366 37. 4  712 3  412 35. 5  423 © McGraw-Hill School Division Estimate. Write  or . 68  4 31. 6  28 5  41 Problem Solving 38. The volunteer ambulance group orders 6 first aid kits. Each kit costs $39. About how much does it cost for 6 kits? Use with Grade 4, Chapter 5, Lesson 4, pages 200–201. (154) 39. An ambulance travels about 386 miles a day. About how many miles does it travel in a week? NS 1.4, 3.2; 3.3 Print This Page Name Print This 5–4 Page Estimate Products R RETEACH You can round to estimate products. Round the greater factor to its greatest place and multiply using patterns. Estimate 8  287. 8  287 Round 287 to the nearest hundred. ↓ ↓ 8  300 287 200 210 220 230 240 250 260 270 280 290 300 Multiply using the rounded number 8  300  2,400 So, 8  287 is about 2,400. © McGraw-Hill School Division Estimate each product. 1. 2  74 2. 3  42 3. 6  36 4. 6  $58 5. 9  18 6. 3  71 7. 3  198 8. 2  $405 9. 4  378 10. 5  2,987 11. 8  2,126 12. 7  $2,905 13. 31 2 14. 58 3 15. $66  4 16. 17 5 17. 51 6 18. $454  7 19. 512  8 20. 498  9 21. $637  4 22. 845  2 23. 7,809  6 24. $6,047  3 25. 4,524  8 26. $2,107  6 27. 8,596  4 28. 2,537  4 29. 5,088  2 30. $6,409 31. 3,623  8 32. $7,522  7 Use with Grade 4, Chapter 5, Lesson 4, pages 200–201. (155)  9 NS 1.4, 3.2; 3.3 Print This Page Name Print This 5–4 Page Estimate Products E ENRICH Target Practice Estimate to find the factors whose product is closer to the target number. Circle the letter of the answer. 1. Target Number: 150 2. Target Number: 160 3. Target Number: 180 S. 57  3 H. 37  4 D. 3  67 T. 52  3 I. 32  4 E. 3  61 4. Target Number: 540 5. Target Number: 420 6. Target Number: 560 S. 88  6 T. 7  62 O. 76  8 T. 83  6 U. 7  68 A. 72  8 7. Target Number: 2,700 8. Target Number: 630 9. Target Number: 4,500 T. 3  879 T. 79  9 E. 9  490 U. 3  849 U. 72  9 F. 9  430 10. Target Number: 3,600 11. Target Number: 5,600 12. Target Number: 6,000 N. 849  4 E. 770  8 L. 2,181  3 O. 889  4 F. 680  8 M. 2,898  3 13. Target Number: 6,400 14. Target Number: 7,200 15. Target Number: 2,400 I. 839  8 A. 711  9 E. 303  8 J. 899  8 B. 782  9 F. 352  8 © McGraw-Hill School Division 16. Target Number: 25,000 17. Target Number: 32,000 18. Target Number: 35,000 Q. 4,175  5 T. 7,825  4 Y. 4,762  7 R. 4,899  5 U. 7,239  4 Z. 4,097  7 Write the circled letters above each exercise number to answer the question. “I lift my lamp beside the golden door!” Who am I? 1 2 3 4 5 6 7 8 9 10 11 Use with Grade 4, Chapter 5, Lesson 4, pages 200–201. (156) 12 13 14 15 16 17 18 NS 1.4, 3.2, 3.3 Print This Page Name Problem Solving: Reading for Math Use an Overestimate or Underestimate Print This 5–5 Page P PRACTICE Reading Skill Form a conclusion about whether you would use an overestimate or an underestimate. Then solve each problem. 1. On Wednesday, a group of 98 students will visit the national forest. Each student will get a nature guide fact book. These books come in boxes of 32. The park rangers have 3 boxes of fact books. Are there enough fact books so each student can get a book? Should you use an overestimate or an underestimate to solve this problem? Explain. Are there enough fact books so each student can get a book? 2. The park charges $16 per day to use a campsite. The Nolans want to use a campsite for 4 nights. They have $80 set aside for using a campsite. Have the Nolans set aside enough money? Should you use an overestimate or an underestimate to solve this problem? Explain. Have the Nolans set aside enough money? © McGraw-Hill School Division 3. A total of 184 people are taking a desert hike. Each hiking group can have up to 36 people. There are enough hike leaders and helpers to lead 6 groups. Are there enough hike leaders and helpers so that all of the people can go on a hike? Should you use an overestimate or an underestimate to solve this problem? Explain. Are there enough hike leaders and helpers so that all of the people can go on a hike? Use with Grade 4, Chapter 5, Lesson 5, pages 202–203. (157) MR 1.1, 2.4, 3.2 Print This Page Name Problem Solving: Reading for Math Use an Overestimate or Underestimate Print This 5–5 Page P PRACTICE Math Skills Test Prep Choose the correct answer. There are 146 students going on a trip to the desert. The school has 3 buses. Each bus can hold 48 students. Should a fourth bus be ordered for the trip? 1. Which statement is true? A There are 48 students going on a trip to the desert. B Each bus can hold 48 students. C Three buses can hold exactly 150 students. 2. To make sure that 3 buses are enough to hold 148 students, you should F underestimate the number of students the buses can hold. G overestimate the number of students the buses can hold. H underestimate the number of students going on the trip. The cafeteria in the national forest visitors’ center has 23 tables. Each table seats 6 people. A group of 120 is visiting the forest. Are there enough tables so that all 120 people can eat in the cafeteria at once? 3. Which statement is not true? © McGraw-Hill School Division A Each table can seat 23 people. B The cafeteria has 23 tables. C Each table can seat 6 people. 4. To make sure there are enough tables to seat 120 people, you should F overestimate the number of seats. G underestimate the number of tables. H overestimate the number of tables. There are 7 river tours per day. Each river tour has room for 48 people. Each person on the river tour receives a pamphlet. The tour leaders have 400 pamphlets. Are there enough pamphlets for a day of river tours? 5. How would you use estimation to solve this problem? A overestimate the number of people B underestimate the number of tours C underestimate the number of people Use with Grade 4, Chapter 5, Lesson 5, pages 202–203. (158) 6. Which estimate would you use to solve the problem? F 7  40  280 G 6  50  300 H 7  50  350 MR 1.1, 2.4, 3.2 Print This Page Name Problem Solving: Reading for Math Use an Overestimate or Underestimate Print This 5–5 Page P PRACTICE Math Skills Test Prep Choose the correct answer. The Wildlife Committee is selling books to raise $400. The committee makes $8.75 on each book it sells. If the committee sells 50 books, will that be enough to raise $400? 7. How would you use estimation to 8. Which estimate would you use to solve this problem? solve the problem? A overestimate the amount made on each book F $9 x 50 = $450 B underestimate the amount made on each book G $8 x 50 = $400 H $8 x 40 = $320 C underestimate the number of books Solve. 9. The river tour has 4 boats. Each boat has room for 24 people. Are there enough boats to take 76 people on a tour? © McGraw-Hill School Division 11. The forest rangers have 5 boxes of wildlife guides. Each box contains 36 pamphlets. The rangers need 200 pamphlets. Should they order another box? 13. The motel in the national park costs $39 per night. Nick sets aside $150 to pay for the motel. Is this enough money to pay for 5 nights? Use with Grade 4, Chapter 5, Lesson 5, pages 202–203. (159) 10. There are 5 groups of 25 students each. The rangers have 150 forest T-shirts. Do they have enough T-shirts to give a T-shirt to each student? 12. Phyllis takes 118 photos of the desert. She buys a photo album with 24 pages. Each page can hold 6 photos. Can all the photos fit in the album? 14. It costs $89 to rent a sport utility vehicle (SUV) for one day. Will $650 be enough to rent an SUV for a 7-day trip through the desert? MR 1.1, 2.4, 3.2 Print This Page Name Print This 5–6 Page Multiply Greater Numbers P PRACTICE Multiply. Check for reasonableness. 1. 693  4 2. 907  5 3. 368  9 4. $601  3 5. 2,901  2 6. 1,999  7 7. 8,072  8 8. $38.88  4 9. 6  2,369  10. 7 5,786  11. 3  4,964  12. 9  $1,288  13. 5  19,091  14. 8  12,967  15. Multiply 3,687 by 8. 16. Multiply 1,096 by 9. Algebra & Functions Complete the table. 17. © McGraw-Hill School Division 18. Input 12 15 Output 48 60 Input 1 2 Output 37 74 18 21 24 3 4 5 Problem Solving 19. Maria made 9 trips between New York City and Los Angeles. Each trip cost $498. How much did the 9 trips cost? Use with Grade 4, Chapter 5, Lesson 6, pages 206–209. (160) 20. A company buys 8 computers. Each computer costs $2,245. How much does the company spend on the 8 computers? NS 3.2, 3.3 Print This Page Name Print This 5–6 Page Multiply Greater Numbers R RETEACH You can use models to help you multiply greater numbers. Find 2  357. Show 2 groups of 357. You can record this way: Step 1 Multiply the ones. 2  7 ones  14 ones Regroup. 14 ones  1 ten 4 ones 1 357  2 4 Step 2 Multiply the tens. 2  5 tens  10 tens 11 357  2 14 Add the tens. 10 tens  1 ten  11 tens Step 3 Multiply the hundreds. 2  3 hundreds  6 hundreds 11 357  2 714 Add the hundreds. 6 hundreds  1 hundred  7 hundreds © McGraw-Hill School Division Multiply. Check for reasonableness. 1. 234  5 2. 146  3 3. 357  4 4. $4.62  6 5. 3,548  2 6. $6,164  7 7. 2,781  8 8. 4,862  9 9. $1,530 10. 2,681  2 11. 9,275  6  4 Use with Grade 4, Chapter 5, Lesson 6, pages 206–209. (161) 12. $7,452  5 NS 3.2, 3.3 Print This Page Name Print This 5–6 Page Multiply Greater Numbers E ENRICH Deducing Digits Find the missing digits. Write them in the boxes. 1. 3  8 184 2. 4 5 0 6. 4  6 744 10. 2 14. 5.  1 9. © McGraw-Hill School Division  17.  $5,  31 1   3 11.  7 5 25 9 5  7, 4 64 2 6, 19.  12. 7 1,666 15. ,6 22. 8. 7 434 416 4 , 9 ,6 2 7. 46 18. 111   8 5  3 174 770 4,38 21.  3 3 4. 138 3 735 $1,0 3.  1 13. 1  7 98 7, 56 29, 75  74,450 Use with Grade 4, Chapter 5, Lesson 6, pages 206–209. (162) 5 23. $3  $1 16.  7 9  ,06 ,3 3, 3 1  1,564 3 2,400 8, 20.  7 3 24. 4  32 76 ,184 0,3 9 82,472 NS 3.2, 3.3 Print This Page Name Print This 5–7 Page Problem Solving: Strategy P PRACTICE Find a Pattern Use find a pattern to solve. 1. Annie makes an arrangement of chestnuts. She puts 3 chestnuts in the first row, 6 chestnuts in the second row, and 9 chestnuts in the third row. Describe the pattern. How many chestnuts will be in the fourth row? 3. Rangers examine trees that fell during a storm. The first tree has 3 annual rings. The second tree has 9 rings. The third tree has 27 rings. The fourth tree has 81 rings. If the pattern continues, how many annual rings does the fourth tree have? 2. In one desert area, the rabbit population is estimated at 25 in one year, 50 the next year, 100 the third year, and 200 the next year. Describe the pattern. Then estimate the rabbit population for the fifth year. 4. Stan counts robins’ nests on his block. One year he counts 4 nests. The next year he counts 9 nests. The third year Stan counts 14 nests. The fourth year he counts 19 nests. If the pattern continues, how many nests will he count in the fifth year? Mixed Strategy Review Solve. Use any strategy. © McGraw-Hill School Division 5. Nick took 40 photos of the desert. 6. Social Studies Colorado’s state He has one photo album with 8 pages and another with 12 pages. Nick wants to put the same number of photos on each page. Which album should he use? parks cover 347,000 acres. Connecticut’s state parks cover 176,000 acres. How many more acres do state parks cover in Colorado than in Connecticut? Strategy: Strategy: 7. Create a problem for which you would find a pattern to solve. Share it with others. Use with Grade 4, Chapter 5, Lesson 7, pages 210–211. (163) NS 3.2; MR 1.1, 2.4, 3.2 Print This Page Name Print This 5–7 Page Problem Solving: Strategy R RETEACH Find a Pattern Page 211, Problem 1 As a plant cell grows, one cell divides into two cells. Two cells divide into four cells, four into eight, and so on. Describe the pattern. How many cells will there be after seven divisions? Step 1 Read Be sure you understand the problem. Read carefully. What do you know? • One cell divides into cells, two cells divide into cells, and four cells divide into cells. What do you need to find? • You need to find how many . Step 2 Plan ■ ■ ■ ■ © McGraw-Hill School Division ■ ■ ■ ■ ■ ■ Find a Pattern Guess and Check Work Backward Make a Graph Make a Table or List Write a Number Sentence Draw a Picture Solve a Simpler Problem Logical Reasoning Act it out Make a plan. Choose a strategy. Finding a pattern will help you solve the problem. Start 1st cell 2nd cell 3rd cell 4th cell 5th cell 6th cell 7th cell division division division division division division division Number of Cells 1 2 4 8 Find the pattern in the number of cells after the 1st, 2nd, and 3rd cell divisions. Continue the pattern to find the number of cells after the 7th cell division. Use with Grade 4, Chapter 5, Lesson 7, pages 210–211. (164) NS 3.2; MR 1.1, 2.4, 3.2 Print This Page Name Print This 5–7 Page Problem Solving: Strategy R RETEACH Find a Pattern Step 3 Solve Carry out your plan. You know the number of cells after the 1st, 2nd, and 3rd cell divisions. 1st cell 2nd cell 3rd cell 4th cell 5th cell 6th cell 7th cell Start division division division division division division division Number of Cells 1 2 4 8 Find the pattern in the number of cells after the 1st, 2nd, and 3rd cell divisions. What pattern do you see? Continue the pattern to complete the chart. If the pattern continues, there will be cells after the 7th cell division. Step 4 Look Back Is the solution reasonable? Reread the problem. Did you find a pattern and continue it? Yes No © McGraw-Hill School Division What other strategies could you use to solve the problem? Practice 1. Kate hikes 2 miles the first day, 5 miles the second day, and 8 miles the third day. If the pattern continues, how many miles will she hike the fourth day? Use with Grade 4, Chapter 5, Lesson 7, pages 210–211. (165) 2. The Support-Our-Forests Fund has goals of $3,000, $6,000, $12,000, and $24,000 for its first four fund drives. If the pattern continues, what will the goal be for the fifth fund drive? NS 3.2; MR 1.1, 2.4, 3.2 Print This Page Name Print This 5–8 Page Functions and Graphs P PRACTICE Complete each table. Then write an equation. 1. Roger runs 7 miles more each week 2. One plant produces 8 times more than another boy. x 1 2 y 8 9 peppers than another plant. 3 4 5 3. One number is 4 less than 3 times 4 5 d 8 11 1 2 s 8 16 3 4 5 4. One number is 8 greater than 2 times another number. c r another number. 6 7 8 m 1 2 n 10 12 3 4 5 Complete each table. Then graph the function. 5. Stella works 4 times as many hours as 6. Liz swims 2 more than 2 times as Jana does. © McGraw-Hill School Division 7. many laps as Sunny does. y  4x x 0 1 y 4 0 2 3 a  2b  2 b 0 1 4 a s  2r  2 8. r 1 2 s 0 2 3 4 5 2 2 3 4 3 4 5 4 n  3t  1 t 1 2 n 4 7 Problem Solving 9. Each of 4 people orders a $8.95 lunch. How much do the 4 lunches cost? Write and solve an equation. Use with Grade 4, Chapter 5, Lesson 8, pages 212–215. (166) 10. Ben buys 3 toys that cost $3 each. How much do the toys cost? Write and solve an equation. AF 1.1, 1.5; SDP 2.1 Print This Page Name Print This 5–8 Page Functions and Graphs R RETEACH The numbers in a function table relate to one another to form a pattern. One number is 1 greater than 2 times a number. x 1 2 3 4 5 y 3 5 7 9 11 Think: How can I find the value of y? x 1 2 ↓ Equation  ↓ 4 5 ↓ ↓ 2x  1 2x  1 2x  1 2x  1 2x  1 3 5 7 9 11 ↓ y ↓ 3 ↓ ↓ ↓ ↓ In each case, multiply by 2 and add 1. The values in the table form ordered pairs. x 1 2 3 4 5 y 3 5 7 9 11 (x, y) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11) You can graph these ordered pairs Complete each table. Then write an equation. 1. One number is 2 greater than 2. One number is 4 times another © McGraw-Hill School Division another number. Think: Add 2 to x to get y. x 1 2 y 3 4 3 4 number. Think: Multiply x by 4 to get y. 5 x 1 2 y 4 8 3 4 5 3 4 Complete each table. Write the ordered pairs. Then graph the function. 3.y  2x 4.y  2x  2 x 0 1 y 0 2 2 3 4 Use with Grade 4, Chapter 5, Lesson 8, pages 212–215. (167) x 0 1 y 2 4 2 AF 1.1, 1.5; SDP 2.1 Print This Page Name Print This 5–8 Page Functions and Graphs E ENRICH When Are Houses Like Books? To answer this riddle, find the points on the grid. Then write the letter for each point on the lines. (1, 3) (7, 8) (0, 6) (7, 1) (7, 8) (4, 7) (2, 2) (0, 6) (3, 0) (7, 8) (0, 6) (4, 4) (6, 5) (3, 0) (1, 1) (6, 2) (9, 5) (0, 6) (6, 5) 12 11 10 9 H 8 A 7 E 6 S 5 Y 4 W 3 © McGraw-Hill School Division I V 2 R O 1 N T 0 1 2 3 4 5 6 7 8 9 10 11 12 If you are given the points (2, 2) and (6, 2), name two other points that would make a square. Use with Grade 4, Chapter 5, Lesson 8, pages 212–215. (168) AF 1.1, 1.5; SDP 2.1 Print This Page Name Print This Page 5–9 Part A WORKSHEET Problem Solving: Application Decision Making Analyze and Make Decisions Record your data. Item Name Cost of Item per Unit Number of Units Total Cost of Item Total Cost of Meal or Snack Breakfast Items Lunch Items Dinner Items © McGraw-Hill School Division Snack Items Your Decision What is your recommendation for the menus (one breakfast, one lunch, one dinner, and snacks)? Use with Grade 4, Chapter 5, Lesson 9, pages 216–217. (169) NS 1.2, 3.2; MR 1.1, 2.3, 3.1 Print This Page Name Problem Solving: Application How much water do you use each day? Print This Page 5–9 Part B WORKSHEET Math & Science Record your data. Number of Times Amount of Water a Day You Use This for Each Use Source of Water Total Amount of Water © McGraw-Hill School Division Place You Use Water Use with Grade 4, Chapter 5, Lesson 9, pages 218–219. (170) NS 1.2, 3.2; MR 1.1, 3.3 Print This Page Name Problem Solving: Application Print This Page 5–9 Part B WORKSHEET Math & Science How much water do you use each day? 1. How much water do you use each day? 2. If a cup of water costs $0.10, how much money do you spend on water each day? Show your work. Work Space 3. How much water is being used by your whole class each day? © McGraw-Hill School Division 4. Is clean water a renewable or nonrenewable resource? Explain. 5. Give some other examples of renewable and nonrenewable resources. Use with Grade 4, Chapter 5, Lesson 9, pages 218–219. (171) NS 1.2, 3.2; MR 1.1, 3.3 Print This Page Name Print This 6-1 Page Patterns of Multiplication P PRACTICE Complete. 1. 6  8  s s 2. w  3  21 w 60  t  480 t 70  3  x x 60  80  u u y  30  2,100 y 60  800  v v 70  300  z z © McGraw-Hill School Division Multiply. Use mental math. 3. 60  70  4. 20  60  5. 80  800  6. 30  200  7. 50  40  8. 400  30  9. 600  50  10. 90  70  11. 20  4,000  12. 9,000  30  13. 3,000  70  14. 900  60  15. 80  5,000  16. 7,000  80  17. 40  800  18. 30  6,000  19. 20  500  20. 6,000  90  21. 700  40  22. 80  2,000  23. 50  5,000  Algebra & Functions Find each missing number. 24. 30  j  9,000 j 25. s  70  2,800 s 26. 60  b  24,000 b 27. 400  t  12,000 t 28. 90  q  8,100 q 29. p  600  30,000 p  n  300  6,000 n  31. r  800  40,000 30. r Problem Solving 32. ABC Hardware has 50 cartons of nails. There are 4,000 nails in each carton. How many nails does the store have? Use with Grade 4, Chapter 6, Lesson 1, pages 234–235. (172) 33. Handy Hardware has 500 boxes of hinges. Each box has 90 hinges. How many hinges does the store have? NS 3.2 Print This Page Name Print This 6–1 Page Patterns of Multiplication R RETEACH You can use basic facts and patterns to help you multiply. 2  3  6 basic fact 4  5  20 basic fact 20  30  600 1 zero 1 zero 2 zeros 40  50  2,000 1 zero 1 zero 2 zeros 20  300  6,000 1 zero 2 zeros 3 zeros 40  500  20,000 1 zero 2 zeros 3 zeros 20  3,000  60,000 1 zero 3 zeros 4 zeros 40  5,000  200,000 1 zero 3 zeros 4 zeros Complete the pattern. 1. 4  3  2. 7  2  40  30  70  20  40  300  70  200  40  3,000  70  2,000  3. 5  6  4. 8  5  50  60  80  50  50  600  80  500  50  6,000  80  5,000  © McGraw-Hill School Division Multiply. Use mental math. 5. 3  6  6. 30  60  7. 30  600  8. 4  9  9. 40  90  10. 40  900  11. 80  30  12. 700  30  13. 20  50  14. 300  9  15. 80  600  16. 70  800  17. 30  8,000  18. 2,000  90  19. 20. 70  7,000  21. 7,000  60  22. 90  8,000 Use with Grade 4, Chapter 6, Lesson 1, pages 234–235. (173) 4,000  50  NS 3.2 Print This Page Name Print This 6–1 Page Patterns of Multiplication E ENRICH Clueless Puzzle This puzzle has all the answers, but no clues. Each answer is a product of two factors. Make up clues for each answer. 1 2 3 4 5 6 © McGraw-Hill School Division Across Down 1. 80  8,000 1. 70  90,000 2. 2. 3. 3. 4. 4. 5. 5. 6. 6. Use with Grade 4, Chapter 6, Lesson 1, pages 234–235. (174) NS 3.2 Print This Page Name Explore Multiplying by 2-Digit Numbers Print This 6–2 Page P PRACTICE © McGraw-Hill School Division Multiply. 1. 36  12 2. 27  41 3. 38  14 4. 23  22 5. 49  13 6. 47  34 7. 46  14 8. 17  25 9. 45  35 10. 48  20 11. 38  27 12. 32  15 13. 45  25 14. 14  15 15. 26  34 16. 32  18 17. 31  25 18. 12  46 19. 36  36 20. 28  44 21. 16  40 22. 17  17 23. 37  26 24. 19  27 25. 49  30 26. 15  23  27. 30  13  28. 14  22  29. 26  21  30. 30  24  31. 42  17  32. 63  15  33. 50  23  34. 13  13  35. 70  14  36. 32  20  37. 25  25  Problem Solving 38. The art teacher wants to decorate each classroom with 28 balloons. How many balloons does he need for 18 classrooms? Use with Grade 4, Chapter 6, Lesson 2, pages 236–237. (175) 39. There are 35 buses waiting for students after school. Each bus carries 45 students. How many students ride the buses? NS 3.2, 3.3 Print This Page Name Print This 6–2 Page Explore Multiplying by 2-Digit Numbers R 19 2 An array can help you multiply. Find 12  19. Think: 12  10  2 19  12 38  190 228 RETEACH 10 2 19 10 19 38  190  228 Find each product. Draw an array diagram to help you. 1. 14  15  2. 11  19  © McGraw-Hill School Division Multiply. 3. 28  14 4. 35  26 5. 42  33 6. 49  27 7. 32  18 8. 18  41 9. 23  17 10. 24  52 11. 45  28 12. 27  27 13. 32  21  14. 41  32  Use with Grade 4, Chapter 6, Lesson 2, pages 236–237. (176) 15. 26  17  NS 3.2, 3.3 Print This Page Name Print This 6–2 Page Explore Multiplying by 2-Digit Numbers E ENRICH Napier’s Bones In the seventeenth century, John Napier invented a simple calculator that multiplied by adding. It became known as Napier’s Bones. Here is a way to use Napier’s Bones to multiply 49  37. Place the strips headed 4 and 9 next to each other. Place the index beside the two strips. Fold the strips so that the rows headed 3 and 7 on the index are next to each other. INDEX INDEX 4 9 8 1 2 1 6 2 0 2 4 2 8 3 2 3 6 1 8 2 7 3 6 4 5 5 4 6 3 7 2 8 1 1 2 3 4 5 6 7 8 9 4 9 1 2 2 8 2 7 6 3 Add diagonally to find the product. Start at the bottom with the ones. Remember to carry. INDEX 1 3 7 4 9 1 2 2 8 2 7 6 3 1 3 7 37  49 Cut out the ten strips of Napier’s Bones below. Use them to find each product. 1. 57  34  2. 61  76  3. 85  29  4. 32  33  5. 94  65  6. 56  48  7. 39  68  8. 75  38  9. 89  21  Napier’s Bones © McGraw-Hill School Division INDEX 1 2 3 4 5 6 7 8 8 7 6 5 4 3 2 1 1 2 3 4 4 5 6 7 6 4 2 0 8 6 4 2 1 2 2 3 4 4 5 6 4 1 8 5 2 9 6 3 1 1 2 3 3 4 4 5 2 8 4 0 6 2 8 4 1 1 2 2 3 3 4 4 8 0 5 0 5 0 5 0 5 Use with Grade 4, Chapter 6, Lesson 2, pages 236–237. (177) 1 1 2 2 2 3 3 2 6 0 4 8 2 6 1 1 1 2 2 2 6 4 2 9 6 3 8 4 0 5 2 6 4 7 6 8 8 9 2 5 8 1 4 7 1 1 1 1 1 NS 3.2, 3.3 Print This Page Name Print This 6–3 Page Multiply by Multiples of 10 P PRACTICE Multiply. 1. 26  40 2. 47  30 3. 91  20 4. 87  10 5. 6. 17  80 7. 135  50 8. 207  60 9. 399  50 10. 756  30 15. 5,503  50 20. 9,075  80 11. 498  70 12. 1,038  40 13. 2,226  20 14. 16. 2,375  20 17. 4,009  40 18. 2,490  70 19. 6,967  10 21. 51  30  22. 39  80  23. 67  20  24. 325  60  25. 40  608  26. 999  10  27. 712  30 28. 10  3,116  29. 80  1,185  30. 90  4,090  31. 2,111  70  32. 50  5,549  Algebra & Functions © McGraw-Hill School Division 3,510  60 23  90 Find the missing number. 33. 34  j  680 j 34. 35. 99  a  7,920 a 36. 56  m  1,680 m 37. 861  b  77,490 b 38. 1,002  n  70,140 n 40. 898  c  53,880 c 39. s  2,108  63,240 s  q  72  2,160 q Problem Solving 41. Classroom chairs cost $39. How much will 30 chairs cost? Use with Grade 4, Chapter 6, Lesson 3, pages 238–239. (178) 42. A computer costs $2,345. How much will 20 computers cost? NS 3.2, 3.3 Print This Page Name Print This 6–3 Page Multiply by Multiples of 10 R RETEACH An expanded form can help you multiply. Find 20  37. Think: 37  30  7 20  (30  7) (20  30) (20  7) 6 0 0  1 4 0  740 37  20 740 Complete to find each product. 1. 10  28 10  ( ( 2. 30  33  8)  20)  (  8)  (  ) (  )   4. 50  64  (20    3)  3. 80  27 ( (  (60  ) )(   ) (  ) ) (     ) © McGraw-Hill School Division Multiply. 5. 34  40 6. 27  30 7. 38  40 8. 43  10 9. 18  50 10. 24  80 11. 35  20 12. 19  30 13. 22  10 14. 57  60 15. 40  18  16. 28  30  17. 30  32  18. 10  39  19. 16  30  20. 20  39  Use with Grade 4, Chapter 6, Lesson 3, pages 238–239. (179) NS 3.2, 3.3 Print This Page Name Print This 6–3 Page Multiply by Multiples of 10 E ENRICH Missing Digits © McGraw-Hill School Division Find each missing digit. 1. 7 4  1 7 4 0 2. 8  3 0 2, 4 9 0 3. 6 2  0 3, 7 2 0 4. 3  5 0 1, 6 5 0 5. 9  9 0 6, 2 1 0 6. 4 6  0 1, 8 4 0 7. 8 1  0 1, 6 2 0 8. 4  7 0 6, 5 8 0 9. 4 8  8 0 3 8, 6 4 0 10. 13. 2 1 1  0 1 0, 5 5 0 14. 17. 4 6  7 0 5 2, 2 2 0 21. 25. 11. 9 1  9 0 8 2, 0 8 0 12. 7 2 1  0 2 1, 6 3 0 3  6 0 3 3, 7 8 0 15. 6 7  3 0 2 0, 1 9 0 16. 8 6  8 0 6 6, 8 8 0 18. 8 3  4 0 3 3, 5 6 0 19. 7 8  8 0 3 8, 2 4 0 20. 5 6  9 0 5 0, 4 9 0 1 4  8 0 2 5, 1 2 0 22. 9 5  2 0 1 8, 5 0 0 23. 7 1 6  0 6 4, 4 4 0 24. 5  7 0 4 7, 2 5 0 2 5  8 0 7 4, 0 0 0 26. 5 4  4 0 2 1, 7 6 0 27. 6 3 6  0 5 7, 2 4 0 28. 7 5 8 4  0 3 5, 0 4 0 5 Use with Grade 4, Chapter 6, Lesson 3, pages 238–239. (180) 6 4  5 0 3 9, 2 0 0 NS 3.2, 3.3 Print This Page Name Problem Solving: Reading for Math Solve Multistep Problems Print This 6–4 Page P PRACTICE Reading Skill Circle the hidden question that can help you solve the problem. Then solve the problem. 1. A group of travelers rents 5 boats for 8 hours each. Boats cost $12 an hour to rent. What is the total fee for this rental? What is the total number of hours that the 5 boats are rented for? What is the total number of boats that are rented in a day? Solution: 2. A swimming instructor has 4 classes with 8 students in each class. Each student pays a total of $50 for the classes for the season. How much money does the swimming instructor receive? What amount does the instructor charge per hour? How many students in all does the swimming instructor have? Solution: 3. Burke’s Bluff Beach sells 25 guest passes in one day. Condor Cove Beach sells 2 times as many guest passes that same day. Estimate the total number of guest passes that beaches will sell in 3 days. How many guest passes does Condor Cove Beach sell in 1 day? How many guest passes will Burke’s Bluff Beach sell in 2 days? © McGraw-Hill School Division Solution: 4. Miguel charges $30 per hour to take people on his boat. Miguel rents his boat for 3 hours per day for 12 days. How much money does Miguel receive? How many hours in all does Miguel rent his boat? How much would Miguel receive if he rented his boat 12 hours per day? Solution: Use with Grade 4, Chapter 6, Lesson 4, pages 240–241. (181) MR 1.2, 2.4, 3.2 Print This Page Name Problem Solving: Reading for Math Solve Multistep Problems Print This 6–4 Page P PRACTICE Math Skills Test Prep Choose the correct answer. Lana and Ken rent 2 sets of scuba equipment for $16 an hour each. They rent a boat for $24 per hour. They use the boat and the equipment for 7 hours. 1. Which of the following statements 2. One “hidden question” you must is true? A Lana and Ken pay $40 per hour to rent a boat. B Lana and Ken pay $168 to rent the boat. C Lana and Ken rent the boat and equipment for 16 hours. solve is: F How much do they pay to rent 2 sets of scuba equipment for 7 hours? G How many hours do they use the boat? H How much do they pay for the boat each hour? On a school trip, 3 buses of students go to Ocean Land. Each bus has 44 students. Each student spends $10 on admission and a special show. How much money do the students spend altogether? 3. Which question do you have to answer © McGraw-Hill School Division before you can solve the problem? A How many students are in each bus? B How many hours are the students at Ocean Land? C How many students in all visit Ocean Land? 4. How much money do the students spend altogether? F $1,320 G $440 H $10 Olive catches 3 fish in 1 hour. Her sister catches 3 times as many fish. Estimate the number of fish the girls will catch if they fish for 3 hours. 5. Which of the following statements is true? A Olive and her sister catch 9 fish. B Olive’s sister catches 3 fish. C Olive’s sister catches 3 times as many fish as Olive does. Use with Grade 4, Chapter 6, Lesson 4, pages 240–241. (182) 6. One “hidden question” you must solve is: F How many fish did Olive catch in 1 hour? G How many fish did Olive’s sister catch in 1 hour? H How many hours have they fished so far? MR 1.2, 2.4, 3.2 Print This Page Name Problem Solving: Reading for Math Solve Multistep Problems Print This 6–4 Page P PRACTICE Math Skills Test Prep Choose the correct answer. The Beach Shack rents out 12 umbrellas for 5 hours each. Umbrellas cost $6 per hour. How much money does The Beach Shack make? 7. Which question do you have to answer before you can solve the problem? A How much does it cost to rent 1 umbrella for 12 hours? B How much does it cost to rent 1 umbrella for 5 hours? 8. How much money does The Beach Shack make? F $30 G $72 H $360 C How many umbrellas does The Beach Shack have? Solve. 9. The Diving Club offers 4 beginning diving classes each day. Each class has room for 6 people. How many people can take classes in 30 days? © McGraw-Hill School Division 11. During one week, 5 sailboats are rented for a total of 16 hours each. The rental cost is $25 per hour. Altogether, how much is paid for these rentals? 13. Amanda rents a canoe and a life preserver from 2:00 P.M. to 5:00 P.M. A canoe costs $12 per hour. A life preserver costs $2 per hour. How much does Amanda spend? Use with Grade 4, Chapter 6, Lesson 4, pages 240–241. (183) 10. A fishing guide charges $25 per hour. He works 6 hours per day for 5 days. How much money does the guide earn? 12. The aquarium charges $12 admission and $6 for a tour. A group of 20 people goes to the aquarium and takes the tour. How much money does the group spend? 14. Jenny rented a rowboat from 10:45 A.M. to 1:00 P.M. After lunch, she rented another rowboat from 1:45 P.M. to 4:45 P.M. For how many minutes did she rent the boat? MR 1.2, 2.4, 3.2 Print This Page Name Print This 6-5 Page Multiply by 2-Digit Numbers P PRACTICE Find each product 1. 26  35 2. 73  51 3. 6. $46  35 7. 59  47 8. 11. 79  73 12. 16. 18  92  94  61 17. 13. 44  87 77  22 $0.63  58 28  19  29  19 55  15 10. 44  46 68  24 15. 51  34 $0.56  83 9. 14. 18. 86  43  19. 74  33  20. 48  26  21. 31  $0.18  22. 77  94  23. 88  62  24. 27  34  Algebra & Functions Find each product. 25. (30  7)  (10  8)  n 26. (60  4)  (20  9) = v 27. (80  1)  (40  2)  p 28. (50  6)  (70  3) = r 29. (90  5)  (10  1)  q © McGraw-Hill School Division 5. 4. 31. (20  8)  (70  7)  s 30. (60  6)  (50  5)  c 32. (40  3)  (80  4)  b Problem Solving 33. A fence has 28 sections with 18 boards in each section. How many boards are in the fence? Use with Grade 4, Chapter 6, Lesson 5, pages 242–245. (184) 34. Horses on a ranch eat 28 bales of hay each day. How many bales do they eat in 31 days? NS 3.2, 3.3 Print This Page Name Print This 6–5 Page Multiply by 2-Digit Numbers R RETEACH You can use a place-value chart to help you multiply 2-digit numbers. Multiply 47  25. Step 1 Multiply by the ones. Regroup if necessary. TH H T Step 2 Multiply by the tens. O TH H 3 2 4 7  1  5 7 5  T O TH H T 2 2 3 3 2 4 7 0 5 7 5 0 1 1 0 TH H T O 5 3 8 2 6  Step 3 Add the products.   2 4 7 0 7 O 5 7 5 0 5 1 1 1 0 1 TH H T O 3 5 9 7 1 Complete. Find each product. 1. H   © McGraw-Hill School Division 4. 9. 14. 6 T O 1 4 5 5 5 0 0 16  23 46  44 85  43  2.   2 2 7 4 0 5. $15  42 6. 23  39 7. 10. 67  29 11. 59  31 12. 15. 96  35  Use with Grade 4, Chapter 6, Lesson 5, pages 242–245. (185) 3.   $0.27  51 $31  28 16. 5 8. 38  26 13. 72  53 9 3 7 0 $0.39  66  NS 3.2, 3.3 Print This Page Name Print This 6–5 Page Multiply by 2-Digit Numbers E ENRICH Patterns for Eleven Multiply 11 by a 1-digit number. 1. 2  11  2. 3  11  3. 4  11  4. 5  11  5. 6  11  6. 7  11  7. 8  11  8. 9  11  What pattern do you see? Multiply 11 by a 2-digit number. 9. 11  31 10. 11  32 11. 11  33 12. 11  34 13. 11  53 14. 11  62 15. 11  27 16. 11  18 19. 11  38 20. 11  16 What pattern do you see? Use the pattern to find these products. © McGraw-Hill School Division 17. 11  41 18. 11  22 21. 44  11  22. 55  11  23. 64  11  24. 72  11  Use with Grade 4, Chapter 6, Lesson 5, pages 242–245. (186) NS 3.2, 3.3 Print This Page Name Print This 6–6 Page P Estimate Products PRACTICE Estimate each product. 1. 49  59 2. 55  65 3. 41  52 4. 18  29 5. 98  402 6. 71  874 7. 61  $216 8. 42  605 9. 81  350 10. 23  999 11. 85  1,211 12. 71  2,118  13. 19  6,302 14. 29  7,907 Algebra & Functions © McGraw-Hill School Division 15. 98  27 Estimate to compare. Write  or . 3,000 16. 37  196 8,000 17. 42  84 3,200 18. 498  16 100,000 19. 21  423 8,000 20. 589  36 24,000 21. 59  689 42,000 22. 49  188 10,000 23. 224  41 8,000 24. 26  42 34  21 25. 15  47 59  68 26. 34  82 37  58 Problem Solving 27. The price of a bus ticket is $58. About how much will tickets for a group of 62 passengers cost? Use with Grade 4, Chapter 6, Lesson 6, pages 246–247. (187) 28. An airline ticket costs $375. About how much will tickets cost for a group of 25 people? NS 3.2, 3.3 Print This Page Name Print This 6–6 Page Estimate Products R RETEACH You can round to estimate products. Round each number to its greatest place. Then multiply using patterns with zeros Estimate 42  59. 42  59 40  60 2,400 Estimate 74  229. 1 zero  1 zero 2 zeros 227  74 200  70 14,000 2 zeros  1 zero 3 zeros Estimate each product by rounding. 3. 2. 1. 54  19 788  51 $29  32 © McGraw-Hill School Division Estimate each product. 4. 37  49 5. 23  51 6. 69  19 7. 26  $72 8. 19  315 9. 85  263 10. 72  803 11. 48  1,056 12. 92  2,228 13. 57  $5,698 14. 76  6,419 15. 12  9,058 16. 55  4,830 17. 92  1,568 Use with Grade 4, Chapter 6, Lesson 6, pages 246–247. (188) NS 3.2, 3.3 Print This Page Name Print This 6–6 Page Estimate Products E ENRICH Estimation Maze Estimate to find your way out of the maze. First, estimate to find the box in which the answer could be 858. Start in that box. Then, in order, estimate to find and go through the boxes in which the answers are: 3,060 7,308 3,822 78  11 2,278 16,910 34  90 I 26  34 953  48 W U H T 196  77 F O 616  59 819  64 E C 67  34 157  39 706  48 36,344 57  14 39  98 178  95 52,416 P O R 33,888 42  19 87  84 172  24 15,092 M B © McGraw-Hill School Division 6,123 R E Write the letters from the boxes you go through in order. What message do you find? ’ Use with Grade 4, Chapter 6, Lesson 6, pages 246–247. (189) ! NS 3.2, 3.3 Print This Page Name Print This 6–7 Page Multiply Greater Numbers P PRACTICE Multiply. Check that each answer is reasonable 1. 653  27 2. 908  43 3. 412  65 4. 714  36 5. 279  64 6. 309  32 7. $1.26  98 8. 305  77 9. 4,084  43 10. 11. 9,148  16 12. $50.09  31 13. 2,007  75 14. $39.85 15. 6,618  91 16. $82.35  72 21,107  42 18. 46,118 19. 92,306  31 20. $123.95  18 17. 7,016  25   74 27 21. 53  36,219  22. 26  $591.05  23. 36  19,962  24. 71  23,401  © McGraw-Hill School Division Algebra & Functions Given each set of digits, make the greatest and least product possible by multiplying by a 2-digit number. Use each digit one time. 25. 5, 2, 6, 1 26. 7, 9, 2, 0 Problem Solving 27. A box holds 250 ping pong balls. How many ping pong balls can be packaged in 85 boxes? Use with Grade 4, Chapter 6, Lesson 7, pages 250–253. (190) 28. Pencils are packaged with 144 pencils in a box. How many pencils are there in 50 boxes? NS 3.2, 3.3 Print This Page Name Print This 6–7 Page Multiply by Greater Numbers R RETEACH You can use a place-value chart to multiply greater numbers. Multiply 25  3,188. Estimate: 30  3,000  90,000 Step 1 Multiply by the ones. Regroup if necessary. Thousands 1. Step 2 Multiply by the tens. Regroup if necessary. Ones Thousands H T O H T O 3  Step 3 Add the products. Ones Thousands H T O H T O 4 3 1 7 8 2 5 1 5 8 9 0  Ones H T O H T O 1 1 1 1 3 4 3 4  3 1 7 8 2 5 1 5 8 9 0   6 3 5 6 0  3 1 7 8 2 5 1 5 8 9 0 6 3 5 6 0 7 9 4 5 0 Since 79,450 is close to the estimate of 90,000, the answer is reasonable. Multiply. Thousands 1. Ones Thousands 2. H T O H T O Ones Thousands 3. H T O H T O Ones H T O H T O 2 1 4 5 7 2 5 © McGraw-Hill School Division  1 2 9 3 1 8     4. $3.69  18 8. 4,484  72  5. 518  49 9. 85  2 0 0 6 1 3  6. 6,735  37 $116.95  Use with Grade 4, Chapter 6, Lesson 7, pages 250–253. (191) 7. 8,098  66 10. 52  19,071 NS 3.2, 3.3 Print This Page Name Print This 6–7 Page Multiply Greater Numbers E ENRICH Quick Check Here is a quick way to check the product for 14  1,456. Step 1 Add the digits in each number. Add again if the sum has two digits. 1,456 ← 1  4  5  6  16,  14 ← 1  4  5 20,384 ← 2  0  3  8  4  17, 167 178 Step 2 Step 3 Multiply the two numbers you got from adding the factors. Compare the sum you got from adding the digits in the product for 14  1,456 to the sum you got in Step 2. Then add the digits in the product. 7 5 35 8  8, so the product 20,384 is correct. 3 5 8 © McGraw-Hill School Division Use the method shown above to check each problem. Draw an X next to any incorrect product. Then find the correct product. 1. 314  57 17,896 2. 815  32 26,090 3. 742  68 50,456 4. 689  24 16,536 5. 537  49 26,213 6. 496  71 35,216 7. 2,214  88 193,832 8. 3,418  92 314,456 9. 4,372  15 65,480 11. 7,498  45 337,410 12. 9,455  76 707,580 10. 8,432  37 311,984 Use with Grade 4, Chapter 6, Lesson 7, pages 250–253. (192) NS 3.2, 3.3 Print This Page Name Print This 6–8 Page Problem Solving: Strategy P PRACTICE Make a Graph Make a graph for the data in the table. Use data from the graph to solve problems 1 and 2. Boat Rentals at Lake Willow in July and August Type of Boat Income from Boat Rentals Sailboats $1,300 Rowboats $1,100 Paddle boats Canoes 1. Which type of boat generated the most income? 3. A beach sells 1,000 passes in 1998; © McGraw-Hill School Division 1,200 passes in 1999; and 1,100 passes in 2000. Suppose you make a pictograph in which each symbol stands for 200 passes. How many symbols would you make for each year? $800 $1,000 2. Which type of boat generated the least income? 4. Suppose you make a graph for the data in problem 3 in which each symbol stands for 100 passes. How many symbols would you make for each year? Mixed Strategy Review Solve. Use any strategy. 5. Time Elliot returns from the beach at 4:30 P.M. He spent 2 hours at the beach. It takes 15 minutes for Elliot to travel from his home to the beach. What time did Elliot leave home to go to the beach? 6. Create a problem for which you would make a graph to solve. Share it with others. Strategy: Use with Grade 4, Chapter 6, Lesson 8, pages 254–255. (193) SDP 1.1; MR 2.3, 2.4, 3.2 Print This Page Name Print This 6–8 Page Problem Solving: Strategy R RETEACH Make a Graph Page 255, Problem 2 Which contest had the most people? The least? Sandcastle Building Contests Location Number of People Port Aransas, TX Wenatchee, WA Seal Beach, CA Atlantic City, NJ Malibu, CA 1,250 1,675 1,775 1,525 1,375 Step 1 Read Be sure you understand the problem. Read carefully. What do you know? • You know how many . What do you need to find? • You need to find . Step 2 Plan © McGraw-Hill School Division ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ Find a Pattern Guess and Check Work Backward Make a Graph Make a Table or List Write a Number Sentence Draw a Diagram Solve a Simpler Problem Logical Reasoning Act it Out Make a plan. Choose a strategy. A graph can help you compare data quickly. Make a bar graph to solve the problem. Use with Grade 4, Chapter 6, Lesson 8, pages 254–255. (194) SDP 1.1; MR 2.3, 2.4, 3.2 Print This Page Name Print This 6–8 Page Problem Solving: Strategy R RETEACH Make a Graph Step 3 Carry out your plan. Make a bar graph. Solve Sandcastle Building Contest Location Port Aransas,TK Wenatchee, WA Seal Beach, CA Atlantic City, NJ Malibu, CA 100 200 300 400 500 600 700 800 900 1,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 Number of People The contest at: has the most people. has the least people. Step 4 © McGraw-Hill School Division Look Back Is the solution reasonable? Reread the problem. Does your answer match the data given in the problem? Yes No What other kind of graph could you use to compare the data? Practice 1. The Lakefront Swim Club had 400 members in 1970, 250 members in 1980, 600 members in 1990, and 550 members in 2000. Make a graph that displays this data. Use with Grade 4, Chapter 6, Lesson 8, pages 254–255. (195) 2. In which year did the Lakefront Swim Club have the most members? the least members? SDP 1.1; MR 2.3, 2.4, 3.2 Print This Page Name Print This 6–9 Page P Multiply Using Mental Math PRACTICE Multiply. Use mental math. 1. 12  30  2. 40  21  3. 34  11  4. 55  18  5. 60  14  6. 70  31  7. 44  22  8. 80  51  9. 90  9  10. 25  50  11. 30  26  12. 24  40  13. 44  15  14. 52  11  15. 15  16  16. 35  22  17. 61  30  18. 20  48  19. 30  19  20. 65  40  21. 48  40  22. 16  21  23. 25  28  24. 59  61  25. 50  14  26. 35  21  27. 70  49  28. 11  62  29. 90  42  30. 22  55  Algebra & Functions 31. Rule: Multiply by 35. Input Output © McGraw-Hill School Division 32. Complete each table. 20 700 31 1,085 42 1,470 110 3,850 130 4,550 75 1,200 100 1,600 220 3,520 Rule: Multiply by 16. Input Output 15 240 25 400 Problem Solving 33. Teams of 16 students are helping clean the park. There are 21 teams. How many students in all are helping clean the park? Use with Grade 4, Chapter 6, Lesson 9, pages 256–257. (196) 34. Students are going on a field trip in 20 buses. Each bus carries 35 students. How many students are going on the field trip? NS 3.2, 3.3 Print This Page Name Print This 6–9 Page Multiply Using Mental Math R RETEACH You can multiply using mental math. Compensation Multiply one factor by a number. Divide another factor by the same number. Compatible Numbers Break apart one number and multiply. Then add. 25  16  (25  2)  (16  2) 25  16  (25  10)  (25  6) 50   400 8  250 150  400 Multiply mentally. Use compensation. 1. 35  40  (35   )  (40   )  2. 60  25  (60   )  (25   )  Multiply mentally. Use compatible numbers. 3. 15  16  (   16)  (5   )  4. 22  30  (   30)  (   30)  © McGraw-Hill School Division Multiply. Use mental math. 5. 20  45  6. 15  28  7. 11  72  8. 75  20  9. 36  40  10. 50  23  11. 44  25  12. 70  18  13. 59  71  14. 99  10  15. 60  73  16. 45  36  17. 53  11  18. 32  26  19. 80  61  20. 70  19  21. 65  16  22. 35  90  23. 25  25  24. 80  18  25. 26  23  26. 11  37  27. 55  27  28. 75  30  29. 62  10  30. 25  45  31. 50  88  Use with Grade 4, Chapter 6, Lesson 9, pages 256–257. (197) NS 3.2, 3.3 Print This Page Name Print This 6–9 Page Multiply Using Mental Math E ENRICH Circle Race You will need: Play with a partner. • Write each of these numbers on an index card: 12 15 18 25 30 35 10 index cards 50 60 200 400 • Mix up the cards and then place them facedown between you and your partner. Draw a card. Write the number in the center of your circle. Use mental math to multiply each number on the circle by the number in the center. The first person to complete the circle with correct answers scores 1 point. • Erase the number in the center. Repeat the activity until all the cards have been drawn. The person with the greater number of points wins. 18 33 © McGraw-Hill School Division 24 16  14 40 300 22 Use with Grade 4, Chapter 6, Lesson 9, pages 256–257. (198) NS 3.2, 3.3 Print This Page Name Problem Solving: Application Print This Page 6–10 Part A WORKSHEET Decision Making Applying Multiplication Record your data. © McGraw-Hill School Division Sailboats Rowboats Paddle boats Canoes Your Decision Which boat or boats will the family rent? How long will they ride? Explain. Use with Grade 4, Chapter 6, Lesson 10, pages 258–259. (199) NS 1.2, 3.3; MR 1.1, 2.3 Print This Page Name Print This Page 6–10 Part B WORKSHEET Problem Solving: Application Math & Science How many times does your heart beat each day? Record your data in the table below. Time Estimate Actual Heart Beats Each minute Each hour Each day Each year Show how you estimated the number of heart beats in each hour, each day, and each year. Each day Each year © McGraw-Hill School Division Each hour Use with Grade 4, Chapter 6, Lesson 10, pages 260–261. (200) NS 3.2, 3.3; MR 1.1, 3.3 Print This Page Name Print This Page 6–10 Part B WORKSHEET Problem Solving: Application Math & Science How many times does your heart beat each day? 1. Why would it be difficult to count the number of heart beats in a day? Explain how math made your job easier. 2. Round the number of beats for a day to the nearest 10,000. Collect the data for the whole class. What was the range of heartbeats? What number was most common? 3. Make a bar graph to display the data © McGraw-Hill School Division from the class. 4. Marty’s heart beats 70 times each minute. Tamara’s heart beats 60 times each minute. How many more times does Marty’s heart beat each day? Show your work. 5. Explain how exercise can reduce the number of times your heart beats each day. Use with Grade 4, Chapter 6, Lesson 10, pages 260–261. (201) NS 3.2, 3.3; MR 1.1, 3.3 Print This Page Name Print This 7–1 Page Division Patterns P PRACTICE Complete. 1. 48  6  2. 35  5  3. 16  4  480  6  350  5  160  4  4,800  6  3,500  5  1,600  4  Divide. 206 R2 50 4. 3 620 5. 5 250 $70 $90 80 9. 3 $270 8. 2 160 700 800 13. 5 3,500 12. 9 7,200 $600 400 16. 7 $4,200 17. 9 3,600 80 6. 6 $420 7. 7 560 70 60 11. 8 560 10. 4 240 700 14. 4 2,800 600 18. 3 1,800 $700 15. 6 $4,200 4,000 19. 2 8,000 20. 120  2  21. $240  3  22. 810  9  23. $450  5  24. 630  7  25. 540  9  26. 3,000  6  27. $7,200  8  28. 4,800  8  29. 3,200  8  30. 5,600  7  31. $3,600  4  Algebra & Functions Write the missing number. © McGraw-Hill School Division 32. 200   50 33. 450  5  35.  6  40 36. 200  38.  4  600 39. 1,500  34. 630   40 37.  500  90  8  80 40. 3,000  5  Problem Solving 41. There are 150 students in 3 buses. Each bus carries the same number of students. How many students are on each bus? Use with Grade 4, Chapter 7, Lesson 1, pages 276–277. (202) 42. A pet shop has 160 fish in aquariums. Each aquarium has 40 fish. How many aquariums of fish are there? NS 3.2, 3.4; MR 3.2 Print This Page Name Print This 7–1 Page Division Patterns R RETEACH You can divide mentally by using basic division facts and looking for a pattern. Divide. Count the zeros. 120  3  40 1,200  3  400 → → → 12  3  4 Think: The basic fact is 40  8  5. no zeros 40  8  5 1 zero 400  8  50 2 zeros 4,000  8  500 → → → Think: The basic fact is 12  3  4. no extra zeros 1 extra zero 2 extra zeros Complete. 1. 15  3  150  3  200  5  1,500  3  2,000  5  3. 32  4  4. 30  6  320  4  300  6  3,200  4  3,000  6  5. 35  5  © McGraw-Hill School Division 2. 20  5  6. 45  9  350  5  450  9  3,500  5  4,500  9  7. 48  8  8. 64  8  480  8  640  8  4,800  8  6,400  8  9. 180  2  10. 360  4  11. 700  7  1 2. 360  6  13. 540  9  14. 1,400  2  15. 4,200  7  16. 2,700  9  17. 4,900  7  Use with Grade 4, Chapter 7, Lesson 1, pages 276–277. (203) NS 3.2, 3.4; MR 3.2 Print This Page Name Print This 7–1 Page Division Patterns E ENRICH Geography Riddles Find each missing number. Solve the riddles by placing the letter from each exercise in the blank above the matching answer number. M 1. 140  7  3. 4,200  700 5. 3,500   700 7.  3  700 O H E  9  40 4.  2  800 6.  4  30 8. 320   400 S 10. 11. 5,600   700 S 12. 240  13. 5,400   600 L 14. 2,700  3  N  9  90  80 16. 800  17. 150  3  M 18.  7  60 19. 120  2  S 20.  8  400 C 22. 810  9  What city likes to wander? Which people are always in a hurry? What country is always cold? Use with Grade 4, Chapter 7, Lesson 1, pages 276–277. (204) I E I What state reminds you of part of a lion? A R 15. 720  9   5  800 A  80 9. 2,800  21. © McGraw-Hill School Division U 2. R  400 E I N 20 4 3 120 420 2 6 50 900 810 360 60 4,000 5 80 7 3,2001,600 90 9 8 2,100 NS 3.2, 3.4; MR 3.2 Print This Page Name Print This 7–2 Page Explore Division P PRACTICE Write a division sentence for each model. 1. 2. 3. 4. 5. 6. Find each quotient. You may draw place-value models. 3 R2 7. 6 20 12 R3 11. 4 51 16 R3 © McGraw-Hill School Division 15. 6 99 3 R5 9 R1 8. 8 29 9. 4 37 13 R1 13 12. 5 66 13. 6 78 14 27 R1 16. 7 98 17. 2 55 3 R6 10. 9 33 11 R6 14. 7 83 49 R1 18. 2 99 19. 41  9  20. 62  9  21. 59  7  22. 88  3  23. 73  5  24. 58  4  25. 67  6  26. 77  7  27. 43  2  Problem Solving 28. Books are packed in boxes of 9. If 67 books are packed, how many full boxes will there be? How many books will be left over? Use with Grade 4, Chapter 7, Lesson 2, pages 278–279. (205) 29. Ping pong balls are packed in boxes of 6. If 59 ping pong balls are packed, how many full boxes will there be? How many ping pong balls will be left over? NS 3.2, 3.4 Print This Page Name Print This 7–2 Page Explore Division R RETEACH You can use models to help you divide. Divide 86  3. Show 86. Place 2 tens in each of 3 groups. Regroup the 2 tens that are left as 20 ones. You can divide the 26 ones into 3 groups of 8 with 2 left over. You can divide 86 cubes into 3 groups of 28 with 2 left over. So, 86  3  28 R2. Divide. You may use models to help you. 1. 2. 58  4  37  2  © McGraw-Hill School Division 3. 4. 49  4  68  3  Divide. 5. 43  2  6. 25  2  7. 42  4  8. 82  5  9. 48  4  10. 78  9  Use with Grade 4, Chapter 7, Lesson 2, pages 278–279. (206) NS 3.2, 3.4 Print This Page Name Explore Division Print This 7–2 Page E ENRICH Remainder Rules You can use divisibility rules to find out if a number will have a remainder. Divisibility Rules A number is divisible by: 2 if the ones digit is 0, 2, 4, 6, or 8. 6 if it is divisible by both 2 and 3. 3 if the sum of its digits is divisible by 3. 9 if the sum of its digits is divisible by 9. 5 if the ones digit is 0 or 5. 10 if the ones digit is 0. 1. If you divide 315 by 5, will there be a remainder? How do you know? Divide to prove your answers. 2. If you divide 691 by any 1-digit number, will there be a remainder? How do you know? © McGraw-Hill School Division Divide to prove your answer. 3. Think about dividing a 3-digit number by each of the following 1-digit numbers: 2, 3, 4, 5, 6, 7, 8, 9. Which divisions will have remainders? Which divisions will not have remainders? Prove your answers. Use with Grade 4, Chapter 7, Lesson 2, pages 278–279. (207) NS 3.2, 3.4 Print This Page Name Print This 7–3 Page Divide 3-Digit Numbers P PRACTICE Divide. Check your work. $135 349 1. 2 698 130 R1 2. 5 $675 3. 3 391 28 R7 111 R2 $0.67 6. 8 231 5. 5 557 11. 3 935 119 R3 361 R1 13. 7 903 15. 7 836 14. 2 723 111 $37 62 R5 17. 9 999 8. 8 995 311 R2 10. 6 $6.72 129 124 R3 7. 4 $2.68 $1.12 99 R2 9. 4 398 18. 6 377 112 R1 4. 7 785 91 R2 12. 5 457 93 R1 16. 8 745 111 R2 19. 8 $296 20. 7 779 21. 215  3  22. 367  5  23. 467  2  24. 593  4  25. 298  6  26. 506  7  27. Divide 726 by 7. 28. Divide 834 by 5. 29. Divide 909 by 8. Algebra & Functions Find each missing number. 30. 1,065  © McGraw-Hill School Division 33. n  213 b  8  116 36. (250 + 14)  31. c  4  168 34. 585  x  44 32. 690  d  195 37. (700 + y)  7  106 35. m  345 t  9  111 38. 756  (r + 3)  126 Problem Solving 39. Morgan is planting 906 pine seedlings in rows. She plants 8 pine seedlings in each row. How many rows are there? How many seedlings are left? Use with Grade 4, Chapter 7, Lesson 3, pages 280–283. (208) 40. The school bought 2,880 tickets to the circus. The tickets will be divided equally among 9 classes. How many tickets will each class get? NS 3.2, 3.4 Print This Page Name Print This 7–3 Page Divide 3-Digit Numbers R RETEACH Divide 8 425 . Step 1 Divide the hundreds. Think: 4  8. There aren’t enough hundreds. 8 425 Step 2 Divide the tens. Bring down the tens. Divide the tens. Step 3 Divide the ones. Bring down the ones. Divide the ones. 5 8 425 40 Multiply: 8  5  40 2 Subtract: 42  40  2 53 R1 8 425 40 25 24 Multiply: 8  3  24 1 Subtract: 25  24  1 The remainder is 1. Check your answer: 53  8  1  425 Complete. 1. 2 2 8 36 8 4 6   2. 8 6 2 4 2 4 0 1 4 3 R 57 1 7 5  2 3. 8 9 R 76 2 4 5 6 2 1 2 0 1 7  1 5 2  1 6 4 6 3 1 © McGraw-Hill School Division Find each quotient. 143 R1 4. 4 573 248 R1 8. 3 745 69 R4 152 R4 5. 5 349 139 9. 7 973 6. 5 764 94 R8 10. 9 854 41 R6 7. 7 293 288 R2 11. 3 866 12. 662  5  13. 571  8  14. 927  4  15. 745  3  16. 680  5  17. 571  6  Use with Grade 4, Chapter 7, Lesson 3, pages 280–283. (209) NS 3.2, 3.4 Print This Page Name Print This 7–3 Page Divide 3-Digit Numbers E ENRICH Short Division Short division is a quick way to divide. Here is how it works. Divide 6 892 . Step 1 Step 2 Step 3 Divide the hundreds. Multiply and subtract mentally. Write the difference in front of the digit in the tens place. Divide the tens. Multiply and subtract mentally. Write the difference in front of the digit in the ones place. Divide the ones. Multiply and subtract mentally. Write the remainder as part of the quotient. 1 6 8292 Think: 6  1  6 862 14 6 82952 Think: 6  4  24 29  24  5 1 4 8 R4 6 82952 Think: 6  8  48 52  48  4 Step 1 Step 2 Step 3 Divide the hundreds. Divide the tens. Divide the ones. 8 653 Think: 8  1  8, not enough hundreds. 8 8 6513 Think: 8  8  64, 65  64  1. 8 1R5 8 6513 Think: 8  1  8, 13  8  5. Divide 8 653 . Use short division to divide. 171 1. 2 342 164 R3 © McGraw-Hill School Division 4. 5 823 111 R6 7. 8 894 72 10. 6 432 65 R2 13. 5 327 118 16. 8 944 253 R2 2. 3 761 157 5. 6 942 96 R3 8. 9 867 52 R1 11. 7 365 69 R3 14. 9 624 95 R7 17. 9 862 Use with Grade 4, Chapter 7, Lesson 3, pages 280–283. (210) 155 R3 3. 4 623 131 R1 6. 7 918 73 R5 9. 6 443 61 R4 12. 7 431 61 R4 15. 8 492 131 R5 18. 6 791 NS 3.2, 3.4 Print This Page Name Print This 7–4 Page Zeros in the Quotient P PRACTICE Divide. Check your answer. 1. 206 R2 2. $105 6. 3 620 5. 109 R4 10. 103 R2 14. 108 R4 18. 490 R1 22. 2 981 4. $1.09 8. 106 R6 11. 10 R8 15. 106 R7 19. 208 R3 23. 101 R4 12. 70 R1 16. 109 R3 20. 103 R6 24. 206 R3 4 827 6 657 7 727 409 R1 2 819 3 211 4 835 102 9 918 8 812 8 855 209 R3 4 839 7 $7.63 9 98 5 544 21. 7. 7 748 6 620 17. $1.07 10 R2 9 92 8 $8.56 5 549 13. 3. 2 419 6 $630 9. 209 R1 305 R2 3 917 50 R6 8 406 25. 823  4  26. 704  5  27. 981  2  28. 920  3  29. 916  7  30. 845  6  31. 885  8  32. 954  5  33. 965  6  © McGraw-Hill School Division Find only those quotients that are greater than 200. 34. 992  3  35. 920  9  36. 619  3  37. 747  4  38. 818  2  39. 540  2  Problem Solving 40. Jenna earns $636 in 6 months by babysitting. If divided evenly, how much is that a month? Use with Grade 4, Chapter 7, Lesson 4, pages 284–285. (211) 41. A family of 4 spent $824 during their vacation. If divided evenly, how much is that per person? NS 3.2, 3.4 Print This Page Name Print This 7–4 Page Zeros in the Quotient R RETEACH Divide 3 629 . Follow the steps below. Step 1 Divide the hundreds. Step 2 Divide the tens. Step 3 Divide the ones. Think: 3  2  600 The first digit is in the hundreds place. Bring down the tens. There are not enough tens to divide. Trade 2 tens for 20 ones. Bring down the ones. Divide the ones. 2 3 629 Multiply: 3  2  6 6 Subtract: 6  6  0 0 Compare: 0  6 20 3 629 There are not enough 6 tens to divide. Write 02 a 0 in the quotient. Compare: 0  4 209 R2 3 629 6 029 27 Multiply: 3  9  27 2 Subtract: 29  27  2 Check your answer: 209  3  2  629 Complete. 1. 3 0 8 R 39 2 6 9  2 2. 2 6 2 4 2 3. 1 0 7 66 4 2 6  2 0 R 3 71 4 3 1 4 4 2 4 2 0 3 Divide. © McGraw-Hill School Division $204 4. 4 $816 307 R1 8. 2 615 109 R2 105 R1 5. 4 438 180 R1 9. 2 361 6. 3 316 209 R1 10. 3 628 109 R2 7. 7 765 $70 11. 3 $210 12. 912  9  13. 452  5  14. 662  3  15. 965  6  16. 905  3  17. 734  7  Use with Grade 4, Chapter 7, Lesson 4, pages 284–285. (212) NS 3.2, 3.4 Print This Page Name Print This 7–4 Page Zeros in the Quotient E ENRICH Pick a Winner Pick divisors from the list below to create 20 division exercises. Then complete the exercises. If you have a zero in the quotient, give yourself 2 points. If you do not have a zero in the quotient, give yourself 1 point. Divisors: 1, 2, 3, 4, 5, 6, 7, 8, 9 1. 6. 302 2 604 110 R5 7 775 106 R4 8 852 101 R4 5. 103 R1 6 619 10. 201R6 9 1,815 2. 390 R1 2 781 3. 7. 105 R3 4 423 8. 13. 3 211 14. 2 321 15. 7 354 18. 40 R3 8 323 19. 302 3 906 20. 403 2 806 11. 4 363 12. 120 R5 6 725 16. 20 R4 5 104 17. 109 5 545 90 R3 4. 170 1 170 5 509 109 R3 9. 70 R1 8 875 160 R1 50 R4 Total Points Earned: © McGraw-Hill School Division 21. Think about dividing a 3-digit number by a 1-digit number. When will you get a quotient with a zero in the tens place? Give an example. Use with Grade 4, Chapter 7, Lesson 4, pages 284–285. (213) NS 3.2, 3.4 Print This Page Name Print This 7–5 Page Problem Solving: Reading for Math P PRACTICE Reading Skill Interpret the Remainders Circle the correct word(s) or number(s) to make each statement true. 1. The Art Club sells T-shirts for $8. Ms. Demming has $92. Ms. Demming can buy 11 1 11 2 12 T-shirts. If Ms. Demming buys the greatest possible number of T-shirts, she will have $ 0 $4 $8 left. Explain your thinking: 2. There are 124 people at the Howard School Sports Dinner. They sit at tables that have 8 seats each. The school needs There are 7 15 16 7 or 8 tables. people at each table. Explain your thinking: 3. Manny and two friends are paid $100 for setting up a new computer in the school’s math lab. They each do the same amount of work. Manny earns more than Each friend earns the same as more than his friends. less than $30. © McGraw-Hill School Division Explain your thinking: 4. There are 75 students going to the art museum. They will ride in vans that can hold 6 students. There will be 12 13 There are 5 5 or 6 Explain your thinking: vans. students in each van. Use with Grade 4, Chapter 7, Lesson 5, pages 286–287. (214) NS 3.4; MR 1.1, 2.4, 2.6, 3.1, 3.2 Print This Page Name Print This 7–5 Page Problem Solving: Reading for Math P Interpret the Remainders PRACTICE Math Skills Test Prep Choose the correct answer. There are 94 people who volunteer to clean the park. They will form as many groups of 4 as possible. How many groups of 4 can they make? 1. Which of the following statements 2. How do you interpret the remainder is true? to solve this problem? A They will make 4 groups. F Use only the quotient. B Everyone can be in a group of 4. G Use only the remainder C There are 94 volunteers. H Add 1 to the quotient. The after-school baseball league wants to buy 250 baseballs. The baseballs come in boxes of 6. How many boxes will the league need? 3. How do you interpret the remainder 4. How many boxes will the to solve this problem? league need? A Use only the quotient. F 41 boxes B Use only the remainder. G 42 boxes C Add 1 to the quotient. H 43 boxes The Computer Club has $80 to buy disks. A box of disks costs $7. There is no sales tax. How many boxes of disks can the club buy? © McGraw-Hill School Division 5. Which of the following statements 6. How do you interpret the remainder is false? to solve this problem? A Each box of disks costs $7. F Add 1 to the quotient. B All of the money will be spent. G Use only the quotient. C The computer club has $80 to buy disks. H Use only the remainder. Use with Grade 4, Chapter 7, Lesson 5, pages 286–287. (215) NS 3.4; MR 1.1, 2.4, 2.6, 3.1, 3.2 Print This Page Name Print This 7–5 Page Problem Solving: Reading for Math P Interpret the Remainders PRACTICE Math Skills Test Prep Choose the correct answer. The Art Club makes $4 on each T-shirt it sells. How many shirts does the club need to sell to raise $75? 7. How do you interpret the remainder 8. How many shirts does the club need to solve this problem? to sell to raise $75? A Add 1 to the quotient. F 3 shirts B Use only the quotient. G 18 shirts C Use only the remainder. H 19 shirts Solve. 9. There are 72 students in the Hockey Club. How many teams of 5 can they make? 11. Paint sets cost $6. The Art Club has $93. If the club buys as many paint sets as it can, how much money will be left over? © McGraw-Hill School Division 13. There are 64 members in the Science Club. They travel to the science fair in cars that can hold 5 members each. How many cars are needed? 15. Each song played by a DJ is 4 minutes long. How many songs does he play in a music set that is 30 minutes long? Use with Grade 4, Chapter 7, Lesson 5, pages 286–287. (216) 10. The Hockey Club buys 128 ounces of juice. How many 7-ounce cups can they pour? 12. There are 132 students at a meeting. The seats are arranged in rows of 8. How many rows of seats are needed? 14. There are 83 students. They will sit in rows of 6 seats each. They will start at the front row and fill as many rows as they can. How many students will be in the last row? 16. The DJ’s assistant distributes neon sunglasses to 50 people at a party. There are 6 glasses in a box. How many boxes should she open? NS 3.4; MR 1.1, 2.4, 2.6, 3.1, 3.2 Print This Page Name Print This 7–6 Page Estimate Quotients P PRACTICE Estimate. Choose compatible numbers. 20 1. 2 43 6. 3 159 40 8 650 5 209 4 3,105 2,000 15. 5,000 16. 3 5,896 © McGraw-Hill School Division 7 2,011 800 14. 6 3,124 300 12. 9 831 500 13. 9 286 90 11. 30 8. 2 131 40 10. 7 501 70 7. 70 4. 6 521 4 171 80 9. 90 3. 4 71 50 5. 20 2. 9 46,999 17. 65  3 18. 98  5 19. 22  3 20. 381  8 21. 555  6 22. 640  7 23. 468  9 24. 309  5 25. 481  7 26. 281  3 27. 349  4 28. 412  5 29. 4,124  6 30. 1,912  9 31. 1,714  2 32. 2,186  4 33. 2,904  7 34. 4,711  8 Problem Solving 35. Marta travels a total of 850 miles every month to San Francisco for business. If she goes 3 times a month, about how many miles is each round trip? Use with Grade 4, Chapter 7, Lesson 6, pages 288–289. (217) 36. Jeff went on a bike trip of 173 miles to Austin. It took him 9 days. About how many miles did he travel each day? NS 3.2, 3.4 Print This Page Name Print This 7–6 Page Estimate Quotients R RETEACH Compatible numbers are numbers you can divide easily. You can use compatible numbers to estimate quotients. Estimate 351  4. Think: What basic division fact is close to 35  4? 36  4  9 360  4  90 So, 351  4 is about 90. Estimate 435  7. Think: What basic division fact is close to 43  7? 42  7  6 420  7  60 So, 435  7 is about 60. Complete. 1. Estimate 430  9. 2. Estimate 279  3. Division fact: 45  9  Division fact: 27  3  Estimate: 450  9  Estimate: 270  3  3. Estimate 299  5 4. Estimate 319  4. Division fact: Division fact: Estimate: Estimate: 5. Estimate 562  6. 6. Estimate 631  8. Division fact: Division fact: Estimate: Estimate: © McGraw-Hill School Division Estimate. Circle the letter of the division sentence with the compatible number. Then complete the division. 7. 122  4 a. 120  4  b. 100  4  8. 349  7 a. 360  7  b. 350  7 9. 272  9 a. 270  9  b. 280  9  10. 292  5 a. 300  5  b. 290  5  11. 453  9 a. 480  9  b. 450  9  Use with Grade 4, Chapter 7, Lesson 6, pages 288–289 (218) NS 3.2, 3.4 Print This Page Name Print This 7–6 Page Estimate Quotients E ENRICH The Treasure State Rewrite each exercise using compatible numbers. Write the estimated quotient. 1. 7 428 60 420 2. 3 605 5. 9 8,140 900 8,100 8. 6 3,546 600 3,600 4. 7. 10. 9 98 5 5,165 10 90 200 600 4 316 1,000 5,000 500 4,000 6. 8 3,999 9. 2 196 100 200 12. 8 725 90 720 11. 80 320 3. 20 80 4 85 5 5,620 1,100 5,500 13. Write the estimated quotient beside each exercise number below. The first one is done for you. Then cross out the letters above quotients with two digits. Circle the letters above quotients with three or more digits. H © McGraw-Hill School Division 11. 90 I 9. T 6. A 5. M 8. D 10. O 7. N 2. B 1. N 4. P 3. A 12. 14. Rearrange the circled letters to spell the name of the Treasure State. 15. Show how to estimate 605  3. Use with Grade 4, Chapter 7, Lesson 6, pages 288–289. (219) NS 3.2, 3.4 Print This Page Name Print This 7–7 Page Divide 4-Digit Numbers P PRACTICE Divide. Check your answer. 1. 2. 1,487 5 7,435 5. $4,028 3. 431 7. 2 $8,056 6. 303 7 2,121 1,306 R3 901 R5 6 5,411 2,027 R2 3 6,083 4 5,227 8 3,448 8. $811 9 $7,299 9. 5,647  4  10. 3,409  2  11. $6,456  8  12. 3,568  6  13. 5,598  5  14. 1,841  2  15. 9,049  7  16. $1,350  5  17. Divide $4,032 by 8. 4. 18. Divide 1,526 by 3. 19. Divide 5,732 by 9. 21. 2,814 7 22. 4,9497 Compare. Write  or . © McGraw-Hill School Division 20. 1,6442 1,9323 2,4186 3,598  4 Problem Solving 23. The mountain bike club wants to raise $4,464 for 9 new bicycles. If each bicycle costs the same amount, how much does each bicycle cost? Use with Grade 4, Chapter 7, Lesson 7, pages 290–293. (220) 24. The Let’s Grow club makes and sells hot sauce. The club grows 1,083 peppers. Each jar of hot sauce contains 3 peppers. How many jars can the club make? NS 3.2, 3.4 Print This Page Name Print This 7–7 Page Divide 4-Digit Numbers R RETEACH When you divide 4-digit numbers, begin by deciding where to place the first digit in the quotient. You can see the quotient will have 3 digits. Divide 3,154  6. Think: You cannot divide 3 by 6. Divide 31 by 6. Write 5 in the quotient above the 1. 5_ _ 6 3,154 Complete. 1. 5 1 6 3 1, 5 4 9 1 5   R 1 2. 1 9 1 3 4 7, 6 5 3 4 4 3 1 9 1 8 1  R 1 3. 3 6 3 6 0 5  4 1 3  1 2 1  Divide. © McGraw-Hill School Division 4. 694 R2 5. 1,159 R3 9. 5 3,472 8. 8 9,275 712 R2 6. 1,009 R1 10. 7 4,986 6 6,055 $656 2,558 R1 2 5,117 13. 7,087  5  14. 3,393  4  15. $6,426  3  R 1 1 5 1 4 1 6  1 6 0 3  2 1 7. 4 $2,624 12. 1,671  8  Use with Grade 4, Chapter 7, Lesson 7, pages 290–293. (221) 4 7 8 1 2 9, 5 6 3 8 457 R2 3 1,373 11. 1,090 R8 9 9,818 NS 3.2, 3.4 Print This Page Name Print This 7–7 Page Divide 4-Digit Numbers E ENRICH Greatest Remainder Game Play with a partner. Take turns. • Place your marker on START. Solve one of the exercises below. Then move your marker the same number of spaces as the remainder. • The winner is the first player to reach END. 203 R1 6 1,219 965 R3 4 3,863 967 R2 6 5,804 674 R1 4 2,697 349 R3 5 1,748 1,377 R1 © McGraw-Hill School Division 7 9,640 868 R3 8 6,947 285 R7 8 2,287 606 R5 6 3,641 1,222 R5 6 7,337 877 R1 3 2,632 1,151 R2 5 5,757 T AR ST Use with Grade 4, Chapter 7, Lesson 7, pages 290–293. (222) 1,165 R4 5 5,829 863 R7 9 7,774 985 653 R3 7 4,574 1,084 R3 4 4,339 451 R4 7 6,895 5 2,259 904 R3 4 3,619 709 R2 8 5,674 607 R3 5 3,038 921 R4 9 8,293 665 R5 6 3,995 430 R3 4 1,723 D EN NS 3.2, 3.4 Print This Page Name Print This 7–8 Page Divide 5-Digit Numbers P PRACTICE Divide. Check your answer. 1. 13,168 2. 4,220 R7 6. 7,073 R1 10. 2 14,147 6,447 R2 5,333 4. 26,994 2 53,988 7. 7 45,131 8 33,767 9. 3. 4 76,832 5 65,840 5. 19,208 6 $90,384 8. $6,475 3 $19,425 11. 6 31,998 $15,064 3,056 R1 9 27,505 4,615 R4 12. 5 23,079 13. $19,328  4  14. 73,895  9  15. 54,620  5  16. 41,183  2  17. 16,697  6  18. 37,986  8  9,316 R1 7 65,213 Algebra & Functions Find each missing number. 19. $26,480  n  $5,296 20. 71,910  v  7,990 21. 44,356  r  11,089 © McGraw-Hill School Division Problem Solving 22. The King School held Junior Olympic games in its sports stadium for 3 days. Each day, every seat in the stadium was full. A total of 17,748 people sat in the stadium. How many seats does the stadium have? Use with Grade 4, Chapter 7, Lesson 8, pages 294–295. (223) 23. The King School raised $75,288 by selling Junior Olympic banners. Each banner cost $6. How many banners did the school sell? NS 3.2, 3.4 Print This Page Name Print This 7–8 Page Divide 5-Digit Numbers R RETEACH Divide 19,834  4. Step 1: Decide where to place the first digit in the quotient. Think: You cannot divide 1 by 4. Divide 19 by 4. Write 4 in the quotient above the 9. Step 2: Divide. The quotient will have 4 digits. 4,958 R2 4 19,834  16 38 36 23  20 34  32 2 Step 3: Check your work. 4,958  4  19,832; 19,832  2  19,834 Divide. 1. 2. 5 68,084 © McGraw-Hill School Division 5. 3. 3 94,391 6. 7 23,042 4. 7. 6 44,738 8. 5 31,619 9. 15,275  8  10. 39,021  9  11. $45,222  3  12. 19,217  3  13. 74,472  8  14. $33,496  4  Use with Grade 4, Chapter 7, Lesson 8, pages 294–295. (224) 2 $26,856 4 52,273 9 82,445 NS 3.2, 3.4 Print This Page Name Print This 7–8 Page Divide 5-Digit Numbers E ENRICH Crossnumber Puzzle Divide to complete the crossnumber puzzle. Then create and solve your own Across and Down clues. © McGraw-Hill School Division Across Down 1. 37,351  6  1. 43,393  7  31. 47,338  5  4. 20,150  4  54. 65,829  3  6. 17,037  9  1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. Use with Grade 4, Chapter 7, Lesson 8, pages 294–295. (225) NS 3.2, 3.4 Print This Page Name Print This 7–9 Page Find the Better Buy P PRACTICE Find each unit price. Compare to find the better buy. 1. 2 ounces for $6.80 2. 3 gallons for $59.91 4 ounces for $14.00 5 gallons for $94.90 Better buy: Better buy: 3. 4 pounds for $10.92 4. 6 pints for $7.14 7 pounds for $19.53 9 pints for $14.31 Better buy: Better buy: 5. 3 yards for $157.44 6. 5 inches for $48.40 4 yards for $199.80 9 inches for $78.21 Better buy: Better buy: 7. 2 quarts for $99.50 8. 4 feet for $2.08 6 quarts for $315.00 5 feet for $2.10 Better buy: Better buy: Solve. Use the ad to answer exercises 9–12. 9. What is the unit price for a 2-pound bag of wild bird seed? © McGraw-Hill School Division 10. What is the unit price for a 5-pound bag of wild bird seed? 11. What is the unit price of a 9-pound bag of wild bird seed? Sa Wild le on Bird Seed ! 2-pou nd ba g $3.96 for 5-pou nd ba g for $9.4 5 9-pou nd ba g for $15.7 5 12. Which bag of wild bird seed is the best buy? Use with Grade 4, Chapter 7, Lesson 9, pages 298–299. (226) NS 3.2, 3.4; MR 3.2, 3.3 Print This Page Name Print This 7–9 Page Find the Better Buy R RETEACH Products often come in different sizes. You can find the better buy by comparing the unit price of each size. Find the better buy: a 6-ounce jar of pickles for $1.92, or an 8-ounce jar of pickles for $2.80. Step 1 Find the unit prices. Divide the price by the number of ounces. $0.32 6 $1.92 18 12  12 0 $0.35 8 $2.80 24 40  40 0 Step 2 Compare the unit prices. $0.32  $0.35 Think: Write the dollar sign and the decimal point in the quotient. So, the 6-ounce jar of pickles is the better buy. Find each unit price. Compare to find the better buy. 1. 3 gallons of paint for $43.62 unit price: 5 gallons of paint for $75.00 unit price: © McGraw-Hill School Division Better buy: 2. 2 pints for $2.98 3. 3 gallons for $3.69 4 pints for $4.96 5 gallons for $6.60 Better buy: Better buy: 4. 4 yards for $12.72 5. 5 feet for $46.25 6 yards for $20.70 7 feet for $63.35 Better buy: Better buy: 6. 3 cups for $11.22 7. 6 quarts for $55.38 8 cups for $31.52 9 quarts for $80.01 Better buy: Better buy: Use with Grade 4, Chapter 7, Lesson 9, pages 298–299. (227) NS 3.2, 3.4; MR 3.2, 3.3 Print This Page Name Print This 7–9 Page Find the Better Buy E ENRICH Beat This Price! Two grocery stores, the Food Barn and Best Foods, are across the street from each other. The Food Barn placed the ad below in the newspaper. Dog food $10.88 for a 8-pound bag T UNA $1.36/pound T UNA T UNA $0.79/box Three cans of tuna $4.86 NEW! Fresh pasta $3.15 for 9 inches $1.62/can a Dog Food $6.95/pound st $0.65/ounce Six-pack of cranberry juice boxes $4.74 Ju ice Cheddar cheese $34.75 for a 5-pound wheel pa Greek olives $2.60 for a O lives 4-ounce jar Ju ice Food Barn s Weekend Specials! $0.35/inch Best Foods says its prices are lower than the Food Barn’s prices. Find the unit price for each item in the Food Barn ad. Then create an ad for Best Foods. Use the same items, but different amounts; for example, a 7-ounce jar of Greek olives. Best Foods—Our Prices Are Always Lower! © McGraw-Hill School Division Item/Amount Our Price Greek olives: oz Cheddar cheese: pounds Cranberry juice: boxes Dog food: Tuna: Fresh pasta: Our Unit Price pounds cans inches Use with Grade 4, Chapter 7, Lesson 9, pages 298–299. (228) NS 3.2, 3.4; MR 3.2, 3.3 Print This Page Name Print This 7–10 Page P Problem Solving: Strategy PRACTICE Guess and Check Use the guess-and-check strategy to solve. 1. Teri is putting 57 dolls in a display case. She puts the same number on each shelf and has 3 dolls left. The case has more than 7 shelves. How many shelves does the case have? How many dolls does each shelf hold? 3. Jamal buys 59 stickers. Stickers come in packs of 5 or 8. How many of each kind of pack does Jamal buy? 2. A group of friends choose cards equally from a deck of 52 cards. There are more than 6 friends. After they have chosen, 4 cards are left. How many friends are there? How many cards does each friend have? 4. There are 36 students in an auditorium. There are twice as many girls as boys. How many girls are there? How many boys are there? Mixed Strategy Review Solve. Use any strategy. © McGraw-Hill School Division 5. Warren is making a display. He puts 6. Social Studies Each of the 50 1 photo in the first row, 4 photos in the second row, 7 in the third row, and 10 in the fourth row. If the pattern continues, how many photos will Warren put in the fifth row? states in the United States has a state flag. Evelyn wants to make a drawing of each state flag. She has 3 more flags to draw. How many flags has Evelyn drawn? Strategy: Strategy: 7. Sally wants to arrive 20 minutes early for her job. She starts work at 4:15 P.M. It will take her about 20 minutes to walk from school to the job. When should Sally leave? 8. Create a problem which can be solved by using the guess-and-check strategy. Share it with others. Strategy: Use with Grade 4, Chapter 7, Lesson 10, pages 300–301. (229) NS 3.4; MR 1.1, 2.3, 2.4, 3.1, 3.2 Print This Page Name Print This 7–10 Page Problem Solving: Strategy R RETEACH Guess and Check Page 301, Problem 2 Jenny is making sand art. A bottle holds 8 inches of sand. Jenny wants to have 2 inches more of red sand than blue sand. How many inches of sand will she pour? Step 1 Read Be sure you understand the problem. Read carefully. What do you know? • A bottle holds inches of sand. • There will be blue sand. of red sand than What do you need to find? • You need to find how many . Step 2 Plan ■ ■ © McGraw-Hill School Division ■ ■ ■ ■ ■ ■ ■ ■ Find a Pattern Work Backward Use Logical Reasoning Write a Number Sentence Make a Table or List Guess and Check Make a Graph Solve a Simpler Problem Draw a Diagram Act it Out Make a plan. Choose a strategy. List the information you know. Use what you know to make a guess. Guess how many inches of each color sand can be used to make a total of 8 inches. Check your guess. Revise the guess and try again if it is wrong. Guess, check, and revise until you find the answer that makes sense. Use with Grade 4, Chapter 7, Lesson 10, pages 300–301. (230) NS 3.4; MR 1.1, 2.3, 2.4, 3.1, 3.2 Print This Page Name Print This 7–10 Page Problem Solving: Strategy R RETEACH Guess and Check Step 3 Solve Carry out your plan. You know that the bottle holds inches of sand. You know that Jenny wants to have inches of sand than more sand. Guess Start with two numbers that have a sum of 8. Try 6 and 2. Check 6 + 2 = 8 inches of red sand, There are inches of blue sand more inches of red sand. Does that answer fit the problem? Revise 5 + 3 = 8 inches of red sand, There are inches of blue sand more inches of red sand. Does that answer fit the problem? Step 4 © McGraw-Hill School Division Look Back Is the solution reasonable? Reread the problem. Does your answer make all of the statements true? Practice 1. A group of friends share 30 stickers equally, with 3 stickers left over. There are more than 5 friends. How many friends are there? How many stickers does each friend get? Use with Grade 4, Chapter 7, Lesson 10, pages 300–301. (231) 2. Erica bought 9 pens. Each pen costs either $2 or $3. If the total cost was $23, how many $2 and $3 pens did Erica buy? NS 3.4; MR 1.1, 2.3, 2.4, 3.1, 3.2 Print This Page Name Print This 7–11 Page Explore Finding the Mean P PRACTICE Use the connecting cubes to find the mean. Redraw the cubes so that the rows are all the same length. 1. 4, 9, 5 Mean: 2. 7, 6, 3, 4 3. 5, 6, 4, 3, 2 Mean: Mean: © McGraw-Hill School Division Find the mean. You may use connecting cubes. 4. 2, 2, 9, 9, 8 5. 15, 0, 6 6. 1, 9, 12, 5, 3 7. 5, 10, 15, 20, 0 8. 1, 9, 2, 8, 3, 7 9. 4, 6, 3, 7, 2, 9, 1, 8 10. 10, 10, 30, 30 11. 1, 1, 1, 9, 9, 9, 8, 2 12. 24, 36 13. 20, 15, 20, 25 14. 4, 3, 2, 5, 1, 6, 2, 9 15. 5, 5, 6, 6, 9, 9, 2 16. 5, 10, 15, 20, 30 17. 1, 2, 3, 4, 5, 6, 7, 8, 9 18. 10, 8, 6, 4, 2 Problem Solving 19. The students in Homeroom 101 collected soup labels this week. The number of labels brought in to class each day were 8, 6, 10, 6, and 5. What was the mean number of labels brought in each day? Use with Grade 4, Chapter 7, Lesson 11, pages 302–303. (232) 20. Alison played in a basketball tournament this week. She scored the following numbers of points in 5 games: 20, 17, 12, 8, and 18. What was her average point total? NS 3.4; SDP 1.2 Print This Page Name Print This 7–11 Page Explore Finding the Mean R RETEACH You can find the mean of a set of numbers by finding the sum of the numbers and then dividing the sum by the number of addends. Here is how to find the mean of 2, 3, 5, and 6 using connecting cubes. Connect cubes to represent each number. Connect the cubes into one long row. You should have 16 cubes connected together. Divide the cubes into 4 equal groups. You should have 4 cubes in each group. So, the mean of 2, 3, 5, and 6 is 4. © McGraw-Hill School Division Find the mean. You may draw cubes to help you. 1. 5, 6, 8, 1 2. 4, 8, 5, 7 3. 12, 10, 2 4. 2, 9, 3, 5, 6 5. 11, 5, 2, 2, 10 6. 5, 5, 3, 3, 9 7. 7, 6, 3, 4 8. 7, 8, 2, 4, 3, 6 9. 10, 15, 5 10. 5, 5, 0, 1, 4, 3 11. 10, 20, 40, 2, 10, 20 Use with Grade 4, Chapter 7, Lesson 11, pages 302–303. (233) NS 3.4; SDP 1.2 Print This Page Name Print This 7–11 Page Explore Finding the Mean E ENRICH January in Los Angeles In Los Angeles, California, from 1961 to 1990, the average, or mean, high temperature in January was 68° Fahrenheit. 1. Imagine that the average high temperature for the month below is 68°F. Complete the calendar by writing different temperatures for the days. When you add the temperatures and divide by 31, you should have an average temperature of 68°F. January Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1 2 3 4 5 6 7 11 12 13 14 70° 8 9 10 73° 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 © McGraw-Hill School Division 63° 68° 2. Explain how you chose the temperatures. Use with Grade 4, Chapter 7, Lesson 11, pages 302–303. (234) NS 3.4; SDP 1.2 Print This Page Name Print This 7–12 Page Find the Mean P PRACTICE Find the mean. 1. 8, 4, 6, 7, 5 2. 11, 18, 13, 14 3. $25, $48, $77 4. 33, 72, 67, 88 5. $120, $308, $446, $506 6. 823, 665, 482, 619, 781 7. Number of minutes Jason practiced 8. Number of miles traveled each day: violin this week: 30, 40, 20, 40, 20. 9. Number of rolls of film used each day to take class pictures: 6, 4, 8, 3, 2, 1, 4 11. Number of miles Dorothy ran each day: 6, 8, 7, 9, 10, 11, 12 13. Number of books Emily read each month: 2, 3, 5, 6, 1, 1. 15. Number of bottles of juice on © McGraw-Hill School Division each shelf: 60, 80, 120, 40, 70, 80, 90, 140 125, 85, 115, 100, 85, 90 10. Number of gallons of gas used each day: 8, 6, 9, 11, 11, 9 12. Number of miles a pilot flew each day: 980, 760, 590, 910, 630 14. Height of six boys in inches: 60, 54, 62, 64, 66, 60 16. Number of boxes of cereal eaten by campers each week: 24, 14, 18, 26, 13 Problem Solving 17. Kathy trades baseball cards. She traded 42, 38, and 40 cards the last three Saturdays. What is the mean number of cards she trades on a Saturday? Use with Grade 4, Chapter 7, Lesson 12, pages 304–305. (235) 18. From Thursday through Sunday, Pizza Guy sold 97, 116, 208, and 151 pizzas. What is the average number of pizzas sold each day? NS 3.4; SDP 1.2 Print This Page Name Print This 7–12 Page Find the Mean R RETEACH You can use connecting cubes to help you record the steps for finding a mean. Find the mean of 7, 6, 3, and 4. Using Connecting Cubes Step 1 Build each number with connecting cubes. Connect the cubes into one long row. You should have 20 cubes connected together. Step 2 Divide the cubes into 4 equal groups. You should have 5 cubes in each group. Using Pencil and Paper Step 1 Add the numbers. 7 6 3 4 20 Step 2 Divide the sum by the number of addends. 5 4 20 So, the mean of 7, 6, 3, and 4 is 5. So, the mean of 7, 6, 3, and 4 is 5. © McGraw-Hill School Division Find the mean. 1. 4, 5, 7, 4, 5 2. 12, 10, 2 3. 16, 13, 12, 15 4. 21, 15, 12, 12, 20 5. 3, 14, 12, 11 6. 16, 15, 19, 13, 27 7. Weight of five dogs in pounds: 42, 35, 21, 38, 54 9. Number of hawks the ranger saw each day: 19, 7, 22, 8, 9, 13, 13 Use with Grade 4, Chapter 7, Lesson 12, pages 304–305. (236) 8. Number of miles Lance bicycled each day: 74, 69, 80, 57 10. Number of cars that used the parking garage each day: 563, 709, 661, 842, 805 NS 3.4; SDP 1.2 Print This Page Name Print This 7–12 Page Find the Mean E ENRICH Missing Pins The computer at the bowling alley is down, so teams have to keep track of their scores on cards. The scorecards below show the scores for the first five frames, or rounds. A cat with muddy paws ran across the cards. Complete the scorecards by writing the correct numbers in the paw prints. Then fill in the team’s total score and mean score. Team A Jason Total: Mean: Deanna 21 13 5 10 7 8 50 18 16 5 60 Mean: Total: Mean: 30 15 10 Total: Mean: 80 9 Chris Mean: 16 50 Lindsey 16 18 20 17 9 18 15 15 10 12 10 12 Team B’s 45 5 12 11 12 Total: 19 Mean Score per Person: Annie 12 13 9 10 16 6 Total: 13 Total Score: Team B Steven © McGraw-Hill School Division Mean: eric 6 4 22 9 4 Total: 65 10 Team A’s Serena 12 Total: Total: 65 10 Total Score: Use with Grade 4, Chapter 7, Lesson 12, pages 304–305. (237) Mean: 13 85 Mean: 17 Mean Score per Person: NS 3.4; SDP 1.2 Print This Page Name Problem Solving: Application Print This Page 7–13 Part A WORKSHEET Decision Making Applying Division Record your data and notes. Cost Advantages and Disadvantages Bus Train © McGraw-Hill School Division Car Your Decision What is your recommendation for the club? Should they take a bus, train, or car to the aquarium? Explain. Use with Grade 4, Chapter 7, Lesson 13, pages 306–307. (238) NS 3.4; MR 1.1, 2.3, 3.1 Print This Page Name Print This Page 7–13 Part B WORKSHEET Problem Solving: Application Math & Science Do light or heavy objects fly farther? Safety: Wear goggles to protect your eyes and work away from other people. Record your data in the table below. Distance Traveled Object 1 2 3 4 5 Mean Paper Clip Eraser 1. Show how you found the mean or average distance for each object. Eraser © McGraw-Hill School Division Paper Clip Use with Grade 4, Chapter 7, Lesson 13, pages 308–309. (239) NS 1.2; SDP 1.2; MR 1.1, 2.3, 3.2 Print This Page Name Problem Solving: Application Do light or heavy objects fly farther? Print This Page 7–13 Part B WORKSHEET Math & Science 2. Which object traveled farther? How do you know? 3. Use division to decide how many times farther one object traveled than the other. Show your work. Work Space © McGraw-Hill School Division 4. In your own words, explain what gravity is. 5. Explain the results of the activity in terms of gravity. Use with Grade 4, Chapter 7, Lesson 13, pages 308–309. (240) NS 1.2; SDP 1.2; MR 1.1, 2.3, 3.2 Print This Page Name Print This 8–1 Page Division Patterns P PRACTICE Complete. 1. 36  9  n 2. 64  8  s 3. 18  b  6 360  90  n 640  80  s b  30  6 3,600  90  n 6,400  80  s 1,800  30  b 36,000  90  n 64,000  80  s 18,000  30  b 360,000  90  n 640,000  80  s 180,000  30  b Divide. Use mental math. 4. 5. 2 60 120 8. $40 10 $400 6. 70 40 2,800 9. 500 7. $50 11. 70 35,000 10. $300 70 $21,000 40 $2,000 12. 150  30  13. 16,000  80  14. 2,700  90  15. 18,000  20  16. 1,200  20  17. 56,000  70  18. 810  90  19. 42,000  70  20. 3,600  40  21. 45,000  50  7,000 80 560,000 5,000 90 450,000 Algebra & Functions Find each missing number. © McGraw-Hill School Division 22. 140  25. a2 t  60  70 23. d  70  7 26. 28,000  24. 3,000  60  b  400 x 27. 40,000  50  y Problem Solving 28. A box of 400 stickers is to be divided equally among 80 students. How many stickers will each student receive? Use with Grade 4, Chapter 8, Lesson 1, pages 324–325. (241) 29. If 6,300 books are divided equally among 90 libraries, how many books will each library get? NS 3.2 Print This Page Name Print This 8–1 Page Division Patterns R RETEACH To divide mentally, you can use basic division facts and look for a pattern. Find the basic division fact. Then count and subtract zeros. This will tell you how many zeros the quotient will have. The basic fact is 6  2  3. 60  20  3 → 600  20  30 → 6,000  20  300 → 1 zero  1 zero  0 zeros 2 zeros  1 zero  1 zero 3 zeros  1 zero  2 zeros The basic fact is 20  4  5. 200  40  5 → 1 extra zero – 1 zero  0 zeros 2,000  40  50 → 2 extra zeros – 1 zero  1 zero 20,000  40  500 → 3 extra zeros – 1 zero  2 zeros Complete the pattern. Count and subtract the zeros. 1. 24  3  2. 12  4  240  30  120  40  2,400  30  1,200  40  24,000  30  12,000  40  © McGraw-Hill School Division 3. 63  9  4. 30  5  630  90  300  50  6,300  90  3,000  50  63,000  90  30,000  50  5. 9  3  6. 90  30  8. 18  3  9. 180  30  10. 1,800  30  11. 42  6  12. 420  60  13. 4,200  60  14. 40  8  15. 400  80  16. 4,000  80  Use with Grade 4, Chapter 8, Lesson 1, pages 324–325. (242) 7. 900  30  NS 3.2 Print This Page Name Print This 8–1 Page Division Patterns E ENRICH Move Along Circle the correct answer for each exercise. Then use the remaining two answers to write the next division sentence. Repeat until you finish the page. 1. 8,000  10 = 800 a. 3,200 b. 800 2. 3,200  80 = c. 80 3. b. 4,000 c. 50 a. 4,200 b. 60 c. 50 a. 50 b. 2,800 c. 40 a. 900 b. 90 c. 81,000 a. 10 b. 10,000 c. 100,000 a. 5,000 b. 500 c. 50 4. a. 90 b. 80 c. 4,500 5. 6. a. 70 b. 4,000 c. 80 7. 8. a. 54,000 b. 60 c. 70 9. 10. a. 900,000 b. 900 c. 90 11. © McGraw-Hill School Division a. 40 12. a. 100,000 b. 10,000 c. 20 13. Look at exercise 12. How did you decide how many zeros were in the quotient? Use with Grade 4, Chapter 8, Lesson 1, pages 324–325. (243) NS 3.2 Print This Page Name Print This 8–2 Page Explore Dividing by 2-Digit Numbers P PRACTICE Divide. 1. 2. 130  10  143  30  3. 4. 121  14  156  18  Divide. You may use place-value models. 5. 6 R9 6. 13 87 9. 18 R5 © McGraw-Hill School Division 16 293 9 R2 7. 15 137 10. 13 R14 7 R9 8. 12 93 11. 17 235 13 R11 19 258 8 R13 14 125 12. 17 R16 25 441 13. 135  16  14. 134  14  15. 115  15  16. 282  18  17. 230  19  18. 269  24  Problem Solving 19. The dividend is 280. The divisor is 23. What are the quotient and remainder? Use with Grade 4, Chapter 8, Lesson 2, pages 326–327. (244) 20. The dividend is 160. The divisor is 12. What are the quotient and remainder? NS 3.2 Print This Page Name Print This 8–2 Page Explore Dividing by 2-Digit Numbers R RETEACH You can use estimation and models to help you divide. Find 148  12. Show 148 using place-value models. Think: How many groups of 12 are there in 148? Exchange 1 hundred for 10 tens. Divide the tens. Make as many groups of 12 as you can. Exchange tens for ones so you can keep grouping 1 ten and 2 ones. You can make 12 equal groups of 12 with 4 ones remaining. So, 148  12  12 R4. © McGraw-Hill School Division Divide. You may use place-value models to help you. 1. 163  13  2. 158  10  3. 214  12  4. 285  14  5. 352  16  6. 385  15  7. 183  17  8. 268  11  9. 376  18  Use with Grade 4, Chapter 8, Lesson 2, pages 326–327. (245) NS 3.2 Print This Page Name Print This 8–2 Page Explore Dividing by 2-Digit Numbers E ENRICH Stick Division What if we used a number system that used symbols instead of numerals? In this Chinese system, numbers are written using the symbols shown. 1 10 2 3 20 4 50 5 60 Using these symbols, 21 is shown as Example: 426 21 8,946 6 7 70 8 90 9 100 and 8,946 is shown as . → © McGraw-Hill School Division Use the number system above to create four division exercises where the divisor is a 2-digit number. Then exchange exercises with a partner and find the quotient using symbols. 1. 2. 3. 4. 5. Is it easier or harder to divide using the number system above? Explain. Use with Grade 4, Chapter 8, Lesson 2, pages 326–327. (246) NS 3.2 Print This Page Name 8–3 Page Divide 2-Digit Numbers by Multiples of 10 Print P This PRACTICE Divide. 1. 82  20  2. 75  10  3. 51  20  4. 94  30  5. 88  20  6. 87  10  7. 93  40  8. 71  30  9. 97  20  10. 74  20  11. 52  10  12. 67  30  13. 91  10  14. 62  40  15. 94  40  16. 3 R1 17. 7 R6 21. 9 R6 25. 20 61 20. 10 96 18. 4 R15 22. 1 R29 26. 50 78 10 76 24. 1 R28 2 R1 19. 1 R24 23. 2 R4 27. 40 81 20 95 60 84 30 59 20 44 2 R3 30 63 1 R9 40 49 1 R9 50 59 © McGraw-Hill School Division Algebra & Functions Find the missing number. 28. 27  m  2 R7 29. 51  k  1 R21 30. 63  a  1 R13 31. 74  p  3 R14 32. 71  y  3 R11 33. 90  r  2 R10 Problem Solving 34. Sam needs to put 76 pencils in packages. Each package should have 10 pencils. How many packages will there be? How many pencils will be left over? Use with Grade 4, Chapter 8, Lesson 3, pages 328–329. (247) 35. Kenya needs to put 84 cans of tennis balls in boxes. Each box should have 20 cans. How many boxes will Kenya fill? How many cans will she have left over? NS 3.2 Print This Page Name 8–3 Page Divide 2-Digit Numbers by Multiples of 10 Print R This RETEACH You can use models to help you divide by multiples of 10. Find 74  20. Think: How many groups of 20 are in 74? Using Models Using Pencil and Paper Show 74 using place-value models. Step 1: Divide 74 by 20. Then make as many groups of 20 as you can. Think: 60  20  3. 3 20 74  60 Step 2: Subtract. Write the remainder in the quotient. 3 R14 20 74  60 14 You can make 3 equal groups of 20 with 14 remaining. © McGraw-Hill School Division Divide. You can use place-value models. 1. 63  30  2. 88  40  3. 55  10  4. 48  20  5. 74  10  6. 93  30  7. 85  30  8. 81  20  9. 76  10  10. 51  30  11. 63  50  12. 84  60  13. 90  40  14. 74  20  15. 71  20  16. 27  10  17. 59  50  18. 59  30  Use with Grade 4, Chapter 8, Lesson 3, pages 328–329. (248) NS 3.2 Print This Page Name Divide 2-Digit Numbers by Multiples of 10 Print This 8–3 Page E ENRICH Winning Start • Label the faces of a number cube 20, 30, 40, 50, 60, and 70. • Place a marker on 72, the starting position. Take turns tossing the number cube. Divide the number your marker is on by the number tossed. Find the whole number quotient. Move forward that number of spaces. • Continue moving forward until you have gone around the board once. After passing "Start", you may move forward or backward. The winner is the person who lands directly on "Start". © McGraw-Hill School Division Start 72 85 97 100 115 120 260 138 253 149 250 150 235 164 226 219 205 Use with Grade 4, Chapter 8, Lesson 3, pages 328–329. (249) 197 186 173 NS 3.2 Print This Page Name Print This 8–4 Page Divide by 2-Digit Divisors P PRACTICE Divide. 1. 43 R6 2. 22 952 5. 11 7. 10. 96 R1 14. 4. 12 R2 11. 71 15. 17 $11.39 8. 12. $0.89 16. 39 2,381 17. 895  24  18. 907  31  19. 367  14  20. $7.08  59  21. 814  36  22. 531  45  23. 1,467  24  24. $37.76  64  25. 4,780  77  26. $48.59  43  27. 7,900  84  28. 8,930  92  13 R9 75 984 61 R2 62 $55.18 14 R4 54 760 44 530 $0.67 51 3,621 $0.11 66 $7.26 29 496 75 R4 93 8,929 17 R3 6. 26 1,954 13. 3. 31 784 81 891 9. 25 R9 83 46 3,818 74 R6 88 6,518 Algebra & Functions Solve. 29. (1,700  53)  37  w © McGraw-Hill School Division 31. (1,900  100)  29  v 33. (2,300  70)  (12  4)  n 34. (1,500  80)  (11  5)  c 30. (1,000  160)  46  d 32. (1,600  240)  83  x Problem Solving 35. Mrs. Tallo’s class made 234 ribbons for the Sports Fair. Each student made the same number of ribbons. There are 18 students in the class. How many ribbons did each student make? Use with Grade 4, Chapter 8, Lesson 4, pages 330–333. (250) 36. Mr. Willow’s class wants to sell 200 tickets to the Winter Sports Fair. There are 25 students in the class. How many tickets will each student need to sell? NS 3.2 Print This Page Name Print This 8–4 Page Divide by 2-Digit Divisors R RETEACH You can use models to help you understand dividing by 2-digit numbers. Find 165  25. Using Models Use place-value models to show 165. Using Pencil and Paper Step 1: Divide, Think: 180  30  6 6 25 165 Exchange the one hundred for 10 tens. Step 2: Multiply. 6 25 165  150 ← 6  25  150 © McGraw-Hill School Division Then make as many groups of 25 as you can. Exchange tens for ones. You can make 6 equal groups of 25 with 15 remaining. Step 3: Subtract. Write the remainder in the quotient. 6 R15 25 165  150 15 ← 165  150  15 Divide. You can use place-value models. 1. 164  12  2. 174  18  3. 318  21  4. 135  14  5. 372  23  6. 243  17  7. 212  24  8. 435  16  9. 166  13  Use with Grade 4, Chapter 8, Lesson 4, pages 330–333. (251) NS 3.2 Print This Page Name Divide by 2-Digit Divisors Print This 8–4 Page E ENRICH What Number Am I? Solve. What number am I? 1. I am a number between 10 and 20. 2. I am a number between 10 and 20. If you divide either 61 or 73 by me, the remainder is 1. If you divide either 45 or 56 by me, the remainder is 1. 3. I am a number between 20 and 30. 4. I am a number between 20 and 30. If you divide either 107 or 128 by me, the remainder is 2. 5. I am a number between 20 and 30. If you divide either 76 or 126 by me, the remainder is 1. 7. I am a number between 10 and 20. If you divide either 74 or 110 by me, the remainder is 2. 9. I am a number between 20 and 30. © McGraw-Hill School Division If you divide either 175 or 204 by me, the remainder is 1. 11. I am a number between 10 and 20. If you divide either 69 or 88 by me, the remainder is 12. 13. I am a number between 10 and 20. If you divide either 110 or 144 by me, the remainder is 8. Use with Grade 4, Chapter 8, Lesson 4, pages 330–333. (252) If you divide either 68 or 134 by me, the remainder is 2. 6. I am a number between 30 and 40. If you divide either 147 or 255 by me, the remainder is 3. 8. I am a number between 40 and 50. If you divide either 221 or 265 by me, the remainder is 1. 10. I am a number between 30 and 40. If you divide either 74 or 214 by me, the remainder is 4. 12. I am a number between 20 and 30. If you divide either 131 or 154 by me, the remainder is 16. 14. I am a number between 20 and 30. If you divide either 295 or 322 by me, the remainder is 25. NS 3.2 Print This Page Name Print This 8–5 Page Estimate Quotients P PRACTICE Estimate the quotient. Choose compatible numbers. 1. 19 389 2. 17 211 3. 18 586 4. 16 789 5. 49 1,585 6. 72 6,280 7. 32 8,920 8. 61 3,256 9. 68 34,912 10. 2,806  38 11. 7,903  86 12. 1,113  31 13. 7,160  93 14. 2,806  56 15. 2,210  48 16. 21 1,732 17. 63 546 18. 53 2,612 19. 41 1,512 20. 78 4,106 21. 86 1,709 Algebra & Functions Estimate to compare. Write  or . © McGraw-Hill School Division 22. 396  21 914  31 23. 492  68 24. 1,947  38 2,011  48 25. 1,300  21 26. 5,106  82 6,206  91 27. 3,100  82 556  71 2,300  13 4,700  71 Problem Solving 28. Karen drove 283 miles at a speed of 46 miles per hour. About how many hours did she drive? Use with Grade 4, Chapter 8, Lesson 5, pages 334–335. (253) 29. A jet flew 3,116 miles in 6 hours. About how many miles per hour did it fly? NS 3.2 Print This Page Name Print This 8–5 Page Estimate Quotients R RETEACH Compatible numbers are numbers you can divide easily. You can use compatible numbers to estimate quotients. Estimate 3,463  73. 3,463  73 Think: A basic fact that is close is 35  7. 3,500  70  50 So, 3,463  73 is about 50. Complete. 1. Estimate 1,785  31. 2. Estimate 2,880  29. Division fact: 18  3  Division fact: 27  3  Estimate: 1,800  30  Estimate: 2,700  30  3. Estimate 5,726  72. 4. Estimate 3,952  79. Division fact: Division fact: Estimate: Estimate: © McGraw-Hill School Division Use compatible numbers to estimate each quotient. 5. 1,482  33 6. 6,512  78 7. 7,164  89 8. 2,207  68 9. 3,512  42 10. 2,587  53 11. 3,123  64 12. 4,132  71 13. 2,712  32 14. 1,789  27 15. 2,797  43 16. 6,432  92 Use with Grade 4, Chapter 8, Lesson 5, pages 334–335. (254) NS 3.2 Print This Page Name Print This 8–5 Page Estimate Quotients E ENRICH Box Estimation Choose the best estimate from each box to complete the sentence. Then write the answer next to the letter of the box to make a code. Use the code to answer the question. Who was the first American in space? A. 24 33 D. 63 53 E. 82 75 42 51 71 48 64 92 2,430  is about 80. is about 70. 3,575  is about 40. H. 27 44 L. 24 32 N. 31 42 52 38 58 44 52 28 2,277  is about 40. 12,250  is about 600. 15,880  P. 68 72 R. 68 74 84 91 47 59 25,370  © McGraw-Hill School Division 4,356  is about 300. 29,790  is about 400. S. 7 72 is about 500. 34,841  A D E H L N P R S 24 33 42 64 is about 500. , JR. B. 33 81 72 52 92 84 33 59 63 Explain how you estimated the divisors. Use with Grade 4, Chapter 8, Lesson 5, pages 334–335. (255) NS 3.2 Print This Page Name Print This 8–6 Page Adjust the Quotient P PRACTICE Divide. 1. 7 R11 2. 2 R44 6. 8 R74 10. 8 R28 14. 8 R19 18. 5 R77 22. 34 249 5. 3 R70 11. 7 R24 15. 5 R9 19. 8 R10 23. 4 R34 8. 5 R35 12. 5 R86 16. 3 R52 20. 8 R35 24. 3 R49 63 238 7 R11 25 186 92 546 3 R75 88 339 65 247 22 186 8 R39 41 367 39 230 24 129 81 482 4. 79 350 69 507 44 371 21. 7. 75 295 56 476 17. 7 R38 8 R21 56 469 84 626 92 810 13. 3. 26 189 51 146 9. 7 R7 4 R56 57 284 45 395 8 R11 36 299 Algebra & Functions Divide only those with quotients between $5.00 and $8.00. 25. $5.25 26. $7.15 30. © McGraw-Hill School Division 18 $94.50 29. 13 $92.95 $6.15 27. 16 $98.40 no 11 $99.11 no 28. no 32. 14 $60.90 31. 15 $56.25 no 25 $93.75 $7.76 12 $93.12 Problem Solving 33. Candy wants to walk 220 miles in 30 days. If she walks 7 miles every day, will she meet her goal? Use with Grade 4, Chapter 8, Lesson 6, pages 336–337. (256) 34. Jason wants to save $180 in 12 months. How much should he save each month? NS 3.2 Print This Page Name Print This 8–6 Page Adjust the Quotient R RETEACH When you divide, sometimes your first estimate is too high or too low. Then you must adjust the quotient. Divide 125  43. Step 1: 3 43 125 Estimate: 120  40  3 Step 2: Use your estimate to divide. 3 43 125  129 ← Multiply: 3  43  129 Compare: 129  125. You cannot subtract. The estimate of 3 is too high. Step 3: Adjust your estimate and divide. Multiply to check the answer. 2 R39 43 125  86 ← Multiply: 2  43  86 39 Subtract: 125  86  39 Compare: 39  43 43 2 86  39 125 © McGraw-Hill School Division Divide. Check your answer. 1. 4 R14 2. 6 R8 6. 24 110 5. 57 350 9. 173  19  7 R1 3. 8 R1 7. 27 190 4. 6 R1 8. 29 148 16 129 10. 293  44  Use with Grade 4, Chapter 8, Lesson 6, pages 336–337. (257) 5 R3 37 223 1 R59 61 120 1 R61 63 124 11. 208  25  NS 3.2 Print This Page Name Adjust the Quotient Print This 8–6 Page E Hi Lo ENRICH Estimate each quotient. Write your estimate. Then divide. If your estimate was too high, circle "Too High." If your estimate was too low, circle "Too Low." Use the circled answers to complete the maze below. 1. 5. 3 R71 2. 9 R10 3. 7 R30 4. $3.25 73 290 65 595 31 247 21 $68.25 Too High Down Too High Left Too High Down Too High Left Too Low Up Too Low Right Too Low Up Too Low Right 6 R2 6. $2.13 7. 7 R7 8. 7 R2 88 530 91 $25.56 48 343 26 184 Too High Down Too High Right Too High Up Too High Left Too Low Up Too Low Left Too Low Down Too Low Right What is the fastest fish, the tallest tree, the biggest dog, and the smallest bird? To find out, begin at Start. Move one space in the direction given next to each circled answer. © McGraw-Hill School Division Start sailfish redwood St. Bernard hummingbird swordfish Maple dolphin oak greyhound parakeet Great Dane sparrow Use with Grade 4, Chapter 8, Lesson 6, pages 336–337. (258) NS 3.2 Print This Page Name Print This 8–7 Page Problem Solving: Reading for Math P PRACTICE Reading Skill Use an Overestimate or Underestimate Form a conclusion about whether you would overestimate or underestimate. Then solve the problem. 1. A group of 118 people have signed up for the 5-kilometer run. Each person will receive a special cap. Caps are sold in boxes of 36. How many boxes are needed? Should you overestimate or underestimate to solve this problem? Explain. How many boxes are needed? 2. The Flying Disk Club has saved $90 to buy Disks for its members. A package of 2 Disks costs $8. How many packages of Disks can the club buy? Should you overestimate or underestimate to solve this problem? Explain. How many packages of Frisbees can the club buy? 3. Trophies cost $9 each. The tournament organizers have $60 © McGraw-Hill School Division budgeted for trophies. How many trophies can they buy? Should you overestimate or underestimate to solve this problem? Explain. How many trophies can they buy? 4. A group of 24 students is playing catch. They share 7 softballs. What is the least number of students who can share each softball? Should you overestimate or underestimate to solve this problem? Explain. What is the least number of students who can share a softball? Use with Grade 4, Chapter 8, Lesson 7, pages 338–339. (259) MR 1.1, 2.1, 2.4, 2.5, 3.1, 3.2 Print This Page Name Print This 8–7 Page Problem Solving: Reading for Math P Use an Overestimate or Underestimate PRACTICE Math Skills Test Prep Choose the correct answer. There are 95 volunteers working at the marathon. Each volunteer will get a water bottle. A box contains 24 water bottles. How many boxes are needed? 1. Which of the following statements 2. To be sure there are enough water is true? bottles for the volunteers, you should: A There are not enough water bottles for the volunteers. F underestimate the number of volunteers. B A box contains 24 water bottles. G overestimate the number of volunteers and underestimate the number of boxes needed. C There are 95 water bottles. D Four water bottles are needed. H underestimate the number of boxes needed. J overestimate the number of boxes needed. At the game, there are 44 color guards. Each color guard will help carry flags. There are 21 flags on 6-foot poles. What is the greatest number of students that will have to share a flag? © McGraw-Hill School Division 3. Which of the following is not 4. To find the greatest number of students important to solving the problem? who will share a flag, you should: A There are 44 students carrying flags. F overestimate the number of students per flag. B Each color guard will help carry a flag. C There are 21 flags. D The flags are on 6-foot poles. G underestimate the number of students per flag. H overestimate the number of flags and underestimate the number of students. J underestimate the number of flags per student. Use with Grade 4, Chapter 8, Lesson 7, pages 338–339. (260) MR 1.1, 2.1, 2.4, 2.5, 3.1, 3.2 Print This Page Name Print This 8–7 Page Problem Solving: Reading for Math P Use an Overestimate or Underestimate PRACTICE Math Skills Test Prep Choose the correct answer. The sports committee buys a piece of fabric that is 60 feet long. Underestimate the number of 9-foot banners that can be made from the fabric. 5. To underestimate the number of banners that can be made, you: A use 63 feet for the length of the fabric. B round down the length of the fabric to 50 feet. C round up the length of each banner to 10 feet. D use 6 feet for the length of each banner. Solve. 7. Travis is making first-place ribbons for Sports Day. He has 111 inches of blue ribbon. Each blue ribbon will be 8 inches long. Underestimate the number of ribbons he can make. © McGraw-Hill School Division 9. There are 152 people at the Sports Night Dinner. There are 33 tables. What is the greatest number of people that can sit at a table? Explain. 11. A pack of 3 pennants costs $8. Maryanne has $30. Is this enough to buy 4 packs of pennants? Explain. Use with Grade 4, Chapter 8, Lesson 7, pages 338–339. (261) 6. How many 9-foot banners can be made from the fabric? F 5 G 6 H 7 J 8 8. The soccer club makes 100 cups of fruit drink. There are 46 students in the soccer club. Is there enough fruit drink for each student to have 2 cups? Explain. 10. Mark wants to buy baseball shirts of different teams. Each shirt costs $18. Mark has $62. How many shirts can he buy? Explain. 12. A box of gold medals costs $56. The Sports Committee has $185 to spend on medals. How many boxes can the committee buy? Explain. MR 1.1, 2.1, 2.4, 2.5, 3.1, 3.2 Print This Page Name Print This 8–8 Page Problem Solving: Strategy P PRACTICE Choose a Strategy Choose a strategy. Use it to solve the problem. 1. The Sports Committee buys 30 yards of material. The material will be cut into banners that are 5 feet long. How many banners can be made? 3. Liam is building a fence around his backyard. The backyard is 24 feet wide and 60 feet long. If Liam uses sections of fencing that are 12 feet long, how many sections will he need? Mixed Strategy Review Solve. Use any strategy. 5. Art Tina makes a display of 36 autographed baseballs. She puts 12 baseballs in a large display case. Tina also has 4 smaller display cases. How can she arrange the baseballs in the smaller cases so that each smaller case has an equal number of baseballs? 2. The Sand Trap Golf Shop has 132 golf balls in stock. The golf balls are packed in tubes of 6. How many tubes of golf balls does the store have? 4. There are 115 students who want to go to the basketball tournament. One bus can carry 26 students. How many buses will be needed? 6. Francine uses a pattern to make a window display for a sneaker store. The first row has 2 sneakers, the second row has 6 sneakers, the third row has 10, and the fourth row has 14. How many sneakers will be in the fifth row? © McGraw-Hill School Division Strategy: Strategy: 7. The Stadium Store sells 450 team photos and 369 individual photos. How many photos does it sell in all? 8. Create a problem which you could solve by drawing a diagram or by writing a division sentence. Share it with others. Strategy: Use with Grade 4, Chapter 8, Lesson 8, pages 342–343. (262) NS 3.2; MR 2.4 Print This Page Name Print This 8–8 Page Problem Solving: Strategy R RETEACH Choose a Strategy Page 343, Problem 1 Camille wants to practice sharper turns. She uses the same 20-yard distance in the driveway and begins at the starting line. This time she places the cones 3 feet apart. How many cones will she use? Step 1 Read Be sure you understand the problem. Read carefully. What do you know? • The total distance is yards. • Camille will start at the starting line and place cones feet apart. What do you need to find? • You need to find the number of feet in yards. • You need to find how many . Step 2 Plan ■ ■ © McGraw-Hill School Division ■ ■ ■ ■ ■ ■ Find a Pattern Work Backward Use Logical Reasoning Write a Number Sentence Make a Table or List Guess and Check Make a Graph Solve Simpler Problem Make a plan. Choose a strategy. To find the answer, you may draw a diagram. Find the number of feet in 20 yards. Show a distance that is that many feet long. Count by 3s to see how many cones Camille will use if they are placed 3 feet apart. To find the answer, you can also write a number sentence. All the cones are the same distance apart. Use division to find how many cones Camille will use. Use with Grade 4, Chapter 8, Lesson 8, pages 342–343. (263) NS 3.2; MR 2.4 Print This Page Name Print This 8–8 Page Problem Solving: Strategy R RETEACH Choose a Strategy Step 3 Carry out your plan. Solve How many feet are in 20 yards? 1 yard  3 feet 20  3  60 Draw a diagram. Show a 60-foot distance. Count by 3s to see how many cones Camille will use. 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 Count. Camille will use a total of cones. Write a number sentence. The distance is feet. There will be 1 cone every Write a division sentence.  Camille will use a total of cones feet.  Step 4 Look Back Is the solution reasonable? Reread the problem. © McGraw-Hill School Division Does your answer make sense? Yes No Which method do you prefer? Explain. Practice 1. The parks department builds stands next to a baseball field. There will be 5 rows of stands. Each row will be 20 feet long. How many 10-foot long boards will they need to build the stands? Use with Grade 4, Chapter 8, Lesson 8, pages 342–343. (264) 2. Ed has 4 packs of sports stickers. There are 24 stickers in each pack. He divides the stickers among 3 friends. How many stickers does each friend get? NS 3.2; MR 2.4 Print This Page Name Print This 8–9 Page Order of Operations P PRACTICE Write which operation should be done first. 1. 2  8  7 2. 2  3  9 3. 4  10  2 4. 9  2  3 5. (3  2)  9 6. 8  (2  2) 7. 6  2  1 8. 1  3  5 9. 10  5  2 10. 7  8  2 11. (12  4)  2 12. 9  2  6 © McGraw-Hill School Division Simplify. Use order of operations. 13. 3  2  7  14. 10  2  1  15. 9  6  2  16. 24  2  8  17. (2  6)  7  18. 12  12  3  19. (4  6)  5  20. 12  3  9  21. 20  5  2  22. 18  9  6  23. 2  8  4  24. 20  5  4  25. 2  6  4  3  26. 20  2  3  6  27. (2  9)  (7  3)  28. 4  (14  6)  2  5  29. 2  9  10  5  (3  2)  Problem Solving 30. Tamara buys 6 apples for $0.40 each. She has a $0.50 off coupon. Write an expression and simplify to find her final cost. Use with Grade 4, Chapter 8, Lesson 9, pages 344–345. (265) 31. Steven has 126 photos to put in an album. He finds 18 more photos. Each page holds 12 photos. Write an expression and simplify to find how many pages Steven will fill. AF 1.3 Print This Page Name Print This 8–9 Page Order of Operations R RETEACH Always use the order of operations to simplify expressions. The rules for the order in which you should perform operations are given below. Simplify (20  8)  4  2. Step 1: Step 2: Step 3: Do the operations in parentheses first. Multiply and divide from left to right. Add and subtract from left to right. (20  8)  4  2 28  4  2 72 28  4  2 72 5 Which operation should you do first? 1. 12  4  2 2. 4  (10  2) 3. 2  8  4 4. (3  7)  2 5. 9  3  2 6. 8  2  4 7. 6  (8  5) 8. 8  4  2 9. 12  (2  2) © McGraw-Hill School Division Simplify. Use the order of operations. 10. 3  (2  5)  11. 14  7  2  12. 9  (6  2)  13. 4  2  5  14. 8  2  2  15. 10  8  4  16.12  3  2  17. (1  5)  4  18. 8  8  4  19. (5  5)  2  20. 14  10  2  21. 16  4  2  Use with Grade 4, Chapter 8, Lesson 9, pages 344–345. (266) AF 1.3 Print This Page Name Order of Operations Print This 8–9 Page E ENRICH Order Counts Rewrite each number sentence. Put in parentheses to make each number sentence true. 1. 3  8  2  1  21 2. 5 x 16 + 14 + 6÷ 2 = 153 3. 6 ÷ 9 – 8 = 6 4. 22 – 3 x 5 + 2 = 1 5. 18 ÷ 2 + 1 + 1 = 7 6. 6 x 5 + 9 ÷ 3 = 28 7. 5 x 10 + 1 ÷ 11 = 5 8. 3 + 40 ÷ 8 x 5 = 4 9. 10 – 6 ÷ 4 = 1 10. 4 x 5 – 2 = 12 11. 40 ÷ 10 – 2 = 5 12. 20 + 8 ÷ 4 = 7 13. 6 + 2 x 7 = 56 © McGraw-Hill School Division 14. 16 – 6 + 2 = 8 In your own words describe the rules for the order of operations. Use with Grade 4, Chapter 8, Lesson 9, pages 344–345. (267) AF 1.3 Print This Page Name Problem Solving: Application Print This Page 8–10 Part A WORKSHEET Decision Making Applying Multiplication Record your data. Cost to the club Profit per bar for the club at a sale price of $1 Sales needed to reach goal for $110 in profits Home-made hiker bars Boxed hiker bars © McGraw-Hill School Division Your Decision What is your recommendation for the hiking club? Explain. Use with Grade 4, Chapter 8, Lesson 10, pages 346–347. (268) NS 1.2, 3.2, 3.3, 3.4; MR 1.1, 2.4 Print This Page Name Problem Solving: Application Does eating improve performance? Print This Page 8–10 Part B WORKSHEET Math & Science Safety: Wait at least 30 minutes after eating before doing vigorous exercise. Record your data. Number of Sit-ups Student Before Lunch After Lunch 1. Did you do more sit-ups before or after lunch? © McGraw-Hill School Division 2. How many more sit-ups did you do? Show your work. Work Space Use with Grade 4, Chapter 8, Lesson 10, pages 348–349. (269) NS 1.2, 3.4; MR 1.1, 2.3, 3.3 Print This Page Name Print This Page 8–10 Part B WORKSHEET Problem Solving: Application Math & Science Does eating improve performance? 3. How many times more sit-ups did you do? Round to the nearest whole number. Show your work. Work Space 4. Can you conclude that the food from lunch gave you more energy? Why or why not? © McGraw-Hill School Division 5. In what ways could you improve this activity? 6. Explain the activity in terms of energy conversion. Use with Grade 4, Chapter 8, Lesson 10, pages 348–349. (270) NS 1.2, 3.4; MR 1.1, 2.3, 3.3 Print This Page Name Print This 9–1 Page Explore Customary Length P PRACTICE Estimate and then measure. Tell what unit and tool you use. 1. length of a pencil 2. height of a desk 3. width of the classroom 4. length of a book 5. distance you go in a stride © McGraw-Hill School Division Circle the letter of the correct estimate. 6. distance you can ride your bike A. 2 mi B. 2 ft C. 2 yd 7. length of a car A. 10 in. B. 10 ft C. 10 yd 8. height of a fourth-grader A. 4 in. B. 4 ft C. 4 yd 9. height of a tree A. 40 mi B. 40 yd C. 40 ft 10. height of a cat A. 1 yd B. 1 mi C. 1 ft 11. length of a worm A. 3 in. B. 3 ft C. 3 yd 12. height of a refrigerator A. 2 ft B. 2 yd C. 2 mi 13. length of a crayon A. 4 ft B. 4 yd C. 4 in. 14. length of a football field A. 100 ft B. 100 yd C. 100 mi Problem Solving 15. Jane can walk a mile in about 15 minutes. About how long would it take her to walk 5 miles? Use with Grade 4, Chapter 9, Lesson 1, pages 364–365. (271) 16. Marta measures the length of her notebook. To the nearest quarter 3 inch, it is 12 4 in. What does it measure to the nearest inch? MR 1.1, 2.3 Print This Page Name Print This 9–1 Page Explore Customary Length R An inch (in.) is used to measure short lengths in the customary system. Customary Units of Length 1 foot (ft)  12 inches (in.) You can use a ruler to measure in inches. 0 1 2 RETEACH 1 yard (yd)  3 feet (ft) 3 1 mile (mi)  1,760 yards (yd) 1 mile (mi)  5,280 feet (ft) 3 14 in. The foot (ft) and yard (yd) are used to measure larger units in the customary system. 1 yd 1 ft Use an inch ruler to measure each object. Measure to the nearest 14 inch. 1. 2. © McGraw-Hill School Division 3. 4. Circle the letter of the correct estimate. 5. length of a person’s foot A. 8 in. B. 8 ft C. 8 yd 6. length of a bed A. 6 in. B. 6 ft C. 6 yd Use with Grade 4, Chapter 9, Lesson 1, pages 364–365. (272) MR 1.1, 2.3 Print This Page Name Print This 9–1 Page Explore Customary Length E ENRICH Early Measurements In early times, distances were measured using fingers, hands, and arms. digit span cubit digit: the width of a finger span: the width of a stretched hand cubit: the distance from fingertip to elbow © McGraw-Hill School Division Choose digit, span, or cubit as the appropriate unit of measure. Then estimate. 1. width of your desk 2. thickness of your math book 3. length of your notebook 4. diameter of an apple 5. height of the classroom 6. length of a car 7. your friend’s height 8. length of your foot 9. What is an advantage of this system? What is a disadvantage? 10. What kinds of distance would be difficult to measure using this system of measurement? Use with Grade 4, Chapter 9, Lesson 1, pages 364–365. (273) MR 1.1, 2.3 Print This Page Name Print This 9–2 Page Customary Capacity and Weight P PRACTICE Estimate and then measure the capacity of each object. 1. a water glass 2. a large pot 3. a cereal bowl 4. a milk carton 5. Order the objects above from least to greatest capacity. Estimate and then measure the weight of each object. 6. an apple 7. four potatoes 8. two envelopes 9. a pencil 10. Order the objects above from least to greatest weight. © McGraw-Hill School Division Circle the letter of the correct estimate. 11. A. 5 c B. 5 pt C. 5 gal 12. A. 1 c B. 1 pt C. 1 qt 13. A. 6 c B. 6 qt C. 6 gal 14. A. 2 fl oz B. 2 c C. 2 pt 15. A. 500 oz B. 500 lb C. 500 T 16. A. 3 oz B. 3 T C. 3 lb Problem Solving 17. A box of Krispy Krunch cereal holds 20 oz. Kyle pours 3 oz of cereal into his bowl. How much cereal is left in the box? Use with Grade 4, Chapter 9, Lesson 2, pages 366–369. (274) 18. Sarah buys a 48 fl oz bottle of apple juice. How many cups of juice can she pour from the bottle? MR 1.1, 2.3 Print This Page Name Print This 9–2 Page Customary Capacity and Weight Capacity is the measure of dry or liquid volume of a container. Pour water into empty milk cartons to model the equivalent units of capacity shown below. 2 cups  1 pint (c) (pt) R RETEACH Customary Units of Capacity 8 fluid ounces (fl oz)  1 cup (c) 2 cups (c)  1 pint (pt) 2 pints (pt)  1 quart (qt) 4 quarts (qt)  1 gallon (gal) 2 pints  1 quart (pt) (qt) Weight is the measure that tells how heavy an object is. A card and envelope weigh about 1 ounce. 4 quarts  1 gallon (qt) (gal) Customary Units of Weight 16 ounces (oz)  1 pound (lb) 2,000 pounds (lb)  1 ton (T) A book weighs about 1 pound. © McGraw-Hill School Division Circle the letter of the correct estimate. 1. weight of an apple A. 5 oz B. 2 lb C. 12 T 2. weight of a fourth grader A. 12 T B. 20 oz C. 60 lb 3. amount of water in a bathtub A. 25 qt B. 25 gal C. 25 pt 4. weight of a refrigerator A. 100 oz B. 100 lb C. 5 T 5. amount of water in a pail A. 5 qt B. 50 gal C. 500 c Use with Grade 4, Chapter 9, Lesson 2, pages 366–369. (275) MR 1.1, 2.3 Print This Page Name Print This 9–2 Page Customary Capacity and Weight E ENRICH Reasonable Measure Maze Shade each box that contains a reasonable measure. The shaded boxes will form a path from start to finish. Finish A living room is 6 yards long. Your smile is 1 yard wide. In an hour, an airplane flew 1,780 miles. A horse weighs 827 oz. A pizza weighs 144 oz. A song is about 3 minutes long. A goldfish bowl holds 18 cups of water. An automobile might weigh 2,545 lb. The pitcher holds 3 qt of lemonade. A football field A frog can jump 475 feet. A girl’s braid was 3 yards long. A dog can jump 17 yards. Jen held her breath for 63 seconds. The gate is 40 inches high. A gallon of paint is enough to paint a large wall. The kitten drank an ounce of milk. The movie lasted 107 minutes. A TV commercial lasts about 600 seconds. A bathtub holds 18 pints of water. The train was 125 yd long. © McGraw-Hill School Division You could walk a mile in 20 seconds. 1 is 4 mile long. The punch bowl holds 24 cups of punch. Pat rode his bike 12 mph. The climbing rope to the tree fort was 37 inches long. The diving pool was 4 yd deep. The subway sandwich was 12 yd long. A light bulb weighs 2 ounces. It took about 3 yards of fabric to make a cape. The newborn baby drank 7 oz of milk. A banana is 9 inches long. Beth ran a distance of 10,525 ft. A sneaker weighs 40 oz. Start How did you decide if running a distance of 10,525 feet was reasonable? Use with Grade 4, Chapter 9, Lesson 2, pages 366–369. (276) MR 1.1, 2.3 Print This Page Name Print This 9–3 Page Convert Customary Units P PRACTICE Complete. 1. 7 ft  in. 4. 60 in.  ft 2. 21 ft  yd 3. 2 mi  yd 5. 13 yd  ft 6. 2 mi  ft 9. 3 pt  c 7. 8 qt  gal 10. 36 ft  yd 11. 4 ft  in. 12. 12 ft  yd 13. 12 pt  qt 14. 2 lb  oz 15. 48 oz  lb 16. 3 T  ft 17. 10,000 lb  lb 19. 3 gal  8. 144 in.  qt T 18. 2 c  20. 2 qt  fl oz 21. 10 c  pt pt 22. 1 lb 10 oz  oz 23. 1 gal 2 pt  pt 24. 10 ft  yd 25. 4 T 800 lb  lb 26. 5 ft 8 in.  in. 27. 13 qt  gal ft qt Algebra & Functions Complete the table. 28. Gallons 29. 1 Quarts Pints 1 Feet 12 9 Inches 16 Cups 30. Yards 72 64 Ounces Pounds 1 2 3 4 31. Tons Pounds 1 6,000 © McGraw-Hill School Division 16 32 48 Problem Solving 32. Amy cuts a piece of ribbon 60 in. long. How many feet long is the piece of ribbon? Use with Grade 4, Chapter 9, Lesson 3, pages 370–373. (277) 33. The 6 members of the Brown family drink a total of 3 gallons of milk each week. How much is that per person? AF 1.3; MR 1.1, 2.3 Print This Page Name Print This 9–3 Page Convert Customary Units R © McGraw-Hill School Division You can use tables to help you convert customary units of measure. To convert a larger unit to a smaller unit, multiply. Think: 2 gallons  4  8 quarts Cups Pints Quarts To convert a smaller unit to a larger unit, 2 1 divide. Think: 8 quarts  4  2 gallons 4 2 1 6 3 24 2 8 4 36 3 10 5 48 4 12 6 60 5 14 7 72 6 16 8 4 84 7 Ounces Cups Pounds 96 8 8 1 108 9 3 16 2 Feet Yards Miles 24 3 5,280 1,760 1 32 4 10,560 3,520 2 40 5 15,840 5,280 3 48 6 Inches Feet 12 Yards 1 2 RETEACH Gallons 1 2 3 1 1 2 3 Complete. 1. 3 ft  in. 4. 5 yd  ft 7. 12 qt  10. 3 pt  gal c 2. 24 in.  5. 8 c  8. 3 mi  11. 2 lb  Use with Grade 4, Chapter 9, Lesson 3, pages 370–373. (278) ft pt yd oz 3. 6 ft  6. 12 pt  9. 2 qt  12. 48 oz  yd qt pt lb AF 1.3; MR 1.1, 2.3 Print This Page Name Print This 9–3 Page Convert Customary Units E ENRICH Can You Convert? Play with a partner. Take turns. • For each turn, roll one number cube. Move that many spaces. • Then roll two number cubes. Convert that number to a larger or smaller unit of measure. For example, you land on a qt square. You roll a 1 and a 7. You can convert 17 or 71 quarts to cups, pints, or gallons, or a combination of units. • If your answer is correct, move ahead 1 space. If it is incorrect, move back 1 space. • The player who reaches FINISH first wins. Start qt oz in. lb c ft gal yd pt © McGraw-Hill School Division qt oz in. lb c ft gal Use with Grade 4, Chapter 9, Lesson 3, pages 370–373. (279) yd pt Finish AF 1.3; MR 1.1, 2.3 Print This Page Name Print This 9–4 Page Problem Solving: Reading for Math P PRACTICE Reading Skill Check for Reasonableness Circle the statement that is reasonable. 1. Robert and Anthony ran 3 miles. Robert says, “We ran about 30,000 feet.” Anthony says, “We ran about 15,000 feet.” Explain your thinking: 2. The distance from April’s home to the school is 10,560 feet. April says “Our home is about 3,500 yards from the school.” April’s sister says, “Our home is about 30,000 yards from the school.” Explain your thinking: 3. A running track is 3,600 yards. Pablo says, “The track is less than 2 miles long.” John says, “The track is more than 2 miles long.” © McGraw-Hill School Division Explain your thinking: 4. A cooler holds 8 gallons of sports drink. Brian says, “The cooler holds 2 quarts.” Rachel says, “The cooler holds 32 quarts.” Explain your thinking: Use with Grade 4, Chapter 9, Lesson 4, pages 374–375. (280) NS 1.2; MR 1.1, 2.3, 2.5, 3.1, 3.2 Print This Page Name Print This 9–4 Page Problem Solving: Reading for Math P Check for Reasonableness PRACTICE Math Skills Test Prep Choose the correct answer. The stage is 31 feet long. The director says the stage is more than 10 yards long. Is this statement reasonable? 1. Which of these statements is true? 2. The director’s statement is A The stage is 11 yards long. reasonable because B The stage is 12 yards long. F 30 feet is less than 10 yards. C The stage is 31 feet long. G 30 feet equals 10 yards. D The stage is 36 inches long. H 31 feet equals 10 yards. J 31 feet equals 11 yards. The television cabinet is 78 inches high. Mary says this is more than 7 feet high. Is this statement reasonable? 3. Which of these statements is true? 4. Mary’s statement is not reasonable A The cabinet is 7 feet high. because B The cabinet is 8 feet high. F 78 inches is less than 7 feet. C The cabinet is more than 8 feet high. G 78 inches is equal to 7 feet. D None of the above J 78 inches is greater than 8 feet. H 78 inches is greater than 7 feet. The refreshment stand sells 36 quarts of punch. Ms. Spencer says the stand sells 9 gallons of punch. Is this statement reasonable? © McGraw-Hill School Division 5. Which of the following is important 6. Ms. Spencer’s statement is to solving this problem? reasonable because A There are 2 gallons in a quart. F You divide quarts by 2 to find gallons. B There are 4 gallons in a quart. C There are 2 quarts in a gallon. D There are 4 quarts in a gallon. G You divide quarts by 4 to find gallons. H You multiply quarts by 2 to find gallons. J You multiply quarts by 4 to find gallons. Use with Grade 4, Chapter 9, Lesson 4, pages 374–375. (281) NS 1.2; MR 1.1, 2.3, 2.5, 3.1, 3.2 Print This Page Name Print This 9–4 Page Problem Solving: Reading for Math P Check for Reasonableness PRACTICE Math Skills Test Prep Choose the correct answer. The theater is 75 feet wide. The theater is twice as long as it is wide. Ned says the theater is 225 yards wide. Is this statement reasonable? 7. Which of these statements is false? A B C D The theater is 75 feet wide. The theater is 75 feet long. The theater is 150 feet long. The theater is twice as long as it is wide. Solve. Explain your answer. 9. Tyler walks 4 miles from his home to the movie theater. He says he walks more than 20,000 feet. Is his statement reasonable? 11. Tammy’s sled is 65 inches long. She © McGraw-Hill School Division says the sled is more than 5 feet long. Is her statement reasonable? 13. The popcorn stand sells 100 ounces of popcorn. Ben says this is 1,600 pounds of popcorn. Is his statement reasonable? Use with Grade 4, Chapter 9, Lesson 4, pages 374–375. (282) 8. Ned’s statement is not reasonable because F You need to divide 75 by 3 to find the width in yards. G You need to multiply 75 by 3 to find the width in feet. H You need to divide 225 by 3 to find the width in yards. J You need to multiply 150 by 3 to find the width in feet. 10. A movie star is 6 feet tall. Meg says that the movie star is more than 80 inches tall. Is her statement reasonable? 12. Earl’s house is 1,200 yards from the bus stop. Earl says that is 3,600 feet. Is his statement reasonable? 14. The refreshment stand sells 144 ounces of peanuts. The manager says that this is more than 10 pounds of peanuts. Is his statement reasonable? NS 3.2; MR 1.1, 2.3, 2.5, 3.1, 3.2 Print This Page Name Print This 9–5 Page Explore Metric Length P PRACTICE Estimate and then measure. Tell what unit and tool you use. 1. the width of your classroom 2. the largest step you can take 3. the width of a window in your classroom 4. the distance from the tip of your hand to the elbow 5. thickness of a nickel © McGraw-Hill School Division Circle the letter of the correct estimate. 6. the distance from Sue’s house to school A. 2,000 mm B. 200 cm C. 2 km 7. the length of a piece of chalk A. 6 cm B. 6 dm C. 6 km 8. the height of a fourth-grader A. 140 mm B. 30 dm C. 140 cm 9. the height of a door A. 30 cm B. 3 m C. 300 mm 10. the length of a classroom A. 7 cm B. 7 m C. 7 km 11. the distance from Chicago to New York A. 1,200 km B. 5,000 m C. 2,000 dm 12. the thickness of a book A. 3 dm B. 3 cm C. 3 mm 13. the width of a pencil point A. 1 dm B. 1 cm C. 1 mm 14. the length of Ben’s foot A. 20 cm B. 20 dm C. 20 m Problem Solving 15. Norma bicycles 1 km in 4 minutes. About how many kilometers will she bicycle in 60 minutes? Use with Grade 4, Chapter 9, Lesson 5, pages 378–379. (283) 16. One brick measures 92 mm. What is its measurement to the nearest cm? MR 1.1, 2.3 Print This Page Name Print This 9–5 Page Explore Metric Length A centimeter (cm), millimeter (mm), decimeter (dm), and kilometer (km) are used to measure lengths in the metric system. 1cm 1 mm R RETEACH Metric Units of Length 10 millimeters (mm)  1 centimeter (cm) 10 centimeters (cm)  1 decimeter (dm) 100 centimeters (cm)  1 meter (m) 1,000 meters (m)  1 kilometer (km) 1 dm A kilometer measures large distances such as the distance from your school to a school in another town or city. Use a centimeter ruler to measure each object. Write the length. 1. 2. © McGraw-Hill School Division 3. 4. Circle the letter of the correct estimate. 5. the width of a button A. 18 cm B. 18 mm C. 2 mm 6. the length of a dollar bill A. 15 dm B. 15 mm C. 15 cm Use with Grade 4, Chapter 9, Lesson 5, pages 378–379. (284) MR 1.1, 2.3 Print This Page Name Print This 9–5 Page Explore Metric Length E ENRICH Connect the Dots Use a centimeter ruler to connect only those dots that are the given distance apart. 2. 2 cm 3. 5 cm 4. 3 cm © McGraw-Hill School Division 1. 4 cm Use with Grade 4, Chapter 9, Lesson 5, pages 378–379. (285) MR 1.1, 2.3 Print This Page Name Print This 9–6 Page Metric Capacity and Mass P PRACTICE Estimate and then measure the capacity of each object. 1. a water glass 2. a large pot 3. a cereal bowl 4. a milk carton 5. Order the objects above from least to greatest capacity. Estimate and then measure the mass of each object. 6. a box of crayons 7. a book 8. a paper clip 9. a pencil 10. Order the objects above from least to greatest mass. © McGraw-Hill School Division Circle the letter of the correct estimate. 11. A. 15 mL B. 15 L C. 2 L 12. A. 3 mL B. 31 L C. 310 mL 13. A. 200 mL B. 200 L C. 2 mL 14. A. 15 g B. 150 g C. 15 kg Algebra & Functions Complete the table. 15. Liters Milliliters 1 2 1,000 Problem Solving 16. Sally buys 1 kg of grapes. She packs 200 g of grapes in her lunch. How many grams of grapes are left? Use with Grade 4, Chapter 9, Lesson 6, pages 380–383. (286) 3 4,000 17. Jim buys 1 L of milk. He drinks 300 mL for breakfast. How many milliliters of milk are left? MR 1.1, 2.3 Print This Page Name Print This 9–6 Page Metric Capacity and Mass R Milliliters and liters measure capacity in the metric system. 1cm RETEACH Metric Units of Capacity 1,000 milliliters (mL)  1 liter (L) 1cm 1cm 1 Liter A cube 1 centimeter (cm) long, 1 centimeter wide, and 1 centimeter high will hold 1 milliliter (mL) of water. This bottle holds 1 liter (L) or 1,000 milliliters (mL) of water. Mass is the amount of matter that makes up an object. The mass of a paper clip is about 1 gram (g). Metric Units of Mass 1,000 grams (g)  1 kilogram (kg) The mass of the book is about 1 kilogram (kg) or 1,000 grams (g). © McGraw-Hill School Division Circle the letter of the correct estimate. 1. mass of a bar of soap A. 120 g B. 120 kg C. 12 kg 2. mass of an iron A. 1 g B. 100 g C. 1 kg 3. amount of water in a bathtub A. 100 mL B. 100 L C. 1,000 mL 4. mass of a horse A. 500 g B. 500 kg C. 1,000 g 5. a bottle cap A. 3 mL B. 300 mL C. 3 L Use with Grade 4, Chapter 9, Lesson 6, pages 380–383. (287) MR 1.1, 2.3 Print This Page Name Print This 9–6 Page Metric Capacity and Mass E ENRICH Who Invented It? Compare. Choose >, <, or . 1. 50 mL 5L  G  W 4. 1 L  B  B 7. 12 L 5. 8 L  T  H 10. 400 g  R 13. 1 kg  H  I 16. 10,000 g  R  C  M  I  U  C  I 8L  O 14. 7 kg  J  H  B  D 9. 5 kg  R  M  F  N 11 L  C 5,000 g  M 12. 6,000 g 6,900 g  E  M 6. 10,000 mL  C 80 L 400 mL  L 7,500 mL 11. 8,400 mL 70 g 3. 3 L 8. 75,000 mL  E 4 kg  U  B  A 12,000 mL  T 3L  A 70 mL  L © McGraw-Hill School Division 2. 4,000 mL  R 15. 5 kg  G  P  A 6 kg  S  T 69,000 g  R  S 12 kg  S  T Your backpack or windbreaker is probably made out of nylon. Who invented nylon? To find out, write the code letter for each answer. Write the letters in the order of the exercises. H. 1 2 3 4 5 6 7 8 Use with Grade 4, Chapter 9, Lesson 6, pages 380–383. (288) 9 10 11 12 13 14 15 16 MR 1.1, 2.3 Print This Page Name Print This 9–7 Page Convert Metric Units P PRACTICE Complete. 1. 5 m  2. 2 L  cm 4. 10 mm  5. 5 kg  cm 7. 3,000 mL  3. 7 kg  g g 6. 2 m  dm 8. 300 cm  L 10. 6,000 mL  mL L 11. 40 kg  13. 700 cm  14. 10 L  m 16. 10,000 g  12. 40 cm  mL 15. 2 km  m 18. 4 m  mm 22. 10 m  m 20. 3 dm  mm cm mm 21. 5 L  23. 5 cm  mm dm mL 24. 600 mm  cm 25. 8,000 mm  26. 4,000 m  km 27. 7,000 mL  L L 29. 70,000 g  kg 28. 20,000 mL  kg g kg 17. 6,000 cm  19. 20 cm  9. 4,000 g  m cm Compare. Write >, <, or . © McGraw-Hill School Division 30. 5,000 g 5 kg 31. 20 L 33. 60 cm 6m 34. 300 cm 36. 3 km 300 m 37. 900 mm 39. 500 dm 5 dm 40. 7 dm 200 mL 3m 9 cm 7,000 mm 32. 50 cm 6 dm 35. 2,500 mL 38. 13 L 2L 1,300 mL 41. 18,000 mL 18 L Problem Solving 42. Dottie has 1 kg 200 g of food for her cat. How many grams of cat food does she have? Use with Grade 4, Chapter 9, Lesson 7, pages 384–385. (289) 43. A 1 L bottle of water is half full. How many milliliters of water are in the bottle? AF 1.3; MR 1.1, 2.3 Print This Page Name Print This 9–7 Page Convert Metric Units R RETEACH You can convert metric units to compare. Metric Units Length 1 centimeter (cm)  10 milliliters (mm) 10 centimeters (cm)  1 decimeter (dm) 10 decimeters (dm)  1 meter (m) 1,000 meters (m)  1 kilometer (km) Mass 1 kilogram (kg)  1,000 grams (g) 1 gram (g)  1,000 milligrams (mg) Capacity 1 liter (L)  1,000 milliliters (mL) Convert 9 dm to centimeters (cm). Convert 6,000 mg to grams (g). To convert a larger unit to a smaller unit, multiply. To convert a smaller unit to a larger unit, divide. Think: 1 dm  10 cm Think: 1 g  1,000 mg 9 dm  ? cm 9 dm  9  10 cm 9 dm  90 cm 6,000 g  ? mg 6,000 g  6,000  1,000 mg 6,000 g  6 mg © McGraw-Hill School Division Complete. 1. 5 m  cm 2. 8 L  3. 6 kg  g 4. 70 mm  5. 8 dm  7. 2,000 mL  9. 9 cm  11. 5,000 g  6. 2 m  cm L mm kg Use with Grade 4, Chapter 9, Lesson 7, pages 384–385. (290) 8. 300 cm  mL cm dm m 10. 70 dm  m 12. 40 cm  dm AF 1.3; MR 1.1, 2.3 Print This Page Name Print This 9–7 Page Convert Metric Units E ENRICH Metric Match Game Use index cards to make the cards shown below. 10 mm 1 cm 5 km 500 cm 1,000 mm 1m 100 cm 1 km 10 cm 100 mm 1m 20 m 40 m 5m 200 dm 4 dm 5,000 m 1m 1,000 m 10 dm 20L 20,000 mL 5L 5,000 mL 500g 0.5 kg 59 kg 59,000 g 150,000 g 150 kg © McGraw-Hill School Division • Mix up the cards and place them facedown. Players take turns turning over two cards. • If all players agree that the measurements on the two cards are equivalent, the player that turned them over keeps the cards and takes another turn. If the cards are not equivalent, turn them facedown again. The next player turns over two cards. • Play until there are no more cards left. The player with the most pairs of cards wins. Use with Grade 4, Chapter 9, Lesson 7, pages 384–385. (291) AF 1.3; MR 1.1, 2.3 Print This Page Name Problem Solving: Strategy Print This 9–8 Page P PRACTICE Logical Reasoning Use logical reasoning to solve each problem. 1. An aquarium worker needs to fill a tank with 10 gallons of water. He has an 8-gallon pail and a 6-gallon pail. How can he use the pails to get exactly 10 gallons of water in the tank? 3. The parrot house has 2 times as many birds as the toucan house. The toucan house has 3 more birds than the jay house. The jay house has 6 birds. How many birds do the other houses have? © McGraw-Hill School Division Mixed Strategy Review Solve. Use any strategy. 5. Language Arts Kenny writes a 740-word review of a play. The review needs to be cut so that it is 500 words. How many words have to be cut? Strategy: 7. A bandstand is 40 feet wide by 80 feet long. It is built from wood planks that are 5 feet wide by 10 feet long. How many planks wide will the platform be? How many planks long? 2. Simon needs to put 9 cups of sea salt into a saltwater tank. He has a 10-cup container and a 7-cup container. How can Simon use the containers to measure 9 cups? 4. The parrots get food 20 minutes before the toucans. The toucans get food 15 minutes after the jays. The jays get food 30 minutes after Bird World opens. Bird World opens at 10:00 A.M. When does each kind of bird get food? 6. There are 24 cars in the theater parking lot. There are 3 times as many 4-door cars as 2-door cars. How many of each kind of car are there? Strategy: 8. Create a problem which you could solve by using logical reasoning. Share it with others. Strategy: Use with Grade 4, Chapter 9, Lesson 8, pages 386–387. (292) MR 1.1, 2.3, 3.1, 3.2 Print This Page Name Print This 9–8 Page Problem Solving: Strategy R RETEACH Logical Reasoning Page 387, Problem 1 Dan needs to put 6 cups of sea salt into the saltwater tank. He has a 7-cup container and a 5-cup container. How can he use the containers to measure 6 cups? Step 1 Read Be sure you understand the problem. Read carefully. What do you know? • Dan needs to put cups of sea salt in a saltwater tank. • Dan has containers that hold cups and cups. What do you need to find? • You need to find how to use the containers to measure cups. Step 2 Plan ■ ■ ■ © McGraw-Hill School Division ■ ■ ■ ■ ■ ■ ■ Make a Table or List Write a Number Sentence Work Backward Act it Out Find a Pattern Make a Graph Guess and Check Logical Reasoning Solve a Simpler Problem Draw a Diagram Make a plan. Choose a strategy. Use logical reasoning to solve the problem. You can use the difference in the amount each container can hold to measure exactly 6 cups. Use with Grade 4, Chapter 9, Lesson 8, pages 386–387. (293) MR 1.1, 2.3, 3.1, 3.2 Print This Page Name Print This 9–8 Page Problem Solving: Strategy R RETEACH Logical Reasoning Step 3 Carry out your plan. Solve Complete the table. It will show how to use the 7-cup container and the 5-cup container to measure exactly 6 cups. Sea Salt in Sea Salt in 7-cup Container 5-cup Container Steps Sea Salt in Tank 1. Fill the 7-cup container. 0 0 2. Fill the 5-cup container 5 cups 0 from the 7-cup container. 3. Pour what is left in the 7-cup container into the tank. 4. Repeat steps 1–3. How much sea salt is in the tank now? 5. Repeat steps 1–3. How much sea salt is in the tank now? 0 5 cups 0 5 cups 0 5 cups Step 4 Look Back Is the solution reasonable? Reread the problem. © McGraw-Hill School Division How can you check your answers? Practice 1. A worker has a 4-gallon pail and a 9-gallon pail. How can he use pails to fill a 10-gallon tank with water? Use with Grade 4, Chapter 9, Lesson 8, pages 386–387. (294) 2. Marcia arrives at the theater 10 minutes before Sam. Sam arrives 25 minutes after Lynn. Paul arrives 10 minutes before Lynn. Lynn gets to the theater at 6:30 P.M. When do the others arrive at the theater? MR 1.1, 2.3, 3.1, 3.2 Print This Page Name Temperature: Fahrenheit and Celsius Print This 9–9 Page P PRACTICE Give a reasonable temperature for each. Then use Fahrenheit and Celsius thermometers to measure each temperature. 1. warm water 2. temperature in freezer 3. cool water 4. temperature in cafeteria 5. temperature outside 6. temperature in classroom © McGraw-Hill School Division Circle the letter of the correct estimate. 7. to go skiing A. 20°C B. 20°F 8. to swim in the swimming pool A. 80°C B. 80°F 9. to go to the beach A. 30°C B. 30°F 10. to sleep comfortably A. 20°C B. 20°F 11. to work in the garden A. 70°C B. 70°F 12. to shiver without a coat A. 20°C B. 20°F 13. to picnic in the park A. 25°C B. 25°F 14. to rake leaves A. 10°C B. 10°F 15. to go sledding in the snow A. 30°C B. 30°F 16. to walk your dog A. 65°C B. 65°F Problem Solving 17. The temperature of a can of soup on the shelf is 45°F. Joy heats the soup to 25°F above its shelf temperature. What is the soup’s temperature now? Use with Grade 4, Chapter 9, Lesson 9, pages 388–389. (295) 18. At noon the temperature of the water in a swimming pool was 25°C. At 9:00 P.M. the temperature was 17°C. By how much did the water temperature drop? NS 1.8; MR 1.1, 2.3 Print This Page Name Print This 9–9 Page Temperature: Fahrenheit and Celsius R RETEACH Temperature is measured in degrees Celsius (°C) or in degrees Fahrenheit (°F). Compare the two scales shown at the right. 230 220 210 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 –10 –20 Fahrenheit Celsius 110 100 90 80 70 60 50 40 30 20 10 0 – 10 – 20 –30 Write the temperature in degrees Celsius (°C) and degrees Fahrenheit (°F). 1. 2. 10 0 – 10 – 20 10 0 – 10 4. 170 160 150 140 130 70 60 50 – 10 – 20 – 20 Circle the letter of the correct estimate. 5. the temperature of cold water 120 20 10 0 –10 –20 © McGraw-Hill School Division 40 30 20 10 0 60 50 40 30 20 3. A. 10°C B. 10°F 6. the temperature of warm water A. 100°C B. 100°F 7. the temperature of a fever A. 39°C B. 39°F 8. room temperature A. 70°C B. 70°F 9. temperature at an outdoor ice rink A. 20°C B. 20°F 10. temperature on a hot beach A. 30°C B. 30°F 11. comfortable outdoor temperature A. 10°C B. 10°F Use with Grade 4, Chapter 9, Lesson 9, pages 388–389. (296) NS 1.8; MR 1.1, 2.3 Print This Page Name Print This 9–9 Page Temperature: Fahrenheit and Celsius E ENRICH Predicting Temperatures Label the thermometers below with the following temperatures: 10°C 20°C 30°C 40°C 50°F 68°F 86°F 104°F 70 0°C 70 60 60 50 50 40 40 30 30 20 20 10 10 0 0 – 10 – 10 – 20 – 20 – 20 – 20 150 140 130 120 110 100 90 80 70 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 60 50 40 30 20 10 0 –10 –20 –10 –20 100°F 32°F Fahrenheit Celsius © McGraw-Hill School Division The thermometers are drawn so that equivalent measures are the same height on both scales. 1. Write the equivalent temperatures in degrees Fahrenheit. Use the thermometers above to help you. 10°C 20°C 30°C  40°C  2. When the Celsius temperature changes 10 degrees, how much does the Fahrenheit temperature change? 3. What pattern do you see that will help you predict Fahrenheit temperatures based on Celsius temperatures? Use with Grade 4, Chapter 9, Lesson 9, pages 388–389. (297) NS 1.8; MR 1.1, 2.3 Print This Page Name Problem Solving: Application Print This Page 9–10 Part A WORKSHEET Decision Making Applying Measurement Record your data. Items Ingredients Amount of Each Cost of Each Ingredient Ingredient Total Cost for Item Sandwiches Fruit Salad © McGraw-Hill School Division Punch Your Decision How much of each item should Mr. Martin make for the birthday party? Explain. Use with Grade 4, Chapter 9, Lesson 10, pages 390–391. (298) MR 1.1, 2.3 Print This Page Name Problem Solving: Application Which color heats up the most? Print This Page 9–10 Part B WORKSHEET Math & Science Record the temperature of each thermometer. Start Temperature Finish Temperature Difference Black Paper White Paper Aluminum Foil 1. Find the difference between each start and finish temperature. Show your work. © McGraw-Hill School Division Work Space 2. Which color heated up the most? The least? Use with Grade 4, Chapter 9, Lesson 10, pages 392–393. (299) NS 1.2; MR 1.2, 2.3, 2.6, 3.3 Print This Page Name Print This Page 9–10 Part B WORKSHEET Problem Solving: Application Math & Science Which color heats up the most? 3. Use subtraction to find how many more degrees the hottest thermometer changed than the coolest. Show your work. Is this a big difference? Work Space 4. Why did you have to put the thermometers under the sun or a lamp? 5. If you were playing outside on a sunny day, which color clothing © McGraw-Hill School Division would you like to wear? Why? 6. Explain the results of the activity in terms of reflection or absorption of light. Use with Grade 4, Chapter 9, Lesson 10, pages 392–393. (300) NS 1.2; MR 1.2, 2.3, 2.6, 3.3 Print This Page Name Print This 10–1 Page 3-Dimensional Figures P PRACTICE Identify the 3-dimensional figure the object looks like. Tell how many faces, edges, and vertices it has. 1. 2. 3. 4. 5. 6. © McGraw-Hill School Division Copy and fold. Identify the 3-dimensional shape. 7. 8. 9. 10. Algebra & Functions 11. What could the next shape be? Use with Grade 4, Chapter 10, Lesson 1, pages 408–411. (301) MG 3.6 Print This Page Name Print This 10–1 Page 3-Dimensional Figures R RETEACH A 3-dimensional figure usually rests on one of its faces, which is called a base. Look at the cube below. Count the number of faces, vertices, and edges it has. face edge A cube has 6 faces. A cube has 12 edges. vertices A cube has 8 vertices. Complete the chart. © McGraw-Hill School Division Name 3Dimensional Figure 1. triangular prism 2. rectangular prism 3. triangular pyramid 4. square pyramid 5. cone 6. cylinder 7. sphere Shape of Base Use with Grade 4, Chapter 10, Lesson 1, pages 408–411. (302) Number of Flat Faces and Bases Number of Straight Edges Number of Vertices MG 3.6 Print This Page Name Print This 10–1 Page 3-Dimensional Figures E ENRICH Polyhedrons The 3-dimensional figures shown below are called polyhedrons. • Each face of a polyhedron is the same size and shape. • Each edge of a polyhedron is the same length. • Each angle of each face is equal. Cube Tetrahedron Dodecahedron Icosahedron Octahedron Look at the cube. • It has 6 square faces. • Each square face has 4 edges. • Since 2 sides meet at each edge, a cube has (6  4)  2  12 edges. Use the information about polyhedrons to complete the sentences. 1. A tetrahedron has 4 triangular faces. © McGraw-Hill School Division Each triangular face has edges. (4  A tetrahedron has edges. 2. An octahedron has Each triangular face has An octahedron has 3. A dodecahedron has Each pentagonal face has A dodecahedron has )2 triangular faces. edges. edges. pentagonal faces. edges. edges. 4. An icosahedron has 20 triangular faces. Each triangular face has An icosahedron has edges. edges. Use with Grade 4, Chapter 10, Lesson 1, pages 408–411. (303) MG 3.6 Print This Page Name 2-Dimensional Figures and Polygons Print This 10–2 Page P PRACTICE Tell whether each figure is open or closed. Is it a polygon? If so, classify the figure. 1. 2. 3. 4. 5. 6. Draw the figure and identify it. Use a separate sheet of paper. 7. a 4-sided figure that is not a square 9. a 6-sided figure 8. a 5-sided figure 10. an 8-sided figure Algebra & Functions Locate each set of points. Then connect the points to make a geometric figure. Identify the figure. © McGraw-Hill School Division 11. (2, 2), (4, 3), (3, 5) 12. (2, 2), (5, 2), (5, 3), (2, 3) 5 4 3 2 1 5 4 3 2 1 O 1 2 3 4 5 Use with Grade 4, Chapter 10, Lesson 2, pages 412–415. (304) O 1 2 3 4 5 MG 3.8 Print This Page Name Print This 10–2 Page 2-Dimensional Figures and Polygons R RETEACH A polygon is a closed 2-dimensional figure that has straight sides. These figures are not polygons. Open Figures Closed Figures These figures are polygons. square 4 straight sides rectangle 4 straight sides triangle 3 straight sides pentagon 5 straight sides hexagon 6 straight sides octagon 8 straight sides © McGraw-Hill School Division Identify each polygon. 1. 2. 3. 4. 5. 6. Use with Grade 4, Chapter 10, Lesson 2, pages 412–415. (305) MG 3.8 Print This Page Name Print This 10–2 Page E 2-Dimensional Figures and Polygons ENRICH Tangrams A tangram is a Chinese puzzle that is made of 2-dimensional figures. The figures can be put together to form different shapes— sometimes even animal shapes! © McGraw-Hill School Division Cut out the five figures at the bottom of the page. Use all five figures to form each of the large polygons shown below. 1. tangram 1 2. tangram 2 3. tangram 3 4. tangram 4 Tangrams: G Use with Grade 4, Chapter 10, Lesson 2, pages 412–415. (306) C MG 3.8 Print This Page Name Print This 10–3 Page Lines, Line Segments, and Rays P PRACTICE Identify each figure. 1. B A 2. C 3. D 4. I L K J 5. Q S l T R 6. M N O P Identify the parts of a circle. 7. 8. © McGraw-Hill School Division G O 9. H K T V S Algebra & Functions Locate the set of points. Then connect the points to draw line segments. Classify the lines as perpendicular or parallel. 10. Line segment OP: 6 (1, 4) (2, 4) (3, 4) (4, 4) 5 Line segment QR: (1, 2) (2, 2) (3, 2) (4, 2) 4 3 2 1 1 Use with Grade 4, Chapter 10, Lesson 3, pages 416–419. (307) 2 3 4 5 6 MG 3.1, 3.2 Print This Page Name Print This 10–3 Page Lines, Line Segments, and Rays R RETEACH A line goes on forever in both directions A line segment is part of a line. It has two endpoints. A ray has one endpoint. Parallel lines never meet. Intersecting lines meet. Perpendicular lines form square corners. A chord is a line that connects two points on a circle. A diameter is a chord that goes through the center of the circle. A radius is the distance from the center of a circle to every point on a circle. © McGraw-Hill School Division Identify each figure. 1. 2. 3. 4. 5. 6. 8. 9. Identify the parts of a circle. 7. Use with Grade 4, Chapter 10, Lesson 3, pages 416–419. (308) MG 3.1, 3.2 Print This Page Name Print This 10–3 Page Lines, Line Segments, and Rays E ENRICH Can You Trace a Figure Without Lifting Your Pencil? 1. Look at Figure A and Figure B below. Can you trace each figure without lifting your pencil or retracing any line? Vertex 2 E O Vertex 3 Vertex 1 O E Vertex 2 Vertex 1 E E Vertex 4 Vertex 5 E E Vertex 3 Vertex 4 E Figure A Figure B 2. Can you trace Figure B without lifting your pencil if you start at any vertex? 3. Can you trace Figure A without lifting your pencil if you start at any vertex? 4. In Figure A, Vertex 4 has an even number of lines that meet at that point. This vertex can be called an even vertex. Vertex 3 has an odd number of lines meeting at that point. Vertex 3 can be called an odd vertex. Label each vertex in the figures. Write E for an even vertex and O for an odd vertex. 5. Can you trace the figures below without lifting your pencil or retracing any line? Label each vertex even or odd. O O E O O O © McGraw-Hill School Division E O Figure C E E O E Figure D O Figure E 6. What conclusion can you draw about whether you can trace a figure without lifting your pencil? Hint: Think about the types of vertices a figure has. Use with Grade 4, Chapter 10, Lesson 3, pages 416–419. (309) MG 3.1, 3.2 Print This Page Name Print This 10–4 Page Angles P PRACTICE Write acute, obtuse, or right for each angle. 1. 2. 3. 4. 5. 6. Write the degree measure and fraction of a turn for each angle. 7. 8. 9. Draw each figure. 11. a 3-sided figure with 3 acute angles © McGraw-Hill School Division 10. a 4-sided figure with 1 right angle Use with Grade 4, Chapter 10, Lesson 4, pages 420–421. (310) MG 3.5 Print This Page Name Print This 10–4 Page Angles R RETEACH Angles are formed by two rays that have the same endpoint. A right angle forms a square corner. An acute angle is less than a right angle. An obtuse angle is greater than a right angle. Identify each angle. Write acute, obtuse, or right. Use the corner of a sheet of paper to help you. 1. 2. 3. 4. 5. 6. 7. 8. © McGraw-Hill School Division Complete. 9. 10. This triangle has 3 11. This kite has 2 angles. This pentagon has angles and 2 angles, angles. 2 angles, and 1 angle. 2 Use with Grade 4, Chapter 10, Lesson 4, pages 420–421. (311) MG 3.5 Print This Page Name Print This 10–4 Page Angles E ENRICH Angle Sums What is the sum of the angles of a triangle? The sum will always be 180º or a straight line. Follow the steps below. 1 1 1 3 2 3 2 2 3 Step 1: Step 2: Step 3 Draw a triangle. Then draw lines to show each angle. Shade and number the 3 angles. Cut along the lines. Place the corners of the pieces together to form a straight line. Follow Steps 1–3 for each triangle below. 1. 2. 3. 2 1 1 3 3 2 1 Triangle 1 Triangle 2 3 2 Triangle 3 © McGraw-Hill School Division 4. What do you think the sum of the angles of a quadrilateral is? 5. Draw a quadrilateral. Draw lines to show the 4 angles. Then shade the corners, cut them out, and put them together to see if you are correct. Use with Grade 4, Chapter 10, Lesson 4, pages 420-421. (312) MG 3.5 Print This Page Name Print This 10–5 Page Triangles and Quadrilaterals P PRACTICE Classify each triangle as equilateral, isosceles, or scalene. Then classify each triangle as right, acute, or obtuse. 1. 2. 3. 5. 6. Identify each quadrilateral. 4. Tell if each statement is true or false. Explain why. 7. All rectangles are parallelograms. 8. All squares are rhombuses. 9. Some right triangles are also equilateral triangles. © McGraw-Hill School Division Problem Solving 10. Sue’s desk has equal sides of 20 inches and 4 right angles. Nancy’s desk has two sides of 20 inches, two sides of 30 inches, and 4 right angles. Both say their desks are rectangles. Who is correct? Use with Grade 4, Chapter 10, Lesson 5, pages 422–425. (313) 11. Mike makes a square out of wooden sticks. He pushes one corner of the square and makes a rhombus. How are the square and rhombus alike? How are they different? MG 3.7, 3.8 Print This Page Name Print This 10–5 Page Triangles and Quadrilaterals R RETEACH You can classify a triangle by the lengths of its sides or the measures of its angles. An equilateral triangle has three sides of equal length. An isosceles triangle has at least two sides of equal length. A scalene triangle has no sides of equal length. An acute triangle has three acute angles (less than 90º). An obtuse triangle has one obtuse angle (greater than 90º and less than 180º). A right triangle has one right angle (exactly 90º). All quadrilaterals have 4 sides and 4 angles. A square has 4 equal sides and 4 right angles. A rectangle has 4 right angles. Its opposite sides are equal and parallel. A rhombus has 4 equal sides. Its opposite sides are parallel. A trapezoid has 1 pair of parallel sides. A parallelogram has opposite sides that are equal and parallel. Classify each triangle by its sides and angles. © McGraw-Hill School Division 1. 2. 3. Identify each quadrilateral in as many ways as you can. 4. 5. Use with Grade 4, Chapter 10, Lesson 5, pages 422–425. (314) 6. MG 3.7, 3.8 Print This Page Name Print This 10–5 Page Triangles and Quadrilaterals E ENRICH Geometry Bingo Play this bingo game with 2–3 players. • Work together to make the bingo game. On an index card, write each of the names for geometric figures shown in the box below. • Then draw each figure in one of the squares on the bingo card below. Be sure to mix up the names. • Shuffle the index cards and place them face down. • Players take turns drawing index cards. Each player places a game marker on the matching figure drawn on the bingo card. • The first player to have markers that fill any row, column, or diagonal wins. parallel lines parallelogram radius rhombus hexagon isosceles triangle © McGraw-Hill School Division B intersecting lines ray right angle octagon acute triangle obtuse triangle I perpendicular lines chord acute angle cube equilateral triangle right triangle N G line segment diameter obtuse angle pentagon trapezoid scalene triangle O FREE Use with Grade 4, Chapter 10, Lesson 5, pages 422–425. (315) MG 3.7, 3.8 Print This Page Name Print This 10–6 Page Problem Solving: Reading for Math P PRACTICE Reading Skill Use a Diagram Use the illustration to solve problems 1–2. 1. Howie used the above figure in a painting. Describe the figure in more than one way. 2. What shape could Howie add to the right side of the figure so that the figure becomes a trapezoid? Add the shape to the figure. Use the illustration below to solve problems 3–4. 4 ft 4 ft © McGraw-Hill School Division 4 ft 6 ft 4 ft 3. Phyllis designed this doorway. What two shapes make up this doorway? 4. What is the length of the missing side of the doorway? Use with Grade 4, Chapter 10, Lesson 6, pages 426–427. (316) MG 3.1, 3.7, 3.8; MR 1.1, 2.3, 2.4, 3.2 Print This Page Name Print This 10–6 Page Problem Solving: Reading for Math P Use a Diagram Math Skills Test Prep Choose the correct answer. This figure is composed of a parallelogram and an equilateral triangle. What is the length of Side A of the triangle? 1. Which statement is true? A All sides of the figure are the same length. B Side A has the same length as one side of parallelogram. C The length of Side A must be greater than 6 inches. PRACTICE 6 in. 4 in. A 2. What is the length of Side A? F 4 inches G 6 inches H 12 inches 4 in. This figure is composed of a rhombus and a triangle. Can the length of side B be 8 inches long? B 4 in. 3. Which statement is true? © McGraw-Hill School Division A The length of side B must be greater than 8 inches. B The length of side B must be less than 8 inches. C The length of side B must be equal to 8 inches. This figure is composed of an isosceles triangle and a rectangle. What is the length of Side C? 5. You can find the length of Side C because A two sides of an isosceles triangle are equal. B the length of Side C is greater than the lengths of the other two sides of the triangle. C no two sides of the triangle have equal lengths. Use with Grade 4, Chapter 10, Lesson 6, pages 426–427. (317) 4. Can the length of side B be 8 inches long? F Yes G No H The answer cannot be found using the information in the diagram. C 10 cm 3 cm 6 cm 6. What is the length of Side C? F 3 centimeters G 6 centimeters H 10 centimeters MG 3.1, 3.7, 3.8; MR 1.1, 2.3, 2.4, 3.2 Print This Page Name Print This 10–6 Page Problem Solving: Reading for Math P Use a Diagram PRACTICE Math Skills Test Prep Choose the correct answer. This figure is a parallelogram. Suppose you draw a line segment from point A to point C. The length of this segment is 5 cm. How would you describe the two new figures you made? 7. Which of these statements is true? A You cannot tell the lengths of the unlabeled sides of the parallelogram. B Only two sides of the parallelogram have a length of 2 centimeters. C Each side of the parallelogram has the length of 2 centimeters. A B 2 cm D C 6 cm 8. How would you describe the two new figures you made? F They are scalene triangles. G They are isosceles triangles. H They are equilateral triangles. Solve. Use data from the illustration to answer problems 9–10. 9. Orson designed this picture frame. What shapes make up the frame? What shape is made by the outer edge of the frame? 10. Suppose Robert added 2 feet to the © McGraw-Hill School Division height of the frame, but kept the width the same. What shape would be made by the outer edge of the frame? 12. Robert drew a square. Then he divided the shape into two parts by drawing a line from one corner of the square, through the center, to the opposite corner. Name two ways to describe the two smaller shapes he created. Use with Grade 4, Chapter 10, Lesson 6, pages 426–427. (318) 3 ft 3 ft 11. Wendy drew a triangle in which three angles were less than 90°. What kind of triangle did she draw? 13. Max draws a rectangle with sides of 6 inches and 9 inches. He uses one of the short sides of the rectangle as a side of a scalene triangle. Can the lengths of the other two sides of the triangle be 6 inches? Explain. MG 3.1, 3.7, 3.8; MR 1.1, 2.3, 2.4, 3.2 Print This Page Name Print This 10–7 Page Congruent and Similar P PRACTICE Write whether the figures are similar. Then write whether the figures are congruent. 1. 2. 3. 4. © McGraw-Hill School Division Copy the figure on a separate piece of dot paper. Then draw one congruent figure and one similar figure. 5. 6. 7. 8. 9. 10. Algebra & Functions Use separate grid paper. 11. Draw a figure on a coordinate grid. Then draw a similar figure that is one half the size of the original. Write the ordered pairs for all vertices. 12. Draw a figure on a coordinate grid. Then draw a similar figure that is two times the size of the original. Write the ordered pairs for all vertices. Use with Grade 4, Chapter 10, Lesson 7, pages 430–433. (319) MG 3.3, 3.4 Print This Page Name Print This 10–7 Page Congruent and Similar R RETEACH Similar Figures Congruent Figures Not congruent Not similar • same shape • may be different sizes • same shape • same size • not the same shape • not the same size To see if figures are congruent, trace one figure. If you can make it fit exactly on top of the other figure, the figures are congruent. © McGraw-Hill School Division Write whether the figures are similar. Then write whether the figures are congruent. You may trace the figures. 1. 2. 3. 4. 5. 6. Use with Grade 4, Chapter 10, Lesson 7, pages 430–433. (320) MG 3.3, 3.4 Print This Page Name Print This 10–7 Page Congruent and Similar E ENRICH Shape Detective Can you find the similar and congruent figures in the drawings below? Each figure in the drawings can be named with one or more letters. Look at the first drawing. Figure A is the rectangle in the upper left corner. Figure AB is the top rectangle. Complete the sentences. The first one is done for you. 1. Figure B is similar to Figure ABCD. 2. Figure C is congruent to Figure A B D C . 3. Figure BC is congruent to Figure . 4. Figure EF is similar to Figure . F G 5. Figure F is congruent to Figure and Figure E H . I 6. Figure I is to Figure EF. 7. How many sets of congruent and similar © McGraw-Hill School Division figures can you find in the drawing at the right? Name each pair or set of figures. J N O Q P M Use with Grade 4, Chapter 10, Lesson 7, pages 430–433. (321) K L MG 3.3, 3.4 Print This Page Name Explore Translations, Reflections, and Rotations Print This 10–8 Page P PRACTICE Write translation, reflection, or rotation to describe how the figure was moved. 1. 2. 3. 4. 5. 6. Draw the movement of each figure on the dot paper. © McGraw-Hill School Division 7. translation 9. translation, then rotation 8. reflection 10. rotation, then reflection Use with Grade 4, Chapter 10, Lesson 8, pages 434–435. (322) MG 3.4 Print This Page Name Explore Translations, Reflections, and Rotations Print This 10–8 Page R RETEACH You can move figures in different ways. You can slide a figure across a line to show a translation. You can flip a figure over a line to show a reflection. You can turn a figure around a point to show a rotation. © McGraw-Hill School Division Write translation, reflection, or rotation to tell how each figure was moved. 1. 2. 3. 4. 5. 6. 7. 8. 9. Use with Grade 4, Chapter 10, Lesson 8, pages 434-435 (323) MG 3.4 Print This Page Name Print This 10–8 Page Explore Translations, Reflections, and Rotations E ENRICH Shape Art Cut out the shape cards and turn them face down. Then cut out the movement cards. Place those cards face down in another pile. Choose one shape card. On another sheet of paper, trace that shape. Then choose a movement card. Follow the instructions on that card. Return the movement card to the bottom of the pile, and choose another movement card. Repeat until you have chosen 4 movement cards. Trade your artwork with a partner. Try to guess which movement cards your partner chose to create the drawing. Movement Cards Translation Reflection Rotation Slide your shape 1 inch to the right. Trace it again. Flip over your shape to the right. Trace it again. Turn your shape around a point. Trace it again. Shape Cards Sample Artwork © McGraw-Hill School Division Which cards were chosen to draw this artwork? Create another shape and another rule for a movement cards. Use with Grade 4, Chapter 10, Lesson 8, pages 434–435. (324) MG 3.4 Print This Page Name Print This 10–9 Page Symmetry P PRACTICE Is the dotted line a line of symmetry? 1. 2. 3. 4. 5. 6. Is the figure symmetrical? If yes, draw its lines of symmetry. 7. 8. 9. © McGraw-Hill School Division 10. On a separate sheet of paper, draw a figure with rotational symmetry. 11. On a separate sheet of paper, draw a figure with bilateral symmetry. Complete the drawing to make it symmetrical. 12. 13. Use with Grade 4, Chapter 10, Lesson 9, pages 436–439. (325) 14. MG 3.4 Print This Page Name Print This 10–9 Page Symmetry R RETEACH Follow these steps to find out if a figure has bilateral symmetry. Step 1: Trace Figure A and cut it out. Step 2: Fold it along one of the dashed lines. The two halves match. The dashed line is a line of symmetry. The figure has bilateral symmetry. Step 3: Unfold the figure. Step 4: Fold the figure along the other dashed lines. The halves match, so all the lines are lines of symmetry. Figure A Follow these steps to find out if Figure B has rotational symmetry. Step 1: Trace Figure B and cut it out. Step 2: Place it on top of the original Figure B. Put your pencil point on the dot in the center. Step 3: Turn the top figure 90º. The top figure matches the original figure. Step 4: Turn the top figure 180º. The figures match. Figure B has rotational symmetry. Figure B © McGraw-Hill School Division 1. Place Figure A you traced on top of original Figure A. Put your pencil point in the center. Turn the top of figure 180º. Does the top figure match the original? Does Figure A have rotational symmetry? 2. Fold Figure B you traced to find its lines of symmetry. How many lines of symmetry does Figure B have? Look at each figure. Is the dashed line a line of symmetry? Then trace each figure. Turn it to see if it has rotational symmetry. 3. 4. Use with Grade 4, Chapter 10, Lesson 9, pages 436–439 (326) 5. MG 3.4 Print This Page Name Print This 10–9 Page Symmetry E ENRICH Circle each letter that has one or more lines of symmetry. © McGraw-Hill School Division Draw the line or lines of symmetry. G4_C10_L09_E01_MA01 Use with Grade 4, Chapter 10, Lesson 9, pages 436–439. (327) MG 3.4 Print This Page Name Print This 10–10Page Problem Solving: Strategy P PRACTICE Find a Pattern Use data from this tessellation to solve problems 1–4. 1. What shapes do you see in a repeated pattern? 2. How are the shapes moved? 3. Complete the missing pieces of the pattern. 4. Suppose you extend this design. You have a total of 20 small right triangles. How many rhombuses will there be in all? © McGraw-Hill School Division Mixed Strategy Review Solve. Use any strategy. 5. Aaron buys 5 Picasso T-shirts for his family. A large T-shirt costs $15 and a small T-shirt costs $12. Aaron spends $69. How many large T-shirts does he buy? How many small T-shirts does he buy? Strategy: 7. Mr. Ervin has 32 jars of paint. He has small boxes that will hold 4 jars and a large box that will hold 6 jars. Which box should Mr. Ervin use if he wants to put an equal number of jars in each box? How many boxes will he need? 6. Art On May 15, 1990, a painting by Van Gogh sold for $75,000,000. Two days later, a painting by Renoir sold for $4,000,000 less than that amount. How much did Renoir’s painting sell for? Strategy: 8. Create a problem which involves finding a pattern in a tessellation. Share it with others. Strategy: Use with Grade 4, Chapter 10, Lesson 10, pages 440–441. (328) MG 3.8; MR 1.1, 2.3, 2.4, 3.2 Print This Page Name Problem Solving: Strategy Print This 10–10Page R RETEACH Find a Pattern Page 441, Problem 1 What shapes do you see in a repeated pattern? How are the figures moved? Step 1 Read Be sure you understand the problem. Read carefully. What do you know? • The illustration shown is a tessellation. What do you need to find? • You need to identify . Step 2 Plan © McGraw-Hill School Division ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ Find a Pattern Guess and Check Work Backward Make a Graph Make a Table or List Write a Number Sentence Draw a Diagram Solve a Simpler Problem Logical Reasoning Act It Out Make a plan. Choose a strategy. Looking for a pattern will help you solve the problem. Find shapes that look familiar. Look for a pattern to see how these shapes have been moved. Use with Grade 4, Chapter 10, Lesson 10, pages 440–441. (329) MG 3.8; MR 1.1, 2.3, 2.4, 3.2 Print This Page Name Print This 10–10Page Problem Solving: Strategy R RETEACH Find a Pattern Step 3 Solve Carry out your plan. Look for shapes you know. What shapes do you see? To find how these shapes have been moved, look for examples of rotations, translations, and reflections. What is one way to describe how the figures moved? Step 4 Look Back Is the solution reasonable? Reread the problem. Did you answer the question? Yes No © McGraw-Hill School Division What other strategies could you use to solve the problem? Practice Use data from this tessellation to solve. 1. What shapes do you see in a repeated pattern? How are they moved? Use with Grade 4, Chapter 10, Lesson 10, pages 440–441. (330) 2. Complete the missing pieces of the tessellation. MG 3.8; MR 1.1, 2.3, 2.4, 3.2 Print This Page Name Print This 10–11 Page Perimeter P PRACTICE Find the perimeter of each figure. 1. 2. 10 cm 3. 10 mm 8 mm 8 mm 5 cm 9 mm 7 cm 4 cm 11 mm 6 mm 4. 8 mm 11 mm 5. 11 mm 6. Algebra & Functions Find the length of each missing side. 7. 8. 8 in. 8 in. 9. 8 ft 11 yd 11 yd 4 ft 11 yd 11 yd perimeter  24 in. perimeter  24 ft perimeter  55 yd © McGraw-Hill School Division Problem Solving 10. Gerry plans a rectangular garden plot that is 30 ft long and 15 ft wide. What is the perimeter of the garden plot? Use with Grade 4, Chapter 10, Lesson 11, pages 442–445. (331) 11. A fence around a rectangular corral has a length of 180 ft and a width of 90 ft. What is the perimeter of the fence? NS 3.1; MG 3.8 Print This Page Name Print This 10–11 Page Perimeter R RETEACH Perimeter is the distance around a closed figure. To find the perimeter, add the lengths of all the sides. To find the perimeter of the rectangle, add the lengths of the sides. 10ft 15ft 10ft  15ft 50ft 15 ft 10 ft 10 ft 15 ft The perimeter of the rectangle is 50 ft. Find the perimeter of each figure. 1. 2. 4 in. 5 in. 4 in. 5 in. 5 in. 5 in. 4 in.   3.   4. 4 ft 4 ft 7m 5m © McGraw-Hill School Division 7. 6 dm 6 dm 6 dm 6 dm 6 dm 6 dm  5. 8 ft 8 ft 5m 8. 4 in. 5 in. 3 in. 6 in. Use with Grade 4, Chapter 10, Lesson 11, pages 442–445. (332)  8 ft 8 ft 7m 3 ft 6.  5 cm 5 cm 6 cm 6 cm 7 cm NS 3.1; MG 3.8 Print This Page Name Perimeter Print This 10–11Page E ENRICH Create a Perimeter Each square at the right is divided into three regions. Each region has a perimeter of 8 units. The square at the right is divided into two regions. Each region has a perimeter of 10 units. Divide each square below into the number of regions and the perimeter given. Try to do this in two different ways. 1. Number of regions: 4 Perimeter of each region: 10 units 2. Number of regions: 5 © McGraw-Hill School Division Perimeter of each region: 12 units 3. Number of regions: 6 Perimeter of each region: 12 units Use with Grade 4, Chapter 10, Lesson 11, pages 442–445. (333) NS 3.1; MG 3.8 Print This Page Name Print This 10–12Page Area P PRACTICE Find the area of each figure. 1. 4. 4 ft 2. 3. 5. 6. 2 yd 2 in. 5 yd 4 ft 2 in. Use graph paper to draw each figure. Tell what the figure is and find the area. 7. length: 5 cm width: 8 cm 8. length:7 cm 9. length: 7 cm width: 7 cm width: 4 cm © McGraw-Hill School Division Find the area and perimeter of each figure. 10. 12 cm 10 cm 11. 1 m 12. 4m Use with Grade 4, Chapter 10, Lesson 12, pages 446–449. (334) 6 mm 25 mm MG 1.2, 1.3; AF 1.4 Print This Page Name Print This 10–12Page Area R RETEACH Area is the number of square units needed to cover a region or figure. You can use these two ways to find the area of a rectangle or square. • Count the number of square units. There are 25 square units. The area is 25 square units. • Multiply the length times the width. 5  5  25 The area is 25 square units. Complete. 1. 2. length: units length: units width: units width: units area  square units area  square units Find the area of each figure. 3. 4. 5. 4 in. 3 ft 2 in. 4 in. © McGraw-Hill School Division 8 ft 7 in. 6. 7. 8. 9 ft 4m 3 yd 6 ft 5 yd Use with Grade 4, Chapter 10, Lesson 12, pages 446–449. (335) 6m MG 1.2, 1.3; AF 1.4 Print This Page Name Print This 10–12Page Area E ENRICH Pick’s Law Pick’s law can be used to find the area of any polygon. Draw the polygon on dot paper. Use this formula: A 1 2  (number of dots on the polygon)  1  (number of dots inside the polygon) Here’s how to use the formula to find the area of this polygon below. A  ( 12  12)  1  3 A  (6  1)  3 A53 A8 © McGraw-Hill School Division Find the area of each polygon. 1. 2. 3. 4. 5. 6. Use with Grade 4, Chapter 10, Lesson 12, pages 446–449. (336) MG 1.2, 1.3; AF 1.4 Print This Page Name Print This 10–13Page Explore Volume P PRACTICE © McGraw-Hill School Division Find the volume of each rectangular prism. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. length: 9 in. 14. length: 5 m 15. length: 7 cm 16. length: 10 ft width: 5 in. width: 8 m width: 2 cm width: 12 ft height: 4 in. height: 6 m height: 8 cm height: 5 ft Use with Grade 4, Chapter 10, Lesson 13, pages 450–451. (337) NS 3.1; MG 1.4 Print This Page Name Print This 10–13Page Explore Volume R RETEACH Volume is the amount of space a 3-dimensional figure encloses. Volume is measured in cubic units. You can use these two ways to find the volume of a rectangular or square prism. • Count the number of cubes in one layer. The bottom layer has 12 cubes. There are 3 layers. 12  12  12  36 The volume of the cube is 36 cubic units. • Multiply: length  width  height V  length  width  height V  4  3  3  36 The volume is 36 cubic units. 3 4 3 Find the volume of each rectangular prism. © McGraw-Hill School Division 1. 2. 3. length: length: length: width: width: width: height: height: height: volume  volume  cm3 4. 5. 2 cm 3 cm 4 cm 4 cm 2 cm 6 cm Use with Grade 4, Chapter 10, Lesson 13, pages 450–451. (338) volume  cm3 6. cm3 2 cm 2 cm 5 cm NS 3.1; MG 1.4 Print This Page Name Print This 10–13Page Explore Volume E ENRICH Volume Patterns 1. What is the volume of Prism A? 3 cm 2 cm 4 cm Prism A 2. What do you think will happen to the volume if you double the length, width, and height of Prism A? 6 cm 4 cm 8 cm Prism A Doubled 3. Find the volume of Prism A doubled. Was your answer to exercise 2 correct? 4. Complete the table. © McGraw-Hill School Division Original Rectangular Prism Length 2 cm 2 cm 1 cm 2 cm Width 2 cm 3 cm 2 cm 2 cm Height 1 cm 3 cm 3 cm 2 cm Volume Doubled Rectangular Prism Length 4 cm 4 cm 2 cm 4 cm Width 4 cm 6 cm 4 cm 4 cm Height 2 cm 6 cm 6 cm 4 cm Volume 5. Compare the volumes of the original and doubled prisms. What pattern do you see? Use with Grade 4, Chapter 10, Lesson 13, pages 450–451. (339) NS 3.1; MG 1.4 Print This Page Name Problem Solving: Application Analyze Data and Make Decisions Print This Page 10–14 Part A WORKSHEET Decision Making Record your data in the chart. © McGraw-Hill School Division Size of Garden Perimeter of Garden Cost of Fencing Material Cost of Fencing and Installation Your Decision What is your recommendation for Mr. Harris’s garden? Explain. Use with Grade 4, Chapter 10, Lesson 10, pages 452–453. (340) MG 1.1, 1.2, 1.3, 1.4; MR 1.1, 2.3 Print This Page Name Problem Solving: Application Print This Page 10–14 Part B WORKSHEET Math & Science How well do you make patterns? Record your ratings. Drawing of Structure Rating: 1 (best)–5 (worst) © McGraw-Hill School Division 1. How well did you follow directions? Do you have enough data to decide? Use with Grade 4, Chapter 10, Lesson 14, pages 454–455. (341) MG 3.3, 3.4, 3.7, 3.8; MR 1.1, 2.3, 3.2 Print This Page Name Print This Page 10–14 Part B WORKSHEET Problem Solving: Application Math & Science How well do you make patterns? 2. What was easy or hard when giving directions? 3. What was easy or hard when following directions? © McGraw-Hill School Division 4. Make a list of words that helped you give directions. 5. Describe how a camouflage pattern gives some animals a survival advantage. Use with Grade 4, Chapter 10, Lesson 14, pages 454–455. (342) MG 3.3, 3.4, 3.7, 3.8; MR 1.1, 2.3, 3.2 Print This Page Name Print This 11–1 Page Parts of a Whole P PRACTICE Write a fraction for the part that is shaded. 1. 2. 3. 4. 5. 6. 7. 8. © McGraw-Hill School Division Draw a rectangle with the fraction shaded. 9. 1 3 10. 4 5 11. 5 7 12. 4 8 13. 4 9 14. 5 6 Use with Grade 4, Chapter 11, Lesson 1, pages 470-471. (343) NS 1.5, 1.7 Print This Page Name Print This 11–1 Page Parts of a Whole R RETEACH A fraction can name parts of a whole. 4 parts shaded 7 parts in all 4 7 shaded 2 parts shaded 5 parts in all 2 5 shaded parts shaded → 4 → numerator parts in all → 7→ denominator parts shaded → 2 → numerator parts in all → 5 → denominator Complete to write a fraction for the part that is shaded. 1. 2. part shaded parts shaded parts shaded parts in all parts in all parts in all fraction 4. © McGraw-Hill School Division 3. fraction 5. fraction 6. part shaded parts shaded parts shaded parts in all parts in all parts in all fraction fraction Use with Grade 4, Chapter 11, Lesson 1, pages 470–471. (344) fraction NS 1.5, 1.7 Print This Page Name Print This 11–1 Page Parts of a Whole E ENRICH Fraction Design Design a quilt. Use red, white, blue, and purple crayons to color the squares below. 1. What part of your quilt is red? blue? purple? white? . © McGraw-Hill School Division Design a flag. Use red, yellow, green, and blue crayons. 2. What part of your flag is red? green? yellow? blue? Use with Grade 4, Chapter 11, Lesson 1, pages 470–471. (345) NS 1.5, 1.7 Print This Page Name Print This 11–2 Page Parts of a Group P PRACTICE Write a fraction that names what part is shaded. 1. 2. 3. 4. 5. 6. Draw a picture, and then write a fraction. 7. Six of eleven balloons are blue. © McGraw-Hill School Division 9. All of five kittens are smiling. 8. Four out of seven hats have stars. 10. One of four animals is a chimpanzee. Problem Solving 11. Five of 12 students are in the school chorus. What part of the students are in the chorus? Use with Grade 4, Chapter 11, Lesson 2, pages 472–473. (346) 12. Twenty of 25 students voted for class president. What part of the class did not vote for president? NS 1.5, 1.7 Print This Page Name Print This 11–2 Page Parts of a Group R RETEACH A fraction can name part of a group. There are 7 squares in all. 3 7 are shaded. 4 7 are not shaded. 5 8 are shaded. 3 8 are not shaded. There are 8 circles in all. Complete. © McGraw-Hill School Division 1. 2. shapes shaded shapes shaded shapes in all shapes in all fraction that is shaded fraction that is shaded fraction that is not shaded fraction that is not shaded Write a fraction that names what part is shaded. 3. 4. Use with Grade 4, Chapter 11, Lesson 2, pages 472–473. (347) 5. NS 1.5, 1.7 Print This Page Name Print This 11–2 Page E Parts of a Group ENRICH Draw the Group © McGraw-Hill School Division Each fraction tells what part of a group the shaded figure or figures represent. Complete the group for each fractional part. 1. 2 5 4 2. 16 3. 1 3 4. 5 6 5. 3 8 6. 1 2 7. 4 7 8. 2 8 9 9. 10 10. How did you decide how many triangles to draw in exercise 1? Use with Grade 4, Chapter 11, Lesson 2, pages 472–473. (348) NS 1.5, 1.7 Print This Page Name Print This 11–3 Page Find Equivalent Fractions and Fractions in Simplest Form P PRACTICE Draw an equivalent fraction for each. 1. 2. 1 2 1 6 1 6 1 4 1 6 1 4 3. 1 4 1 1 1 1 1 1 8 8 8 8 8 8 1 5 1 5 1 5 1 5 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 Complete to find equivalent fractions. 4. 42 10  8. 4  5  2 10 5. 1 28  6. 16 9. 1  6 2 22 8  1 7. 1 54 10. 4  1 11. 9 14. 6  15. 4  4 12   20 4 Name an equivalent fraction for each. 12. 3  7 13. 4  5 15 12 Write each fraction in simplest form. 16. 4  17. 6  18. 3  19. 6  20. 8  21. 3  22. 10  23. 8  24. 5  25. 9  26. 12  27. 24  10 12 © McGraw-Hill School Division 15 12 21 24 18 30 24 18 20 32 Complete the pattern of equivalent fractions. 28. 1      4 8 12 16 20 24 29. 1      3 6 9 12 15 18 Problem Solving 30. A box contains 6 red pencils and 8 black pencils. What fraction of the pencils are red? Use with Grade 4, Chapter 11, Lesson 3, pages 474–477. (349) 31. Paul caught 9 bass and 3 trout. What fraction of the fish were trout? NS 1.5; AF 2.2 Print This Page Name Print This 11–3 Page R Find Equivalent Fractions and Fractions in Simplest Form RETEACH Equivalent Fractions Simplest Form Equivalent fractions name the same part. To find an equivalent fraction, multiply the numerator and denominator by the same number. When a fraction is in simplest form, its numerator and denominator have only 1 as a common factor. Show 12 32 So, 13,  13 33 2 6 2 3 6, 9, and 4 12  3 9 14 34  4 12 6 8 in simplest form. 1. Find the greatest common factor of the numerator and denominator. factors of 6: 1, 2, 3, 6 factors of 8: 1, 2, 4 The greatest common factor is 2. 2. Divide the numerator and denominator by the greatest common factor. So, the simplest 6  62  3 8 4 82 form of 68 is 34 . are equivalent fractions. Complete to find equivalent fractions. 1. 2. © McGraw-Hill School Division 3 4  4. 3  3  4 4 3. 3 5 8   3 6 10 5. 3  3  5 5   6. 3  3  6 6 12  Write each fraction in simplest form. 7. 8. 4 8  9. 2 10  Use with Grade 4, Chapter 11, Lesson 3, pages 474–477. (350) 4 12  NS 1.5; AF 2.2 Print This Page Name Print This 11–3 Page Find Equivalent Fractions and Fractions in Simplest Form E ENRICH Which Does Not Belong? Look at the fractions in each exercise. Cross out the fraction that does not belong. Then write a fraction that does belong. 1. 4. © McGraw-Hill School Division 7. 3 8 5 8 6 7 7 8 2 8 3 12 4 16 5 25 5 9 3 5 5 12 5 6 2. 5. 8. 1 3 2 7 5 6 1 12 2 3 6 9 4 7 8 12 2 3 5 5 8 8 1 1 3. 6. 9. 1 2 5 9 4 8 3 6 6 8 8 12 10 16 3 4 1 3 3 7 4 6 5 8 Cross out each fraction in simplest form and the letter below it. 1 3 4 6 3 7 6 9 8 10 5 8 3 9 10 20 6 13 2 12 8 16 5 6 9 12 15 30 8 15 B E N X C K E L P L E T N T Y Write the letters that are left. Use with Grade 4, Chapter 11, Lesson 3, pages 474–477. (351) NS 1.5; AF 2.2 Print This Page Name Print This 11–4 Page Compare and Order Fractions P PRACTICE Complete. Write , , or . 1. 1 2 1 3 2. 2 5 3. 4 9 2 3 4. 2 5 3 4 7 5. 10 4 5 6. 3 4 2 3 7. 4 5 12 15 8. 1 5 4 20 9. 1 5 2 15 5 10. 12 1 4 11. 3 4 13 16 12. 8 9 7 8 7 13. 12 5 6 3 14. 10 4 9 15. 7 8 3 4 9 16. 10 4 5 17. 1 4 5 16 18. 3 5 7 10 2 7 Order from least to greatest. 1 1 19. 1 4, 2, 5 , 1 3 21. 5 7 , 7 , 20 , , , 3 3 20. 7 8, 4, 8 , , 1 2 22. 4 9, 3, 3 , , 2 5 24. 4 9, 9, 9 , , Order from greatest to least. 2 3 23. 1 2, 3, 4 © McGraw-Hill School Division 3 3 25. 1 4 , 4 , 16 , , , , 7 3 26. 5 6 , 12 , 4 , , Problem Solving 1 27. Sandra eats 1 6 of the cake. Pat eats 3 2 28. Karl eats 1 2 of a pizza. Tim eats 3 of a 3 4 of the cake. Who eats more cake? pizza. Chris eats Explain. the amounts from greatest to least. Use with Grade 4, Chapter 11, Lesson 4, pages 478–481. (352) of a pizza. Order NS 1.5, 1.9 Print This Page Name Print This 11–4 Page Compare and Order Fractions R RETEACH You can use equivalent fractions to compare and order fractions. Order the fractions from least to greatest: 16 , 23 , 36 . Step 1 Step 2 Write each fraction as an equivalent fraction with the same denominator. Compare the numerators. Put the fractions in order from least to greatest. 1 6  1 6 1 6  1 6 2 3  4 6 3 6  3 6 3 6  3 6 4 6  2 3 From least to greatest, the fractions are 16 , 36 , 23 . Complete. Write , , or . 1. 2. 3 4 2 4 4. 5 10 3 10 5. 4 8 © McGraw-Hill School Division 3. 1 2 2 3 1 3 1 4 3 8 6. 2 3 5 6 Write the fractions in order from least to greatest. 2 5 7. 6 6, 6, 6 , 5 3 8. 3 4, 8, 8 , , 1 1 9. 2 3 , 4 , 12 , Use with Grade 4, Chapter 11, Lesson 4, pages 478–481. (353) , , NS 1.5, 1.9 Print This Page Name Print This 11–4 Page Compare and Order Fractions E ENRICH Fraction War Play this game with a partner. • Cut out the cards below. Shuffle them and then place them facedown in a pile in front of you. Your partner will do the same thing. • Each player draws a card at the same time from his or her pile. The player who draws the greater fraction takes both cards. If both fractions are equal, each player draws another card. The player with the greater fraction also takes the fraction cards that were equal. © McGraw-Hill School Division • When the piles of cards are gone, the player with the greater number of cards wins. 1 2 1 3 1 4 1 5 1 6 1 8 1 9 1 12 1 18 2 3 2 4 2 5 2 6 2 8 2 9 2 12 2 18 3 8 3 9 3 10 5 8 3 15 3 6 5 12 8 10 4 12 7 12 6 15 5 6 7 8 5 9 3 4 Use with Grade 4, Chapter 11, Lesson 4, pages 478–481. (354) NS 1.5, 1.9 Print This Page Name Print This 11–5 Page Problem Solving: Reading for Math P PRACTICE Reading Skill Check for Reasonableness Circle the statement that helps you solve the problem. Then solve the problem. 1 1. Jack spends 1 hour in an amusement park. He spends 4 of his time waiting in lines. How many minutes does Jack wait in lines? There are 24 hours in 1 day. There are 60 minutes in 1 hour. Solution: 1 2. Two dozen students went to the amusement park. A group of 3 of those students went on the roller coaster. How many students went on the roller coaster? 1 1 3 is greater than 4 . A dozen is the same as 12. Solution: 3. At the amusement park, Vivian buys a bag of popcorn. The bag holds 14 pound of popcorn. How many ounces is that? Two thousand pounds equal 1 ton. One pound equals 16 ounces. Solution: © McGraw-Hill School Division 4. A flag at the amusement park is 4 yards long. The width of the flag 2 is 3 of its length. How many feet wide is the flag? One yard is the same as 3 feet. A yard is a measure of length. Solution: 5. Leora buys a quart container of iced tea to share with her friends. 1 Each friend drinks 4 of the iced tea. How many ounces did each friend drink? One quart equals 32 ounces. One cup equals 8 ounces. Solution: Use with Grade 4, Chapter 11, Lesson 5, pages 482–483. (355) MR 1.1, 2.3, 3.1, 3.2 Print This Page Name Problem Solving: Reading for Math Check for Reasonableness Print This 11–5 Page P PRACTICE Math Skills Test Prep Choose the correct answer. A group of 18 students goes to the amusement park. Of these students, 5 6 go on the bumper cars. How many students go on the bumper cars? 1. What prior knowledge do you need 2. A reasonable answer for this in order to solve this problem? problem would be A 56 means 5 of 6 equal parts. F greater than 18. B 56 is less than 1. G less than 3. C 56 is greater than 16 . H greater than 3 but less than 9. D 18 is divisible by 9. J greater than 9 but less than 18. Fun Time International has 16 amusement parks. Of these amusement parks, 34 are in the United States. There is a Fun Time Amusement Park in France. How many Fun Time Amusement Parks are in the United States? 3. Which information is not needed in © McGraw-Hill School Division order to solve the problem? A Fun Time has 16 amusement parks. B Of Fun Time’s amusement parks, 3 4 are in the United States. C Fun Time has an amusement park in France. D All of the above 4. A reasonable answer for this problem would be that Fun Time has F 16 amusement parks in the United States. G 12 amusement parks in the United States. H 4 amusement parks in the U.S J no amusement parks in the U.S. Nick spends 2 hours in the amusement park. He spends 23 of his time on rides. How many minutes does Nick spend on rides? 5. Which of the following information is important to solve the problem? A There are 24 hours in 1 day. B Nick goes on 4 rides. C There are 60 minutes in an hour. D There are 36 rides in the amusement park. Use with Grade 4, Chapter 11, Lesson 5, pages 482–483. (356) 6. A reasonable answer for this problem would be F 2 hours. G more than 60 minutes but less than 120 minutes. H greater than 20 minutes but less than 1 hour. J less than 20 minutes. MR 1.1, 2.3, 3.1, 3.2 Print This Page Name Problem Solving: Reading for Math Check for Reasonableness Print This 11–5 Page P PRACTICE Math Skills Test Prep Choose the correct answer. 3 A group of 40 students goes to the amusement park. If 4 of the students go on the Water Slide and 25 of the students go on the Space Shot, how many students go on the Space Shot? 7. What prior knowledge do you need 8. A reasonable answer for this in order to solve this problem? problem would be A 20  25 F 40 students. 3 B 4 means 3  4 2 C 5 means 2 of 5 equal groups 3 D 4 1 G 24 students. H 20 students. J 16 students. Solve. 9. There are 32 rides at an amusement park. Norman goes on 38 of the rides. How many rides does he go on? 11. A dozen students go to the © McGraw-Hill School Division amusement park. A group of 31 of these students goes on the Super Cycle. How many students go on the Super Cycle? 13. Each car of the Sling Shot can hold 15 people. A car is 25 full. How many people are in the car? Use with Grade 4, Chapter 11, Lesson 5, pages 482–483. (357) 10. Donna took 18 rides. She went on the roller coaster 23 of the time. How many roller-coaster rides did Donna take? 12. There were 25 students at the amusement park. Of these students, 2 5 were there for the first time. How many students were there for the first time? 14. An amusement park has 36 rides. Bobby goes on 12 of them. How many rides does he go on? MR 1.1, 2.3, 3.1, 3.2 Print This Page Name Print This 11–6 Page Explore Parts of a Group P PRACTICE Use the squares to help you find the fraction of each group. 1. 2. 1 3 3. 3 4 of 6  4. of 16  5. 3 4 of 18  4 5 of 15  6. 2 3 of 20  2 3 of 24  Find the fraction of each number. 1 8. 3 of 15  5 11. 7 of 14  2 14. 10 of 40  5 17. 3 of 21  2 20. 6 of 36  3 23. 7 of 49  7. 2 of 18  10. 6 of 12  13. 9 of 18  16. 8 of 40  19. 5 of 30  © McGraw-Hill School Division 22. 7 of 28  2 9. 5 of 30  3 3 12. 8 of 32  1 15. 7 of 21  1 18. 4 of 20  1 21. 8 of 16  6 24. 10 of 60  1 4 1 3 7 Problem Solving 25. Of the 24 fourth graders in Mrs. 1 4 Williams’ class, participate in sports. How many fourth-grade students participate in sports? Use with Grade 4, Chapter 11, Lesson 6, pages 484–485. (358) 26. Steven practices cello 15 hours a week. On Monday he practices 15 of that time. How many hours does Steven practice cello on Monday? NS 1.5 Print This Page Name Print This 11–6 Page Explore Parts of a Group R RETEACH You can use counters to find a part of a group. Suppose you have 20 counters. You want to find 2 5 of 20 counters. The denominator tells you how many equal groups to make. Divide the 20 counters into 5 equal groups. There are 8 counters in 2 groups. So, 2 5 of 20 is 8. Complete. Circle the part of each group. 1 2. 5 of 10  2 5. 4 of 12  1 8. 6 of 18  1. 2 of 8  © McGraw-Hill School Division 4. 3 of 15  7. 6 of 30  2 3. 3 of 6  3 6. 4 of 20  5 9. 5 of 10  Use with Grade 4, Chapter 11, Lesson 6, pages 484–485. (359) 1 1 4 NS 1.5 Print This Page Name Print This 11–6 Page Explore Parts of a Group E ENRICH Cooking with Fractions Use the grocery list to answer each question. 3 1. Barb adds salt and pepper to 4 of the ground beef. How much ground beef is that? Grocery List 12 pounds of ground beef 9 pounds of ground turkey 2 2. Mark uses 3 of the ground turkey to 15 pounds of potatoes make meatballs. How many pounds does he use? 36 eggs 16 loaves of bread 18 pounds of chicken 3 3. Melanie uses 5 of the potatoes for potato salad. How many pounds does she use? 20 pounds of sausage 5 4. George boils 6 of the eggs. How many eggs does he boil? 3 5. Sam slices 4 of the bread. How much is that? 1 © McGraw-Hill School Division 6. Sarah uses 8 of the bread for stuffing. How much is that? 3 7. Jon barbecues 4 of the sausage and uses the rest for appetizers. How many pounds does he barbecue? How many pounds does he use for appetizers? 1 1 8. Jan grills 2 of the chicken. Bob cooks 6 of the chicken for chicken salad. How much chicken is left? Use with Grade 4, Chapter 11, Lesson 6, pages 484–485. (360) NS 1.5 Print This Page Name Print This 11–7 Page Mixed Numbers P PRACTICE Rename as a mixed number or fraction in simplest form. 8 9 1. 7  7 2. 2  2 6. 38  22 10. 6  2 14. 28  40 18. 4  5. 66  9. 10  13. 56  17. 6  10 3. 2  6 7. 45  21 11. 2  2 15. 36  30 19. 6  4. 3  1 8. 17  5 13 12. 4  2 16. 84  64 20. 5  19 3 48 Algebra & Functions Use the number line to compare. Write , , or . 1 8 0 1 6 1 4 3 4 1 2 5 8 3 4 21. 1 1 6 1 18 22. 1 24. 1 1 4 1 58 25. 1 1 8 7 8 1 1 18 8 8 1 16 1 14 3 14 1 5 7 2 1 78 23. 2 1 12 3 12 18 14 18 26. 1 3 4 1 78 Problem Solving © McGraw-Hill School Division 27. Ben measures ten one-fourths of a 1 28. Claudia ran 43 miles on Monday. On cup of water. What is this as a mixed Tuesday she ran 412 miles. On which number? day did Claudia run a longer distance? Explain. 29. Jared drank 7 cups of juice. Aida drank 9 6 4 cups. Who drank more juice? Explain. Use with Grade 4, Chapter 11, Lesson 7, pages 486–487. (361) 30. Mary worked 81 hours on Monday 2 and 835 hours on Tuesday. On which day did she work longer? Explain. NS 1.5, 1.9 Print This Page Name Print This 11–7 Page Mixed Numbers R 13 4 You can use models to help you write 13 4 13 4 13 4 RETEACH as a mixed number.  4 4  4 4  4 4   1  1  1   3 14 1 4 1 4 You can also use multiplication and addition to write a mixed number as a fraction. Step 1. Multiply the whole number by the denominator. Step 2. Add the numerator to the product. 1 35 = (5  1)  3 5 = 53 5 = 8 5 Write the fraction as a mixed number or whole number. 1. 7 4 9 © McGraw-Hill School Division 4. 4  2. 7 3 11 5. 3  3. 31 8 8 6. 8  Write the mixed number as a fraction. 7. 1 1 4  8.6 3 5  10. 8 2 3  11. 4 1 3  12.5 2 7  13. 3 5 6  Use with Grade 4, Chapter 11, Lesson 7, pages 486–487. (362) NS 1.5, 1.9 Print This Page Name Mixed Numbers Print This 11–7 Page E ENRICH Fractions Between Shade the fraction bars to show a fraction between the two whole numbers given. Write both the fraction and the mixed number. 1. Shade the fraction bars to show a fraction between 1 and 2. Fraction: Mixed number: 2. Shade the fraction bars to show a fraction between 2 and 3. Fraction: Mixed number: 3. Shade the fraction bars to show a fraction between 2 and 3. Fraction: © McGraw-Hill School Division Mixed number: 4. Shade the fraction bars to show a fraction between 2 and 3. Fraction: Mixed number: Use with Grade 4, Chapter 11, Lesson 7, pages 486–487. (363) NS 1.5, 1.9 Print This Page Name Print This 11–8 Page Likely and Unlikely P PRACTICE Describe the probability of picking a certain shape from the bag. Use the words likely, equally likely, certain, unlikely, or impossible. 1. 2. 3. 4. or , ,or Describe the probability of spinning the number. 2 5. spinning 2 3 2 4 6. spinning 3 2 1 7. spinning 6 2 2 2 8. spinning 1 2 4 3 9. spinning 3 or 4 10. spinning 1, 2, 3, or 4 Describe the probability. 11. The month after September will be November. 12. It will be sunny or rainy tomorrow. © McGraw-Hill School Division 13. It will snow in Alaska this year. Problem Solving 14. A bag contains 3 red and 7 white balls. Is it unlikely, more likely, or equally likely you will pick a red ball? Use with Grade 4, Chapter 11, Lesson 8, pages 490–491. (364) 15. A box contains 6 red pencils and 6 black pencils. Is it unlikely, less likely, or equally likely you will pick a red pencil? NS 1.5; MR 1.1; SDP 2.2 Print This Page Name Print This 11–8 Page Likely and Unlikely R The chance, or likelihood, that something will happen is called probability. 6 Look at the spinner at the right. You could spin 1, 2, 3, 4, 5, or 6. There are 6 possible outcomes. • The probability of spinning each 1 5 2 4 number is equally likely. • It is impossible to spin an 8. • It is certain that you will spin a number greater than 0. Look at the spinner at the right. RETEACH 3 7 8 8 8 • The probability of spinning a 7 is unlikely. • The probability of spinning an 8 is likely. Look at the spinner at the right. Use the words likely, equally likely, certain, unlikely, or impossible to describe the probability. 1. The probability of spinning 12 2. It is that you will land on a number greater than 2. © McGraw-Hill School Division 3. It is that you will land on a number less than 2. 4. It is that you will land on a number less than 9. 8 1 7 2 6 3 5 4 5. It is that you will land on an odd or even number. 6. It is to land on a number greater than 8. Use with Grade 4, Chapter 11, Lesson 8, pages 490–491. (365) NS 1.5; MR 1.1; SDP 2.2 Print This Page Name Print This 11–8 Page Likely and Unlikely E ENRICH Guess the Number • Play this game with a partner. Partner A chooses a secret 4-digit number and writes it on a sheet of paper. • Player B guesses a 4-digit number and writes in the first row of the guess chart. • Player A looks at the 4-digit number and then fills in the second chart. He or she writes the number of digits that are correct. Player A also writes the number of digits that are in the correct position. Example: The secret number is 1,093. The first guess is 6,198. The number of correct digits is 2. The number of digits in the correct position is 1. • Based on that information, Player B makes a second guess. • Continue playing until the secret 4-digit number is guessed, or until 10 guesses have been used. • Players then switch roles. © McGraw-Hill School Division Guess Number of Correct Numbers 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6. 7. 7. 8. 8. 9. 9. 10. 10. Number of Digits in the Correct Position What strategy did you use in guessing the numbers? Use with Grade 4, Chapter 11, Lesson 8, pages 490–491. (366) NS 1.5; MR 1.1; SDP 2.2 Print This Page Name Print This 11–9 Page Explore Probability P Find the probability of spinning the number. 4 PRACTICE 3 3 1 1. 3 3. 4 2. 1 4. 2 4 4 4 4 2 4 5. 3 or 4 2 2 6. 5 Find the probability of picking the shape. 7. circle 9. square 11. hexagon 8. triangle 10. pentagon 12. triangle or square Find the probability of picking the color. © McGraw-Hill School Division 13. blue 14. red 15. green 16. purple 17. red or blue 18. blue or green red blue red blue red blue red green Problem Solving 19. Greg has a coin in one of his closed hands. What is the probability that Greg’s friend will pick the hand the coin is in? Use with Grade 4, Chapter 11, Lesson 9, pages 492–493. (367) 20. Karen turns over 5 paper cups. She hides a coin under one of them. What is the probability that Steven will guess which cup the coin is under? NS 1.5; SDP 1.1, 2.2 Print This Page Name Print This 11–9 Page Explore Probability R RETEACH You can use a fraction to show a probability. Probability  number of favorable outcomes number of possible outcomes You can use probability to predict an outcome. If you pick one of these counters without looking, there are 5 possible outcomes. The probability of picking a is 25 . The probability of picking a is 15 . The probability of picking a is 25 . Find the probability of picking each shape. 1. 2. 3. 4. Find the probability of picking each letter. 5. A 6. B 7. C 8. D A B C C D B C C C B © McGraw-Hill School Division Find the probability of picking each item. 9. a pencil 10. a pen 11. an eraser 12. a pair of scissors 13. a pad of paper 14. a crayon Use with Grade 4, Chapter 11, Lesson 9, pages 492–493. (368) NS 1.5; SDP 1.1, 2.2 Print This Page Name Print This 11–9 Page Explore Probability E ENRICH Experimental Probability 1. What if you toss a number cube numbered 1–6 120 times? About how many times do you think you will toss the number 1? Explain. 2. Toss two number cubes numbered 1–6 120 times. Use tally marks to record your results in the table below. Number Cube (120 tosses) 1 2 3 4 5 6 3. You get the sums 2–12 when you toss two number cubes and add the numbers. What if you toss two number cubes 72 times? Record your sums in the table below. Sum of Numbers on Two Number Cubes (72 tosses) © McGraw-Hill School Division 2 3 4 5 6 7 8 9 10 11 12 4. What if you toss 3 numbers cubes? What sums would be least likely to come up? Explain. Use with Grade 4, Chapter 11, Lesson 9, pages 492–493. (369) NS 1.5; SDP 1.1, 2.2 Print This Page Name Print This 11–10 Page Problem Solving: Strategy P PRACTICE Draw a Tree Diagram Use a tree diagram to solve. 1. You spin a spinner with 4 equal sections marked 1–4. Then you spin another spinner with 3 equal sections colored red, blue, and yellow. What are all of the possible outcomes? 3. The Boardwalk Shop sells souvenir © McGraw-Hill School Division shirts. The shirts come with long sleeves or short sleeves. The shirts come in white, gray, and blue. What are all of the different kinds of shirts? Mixed Strategy Review Solve. Use any strategy. 5. The Target Toss Game has 6 rings. The first ring is worth 4 points, the second ring is worth 8 points, and the third ring is worth 12 points. If the pattern continues, what is the sixth ring worth? Strategy: 7. Marnie brought $75 to the amusement park. She has $39 left. How much money did Marnie spend? 2. Karen throws a dart at a target with 5 equal sections marked 1–5. She then throws a dart at a target with two equal sections colored green and blue. What are all of the possible outcomes? 4. Boardwalk Burgers sells burgers made from beef, turkey, chicken, or soy. Burgers can have no cheese, Swiss cheese, or American cheese. How many different choices are there? 11 6. Social Studies In a recent year, 100 of all U.S. vacations included time at 6 the beach, 100 included time at 8 included time sports events, and 100 at theme parks. Write these activities in order from least to most popular. Strategy: 8. Create a problem which can be solved by drawing a tree diagram. Share it with others. Strategy: Use with Grade 4, Chapter 11, Lesson 10, pages 494–495. (370) SDP 2.1, 2.2; MR 1.1, 2.3, 2.4, 3.1, 3.2 Print This Page Name Print This 11–10 Page Problem Solving: Strategy R RETEACH Draw a Tree Diagram Page 495, Problem 1 What are all of the possible outcomes of tossing a number cube and flipping a coin? Step 1 Read Be sure you understand the problem. Read carefully. What do you know? • When you toss a number cube, you can toss a , , , , . • When you flip a coin, you can get or , . What do you need to find? • You need to find Step 2 Plan ■ ■ © McGraw-Hill School Division ■ ■ ■ ■ ■ ■ ■ ■ Find a Pattern Guess and Check Work Backward Make a Table or List Write a Number Sentence Use Logical Reasoning Solve a Simpler Problem Make a Graph Act it out Draw a Diagram Make a plan. Choose a strategy. A tree diagram can show all of the possible outcomes. Use with Grade 4, Chapter 11, Lesson 10, pages 494–495. (371) SDP 2.1, 2.2; MR 1.1, 2.3, 2.4, 3.1, 3.2 Print This Page Name Print This 11–10 Page Problem Solving: Strategy R RETEACH Draw a Tree Diagram Step 3 Solve Carry out your plan. Number Cube Make branches to show all of the possible outcomes for tossing the number cube. Then make branches to show all of the possible outcomes for flipping the coin. List each outcome. 1 Coin Outcome heads 1-heads tails 1-tails 2 heads tails 4 heads tails 6 Step 4 Look Back Is the solution reasonable? Reread the problem. © McGraw-Hill School Division How can you check to make sure your answer is correct? Practice 1. The amusement park offers discount tickets for 5 rides, 10 rides, or 20 rides. The tickets come as adult tickets or child’s tickets. What are all of the possible discount tickets? Use with Grade 4, Chapter 11, Lesson 10, pages 494–495. (372) 2. Pia wants a fruit drink. She can choose strawberry, banana, orange, grapefruit, or mango. Drinks come in small, medium, or large. What are all of the possible combinations? SDP 2.1, 2.2; MR 1.1, 2.3, 2.4, 3.1, 3.2 Print This Page Name Print This 11–11 Page Explore Making Predictions P PRACTICE Use the spinner for exercises 1–6. 1. If you spin the spinner 100 times, what is the probability you will land on A? 2. If you spin the spinner 50 times, what C is the probability you will land on B? 3. If you spin the spinner 100 times, what is the probability you will land on C? B A A C B C 4. If you spin the spinner 100 times, A A A what is the probability you will land on a shaded section? 6. If you spin the spinner 50 times, what 5. If you spin the spinner 50 times, what is the probability you will land on an A or a B? is the probability you will land on an unshaded section? Use a number cube with the sides labeled 1–6 for problems 7–10. © McGraw-Hill School Division 7. Predict the number of times 3 will 8. If you toss the number cube 60 times, come up if you toss the number cube 30 times. 9. Is it reasonable to predict that you will how often might 4 come up? 10. Can you predict exactly how many toss a 4 on the number cube 2 out 12 tosses? Use with Grade 4, Chapter 11, Lesson 11, pages 496–497. (373) times 5 will come up when you toss a number cube labeled 1–6? NS 1.5; SDP 1.1, 2.1 Print This Page Name Print This 11–11 Page Explore Making Predictions R RETEACH Suppose you toss a coin. There are 2 possible outcomes, heads or tails. You can predict that 1 out of 2 times you will toss heads. As an experiment, you can toss a coin 10 times and record your results. Compare the results with your prediction. Suppose you spin this spinner. You can predict that 2 out of 8 times the spinner will land on 5. There are 2 favorable outcomes and 8 possible outcomes. The probability of spinning a 5 is 2 1 8 , or 4 . You can spin a spinner for 10 or 20 times to check your prediction. 5 1 4 3 3 1 2 5 Use the spinner below to answer the questions. Write true or false. Explain. 1. Is it reasonable to predict that the spinner will land on a shaded section 1 out of 5 times? 2. Is it reasonable to predict that the spinner will land on a dotted section 5 out of 15 times? © McGraw-Hill School Division 3. The probability of landing on a striped section is 2 out of 5. 4. The probability of landing on a red section is 1 out of 5. Use with Grade 4, Chapter 11, Lesson 11, pages 496–497 (374) 5. Is it reasonable to predict that the spinner will land on a section that is not shaded 6 out of 30 times? NS 1.5; SDP 1.1, 2.1 Print This Page Name Explore Making Predictions Print This 11–11 Page E ENRICH Could It Happen? The letters below have been sent to an advice column called “Could It Happen?” Write a response to each letter. Include information about probability in your response. Dear Could It Happen? Dear Could It Happen? My school is having a raffle for a There are 30 people trying out for 15 computer. Each ticket costs $3.00. My parts in the school play. I don’t want to friend says that if each student in our try out unless I have a pretty good chance class buys a ticket our class has a great of getting a part. What do you think chance of winning the computer for our the chances are that I will get the part? classroom. What do you think? Regards, Sincerely, Broadway Bound Mouse Potato Could It Happen? © McGraw-Hill School Division Could It Happen? Write your own probability letter to “Could It Happen?” Use with Grade 4, Chapter 11, Lesson 11, pages 496–497. (375) NS 1.5; SDP 1.1, 2.1 Print This Page Name Problem Solving: Application Print This Page 11–12 Part A WORKSHEET Decision Making Applying Probability Record your data. Game Fair or unfair? Why? If the game is unfair, how can you change it to make it fair? Spinner A Spinner B Spinner C Spinner D Cards A Cards B Checkerboard A © McGraw-Hill School Division Checkerboard B Your Decision Describe three games you would recommend to Reggie and Bianca. Explain. Use with Grade 4, Chapter 11, Lesson 12, pages 498–499. (376) MR1.1; NS 1.5; SDP 1.1, 2.1 Print This Page Name Print This Page 11–12 Part B WORKSHEET Problem Solving: Application How does size affect how fast a solid dissolves? Math & Science © McGraw-Hill School Division Make your own chart to record the dissolving time for each seltzer tablet. 1. Rank the seltzer tablets in order from fastest to slowest. Use with Grade 4, Chapter 11, Lesson 12, pages 500–501. (377) NS 1.5, 1.7; MR 1.1, 2.3, 3.3 Print This Page Name Print This Page 11–12 Part B WORKSHEET Problem Solving: Application How does size affect how fast a solid dissolves? Math & Science 2. What would happen if you broke the seltzer tablet into eighths? Why? 3. Describe a plan to make the seltzer tablet dissolve as fast as possible. 4. Did you collect enough data in this activity to make any strong © McGraw-Hill School Division conclusions? Explain your answer. 5. Explain the results of the activity in terms of surface area. Use with Grade 4, Chapter 11, Lesson 12, pages 500–501. (378) NS 1.5, 1.7; MR 1.1, 2.3, 3.3 Print This Page Name Print This 12–1 Page Add Fractions with Like Denominators P PRACTICE Add. Write each sum in simplest form. 1.  7.  1 3 1 3  1 6 2 6  2 4 2 4 2. 3 9 2 9 8. 3.  9.  2 7 2 7 4.  2 8 4 8 2 12 4 12 10.  3 5 3 5 5.  3 15 3 15 11.  6.  7 9 6 9 12.  13. 2  2  14. 3  2  15. 3  3  16. 1  7  17. 3  3  18. 5  4  19. 3  3  20. 5  5  21. 13  12  22. 7  8  23. 5  7  24. 9  3  16 8 4 16 10 8 9 4 12 8 12 10 18 9 8 8 11 3 12 5 12 18 8 16 11 6 10 8 10 15 16 15 © McGraw-Hill School Division Algebra & Functions Compare. Write , , or . 3 25. 1 4  4 1 2 26. 6 7  7 6 28. 2 9  9 1 2 7 29. 10  10 3 27. 1 6  6 1 1 8 5 30. 12  12 1 1 Problem Solving 1 31. You need at least 1 4 yards of paper for a mural. You tape together 2 pieces of paper that are 34 yard each. Do you have enough paper now? How long is your piece of paper? Use with Grade 4, Chapter 12, Lesson 1, pages 516–517. (379) 32. You want to make some salt ceramic dough. The recipe calls for 23 cup of salt. If you want to double the recipe, how much salt will you need? NS 1.5, 3.1 Print This Page Name Print This 12–1 Page R Add Fractions with Like Denominators RETEACH You can use fraction strips to add fractions with like denominators. 1 1 6 6 1 1 6 6 1 1 1 1 6 6 6 6 1 3  2 6  2 6 1 3 4 6  2 3 Add. Write each sum in simplest form. 1. 1 8 1 8 4.  3 8 7.  1 1 6 6 2 6  3 6 1 6 5.  1 6 8. 1 1 4 4  2 4 1 4   4 10 6.  1 3 1 3  1 1 10 10 2 10 1 1 1 1 1 10 10 10 10 10 5 10 1 1 3 3 2 3 1 4  3.  1 4 1 4 1 1 1 6 6 6  1 4 1 4 1 1 1 1 6 6 6 6 4 6 © McGraw-Hill School Division  2. 1 1 1 8 8 8  3 10 1 1 1 10 10 10  1 1 1 1 10 10 10 10  9. 1  2  10. 1  4  11. 3  4  12. 2  5  13. 2  4  14. 2  6  5 12 5 12 8 8 8 8 Use with Grade 4, Chapter 12, Lesson 1, pages 516–517. (380) 12 10 12 10 NS 1.5, 3.1 Print This Page Name Add Fractions with Like Denominators Print This 12–1 Page E ENRICH Hexagon Roll Game Play with a partner to form hexagons. You will need two number cubes and triangle and hexagon pattern blocks. 2 6 2 6 5 6 5 6 • Write the following fractions on each side of two number cubes: 0, 16 , 26 , 36 , 46 , 56 . • Each triangle pattern block stands for stands for 1. 1 6 and each hexagon © McGraw-Hill School Division • The first player rolls the two number cubes and shows the fractions with the triangle pattern blocks. Then he or she finds the sum of the fractions by combining the pattern blocks. That player should also write a number sentence that shows the addition. • If the triangle pattern blocks form a whole hexagon, call out “Hexagon!” to score 1 point. • Take turns and continue playing for 5 rounds. The player with more points wins the game. Which fractions would you like to roll each time? Explain. Use with Grade 4, Chapter 12, Lesson 1, pages 516–517 (381) NS 1.5, 3.1 Print This Page Name Print This 12–2 Page P Subtract Fractions with Like Denominators PRACTICE Subtract. Write each difference in simplest form. 1.  7.  4 5 2 5 2.  7 10 2 10 8.  5 7 3 7 3.  6 10 4 10 9.  5 8 1 8 4.  7 12 1 12 10.  8 9 2 9 5 6 1 6 5.  4 15 1 15 11.  6.  8 11 4 11 12.  13. 7  2  14. 5  1  15. 7  3  16. 5  4  17. 8  1  18. 4  3  19. 7  5  20. 7  4  21. 10  5  22. 11  8  23. 9  5  24. 7  3  25. 2  2  26. 8  2  27. 9  8  9 7 9 7 12 9 12 12 3 16 16 9 12 12 9 5 11 10 8 9 11 12 8 12 8 5 12 10 3 8 4 9 1 9 11 8 11 11 Algebra & Functions Compare. Write , , or . 28. 5  2  3 9 30. 5  1 12 7 12  32. 7  6 7 11  © McGraw-Hill School Division 9 12 11 6 9 9 11 29. 7  3 10 8 10  2 10 5 12 31. 11  10 15 14 15  13 15 5 11 33. 12  5 9 13  2 13 10 15 13 13 Problem Solving 34. At lunch you cut a sandwich into 4 parts and eat 3 of the parts. What fraction of the sandwich is left? Use with Grade 4, Chapter 12, Lesson 2, pages 518–519. (382) 35. For breakfast and lunch you drink 2 3 of a quart of milk. How much of the quart is left? NS 1.5, 3.1 Print This Page Name Print This 12–2 Page Subtract Fractions with Like Denominators R RETEACH You can use fraction strips to subtract fractions with like denominators. 1 5 4 5  1 5 1 5  1 5 1 5 3 5 Subtract. Write each difference in simplest form. 1. 1 1 1 4 4 4 3 4 4. 1 4 7.  2 8  3 8  8. 1 3  1 8 1 1 1 1 1 6 6 6 6 6 5 6  1 1 1 1 1 1 1 8 8 8 8 8 8 8 7 8  1 1 1 1 1 1 1 8 8 8 8 8 8 8 7 8 5.  3. 1 3 1 3 2 3  1 1 1 1 1 8 8 8 8 8 5 8 © McGraw-Hill School Division  2. 6.   1 1 1 1 1 10 10 10 10 10 5 10  4 6  1 10  1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 9 12  1 12  Subtract. Write each difference in simplest form. 1 9. 3 4  4  7 1 12. 12  12  2 10. 3 3  3  3 11. 5 5  5  7 3 13. 16  16  8 5 14. 10  10  Use with Grade 4, Chapter 12, Lesson 2, pages 518–519. (383) NS 1.5, 3.1 Print This Page Name Subtract Fractions with Like Denominators Print This 12–2 Page E ENRICH Fraction Subtraction Riddle When is it bad luck to have a black cat follow you? Subtract. Write each difference in simplest form. To solve the riddle, find the letter that goes with each difference. Write the letters on the lines below. E A 5 8  2 8  4 10  7 16  3 12 Y  2 8  4 16 5 8 1 4 3 10  4 15 7 8 5 12 3 5 13 15 2 5 Use with Grade 4, Chapter 12, Lesson 2, pages 518–519. (384) 1 16  2 24 6 10  5 10 18 20  2 20 11 12  6 12 U A 13 16 1 3  1 24 23 24 M 13 24 O 7 12  5 16 S 7 8 N  5 10 W 7 16 H 11 16 © McGraw-Hill School Division  3 16 9 10 E 15 16 E 1 10  4 16 U 7 10 O R 5 16 3 8 4 5 9 16 3 4 1 2 1 8 NS 1.5, 3.1 Print This Page Name Print This 12–3 Page Problem Solving: Reading for Math P PRACTICE Reading Skill Choose an Operation Solve. Tell how you chose the operation. 1. Kerstin cuts a pie into a dozen pieces. Her friends eat 7 pieces. What part of the pie is left? of raisins than nuts are needed? 3. A recipe calls for 3 cup of 8 macadamia nuts and 58 cup of 4. Kevin uses 1 stick of butter for 8 one recipe and 58 stick of butter for 5. Mary makes a batch of 16 muffins. 6. Nick buys 3 pound of roast beef and 4 1 4 pound of ham. How many pounds cashew nuts. What is the total amount of nuts in the recipe? She sells 9 of them. What part of the batch is left? © McGraw-Hill School Division 2. A recipe calls for 3 cup of raisins and 4 1 cup of nuts. How many more cups 4 7. Nicole drinks 1 quart of orange juice 8 and 38 quart of water. How much did she drink in all? Use with Grade 4, Chapter 12, Lesson 3, pages 520–521. (385) another recipe. How much butter does he use altogether? of meat does Nick buy? 8. Michael fills 10 bowls with fruit salad. He serves 8 bowls to his guests. What part of the bowls is left? MR 1.1, 2.3, 2.4, 3.1, 3.2 Print This Page Name Print This 12–3 Page Problem Solving: Reading for Math P Choose an Operation PRACTICE Math Skills Test Prep Choose the correct answer. 1 3 A recipe calls for 8 cup of beef broth and 8 cup of water. How much liquid does it call for in all? 1. Which of these statements is true? 2. Which of the following can you use to solve the problem? A The recipe uses more water than beef broth. 3 1 3 1 3 1 F 88 1 G 88 B The recipe uses 8 cup of beef broth. H 88 1 C The recipe uses 8 cup of water 3 1 Tim buys 4 pound of provolone cheese and 4 pound of Swiss cheese. How much more provolone cheese than Swiss cheese does Ted buy? 3. What do you have to do to solve 4. How much more provolone cheese this problem? than Swiss cheese does Ted buy? A Find the difference between two amounts. F 1 pound B Find the total of two equal amounts. 3 G 4 pound 1 H 2 pound © McGraw-Hill School Division C Find the total of two unequal amounts. Ashley cuts a cake into 16 squares. Her family eats 10 squares. What part of the cake is left? 5. Which statement is true? A There is a total of 10 squares of cake. B There is a total of 16 squares of cake. 6. Which of the following can you use to solve the problem? 16 10 16 10 10 6 F 16  16 G 16  16 H 16  16 C Ashley’s family eats 16 squares of cake. Use with Grade 4, Chapter 12, Lesson 3, pages 520–521. (386) MR 1.1, 2.3, 2.4, 3.1, 3.2 Print This Page Name Problem Solving: Reading for Math Choose an Operation Print This 12–3 Page P PRACTICE Math Skills Test Prep Choose the correct answer. 5 7 Janell uses 8 cup of pine nuts and 8 cup of peanuts. What is the total amount of nuts she uses? 7. What operation would you use to 8. What is the total amount of nuts solve this problem? she uses? A addition F 1 2 cups B subtraction G 2 cup C multiplication H 4 cup 1 1 1 Solve. 7 9. Max buys 8 pound of apples and 3 pound of grapes. What is the total 8 amount of fruit he buys? 15 cookies to her friends. What part of the 20 cookies is left? 5 11. Chen buys 8 pound of American cheese and 7 pound of Swiss cheese. 8 12. Kathryn uses 3 tablespoon of nutmeg 4 and 34 tablespoon of cocoa. How 13. Amy buys 1 pound of turkey and 1 pound of4 honey-roasted ham. How 4 14. Marge cuts a cherry pie into 8 slices. 15. A recipe for pudding uses 7 cup 8 3 16. Patrick bought 4 pound of cookies. He ate 14 pound of the cookies. How How much more Swiss cheese than American cheese does he buy? © McGraw-Hill School Division 10. Adela makes 20 cookies. She gives much meat did she buy altogether? of milk. A recipe for custard uses 3 cup of milk. How much more milk 8 does the pudding use than the custard recipe? Use with Grade 4, Chapter 12, Lesson 3, pages 520–521. (387) many tablespoons of nutmeg and cocoa does she use altogether? She eats one slice. What part of the pie is left? much of the cookies is left? MR 1.1, 2.3, 2.4, 3.1, 3.2 Print This Page Name Print This 12–4 Page Explore Adding Fractions with Unlike Denominators P PRACTICE Add. Write each sum in simplest form. 1. 1 2 1 4 2. 1 6 1 1 4 4 1 4 1 6 1 2  1 4 2 4  1 4 4. 1 1 6 6 1 6  1 3 1 6  2 6 1 2 111 888 5. 1 1 1 10 10 10 1111 8888 111 888 111 10 10 10 1 2  3 8 4 8  3 8  1 6  1 5 1 5 1111 10 10 10 10 3 10  2 5 3 10  4 10  1 2 1 1 1 6 6 6 1 6  1 2 1 6  3 6 1 4 1 4 6.  1 4 111 888 111111 888888 3 4  3 8 6 8  3 8 111 888  7. 3  5  8. 7  1  10. 5  1  11. 1  5  12. 1  1  13. 1  3  14. 1  2  15. 1  1  16. 2  5  17. 2  7  18. 3  1  19. 2  1  20. 1  3  21. 3  7  1 22. 3  3  2  5 10 23. 1  1  1  24. 1  1  1  12 6 12 © McGraw-Hill School Division  3. 1 6 1 3 5 3 3 4 10 6 6 9 4 6 3 3 8 3 3 2 12 10 8 9. 2  2  3 5 4 2 Use with Grade 4, Chapter 12, Lesson 4, pages 524–525. (388) 8 4 3 9 12 8 4 8 2 4 NS 1.5, 3.1 Print This Page Name Print This 12–4 Page Explore Adding Fractions with Unlike Denominators R RETEACH You can use fraction strips to find equivalent fractions before you add. 3 4 Add  1 12 . 1 1 4 Compare fourths to twelfths: 9 12 is equivalent to 9 12 Add the twelfths. 3 4  1 12 1 4 1 12 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 12 3 4. 1 6 So, 1 4 1 6  1 12 1 6  1 6 10 12 1 6  5 6 is 56 . Add. You may use fraction strips to help you. Write each answer in simplest form. 1. 3  2  2. 1  2  3. 1  1  4. 3  2  5. 2  1  6. 1  1  7. 3  1  8. 4  1  9. 1  5  5 10 © McGraw-Hill School Division 12 4 6 8 6 3 12 2 10 2 6 4 2 2 2 12 10. 2  2  11. 3  1  12. 1  3  13. 1  1  14. 5  1  15. 2  1  9 6 3 3 8 8 2 4 Use with Grade 4, Chapter 12, Lesson 4, pages 524–525. (389) 10 3 5 9 NS 1.5, 3.1 Print This Page Name Print This 12–4 Page Explore Adding Fractions with Unlike Denominators E ENRICH Hidden Sentences The squares contain hidden addition sentences. Look from left to right and top to bottom to find the hidden addition sentences. Circle each addition sentence you find. Each sum is in simplest form. 1. 2. 1 3 2 8 5 8 7 8 2 8 3 8 5 10 1 4 1 3 3 5 3 5 2 5 4 8 1 8 2 10 1 3 2 3 1 5 1 5 2 5 3 4 1 2 7 10 3 5 1 5 4 5 2 5 4 5 3 10 2 10 1 2 4 10 © McGraw-Hill School Division 3. 4. 3 4 5 12 2 3 1 4 1 3 3 10 1 10 2 5 3 8 1 12 1 8 1 3 1 6 1 3 3 4 1 4 1 18 1 2 1 2 2 3 1 2 1 4 3 4 3 8 3 4 3 4 1 12 1 1 4 3 4 1 5 8 Use with Grade 4, Chapter 12, Lesson 4, pages 524–525. (390) NS 1.5, 3.1 Print This Page Name Print This 12–5 Page Add Fractions with Unlike Denominators P PRACTICE Add. Write each sum in simplest form. 1.  7.  1 4 1 8  2 3 1 2  1 3 2 5 2. 1 6 2 3 8. 3.  9.  2 3 3 4  5 6 1 3  1 2 5 6 4. 1 2 3 5 10. 5.  1 5 2 15 6.  1 2 7 8 11.  12.  13. 1  1  14. 3  1  15. 1  5  16. 1  3  17. 1  2  18. 2  1  19. 3  3  20. 7  1  21. 1  5  22. 10  3  23. 1  5  1  2 4 4 12 4 10 8 4 8 9 4 2 2 6 3 6 3 5 7 10 12 5 3 1 6 1 4 3 4 12 24. 1  1  3  3 8 2 4 © McGraw-Hill School Division Algebra & Functions Compare. Write , , or . 9 25. 1 4  12 1 4 2 27. 12  14 3 12  2 3  1 26. 2 6  6 1 6 4 28. 3 5  10 1 2  1 2 1 4  1 3 Problem Solving 1 29. Your family ate 2 of a box of cereal 1 30. At 6:00 P.M., 6 of the passengers one day and 34 the next. Did you eat boarded the plane. At 6:10 P.M., 23 of more or less than 1 box of cereal? the passengers boarded. What fraction Explain. of the passengers are on the plane? Use with Grade 4, Chapter 12, Lesson 5, pages 526–529. (391) NS 1.5, 3.1 Print This Page Name Print This 12–5 Page Add Fractions with Unlike Denominators R RETEACH You can use fraction strips to help you record the steps when you add unlike fractions. Add 2 3  16 . Using Fraction Strips 1 3 1 3 1 6 1 6   Find equivalent fractions. 1 6 1 1 1 1 6 6 6 6 2 3 4 6 Using Pencil and Paper 2 3 1 6  Add the numerators. Use the common denominator. 4 6  4 6 1 6 5 6 Write the answer in simplest form if necessary.  5 6 Find each equivalent fraction. Then add. Write the sum in simplest form. You may use fraction strips to help you add. 1. 1 8  8  34  8 5. 6 10  10 © McGraw-Hill School Division 7 12  26  12 3 4 6.  1 3 1 6  10 4. 2  10  10  9 7 8 7.  16  2 10. 4 5 3. 7  12  12  15  10 9. 1 3 2.  Use with Grade 4, Chapter 12, Lesson 5, pages 526–529. (392)  1 4 1 2  6  13  6 8.  34  11. 1 2 9 10   35  12. 5 12  14 NS 1.5, 3.1 Print This Page Name Print This 12–5 Page Add Fractions with Unlike Denominators E ENRICH Fraction Magic Squares In a magic square, the sum of each row, column, and diagonal is the same. Complete each magic square. 4 1. The magic sum is 1 11 . 2. The magic sum is 15 16 . 8 11 1 4 9 11 1 16 7 11 7 16 6 11 3. What is the magic sum? 1 8 4. What is the magic sum? 3 5 1 6 1 2 © McGraw-Hill School Division 1 3 7 18 1 9 2 5 1 5 5. How did you find the magic sum in exercise 3? Use with Grade 4, Chapter 12, Lesson 5, pages 526–529. (393) NS 1.5, 3.1 Print This Page Name Print This 12–6 Page Problem Solving: Strategy P PRACTICE Solve a Simpler Problem Solve using a simpler problem. 1. Sandwiches cost $4.95. Drinks cost $0.99. How much does it cost to buy 2 sandwiches and 3 drinks? 1 3. Recipe A uses 2 cup of chicken broth and 41 cup of water. Recipe B uses 1 1 3 cup of chicken broth and 3 cup of water. Which recipe uses more liquid? 2. A customer pays $3.95 for 5 pounds of apples. What is the price for 1 pound of apples? 4. Tracy buys 3 pound of roast beef, 1 pound of4turkey, and 3 pound of 2 8 ham. Ken buys 41 pound of roast beef, 1 pound of turkey, and 3 pound of 2 8 ham. Who buys more meat? How much more does that person buy? Mixed Strategy Review Solve. Use any strategy. 5. There are 24 plants in a garden. © McGraw-Hill School Division There are 4 more tomato plants than red pepper plants. There are twice as many red pepper plants as green pepper plants. How many of each kind of plant is in the garden? Strategy: 7. Health An ounce of cheddar cheese has 114 calories. An ounce of brie cheese has 95 calories. How many more calories does an ounce of cheddar cheese have than an ounce of brie cheese? 6. The Yogurt Cart has the following 3 flavors: chocolate, vanilla, and strawberry. Yogurt comes in a cup or a cone. You can have no sprinkles, chocolate sprinkles, or rainbow sprinkles. How many different choices are there? Strategy: 8. Create a problem for which you could use a simpler problem to help you find the answer. Share it with others. Strategy: Use with Grade 4, Chapter 12, Lesson 6, pages 530–531. (394) NS 1.5; MS 1.1, 1.2, 2.4, 3.2 Print This Page Name Print This 12–6 Page Problem Solving: Strategy R RETEACH Solve a Simpler Problem Page 531, Problem 1 Josh buys a 5-pound watermelon at $0.49 per pound and 2 pounds of grapes at $1.29 per pound. Sabrina buys an 8-pound watermelon at $0.29 per pound and 3 pounds of grapes at $0.99 per pound. Who spends more money? How much more? Step 1 Read Be sure you understand the problem. Read carefully. What do you know? • Josh buys pounds of watermelon at He also buys • Sabrina buys She also buys pounds of grapes at pounds of watermelon at pounds of grapes at per pound. per pound. per pound. per pound. What do you need to find? • You need to find Step 2 Plan ■ ■ © McGraw-Hill School Division ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ Make a Table Write a Number Sentence Work Backward Act It Out Find a Pattern Make a Graph Guess and Check Choose a Strategy Make a Graph Logical Reasoning Draw a Tree Diagram Solve a Simpler Problem Draw a Diagram Make a plan. Choose a strategy. Use simpler numbers to make up a problem similar to the one you need to solve. Then solve the real problem the same way. Use with Grade 4, Chapter 12, Lesson 6, pages 530–531. (395) NS 1.5; MS 1.1, 1.2, 2.4, 3.2 Print This Page Name Print This 12–6 Page Problem Solving: Strategy R RETEACH Solve a Simpler Problem Step 3 Solve Carry out your plan. Josh: watermelon: $0.50 per lb grapes: $1.30 per lb 5  $0.50  $2.50 $2.50  $2.60  $5.10 Sabrina: watermelon: $0.30 per lb 8  $0.30  $2.40 $2.40  $3.00  $5.40 2  $1.30  $2.60 grapes: $1.00 per lb 3  $1.00  $3.00 Now solve the real problem the same way. Josh: 5 lb  $0.49  $2.45 2 lb  $1.29  $2.58 $2.45  $2.58  $5.03 Sabrina: 8 lb  $0.29  $2.32 3 lb  $0.99  $2.97 $2.32  $2.97  $5.29 $5.29  $5.03  $0.26 Sabrina spends $0.26 more. Step 4 © McGraw-Hill School Division Look Back Is the solution reasonable? Reread the problem. Does your answer make sense? Explain. Practice 1. Robert buys 4 pounds of apples for $0.89 per pounds and 3 pounds of grapes for $1.09 per pounds. Which fruit does he spend more on? How much more? 7 2. Kostas buys 8 pound of cashew nuts, 5 1 pound 8 pound of walnuts, and 2 of peanuts. Jane buys 38 pound of cashew nuts, 21 pound of walnuts, 3 and 8 pound of peanuts. Who buys more nuts? How much more? Use with Grade 4, Chapter 12, Lesson 6, pages 530–531. (396) NS 1.5; MS 1.1, 1.2, 2.4, 3.2 Print This Page Name Print This 12–7 Page Explore Subtracting Fractions with Unlike Denominators P PRACTICE Subtract. Write each difference in simplest form. 1. 2. 1 4 1 3 3. 1 3 1 2 1 1 1 1 6 6 6 6 11 88 1 1 1 6 6 6 1 2 1 4  1 8 2 8  1 8 4.  2 3  1 6 4 6  1 6 5. 1 2 111111 12 12 12 12 12 12  1 2  1 3 3 6  2 6 6. 1 5 11 10 10  1 6 11 12 12 1 3 1 2  6 12 2 12  2 12 1 5  © McGraw-Hill School Division 1 7. 1 4  6   2 10 1 6 1 10  1 10   1 12 2 1 12  12  1 8. 1 2  5  1 9. 1 4  12  10. 7  1  2 11. 7 9  3  5 12. 12  14  1 13. 5 6  3  1 14. 3 4  3  1 15. 1 2  12  3 16. 1 2  10  1 17. 5 6  12  3 18. 1 2  8  1 19. 2 3  6  1 20. 4 5  10  1 21. 3 4  8  12 3 Use with Grade 4, Chapter 12, Lesson 7, pages 532–533. (397) NS 1.5, 3.1 Print This Page Name Print This 12–7 Page Explore Subtracting Fractions with Unlike Denominators R RETEACH You can use fraction strips to find equivalent fractions before you subtract fractions with unlike denominators. Subtract 1 4  18 . 1 4 Compare fourths to eighths: 2 8 is equivalent to 1 1 8 8 1 4. Subtract the eighths. 2 8 So, 1 4   1 8 1 8  1 1 8 8 1 8  18 . Subtract. You may use fraction strips to help you. Write each difference in simplest form. 2 1. 1 2  12  1 2. 1 5  10  1 3. 3 4  2  4. 7  1  5 5. 10  12  1 6. 5 6  3  3 7. 1 2  10  5 8. 5 6  12  3 9. 1 2  8  1 10. 2 3  6  1 11. 4 5  10  1 12. 7 9  3  5 13. 3 4  8  3 14. 4 5  10  5 15. 11 12  6  7 16. 10  35  1 17. 2 3  6  5 18. 5 6  12  © McGraw-Hill School Division 12 3 Use with Grade 4, Chapter 12, Lesson 7, pages 532–533. (398) NS 1.5, 3.1 Print This Page Name Print This 12–7 Page Explore Subtracting Fractions with Unlike Denominators E ENRICH Fraction Wheels Subtract the fraction in the center from each fraction in the inner circle. Write the difference in simplest form in the outer circle. 1. 2. 1 12 7 12 5 9 1 18 1 2 5 6 1 2 2 3 1 4 1 6 1 6 3. 1 12 5 6 2 3 3 4 7 12 4. 7 10 9 10 1 2 © McGraw-Hill School Division 5 12 1 3 7 10 1 5 3 10 4 5 1 2 1 8 3 5 5. 5 8 1 4 1 10 3 8 1 4 7 8 7 12 1 3 6. 1 2 1 6 2 3 5 12 7 12 1 6 1 8 1 4 1 3 3 4 1 2 5 6 1 3 Use with Grade 4, Chapter 12, Lesson 7, pages 532–533. (399) 1 3 1 2 5 8 11 12 5 12 NS 1.5, 3.1 Print This Page Name 12–8 Page Subtract Fractions with Unlike DenominatorsPrint P This PRACTICE Subtract. Write each difference in simplest form. 1.  7. 1 3 1 12 2.  9 10  35 3 4 5 12 8.  3 4 1 2 3.  9.  1 5 2 15 3 5 3 10 4. 7 10  15 10.  5. 5 9 1 3 11 12  56 11.  2 3 2 9  5 6 2 3  3 4 1 8 6. 12. 1 13. 5 8  4  1 14. 2 3  6  1 15. 1 4  12  7 16. 4 5  10  1 17. 4 9  3  3 18. 4 5  10  1 19. 1 2  6  1 20. 3 8  4  1 21. 7 9  3  7 22. 12  16  1 23. 1 2  4  5 24. 2 3  12  7 25. 12  12  7 26. 10  25  1 27. 1 2  5  Algebra & Functions Find each missing number. © McGraw-Hill School Division 1 28. 7 8  2  8 1 31. 1  13 2  1 29. 5  23 6  2 30. 3 4  12  3 1 32. 2 3  6  2 1 33. 5  29 9  Problem Solving 34. Pam has 7 yard of ribbon. She uses 8 1 2 yard. How much ribbon does Pam have left? Use with Grade 4, Chapter 12, Lesson 8, pages 534–537. (400) 35. Joe has 5 yard of fabric. He uses 6 2 3 yard to make a kite. How much fabric does Joe have left? NS 1.5, 3.1 Print This Page Name 12–8 Page Subtract Fractions with Unlike DenominatorsPrint R This RETEACH You can use fraction strips to help you record the steps when you subtract unlike fractions. 7 10 Subtract  25 . Using Fraction Strips Using Pencil and Paper 1111111 10 10 10 10 10 10 10 Find equivalent fractions. 1 1 5 5 7 10 1111 10 10 10 10 2 5 1111111 10 10 10 10 10 10 10 7 10  2 5 7 10  4 10   Subtract the numerators. Use the common 7 10 denominator. 4  10 7 10 3 10 4 10 Write the answer in simplest form if necessary.  3 10 Find each equivalent fraction. Then subtract. Write the difference in simplest form. You may use fraction strips to help you subtract. 7 8 1.  8 © McGraw-Hill School Division  34  8 4 5 5.  3 10  1 2 1 5 9.  10 7 12 2.  12  26  12 3 4 6. 10.  1 2 1 3  8  9 7. 7 9  Use with Grade 4, Chapter 12, Lesson 8, pages 534–537. (401) 6 10  15  6  16  6 2 3 8.  13  11. 2 3 4.  18  8  16  2  10 1 2 3.  4   12 12.  4 5 1 2 NS 1.5, 3.1 Print This Page Name 12–8 Page Subtract Fractions with Unlike DenominatorsPrint E This ENRICH Fraction Memory Game How good is your memory? Play this memory game with a partner. • Make up 12 subtraction sentences with unlike denominators on cards like the sample below. Write each subtraction sentence on a separate index card. Also write each difference, in simplest form, on a separate index card. You should have 24 cards. 3 4  1 8 5 8 • Place the 24 cards facedown. Mix them up. Then arrange the cards in 4 rows of 6 cards each. • Take turns turning over two cards. If a player turns over a subtraction sentence and its matching difference, then he or she keeps the cards and takes another turn. If there is no match, the player turns over both cards. The other player takes a turn. © McGraw-Hill School Division • Continue taking turns until all the cards have been matched. The player with more pairs of cards wins. Use with Grade 4, Chapter 12, Lesson 8, pages 534–537. (402) NS 1.5, 3.1 Print This Page Name Print This 12–9 Page Properties of Fractions P PRACTICE Use properties to find each missing number. 7 1. 10   7 10 1 1 1 2. ( 1 2  3)  4  2  ( 3 4 4 3. 10  17  17   ( 47  59 )  ( 34  47 )  5. 7. 1 3   3 5  1 3 4. 5 9 0 2 3  1 2 6. 8 9    14 ) 8 9 1 2 4 8. ( 4 5  2)  3  5  (  23 ) Add. Then use the property to write a different number sentence. 1 10. 1  ( 1 3  2)  3 9. 1  3  4 8 Commutative 1 12. 1  ( 1 3  4)  2 11. 2  1  9 Associative 3 Commutative 13. 2  3  5 Associative 14. 1  2  10 4 © McGraw-Hill School Division Identity Identity 15. 1  ( 1  1 )  12 6 3 2 16. 3  1  Associative Use with Grade 4, Chapter 12, Lesson 9, pages 538–539. (403) 8 2 Commutative NS 1.5, 3.1; MR 1.1; AF 1.2, 1.3 Print This Page Name Print This 12–9 Page Properties of Fractions R RETEACH You can use the Commutative, Identity, and Associative properties to help you add fractions. Commutative Property The order of the addends does not change the sum. 1 4 1 4 1 4 11 11 11 88 88 88 3 4  1 8 = 1 8 1 8 1 8 1 8 7 8 0 1 4 1 4 11 11 11 88 88 88 1 8 Identity Property The sum of 0 and any fraction is that fraction. 4 5 1 4  3 4 = 7 8 Associative Property The way you group the fraction addends does not change the sum. (3  1)  4 5 8 8 4 8  3 8  (1  4)  1 8 8 Add. Then use the property to write a different number sentence. 1 1. 1  ( 1 4  2)  8 2. 3  1  8 Associative Commutative 1 3 4. ( 1 3  6 )  12  3. 3  3  5 10 Identity © McGraw-Hill School Division 2 Associative Use the properties to find each missing number. 5. 4 7   4 7 7. 1 8   3 4 3 9. 12   1 1 1 6. ( 1 3  6)  2  3  (  1 2 1 8  8. 3 12 0 9 10 1 1 2 10. ( 2 5  2)  3  5  ( Use with Grade 4, Chapter 12, Lesson 9, pages 538–539. (404)  12 )  13 ) NS 1.5, 3.1; MR 1.1; AF 1.2, 1.3 Print This Page Name Print This 12–9 Page E Properties of Fractions ENRICH Crossword Property Puzzle Identify the property in each clue. Write it in proper place in the crossword puzzle. Then write a fraction as an example for each property in each clue. 2 3 4 A A S S O C S O C S M I 1 C O M M U T A T 6 5 I I D V E C I U T T I D E N T A A V N I T T E T T I I I Y V E V E T Y © McGraw-Hill School Division Across a c c a 1. b  d  d  b Down a c e r t v m o o a c e 2. ( b  d )  f  b  ( d  f ) r t v 3. s  ( u  w )  ( s  u )  w m 4. n  p  p  n g g 5. h  0  h x x 6. y  0  y Use with Grade 4, Chapter 12, Lesson 9, pages 538–539. (405) NS 1.5, 3.1; MR 1.1; AF 1.2, 1.3 Print This Page Name Problem Solving: Application Analyze and Make Decisions Print This Page 12–10 Part A WORKSHEET Decision Making Record your data. Add Other Juices to This Juice Possible Combinations and Total Amounts of Juice Orange Juice Pineapple Juice Grapefruit Juice Cranberry Juice Grape Juice Apple Juice Mixed Berry Juice Mixed Citrus Juice © McGraw-Hill School Division Your Decision What combinations of juices can Joseph and his sisters use to make exactly one quart of fruit punch? Use with Grade 4, Chapter 12, Lesson 10, pages 540–541. (406) MR 1.1, 2.3, 3.1; NS 1.5, 3.1 Print This Page Name Problem Solving: Application Which objects can hold a static charge? Print This Page 12–10 Part B WORKSHEET Math & Science Safety Be careful when working with scissors. Wear goggles in case the balloon bursts. Record your observations. Material Observations Balloon Cubes Crayons Sock Hand © McGraw-Hill School Division 1. What happened to the string when a charged object came near it? 2. Which objects held a static charge? How do you know? Use with Grade 4, Chapter 12, Lesson 10, pages 542–543. (407) MR 1.1, 2.3, 3.1, 3.2 Print This Page Name Problem Solving: Application Print This Page 12–10 Part B WORKSHEET Math & Science Which objects can hold a static charge? 3. What fraction of the objects held a static charge? Construct a circle graph to display your results. 4. What fraction of all the objects in the world do you think hold a static charge? © McGraw-Hill School Division Think about how the objects you used represent all things in the world. 5. Explain the results of the activity in terms of static electricity. Use with Grade 4, Chapter 12, Lesson 10, pages 542–543. (408) MR 1.1, 2.3, 3.1, 3.2 Print This Page Name Print This 13–1 Page P Explore Fractions and Decimals PRACTICE Write a fraction and a decimal for each shaded part. Then write the fraction in simplest form. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. © McGraw-Hill School Division Write each as a decimal. 70 78 13. 100 14. 100 8 17. 10 18. 10 3 21. 10 4 25. 10 4 29. 5 5 66 22. 100 1 26. 2 10 30. 50 Use with Grade 4, Chapter 13, Lesson 1, pages 558–559. (409) 13 15. 100 1 19. 100 7 23. 10 10 27. 25 3 31. 4 27 16. 100 4 20. 100 90 24. 100 5 28. 20 2 32. 5 NS 1.6 Print This Page Name Print This 13–1 Page Explore Fractions and Decimals R RETEACH You can use models to show decimals. This model shows 1. This model shows 1 divided into 10 equal parts. You can shade the model to 1 1 show 10 . You can write 10 as a decimal: 0.1. This model shows 1 divided into 100 equal parts. You can shade the model to 1 1 show 100 . You can write 100 as a decimal: 0.01. Look at each model. Circle the fraction and the decimal for the shaded part. 1. 2. 4 10 4 100 3. 4. 0.4 0.04 7 10 7 100 52 100 0.7 0.07 5 10 8 10 0.5 0.52 8 100 0.8 0.08 Look at each model. Write a decimal for each shaded part. 6. 7. 8. © McGraw-Hill School Division 5. Use with Grade 4, Chapter 13, Lesson 1, pages 558–559. (410) NS 1.6 Print This Page Name Print This 13–1 Page Explore Fractions and Decimals E ENRICH Riddle Fun Match each of the ten fractions and decimals below with its word name at the right. Write the number of the exercise on the blank. 7 1. 10 C three hundredths 2. 0.5 A eleven hundredths 63 3. 100 4. O ninety-nine hundredths 90 100 I five tenths 2 5. 10 A twenty-two hundredths 6. 0.89 T eight tenths 11 7. 100 P sixty-three hundredths 8. 0.03 T eighty-nine hundredths 9. 0.22 N ninety hundredths 10. 0.99 O seven tenths 11. 0.17 F two tenths 12. 0.8 A seventeen hundredths To solve the riddle below, write the letters above the numbers. The first one is done for you. © McGraw-Hill School Division What kind of coat can be put on only when wet? A 7 8 1 9 6 10 5 3 11 2 4 12 13. Write the decimals in the left-hand column above as fractions. 14. Write the fractions in the left-hand column above as decimals. Use with Grade 4, Chapter 13, Lesson 1, pages 558–559. (411) NS 1.6 Print This Page Name Print This 13–2 Page Tenths and Hundredths P PRACTICE Write a fraction and a decimal for each part that is shaded. Then write the fraction in simple form. 1. 2. 3. 4. Write each as a decimal. 2 7 5. 5 1 6. 10 1 1 9. 2 7 7. 4 8. 100 2 10. 10 96 11. 100 12. 100 13. two tenths 14. fifteen hundredths 15. six hundredths 16. three tenths 17. five tenths 18. seventeen hundredths 19. ninety-nine hundredths 20. two tenths Write a fraction and a decimal for each point. Tell if it is close to 0, 12, or 1. A B 1 2 0 © McGraw-Hill School Division C D 1 21. A 22. B 23. C 24. D Problem Solving 25. Peter’s house is 0.78 mile from school. Write the number in words. Use with Grade 4, Chapter 13, Lesson 2, pages 560–561. (412) 26. Lora walks for five tenths of an hour. Write the number as a decimal. NS 1.6, 1.7 Print This Page Name Print This 13–2 Page Tenths and Hundredths R RETEACH You can use a model and a place-value chart to read and write decimals. A model and a place-value chart can also help you write a fraction for a decimal. Using Models Using Paper and Pencil Ones 0 Think: 5 10  12 • Tenths 5 Think: 0.5  Ones 0 • 5 10 60 100  6 10  12 Tenths 6 Think: 0.60  Think: Hundredths 6 100 Hundredths 0  6 10  35  35 © McGraw-Hill School Division Write a fraction and a decimal for each shaded part. Then write the fraction in simplest form. 1. 2. 3. 4. 5. 6. 7. 8. Use with Grade 4, Chapter 13, Lesson 2, pages 560–561. (413) NS 1.6, 1.7 Print This Page Name Print This 13–2 Page Tenths and Hundredths E ENRICH Decimal History Other symbols for decimals were used in England and Europe before the eighteenth century. Here are some examples of different ways to show 0.45. A. 0.4’ .5" B. 0|45 (1) (2) C. 0.4 .5 D. 0,45 Write the decimals using each of the notations shown above. A B C D (1) 1. 0.6 (1) 2. 0.4 (1) 3. 0.9 (1) 4. 5. © McGraw-Hill School Division 6. 7. 8. 0.5 (1) (2) (1) (2) (1) (2) (1) (2) 0.61 0.95 0.78 0.67 9. Which notation is most like the one we use today? Which notation did you find the most difficult to use? Explain. Use with Grade 4, Chapter 13, Lesson 2, pages 560–561. (414) NS 1.6, 1.7 Print This Page Name Print This 13–3 Page Thousandths P PRACTICE Write each as a decimal. 123 370 1. 1,000 17 6. 1,000 6 1,000 10. 1,000 120 4. 1,000 36 1 7. 1,000 24 8. 1,000 3 12 11. 1,000 999 13. 1,000 4 3. 1,000 225 5. 1,000 9. 25 2. 1,000 12. 1,000 9 14. 1,000 60 15. 1,000 16. 1,000 17. sixteen thousandths 18. twenty-five thousandths 19. nine thousandths 20. three hundred twenty-nine thousandths 21. five hundred thousandths 22. six hundred ninety thousandths 23. ninety-five thousandths 24. two thousandths 25. eleven thousandths 26. four thousandths 27. seventy-two thousandths 28. one hundred ninety-nine thousandths Algebra & Functions Complete. © McGraw-Hill School Division 29. meters decimeters centimeters millimeters 0.06 0.6 6 0.009 14 Problem Solving 30. Joe weighs 0.625 g of rice. Write this in words. Use with Grade 4, Chapter 13, Lesson 3, pages 562–563. (415) 31. Jaime bats three hundred one thousandths for the season. Write this as a decimal. NS 1.6 Print This Page Name Print This 13–3 Page Thousandths R RETEACH You can use models and a place-value chart to read and write decimals. Using Models The first decimal square is divided into hundredths. Think of dividing each hundredth into 10 equal parts. The second decimal square shows thousandths. Think: 7 1,000  0.007 The first decimal square is divided into hundredths. Think of dividing each hundredth into 10 equal parts. The second decimal square shows thousandths. Think: 513 1,000 = 0.513 Using Paper and Pencil Ones • Tenths Hundredths Thousandths 0 Think: 0 7 1,000 0 Ones Tenths Hundredths Thousandths 0 7  0.007 • Think: 5 513 1,000 1 3  0.513 © McGraw-Hill School Division Write each as a decimal and a fraction. 1. 2. 3. 4. Use with Grade 4, Chapter 13, Lesson 3, pages 562–563. (416) NS 1.6 Print This Page Name Print This 13–3 Page Thousandths E ENRICH Decimal Memory Game Play this memory game with a partner. • Cut out the cards below. Mix them up and place them facedown in six rows of six. • The first player turns over two cards. If the cards show an equivalent fraction and decimal, he or she keeps the cards. If the cards do not match, the cards are turned over again and left in the same position. • Try to remember which fractions and decimals have been turned over. • Players take turns until all the cards have been matched. © McGraw-Hill School Division • The player with more cards wins. 0.5 0.3 0.2 0.7 0.8 0.9 1 2 3 10 1 5 7 10 4 5 9 10 0.35 0.85 0.25 0.75 0.40 0.50 35 100 85 100 1 4 3 4 2 5 1 2 5 1,000 255 1,000 10 1,000 600 1,000 345 1,000 850 1,000 0.005 0.255 0.01 0.600 0.345 0.850 Use with Grade 4, Chapter 13, Lesson 3, pages 562–563. (417) NS 1.6 Print This Page Name Print This 13–4 Page Problem Solving: Reading for Math P PRACTICE Reading Skill Choose a Representation Circle the word fraction or decimal to tell how you will represent the numbers in the problem. Write both numbers in that form. Then compare the data to solve the problem. 1. A survey question asked people how they got to work most often. 4 Of those who answered, 0.3 said bus and 10 said subway. Do more riders take the bus or the subway? fraction decimal  4 10 0.3  Answer: 2. A survey question asked bus riders how often they took the bus. Of those who answered, 41 said 5 or more times per week and 0.75 said fewer than 5 times per week. Which answer got the greater number of responses? fraction 1 4 decimal   0.75 Answer: © McGraw-Hill School Division 4 3. Ashley takes the subway to work 5 of the time. Lauren takes the subway to work 0.7 of the time. Who takes the subway to work the greater part of the time? fraction 4 5 decimal   0.7 Answer: Use with Grade 4, Chapter 13, Lesson 4, pages 564–565. (418) NS 1.2; MR 1.1, 2.4, 3.2 Print This Page Name Print This 13–4 Page Problem Solving: Reading for Math P Choose a Representation PRACTICE Math Skills Test Prep Choose the correct answer. In a survey, 10 out of 20 people say they ride the subway at least once a week. Is it reasonable to say that 0.5 of the people surveyed ride the subway? 1. Which statement is true? A Twenty people say they ride the subway at least once a week. B Ten out of 20 people say they ride the subway at least once a week. 2. The statement is reasonable because F 10  20. 1 1 1 G 1  2  2 , and 2  0.5. 10 1 1 H 20  2 , and 2  0.5. C Ten percent of the people ride the subway at least once a week. Tonya takes the subway 8 out of 10 days. Max takes the subway 0.7 of the time. Max says he takes the subway a greater part of the time than Tonya does. Is his statement reasonable? 3. Which of the following plans can help you solve this problem? 8 4. Max’s statement is not reasonable because 8 A Write a decimal for 10 , and compare it to 0.7. F 10  0.7. B Write a fraction for 0.7 and 2 compare it to 10 . H 0.7  10 , and 10  10 . 8 G 10  0.8, and 0.8  0.7. 7 7 8 © McGraw-Hill School Division C Subtract 10  7. In a survey, 10 out of 40 people say they never walk to work. Is it reasonable to say that 0.4 of the people never walk to work? 5. Which statement is true? A Ten out of 40 people say they never walk to work. B Four out of 10 people never walk to work. 6. The statement is not reasonable because 10 1 1 F 40  4 , and 4  0.25, not 0.4. 1 3 3 G 1  4  4 , and 4  0.75, not 0.4. 10 4 4 H 40  10 , and 10  0.4. C Thirty out of 40 people say they never walk to work. Use with Grade 4, Chapter 13, Lesson 4, pages 564–565. (419) NS 1.2; MR 1.1, 2.4, 3.2 Print This Page Name Print This 13–4 Page Problem Solving: Reading for Math P Choose a Representation PRACTICE Math Skills Test Prep Choose the correct answer. A survey question asks people which is faster, the train or the bus. Of the people surveyed, 34 said the train and 0.1 said the bus. The rest of the people said that neither was faster. Which answer got more responses, the train or the bus? 7. Which statement is true? A Of the people surveyed, 14 said neither was faster. B Of the people surveyed, 0.1 said the train was faster. C Of the people surveyed, 0.1 said the bus was faster. 8. Which of the following plans can help you solve this problem? 1 F Write a decimal for 4 , and compare it to 0.1. G Write a fraction for 0.1 and 3 compare it to 4 . 1 H Subtract 4 from 1, and write it as a decimal. Solve. 9. George walks to work 6 out of 10 days. Janice walks to work 0.7 of 10 days. Who walks to work a greater part of the time? © McGraw-Hill School Division 11. In a survey, 0.5 of the people who answer say that they are very satisfied with subway service. Four tenths of the people say that they are somewhat satisfied. Are more people very satisfied or somewhat satisfied? 13. Alfredo walks to work 15 out of 20 days. He says he walks to work 0.9 of those days. Is his statement reasonable? Use with Grade 4, Chapter 13, Lesson 4, pages 564–565. (420) 10. Train Q is on time or early 0.4 of the 1 time. Train Y is on time or early 2 of the time. Which train is on time or early a lesser part of time? 12. Colleen takes the bus 18 of the days 7 in June. Rita takes the bus 10 of the days in June. Who takes the bus more days? [HINT: June has 30 days.] 14. The express bus is late 0.2 of the time. A reporter says that the express 2 bus is late 10 of the time. Is the reporter’s statement reasonable? NS 1.2; MR 1.1, 2.4, 3.2 Print This Page Name Print This 13–5 Page Decimals Greater Than 1 P PRACTICE Write as a mixed number in simplest form and a decimal to tell how much is shaded. 1. 2. 3. Write as a decimal. 4. 7 10 3 5. 1 100 25 2 9. 17 10 8. 6 100 1 13. 2 10 98 16. 18 100 6 20. 6 100 4 24. 24 100 © McGraw-Hill School Division 7 9 12. 9 10 5 7. 8 1,000 5 11. 3 1,000 21 15. 25 1,000 6. 9 100 10. 8 1,000 14. 27 100 5 17. 13 1,000 12 18. 10 1,000 375 22. 23 10 1 26. 9 100 21. 19 1,000 25. 11 100 28. eight and three tenths 8 19 125 37 16 3 19. 11 100 60 23. 76 1,000 26 27. 6 100 29. seven and seventy hundredths Problem Solving 30. Out of 100 pairs of shoes in a sporting goods store, 53 are running shoes. What decimal shows the number of running shoes? Use with Grade 4, Chapter 13, Lesson 5, pages 568–569. (421) 31. Out of 1,000 backpacks, 25 are red and the rest are green. What decimal shows the number of red backpacks? NS 1.6 Print This Page Name Print This 13–5 Page Decimals Greater Than 1 R RETEACH A mixed number is made up of a whole and a part of a whole. You can use models to help you write mixed numbers as decimals. 7 Mixed Number: 1 10 Decimal: 1.7 Read: one and seven tenths 36 Mixed Number: 2 100 Decimal: 2.36 Read: two and thirty-six hundredths © McGraw-Hill School Division Look at each model. Write a mixed number and a decimal to tell how much is shaded. 1. 2. 3. 4. Write a decimal and the word name. 5. 1 9 10 6. 3 5 Use with Grade 4, Chapter 13, Lesson 5, pages 568–569. (422) 100 NS 1.6 Print This Page Name Print This 13–5 Page Decimals Greater Than 1 E ENRICH Decimal Crossword Complete the decimal crossword puzzle. Write the decimal for the fraction or word name given in the ACROSS and DOWN clues below. Each decimal point has a space of its own. 1. 5 . 2. 6. 4 . 7. 3 4 4 . . 5 8 7 . 8. . 2 3 . 3 14. 6 . 16. . 5 1 7 7 3 1 1 . 6 21. 9 9 6 5 10 © McGraw-Hill School Division 8 3. 37 10 9 6. 44 10 7. 5 3 10 5 8. 3 100 7 11. 12 10 75 14. 6 100 37 15. 38 100 28 17. 3 100 18. thirty-five and twenty-one hundredths 19. eleven and six tenths 20. seventy-eight and seventy-nine hundredths 21. ninety-nine and sixty- 5 1 . 5 2 . . 2 8 6 3 Down Across 1. 9. 8 2 9 5 7 7 17. 7 19. . 0 13. . . 7 . . 2 3 8 2 12. . 20. 5. 8 9 1 18. 3 4. 0 11. 3 . 3 . 4 10. 6 15. 7 3 . 3 8 3. 6 48 1. 53 100 2. 43 6 100 51 3. 34 100 37 4. 80 100 5. 27 12. two and thirty- five hundredths 13. fifteen and eight tenths 15. thirty-three and seven tenths 16. seven and nineteen 28 9. 57 100 hundredths 8 10. 36 10 three hundredths Use with Grade 4, Chapter 13, Lesson 5, pages 568–569. (423) NS 1.6 Print This Page Name Print This 13–6 Page Compare and Order Decimals P PRACTICE Compare. Write , , or . 1. 0.2 5. 0.106 9. 9.06 0.02 2. 0.7 0.70 0.160 6. 5.117 9.16 10. 6.5 5.107 5.9 3. 1.78 7. 11.99 11. 2.1 13. 16.75 16.57 14. 14.44 14.54 15. 18.01 17. 21.12 22.13 18. 16.06 16.6 21. 9.01 9.10 22. 14.03 19. 1.1 13.99 23. 2.22 1.87 12.1 0.2 4. 12.16 8. 11.1 2.11 10.1 12. 10.3 18.11 16. 9.1 1.11 12.160 10.300 9.09 20. 9.9 10.0 24. 19.99 18.99 Write in order from greatest to least. 25. 1.78, 1.08, 1.87 26. 0.88, 0.08, 0.98 27. 1.11, 1.21, 0.22 28. 10.02, 9.9, 10.12 29. 7.7, 8.8, 7.07 30. 1.001, 1.011, 1.111 © McGraw-Hill School Division Write in order from least to greatest. 31. 0.01, 0.1, 0.001 32. 2.22, 2.02, 2.12 33. 6.07, 5.99, 6.17 34. 1.06, 1.16, 0.99 35. 11.17, 10.99, 9.99 36. 16.6, 16.61, 16.1 Problem Solving 37. On Monday Ken ran 100 meters in 11.2 seconds. On Tuesday he ran 100 meters in 10.9 seconds. On which day did Ken run faster? Use with Grade 4, Chapter 13, Lesson 6, pages 570–573. (424) 38. Jadwin Bridge is 1.6 km long. Seely Bridge is 1.06 km long. Which bridge is longer? NS 1.2, 1.6, 1.7, 1.9 Print This Page Name Print This 13–6 Page Compare and Order Decimals R RETEACH You can use models to compare and order decimals. Order the numbers from least to greatest. 3.63 3.68 2.75 Compare the decimals. Order the decimals. Since 2  3, 2.75  3.63 and 3.68. Think: 2.75  3.63  3.68. Since 63 100 68  100 , 3.63  3.68. The order from least to greatest is 2.75  3.63  3.68. Compare. Write , , or . 1. 2. 0.75 0.7 © McGraw-Hill School Division 4. 3. 0.66 0.77 5. 0.29 0.25 0.06 0.60 0.03 0.30 6. 0.24 0.33 Write the decimals in order from least to greatest. 7. 0.75, 0.66, 0.7 9. 0.29, 0.25, 0.24 8. 0.06, 0.77, 0.60 10. 0.33, 0.03, 0.30 Use with Grade 4, Chapter 13, Lesson 6, pages 570–573. (425) NS 1.2, 1.6, 1.7, 1.9 Print This Page Name Print This 13–6 Page Compare and Order Decimals E ENRICH Puzzles Choose the decimal from the box that solves each puzzle. Use a decimal only once. © McGraw-Hill School Division 10.79 8.08 0.84 8.01 0.89 10.25 8.43 10.33 10.8 Puzzle 1 The decimal is greater than 0. It is less than 0.85 Puzzle 2 The decimal is less than 10.8. It is greater than 10.75. Puzzle 3 The decimal is greater than 8.02. It is less than 8.1. Puzzle 4 The decimal is less than 10.30. It is greater than 10. Puzzle 5 The decimal is greater than 0.85. It is less than 0.9. Puzzle 6 The decimal is greater than 10. It is less than 10.85. Puzzle 7 The decimal is greater than 8. It is less than 8.07. Puzzle 8 The decimal is less than 10.4. It is greater than 10.25. Puzzle 9 The decimal is greater than 8.35. It is less than 8.5. 1. Arrange the decimals in the box in order from least to greatest. 2. Explain how you found the answer to Puzzle 3. Use with Grade 4, Chapter 13, Lesson 6, pages 570–573. (426) NS 1.2, 1.6, 1.7, 1.9 Print This Page Name Print This 13–7 Page Problem Solving: Strategy P PRACTICE Draw a Diagram Draw a diagram to solve. 1. CD World is 1.8 miles east of the school. William lives 1.4 miles west of the school. Sound City is 2.9 miles east of William. Is William closer to CD World or to Sound City? 3. Ed walks up 2 floors from his office to the storeroom. He walks down 6 floors to the cafeteria. How many floors away is the cafeteria from Ed’s office? 2. Silver Hills is 3.9 miles north of Bay Edge. East Ridge is 1.3 miles south of Silver Hills. East Ridge is 2.8 miles north of Hightown. How far is Bay Edge from Hightown? 4. A cab driver leaves his garage. He goes north 9 blocks, south 6 blocks, and north 8 blocks. How many blocks is he from his garage? Mixed Strategy Review Solve. Use any strategy. 5. The City Sports Center offers season tickets, 20-game tickets, or single game tickets. Seats are available for the lower deck, middle deck, or upper deck. You can buy an individual seat or a pair of seats. How many choices do you have? 6. Social Studies In 1996, Abilene, Texas, had a population of 122,130. Amarillo, Texas has a population that was 83,885 greater than the population of Abilene. What was the population of Amarillo? Strategy: © McGraw-Hill School Division Strategy: 7. There are 48 people at a dinner at City Hall. You want to use small tables that seat 5 people and large tables that seat 8 people. To have full tables, which tables should be used? How many of these tables will be needed? 8. Create a problem which you could solve by drawing a diagram. Share it with others. Strategy: Use with Grade 4, Chapter 13, Lesson 7, pages 574–575. (427) NS 1.2; MR 1.1, 2.3, 2.4, 3.2 Print This Page Name Print This 13–7 Page Problem Solving: Strategy R RETEACH Draw a Diagram Page 575, Problem 1 Kendra wants to go to a mall. The Loews Mall is 3.9 miles east of her town. The Bergen Mall is 1.8 miles west of the Loews Mall. King’s Mall is 2.9 miles east of Bergen Mall. Which mall is the closest to Kendra’s town? the farthest from her town? Step 1 Read Be sure you understand the problem. Read carefully. What do you know? • Loews Mall is • Bergen Mall is • King’s Mall is miles east of Kendra’s town. miles west of the Loews Mall. miles east of Bergen Mall. What do you need to find? • You need to find . Step 2 Make a plan. Plan Choose a strategy. ■ ■ © McGraw-Hill School Division ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ Make a Table Write a Number Sentence Work Backward Act It Out Find a Pattern Make a Graph Guess and Check Choose a Stategy Logical Reasoning Draw a Tree Diagram Solve Simpler Problem Draw a Diagram Drawing a diagram can help you see the solution to a problem. Draw a line segment to show the distance between Kendra’s town and Loews Mall. Along that line, show the distance between Bergen Mall and Loews Mall. Then show the distance between Bergen Mall and King’s Mall. Extend the line in either direction if you need to. Use your drawing to solve the problem. Use with Grade 4, Chapter 12, Lesson 7, pages 574–575. (428) NS 1.2; MR 1.1, 2.3, 2.4, 3.2 Print This Page Name Print This 13–7 Page Problem Solving: Strategy R RETEACH Draw a Diagram Step 3 Solve Carry out your plan. Draw a diagram. Use 1 cm to show 1 mile. Loews Mall 3.9 miles  3.9 cm Bergen Mall 1.8 miles  1.8 cm King’s Mall 2.9 miles  2.9 cm N Kendra‘s Town Bergen Mall Loew‘s Mall King‘s Mall W E S 3.9 cm 1.8 cm 2.9 cm Mall is closest to Kendra’s town. Mall is farthest from her town. Step 4 © McGraw-Hill School Division Look Back Is the solution reasonable? Reread the problem. Does your answer make sense? Did you check your answer? Practice 1. Allison lives 2.6 miles west of the beach. Jerry lives 1.2 miles east of Allison. Phil lives 1.7 miles west of Jerry. Who is farthest from the beach? Use with Grade 4, Chapter 13, Lesson 7, pages 574–575. (429) 2. Norma goes up 4 floors from her office to her manager’s office. She then goes down 7 floors to the copy room. Randi is in the copy room. Randi goes up 1 floor to her office. How many floors away is Randi’s office from Norma’s? NS 1.2; MR 1.1, 2.3, 2.4, 3.2 Print This Page Name Print This 13–8 Page Round Decimals P PRACTICE Round to the nearest whole number. 1. 9.47 2. 2.8 3. 6.01 4. 9.09 5. 1.1 6. 3.51 7. 4.62 8. 1.5 9. 13.61 10. 25.09 11. 37.8 12. 52.4 13. 93.56 14. 88.48 15. 19.71 16. 63.44 Round to the nearest tenth. 17. 7.24 18. 9.43 19. 6.58 20. 8.89 21. 3.25 22. 1.27 23. 3.98 24. 7.24 25. 31.26 26. 71.64 27. 12.55 28. 64.93 29. 47.96 30. 87.54 31. 29.69 32. 36.97 33. 53.84 34. 19.46 35. 61.07 36. 78.85 © McGraw-Hill School Division Round to the nearest hundredth. 37. 8.236 38. 4.186 39. 9.275 40. 1.123 41. 6.008 42. 2.055 43. 7.266 44. 3.199 45. 17.246 46. 26.981 47. 78.006 48. 91.115 49. 53.102 50. 66.666 51. 32.333 52. 45.999 53. 13.462 54. 51.277 55. 90.409 56. 45.555 Problem Solving 57. A vitamin pill weighs 2.346 g. What is its weight to the nearest hundredth of a gram? Use with Grade 4, Chapter 13, Lesson 8, pages 576–577. (430) 58. Jason weighs 152.6 lb. What is his weight to the nearest pound? NS 1.2, 1.3 Print This Page Name Print This 13–8 Page Round Decimals R RETEACH You can use a number line to help you round decimals. To round a decimal to the nearest whole number, look at the digit in the tenths place. If the ones digit is 5 or greater, round up to the nearest one. If the ones digit is less than 5, round down to the nearest one. 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10.0 Round 8.3 to the nearest whole number. Think: 8.3 is closer to 8 than 9. So, 8.3 rounds down to 8. Round 9.8 to the nearest whole number. Think: 9.8 is closer to 10 than 9. So, 9.8 rounds up to 10. To round to the nearest tenth, look at the digit in the hundredths place. If the hundredths digit is 5 or greater, round up to the nearest tenth. If the hundredths digit is less than 5, round down to the nearest tenth. 1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.601.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.70 Think: 1.56 is closer to 1.6 than 1.5. So, 1.56 rounds up to 1.6. Think: 1.61 is closer to 1.6 than 1.7. So, 1.61 rounds down to 1.6. © McGraw-Hill School Division Round each decimal to the nearest whole number. Use the number line above to help you. 1. 8.6 2. 9.1 3. 8.2 4. 9.3 5. 9.8 6. 8.4 7. 9.5 8. 8.7 Round to the nearest tenth. Use the number line above to help you. 9. 1.52 10. 1.64 11. 1.59 12. 1.63 13. 1.55 14. 1.68 15. 1.51 16. 1.66 Use with Grade 4, Chapter 13, Lesson 8, pages 576–577. (431) NS 1.2, 1.3 Print This Page Name Print This 13–8 Page Round Decimals E ENRICH Decimal Detective Use the clues to solve each riddle. Circle the mystery number. 1. Round me to the nearest whole number. You get 5. Round me to the nearest tenth. You get 5.3. Round me to the nearest hundredth. You get 5.32. What number am I? 5.316 5.295 5.334 2. Round me to the nearest whole number. You get 12. Round me to the nearest tenth. You get 12.5. Round me to the nearest hundredth. You get 12.48. What number am I? 12.557 12.479 12.486 3. Round me to the nearest whole number. You get 17. Round me to the nearest tenth. You get 16.9. Round me to the nearest hundredth. You get 16.94. What number am I? 16.937 16.899 16.934 4. Round me to the nearest whole number. You get 28. Round me to the nearest tenth. You get 28.0. Round me to the nearest hundredth. You get 28.00. What number am I? 27.959 28.002 28.008 5. Round me to the nearest whole number. You get 124. © McGraw-Hill School Division Round me to the nearest tenth. You get 124.4. Round me to the nearest hundredth. You get 124.45. What number am I? 124.456 124.444 124.446 6. Round me to the nearest whole number. You get 203. Round me to the nearest tenth. You get 203.5. The sum of my digits is 20. What number am I? 203.456 203.458 203.566 7. Create you own mystery number puzzle. Exchange your puzzle with a friend to solve. Use with Grade 4, Chapter 13, Lesson 8, pages 576–577. (432) NS 1.2, 1.3 Print This Page Name Problem Solving: Application Print This Page 13–9 Part A WORKSHEET Decision Making Applying Decimals Record your data. Name of Item Number Bought Total Cost Items for Business District Items for Area Where People Live Your Decision © McGraw-Hill School Division What models should Kit and Rammel buy for the area where people live? What models should they buy for the business district? Explain. Use with Grade 4, Chapter 13, Lesson 9, pages 578–579. (433) NS 1.2; MR 1.1, 2.3 Print This Page Name Print This Page 13–9 Part B WORKSHEET Problem Solving: Application Math & Science How does distance affect how many strikes you throw? Record your data. Distance Attempts 1.5 m 10 3m 10 4.5 m 10 6m 10 Strikes Strikes Thrown (as a decimal) © McGraw-Hill School Division 1. At which distance was it easiest to make strikes? Explain your answer. In ten tries, how many strikes do you think you will be able to throw from 1.5 meters away? Use with Grade 4, Chapter 13, Lesson 9, pages 580–581. (434) NS 1.2, 1.6; MR 1.1, 2.3, 3.2 Print This Page Name Problem Solving: Application How does distance affect how many strikes you throw? Print This Page 13–9 Part B WORKSHEET Math & Science 2. How did the results compare to what you thought the results would be? 3. Order the decimals in the table from least to greatest. If you made a lot of strikes, was the decimal bigger or smaller than the other numbers? 4. What fraction of all throws are strikes? Write the fraction © McGraw-Hill School Division as a decimal. 5. Use your answer in number 3 to compare your ability to throw strikes with Major League Baseball pitchers. Use with Grade 4, Chapter 13, Lesson 9, pages 580–581. (435) NS 1.2, 1.6; MR 1.1, 2.3, 3.2 Print This Page Name Print This 14–1 Page Explore Adding Decimals P PRACTICE Use the models to find each sum. 1. 2. 1.56  0.43  3. 1.7  1.2  0.76  0.45  © McGraw-Hill School Division Find each sum. 4. 0.3  0.4 5. 0.5  0.4 6. 0.6  0.7 7. 0.8  0.9 8. 0.4  0.6 9. 0.99  0.88 10. 0.62  0.53 11. 0.71  0.59 12. 0.44  0.79 13. 0.86  0.13 14. 2.7  3.8 15. 0.5  1.9 16. 2.6  1.8 17. 1.7  2.8 18. 0.4  0.9 19. 0.85  2.17  20. 2.76  1.32  21. 3.46  1.78  22. 2.96  2.23  23. 0.67  2.98  24. 0.12  2.2  25. 1.5  2.49  26. 2.14  1.9  27. 2.3  1.92  Problem Solving 28. Two strips of paper, 3.6 cm long and 2.8 cm long, are taped together. How long is the entire strip of paper? Use with Grade 4, Chapter 14, Lesson 1, pages 596–597. (436) 29. One apple weighs 0.26 kg. Another apple weighs 0.87 kg. How much do the two apples weigh together? NS 2.1 Print This Page Name Explore Adding Decimals Print This 14–1 Page R RETEACH You can use models to help you add decimals. Add 1.7  0.85. Write a decimal to show the total number of shaded squares. 2.55 Color 1.7 dark gray. Color 0.85 with stripes. So, 1.7  0.85  2.55. © McGraw-Hill School Division Add. Draw 10 by 10 grids to help you. 1. 0.65  0.34  2. 1.3  1.5  3. 2.4  1.36  4. 1.52  0.31  5. 0.77  0.24  6. 0.84  0.39  7. 1.8  0.5  8. 2.5  0.62  9. 2.75  0.45  Use with Grade 4, Chapter 14, Lesson 1, pages 596–597. (437) NS 2.1 Print This Page Name Print This 14–1 Page Explore Adding Decimals E ENRICH Magic Boxes and Mazes Fill in the boxes so that each row, column, and diagonal adds up to the same sum. 1. 2. 0.9 0.6 1.0 0.8 0.8 0.7 0.4 0.7 3. 4. 0.5 0.7 0.1 1.0 1.2 0.9 0.6 1.1 1.3 1.3 0.5 0.3 1.6 © McGraw-Hill School Division Move through the maze from start to finish by adding numbers that will give you the finish number. You may move across, down, up, or diagonally. Start ↓ Start ↓ 5. 6. 2.3 3.1 0.6 0.9 1.4 1.2 0.7 4.1 1.2 2.4 0.3 2.1 2.8 1.7 8.2 7.9 0.6 3.2 ↑ Finish ↑ Finish Use with Grade 4, Chapter 14, Lesson 1, pages 596–597. (438) NS 2.1 Print This Page Name Print This 14–2 Page Add Decimals P PRACTICE Add. 1. 0.36  0.25 2. 0.29  0.44 3. 0.60  0.70 4. 6. 4.2  6.4 7. 1.2  8.3 8. 0.697  9.262 1.67  1.45 5. 2.67  1.38 9. 23.604 10.  5.408 32.75  12.30 11. 25.97 12.  0.12 12.32 13.  1.74 13.407 14.  26.708 21.151 15.  4.774 6.373  5.602 16. 2.874 17.  8.129 36.215 18.  9.759 12.948 19.  7.267 0.254 20.  12.259 3.187  6.975 21. 11.3 22. 6.7  21.6 8.25 23. 4.30  9.20 4.142 24. 8.167  2.94 4.567 25. 7.0 13.621 9.288  21.984 12.6 26. 12.5  11.35  27. 2.7  2.73  28. 3.36  5.031  29. 3.869  9.3  7.76  30. 7.35  8.2  17.314  31. 12.42  7.687  19.3  32. 8.0  4.343  10.5  © McGraw-Hill School Division Find the number you need to add to complete the pattern. 33. 1.3, 1.9, 2.5, 34. 4.12, 4.125, , , , 4.135, Add , Add Problem Solving 35. Lora spends $2.64 on stamps and $1.39 on envelopes. How much does she spend? Use with Grade 4, Chapter 14, Lesson 2, pages 598–601. (439) 36. Ben buys packing tape for $2.97 and boxes for $6.99. How much does he spend? NS 2.1 Print This Page Name Print This 14–2 Page Add Decimals R RETEACH You can use models to help you add decimals. Add 1.34  1.28. Using Models Regroup Color 1.34 dark gray. Color 1.28 with stripes. Count the number of squares you shaded. Using Paper and Pencil Add each place. Regroup if needed. 1 1.34  1.28 2.62 © McGraw-Hill School Division Find each sum. Draw 10 by 10 grids to help you. 1. 1.7  1.4  2. 0.5  0.8  3. 2.25  1.03  4. 0.9  0.8  5. 0.85  0.15  6. 1.24  0.38  7. 1.5  1.35  8. 1.52  0.35  9. 0.6  1.85  Use with Grade 4, Chapter 14, Lesson 2, pages 598–601. (440) NS 2.1 Print This Page Name Print This 14–2 Page Add Decimals E ENRICH Digit Detective Find the missing digits. . 2 1. 6  1. 4  1 . 5. 9 5. 4 .7 6. $ 10. 8 .  7.  . 1 6 9 . 2 . 9 1 .   6 . 5 . 3 7 22.  2 . 1 6 7 7. 1 $2 . 1 4 3 . 6 4  3 . 4 3 . 1 8 $ 23. 4 2 . 9  8 . 0 . 4 1 6  1 . 2 1 Use with Grade 4, Chapter 14, Lesson 2, pages 598–601. (441) 1 8 . 4 12. 6 . 1 5 . 8 7 16. . 3 7 . 7 6 . 2 6  8 3 . 2 . 9 0 . 4 3 4 7 . 24. 3 . 4 2 4 . 20. . 0 8 6 . 2 3 2 7 7 . 5  . 4 5 . 3 7  3. 3 19. 1 1  . 4 3. 8 6 15. 2 . 3 5 4 2 . 6 7 . 8 5 3 1 . 3 . 2 2 . 1 1 . 5 6 . 6 18. 1 . 2 9 . 8. 1 . 9 9 11. 7 7 . . 1 3 $ .5 $ 3 $10 17. 6 9 . 21. 8 2 . 7 1 8  $7 6 . 2  . 6 7 4. $ 6 .3 3 7. $ 8 . 0 14. 1 0 . 3 4 .6 6 . 1 4 . 9 13. 5 9 .   $ 6 2. 9. 2 1 5 8. 9.  3. 4. 7  3 .6 4 1 0 2 9. 6 1 3 .9 © McGraw-Hill School Division . 2 2. 9 3 . 1 8 6 . 8 NS 2.1 Print This Page Name Print This 14–3 Page Estimate Sums P PRACTICE Estimate. Round to the nearest whole number. 1. 5.1  9.4 2. 6.7  8.4 3. 1.9  3.8 4. $6.35  $5.95 5. 7.45  8.56 6. 4.32  7.59 7. 9.3  2.6 8. 22.63  3.46 9. 31.06  9.98 10. 45.92  4.18 11. $33.19  $9.50 12. 6.67  21.15 Add. Estimate to check for reasonableness. 13. 19.76  9.55  14. $10.25  $3.25  15. 19.67  9.94  16. 3.7  5.2  4.6  17. 4.1  9.6  1.9  18. 2.9  6.7  7.3  19. $3.75  $9.90  $8.75  20. 4.76  9.15  8.95  21. 8.12  4.79  7.15  22. $6.30  $7.95  $8.10  23. 7.75  8.90  9.90  24. 2.178  6.472  8.015  © McGraw-Hill School Division Algebra & Functions Compare. Write  or . 25. 3.7  2.5 1.9  4.2 26. 4.9  1.6 5.1  3.1 27. 6.9  7.1 3.8  8.3 28. 9.2  3.6 2.6  9.1 29. 5.5  6.3 8.2  5.2 30. 9.4  2.7 6.8  6.1 31. 1.6  2.9 3.1  1.1 32. 7.7  7.2 8.1  9.1 33. 8.7  9.6 9.1  8.6 Problem Solving 34. The odometer on a new car shows 17.7 miles. Sean drives the car 12.9 miles. About what does the odometer show now? Use with Grade 4, Chapter 14, Lesson 3, pages 602–603. (442) 35. Lenny buys one CD for $12.75 and another CD for $18.90. About how much does Lenny pay for the two CDs? NS 2.1, 2.2, 3.1; MR 2.1 Print This Page Name Print This 14–3 Page Estimate Sums R RETEACH To estimate the sums of decimals, round each decimal to the nearest whole number. Then add the rounded numbers. Estimate 22.52  4.49. ↓ ↓ Round each number 23 4 to the nearest whole number. Add. 23  4  27 So, 22.52  4.49 is about 27. Estimate $7.95  $9.25 ↓ ↓ Round each number $8.00  $9.00 to the nearest dollar. Add. $8.00  $9.00 = $17.00 So, $7.95  $9.25 is about $17.00. Circle the digits in the place to which you will round each number. © McGraw-Hill School Division Estimate each sum. Show how you rounded. 1. $ 5 . 8 9  $ 4 . 2 9 2. 1 7 . 3  5 . 6 7 3. 8 . 4 8  3 . 0 7 4. 5. $ 1 5 . 9 5  $ 2 . 5 9 6. 2 5 . 7  8 . 9 7. 1 5 . 7 5  1 2 . 3 4 8. 9. 11. 6. 7  3.2 9.9 7  8.4 5.6 3  1 8.4 7 10. $ 6 . 5 2  $ 1 . 7 5 4.4 7  6.7 4 12. $ 8 . 5 0  $2 4 . 3 8 Use with Grade 4, Chapter 14, Lesson 3, pages 602–603. (443) NS 2.1, 2.2, 3.1; MR 2.1 Print This Page Name Print This 14–3 Page Estimate Sums E ENRICH Four for 16 Use estimation to try to choose four numbers that will have a sum close to 16. • Player 1 chooses a number from below and writes it in the first box for that round. He or she crosses out the number below. • Player 2 chooses any number that is not crossed out and follows the same steps. • Players take turns until each player has four numbers. • Add the numbers. Then find the difference between each sum and 16. You may check your results with a calculator. • The player with the sum closer to 16 wins that round. Round Players 1 Player 1 Numbers Sum How Close to 16? Player 2 2 Player 1 Player 2 3 Player 1 Player 2 4 Player 1 © McGraw-Hill School Division Player 2 5 Player 1 Player 2 3.38 3.56 1.08 4.5 6.75 2.03 2.58 4.61 3.23 4.89 2.47 4.19 8.48 3.96 4.91 5.57 7.59 2.19 2.64 1.18 1.77 2.63 5.72 5.63 4.24 3.27 5.13 3.76 2.30 4.55 3.69 3.31 4.16 6.89 7.81 7.35 8.74 0.99 3.49 3.98 Use with Grade 4, Chapter 14, Lesson 3, pages 602–603. (444) NS 2.1, 2.2, 3.1; MR 2.1 Print This Page Name Print This 14–4 Page Problem Solving: Reading for Math P PRACTICE Reading Skill Choose the Operation Circle the number sentence you would use to solve the problem. Then tell how you decided whether to use addition or subtraction. 1. Chico bikes 4.6 miles. Tom bikes 3.7 miles. How much farther does Chico bike than Tom? 4.6  3.7  8.3 4.6  3.7  0.9 Explain: 2. Keiko rode her bike 8.4 miles last week. This week, she rode 4.35 miles more than last week. How far did Keiko ride this week? 8.4  4.35  12.75 8.4  4.35  4.05 Explain: 3. Rachel bikes 3.2 miles to the mall. Then she bikes 2.7 miles to the park. How many miles does she bike? 3.2  2.7  5.9 3.2  2.7  0.5 © McGraw-Hill School Division Explain: 4. Mark is biking around a 9.2-mile loop. He has biked 4.5 miles so far. How many miles does Mark have left to finish the loop? 9.3  4.5  13.8 9.3  4.5  4.8 Explain: Use with Grade 4, Chapter 14, Lesson 4, pages 604–605. (445) NS 2.1; MR 1.1, 2.4, 3.2 Print This Page Name Print This 14–4 Page Problem Solving: Reading for Math P Choose the Operation PRACTICE Math Skills Test Prep Choose the correct answer. Mikio rides his bike 4.25 miles from home to school. Then he rides 2.9 miles to the park. How far does Mikio ride? 1. Which of the following statements 2. Which number sentence can you use is true? to solve this problem? A Hiroshi walks to school. F 4.25  2.9  7.15 B Hiroshi rides 4.25 miles in all. G 2.9  2.9  5.8 C The ride from school to the park is 2.9 miles. H 4.25  2.9  1.35 It is 5.6 miles from Sarah’s house to the museum. She has completed 1.75 miles of the trip so far. How many miles does Sarah have left? 3. What do you have to do to solve 4. Which number sentence can you use this problem? to solve this problem? A Add to find the total amount of miles that Sarah travels to the museum. F 5.6  5.6  11.2 B Subtract to find the number of miles Sarah has left. G 5.6  1.75  7.35 H 5.6  1.75  3.85 © McGraw-Hill School Division C Add to find the total number of miles in the round trip. Michael takes the train for 8.4 miles. Then he walks 0.6 miles. How many miles does Michael travel? 5. Which could you use to solve 6. How many miles does Michael the problem? travel? A 8.4  0.6 F 16.8 miles B 8.4  0.6 G 9 miles C 8.4  8.4 H 8.4 miles Use with Grade 4, Chapter 14, Lesson 4, pages 604–605. (446) NS 2.1; MR 1.1, 2.4, 3.2 Print This Page Name Print This 14–4 Page Problem Solving: Reading for Math P Choose the Operation PRACTICE Math Skills Test Prep Choose the correct answer. Roland bikes 8.24 miles. Paul bikes 4.62 miles. How much farther does Roland bike than Paul? 7. Which of the following statements 8. Which number sentence can you use is true? to solve this problem? A Paul bikes farther than Roland. F 8.24  4.62  3.62 B Roland bikes 4.62 miles. G 4.62  4.62  9.24 C Paul bikes 4.62 miles. H 8.24  4.62  12.86 Solve. 9. The train trip from Springfield to Morris Hill is 6.2 miles. The next stop, Peapack, is 3.2 miles from Morris Hills. How long is the train trip from Springfield to Peapack? 11. Daniel biked 6.24 miles last week. © McGraw-Hill School Division This week he biked 1.65 miles less than last week. How far did he bike this week? 13. Eddie rode 1.9 miles more today than he did yesterday. He rode 5.75 miles yesterday. How far did Eddie ride today? Use with Grade 4, Chapter 14, Lesson 4, pages 604–605. (447) 10.The train trip from Point Dume to Snug Harbor is 8.31 miles. The road from Point Dume to Snug Harbor is 9.6 miles. How much longer is the train trip than the road? 12. Myra bikes 3.25 miles from home to the record store. Then she bikes 1.1 miles to the movie theater. How many miles does she bike altogether? 14. Shore Road is 6.3 miles long. Nicole has biked 2.2 miles along Shore Road so far. How many miles does she have left? NS 2.1; MR 1.1, 2.4, 3.2 Print This Page Name Print This 14–5 Page Explore Subtracting Decimals P PRACTICE Use the models to find each difference. 1. 2. 0.68  0.35  3. 1.12  0.7  1.8  1.1  © McGraw-Hill School Division Find each difference. 4. 0.9  0.3 5. 1.2  0.6 6. 2.7  0.9 7. 2.5  1.6 8. 2.1  1.7 9. 1.67  0.48 10. 1.6  1.48 11. 3.11  1.12 12. 3.7  2.91 13. 1.2  1.13 14. 3.6  1.47 15. 2.02  1.79 16. 0.95  0.67 17. 0.8  0.25 18. 0.74  0.59 19. 1.7  0.35 20. 2.04  1.69 21. 1.03 0.6 22. 0.80  0.54 23. 2.0  1.06 24. 2.7  1.6  25. 0.8  0.5  26. 7.66  2.34  27. 1.52  0.57  28. 0.73  0.57  29. 0.70  0.34  30. 0.8  0.07  31. 0.4  0.14  32. 3.7  0.16  Problem Solving 33. A board is 2.12 m long. A piece 1.55 m long is cut from it. How much of the board is left? Use with Grade 4, Chapter 14, Lesson 5, pages 608–609. (448) 34. A piece of wire is 2.6 cm long. A piece 1.9 cm long is cut from it. How much of the wire is left? NS 2.1 Print This Page Name Explore Subtracting Decimals Print This 14–5 Page R RETEACH You can use models to help you subtract decimals. Subtract 1.85  0.9. Write a decimal to show how many squares are not crossed out. 0.95 Shade 1.85. Cross out 0.9. So, 1.85  0.9  0.95. © McGraw-Hill School Division Subtract. Draw 10 by 10 grids to help you. 1. 1.6  1.3  2. 0.8  0.3  3. 1.22  0.55  4. 1.9  0.56  5. 0.80  0.57  6. 1.35  1.07  7. 0.8  0.09  8. 1.85  1.49  9. 1.7  0.45  Use with Grade 4, Chapter 14, Lesson 5, pages 608–609. (449) NS 2.1 Print This Page Name Print This 14–5 Page Explore Subtracting Decimals E ENRICH Magic Triangles In a magic triangle, each side of the triangle has the same sum. Choose numbers from the box so each side of the triangle has a sum of 22.4. 3.8 5.19 6.88 7.22 5.19 0.73 1.6 2.48 4 4.85 5.35 4.3 4 3.6 6.88 2.08 Choose numbers from the box so each side of the triangle has a sum of 24.5. 5.8 0.73 © McGraw-Hill School Division 4.9 5 4.9 4.85 5.05 2 4 8.92 4.3 7.22 2.67 5.84 4 5.35 2.48 Use with Grade 4, Chapter 14, Lesson 5, pages 608–609. (450) 5 1.6 6.5 NS 2.1 Print This Page Name Print This 14–6 Page Subtract Decimals P PRACTICE Subtract. Check each answer. 1. 0.7  0.4 2. 6.3  0.7 3. 9.1  2.3 7. 0.44  0.22 8. 7.04  3.66 9. 13. 9.04  7.50 14. 19. 8.154 20.  2.075 4.5  2.7 1.2  0.7 6. 0.43  0.26 15.03 10. 4.12 11.  3.12  1.27 9.00 12.  0.09 7.17  2.70 6.00 15. 8.20 16. 5.34 17.  4.70  4.96  4.67 1.67 18.  0.50 19.83  3.60 4. 5. 17.076 21. 5.258 22. 8.000 23. 1.755 24. 6.024  0.027  3.129  2.974  0.896  2.402 25. 6.7  2.4  26. 7.6  2.07  27. 8.5  3.08  28. 9.03  3.775  29. 7.44  3.867  30. 4.627  2.88  31. 3.6  2.79  32. 8.36  3.248  33. 4.556  0.93  34. 34.0  2.097  © McGraw-Hill School Division Algebra & Functions Find each missing number. 35. 7.97  n  0.52 36. h  4.64  2.31 37. 5.25  b  10.46 38. a  7.08  18.5 Problem Solving 39. Christine buys a pair of socks for $8.35. What is her change from a $10 bill? Use with Grade 4, Chapter 14, Lesson 6, pages 610–613. (451) 40. Matt buys a pencil for $0.35, a pen for $2.75, and a ruler for $4.36. What is his change from a $20 bill? NS 3.1; MR 2.2 Print This Page Name Print This 14–6 Page Subtract Decimals R RETEACH You can use models to help you subtract decimals. Subtract 1.7  1.59. Using Models Color 1.7. Cross out 1.59. Count the number of squares not crossed out. Using Paper and Pencil Subtract each place. Regroup if necessary. Write zero as a 1.70 ← placeholder.  1.59 0.11 6 10 © McGraw-Hill School Division Find each difference. Draw 10 by 10 grids to help you. 1. 1.8  1.2  2. 0.9  0.5  3. 1.25  0.18  4. 0.8  0.25  5. 1.35  1.08  6. 1.7  0.48  7. 0.5  0.05  8. 1.65  1.3  9. 1.06  0.88  Use with Grade 4, Chapter 14, Lesson 6, pages 610–613. (452) NS 3.1; MR 2.2 Print This Page Name Print This 14–6 Page Subtract Decimals E ENRICH Problem Generator • • • • Cut out the numbered cards below. Mix them up and place them face down. Turn over 8 cards and place them into a. and b. Then solve. Record your work. Repeat several times. a. b. •  •  • • 1. Turn over all the cards. Using b., what is the greatest possible sum you can make? 2. Using a., what is the greatest possible difference you can make without using the zeros? ✄ 0 1 2 3 4 5 6 7 8 9 ✄ © McGraw-Hill School Division 3. What method did you use to find the answer in exercise 2? 0 1 2 3 4 5 6 7 8 9 Use with Grade 4, Chapter 14, Lesson 6, pages 610–613. (453) MR 2.2; NS 3.1 Print This Page Name Print This 14–7 Page Estimate Differences P PRACTICE Estimate. Round to the nearest whole number. 1. 6.3  2.6 2. 7.1  4.8 3. 8.7  5.2 4. 9.0  3.9 5. 4.6  1.5 6. 7.34  5.78 7. 8.57  3.52 8. 17.26  13.78 9. 26.14  12.95 11. 25.60  11.55 12. 47.15  17.11 10. $34.95  $12.20 Subtract. Estimate to check for reasonableness. 13. 7.1  2.70  14. 9.8  4.6  15. 8.5  6.3  16. 5.6  1.75  17. 36.62  23.13  18. 24.35  10.4  19. 77.36  15.93  20. $16.12  $12.80  21. 94.32  22.80  22. $54.10  $34.89  23. 13.4  6.79  24. 47.65  17.93  25. $14.75  $6.90  26. 63.5  18.27  © McGraw-Hill School Division Algebra & Functions Compare. Write  or . 27. 7.2  3.5 8.8  5.4 28. 9.9  4.8 6.4  1.7 29. 7.6  2.2 5.6  1.3 30. 8.3  6.6 4.2  2.3 31. 9.1  8.7 2.1  1.1 32. 7.2  4.5 6.8  5.8 33. 5.2  2.3 9.7  7.9 34. 9.3  3.8 9.9  3.1 35. 8.1  4.6 7.2  5.1 Problem Solving 36. Jake has $25.75. He spends $13.15 on magazines. About how much money does Jake have left? Use with Grade 4, Chapter 14, Lesson 7, pages 614–615. (454) 37. Nancy ran a total of 5.7 miles today. She ran 3.2 miles this morning. About how many miles did Nancy run this afternoon? NS 2.1, 2.2, 3.1; MR 2.1 Print This Page Name Print This 14–7 Page Estimate Differences R RETEACH To estimate differences of decimals, round each decimal to the nearest whole number. Then subtract the rounded numbers. Estimate 12.25  5.79. ↓ ↓ Round each number 12 – 6 to the nearest whole number. Estimate $6.25  $4.79. ↓ ↓ Round each number $6.00  $5.00 to the nearest dollar. Subtract. Subtract. 12 – 6 = 6 So, 12.25  5.79 is about 6. $6.00  $5.00  $1.00 So, $6.25  $4.79 is about $1.00. Circle the digits in the place to which you will round each number. © McGraw-Hill School Division Estimate each difference. Show how you rounded. 1. $ 7 . 2 4  $ 3 . 6 9 2. 2 7 . 3  1 5 . 7 6 3. 1 2 . 4  3 . 7 4. 1 2 . 7  4 . 8 5. $ 2 5 . 7 5  $ 7 . 8 0 6. 2 5 . 8 7  7 . 2 7. 1 4 . 2 5  7 . 8 4 8. 1 0 . 9 7  7 . 4 9. 3 . 6 2  1 . 8 7 11. $1 0 . 5 4  $ 7 . 8 1 10. $1 0 . 2 5  $ 3 . 4 5 12. 4 3 . 7  2 0 . 4 8 Use with Grade 4, Chapter 14, Lesson 7, pages 614–615. (455) NS 2.1, 2.2, 3.1; MR 2.1 Print This Page Name Print This 14–7 Page Estimate Differences E ENRICH Dollars and Sense scissors $7.49 T-Shirt markers $2.89 sweatshirt $3.29 notebook jeans $14.95 paper $0.89 $8.98 $12.98 $11.99 backpack $29.99 sneakers radio $14.98 ruler $0.99 glue $1.59 pencils clock pen $1.29 $5.98 $1.19 About how much more would Group A cost than Group B? © McGraw-Hill School Division Group A Group B Difference 1. paper, glue notebook, ruler 2. sweatshirt, jeans T-Shirt, jeans 3. backpack, pencils clock, pen 4. markers, sneakers radio, scissors 5. clothing and shoes everything but clothing and shoes Estimate to solve. 6. Andy buys a box of markers. He gives the clerk $20. He receives $18.11 in change. Is the amount of change reasonable? Explain. Use with Grade 4, Chapter 14, Lesson 7, pages 614–615. (456) 7. Heidi buys a clock. She gives the clerk $10. She receives $4.02 in change. Is the amount of change reasonable? Explain. NS 2.1, 2.2, 3.1; MR 2.1 Print This Page Name Print This 14–8 Page Problem Solving: Strategy P PRACTICE Solve Simpler Problems Solve using a simpler problem. 1. The tennis team travels to a statewide contest. They buy 8 student bus tickets at $6.95 each and 2 adult bus tickets at $9.50 each. How much does the team spend for tickets? 2. A bus ticket costs $8.75. A train ticket for the same ride costs $12.50. Suppose you buy 4 tickets. How much money would you save by taking the bus instead of the train? 3. A bus driver earns $16.40 per hour 4. The Silver Eagle Express has a dining for the first 7 hours of work each day. She earns $24.60 per hour for each hour over 7 hours. How much does she earn in a 9-hour day? car. Sandwiches cost $5.95. Drinks cost $1.49. How much does a family pay for 3 sandwiches and 4 drinks? Mixed Strategy Review Solve. Use any strategy. 5. Sam spends $18.40 on a train ticket, © McGraw-Hill School Division $5.90 on a cab, and $11.20 on dinner. He has $30 left. How much money did Sam have when he started? 6. Science The first steam-powered railroad engine was built in England 1804. Thomas Edison tested an electricpowered railroad engine 76 years later. When did Edison test his engine? Strategy: 7. Teri has 17 model trains. She has a long shelf that can hold 7 trains. She also has 2 smaller shelves. How can she arrange the trains on shelves so that each smaller shelf has an equal number of trains? Strategy: 8. Create a problem for which you could use a simpler problem to help you find the answer. Share it with others. Strategy: Use with Grade 4, Chapter 14, Lesson 8, pages 616–617. (457) MR 1.1, 1.2, 2.2, 2.4, 3.2 Print This Page Name Print This 14–8 Page Problem Solving: Strategy R RETEACH Solve Simpler Problems Page 616, Problem 2 A train conductor earns $18.45 an hour. A ticket checker earns $12.95 an hour. How much do both workers earn in an 8-hour day? Step 1 Read Be sure you understand the problem. Read carefully. What do you know? • A train conductor works an hour. • A ticket checker works an hour. hours for hours for What do you need to find? • You need to find how much Step 2 Make a plan. Plan Choose a strategy. ■ ■ ■ © McGraw-Hill School Division ■ ■ ■ ■ ■ ■ ■ Find a Pattern Guess and Check Work Backward Make a Graph Make a Table or List Write a Number Sentence Draw a Picture Solve a Simpler Problem Logical Reasoning Act it Out Use simpler numbers to make up a problem similar to the one you need to solve. Then solve the real problem the same way. Use with Grade 4, Chapter 14, Lesson 8, pages 616–617. (458) MR 1.1, 1.2, 2.2, 2.4, 3.2 Print This Page Name Print This 14–8 Page Problem Solving: Strategy R RETEACH Solve Simpler Problems Step 3 Solve Solve this simpler problem. • A conductor works 8 hours for $18 an hour. The conductor earns 8  or . • A ticket checker works 8 hours at $13 an hour. The ticket checker earns 8  or  The total amount is .  . Now solve the real problem the same way. • A conductor works 8 hours at an hour. The conductor earns 8  or . • A ticket checker works 8 hours at an hour. The ticket checker earns 8  or  The total amount is .  Step 4 © McGraw-Hill School Division Look Back Is the solution reasonable? Reread the problem. Does your answer make sense? Did you answer the question? Yes Yes No No What other strategies could you use to solve the problem? Practice 1. The Sheppards buy 2 adult tickets for $8.70 each and 3 children’s tickets for $4.35 each. How much money do they spend? Use with Grade 4, Chapter 14, Lesson 8, pages 616–617. (459) 2. Gina buys 3 model planes for $14.95 each and 4 model trains for $7.29 each. How much money does Gina spend? MR 1.1, 1.2, 2.2, 2.4, 3.2 Print This Page Name Print This 14–9 Page Use Properties to Add and Subtract P PRACTICE Add or subtract mentally. 1. 3.56  0.04  2. 4.12  1.7  3. 4.5  4.5  4. 1.7  1.3  5. 8.87  0.03  6. 5.08  0.9  7. 6.04  6  8. 7.86  1.06  9. 17.23  0  10. 12.13  0.14  11. 11.22  10.02  12. 15.66  10.44  13. 17.01  9.99  14. 10.17  8.18  15. 15.44  3.22  16. 3.6  4.7  0.4  17. 13.1  5.6  3.9  18. 7.9  2.8  0.9  19. 7.5  6.3  4.5  20. 9.3  2.6  4.4  21. 6.3  5.5  1.7  22. 8.7  2.9  5.7  23. 9.1  4.7  9.1  © McGraw-Hill School Division Algebra & Functions Find each missing number. 24. 4.9  b  6.0 25. (f  1.5)  3.5  5 26. 2.7  c  2.7 27. 10.6  d  5 28. 14.12  m  0 29. 3.7  h  6.3  3.7 30. 6.3  w  6.3 31. 4.2  t  10 32. 2.7  9.3  9.3  n 33. a  7.9  0 Problem Solving 34. It takes Anita 11.6 seconds to sprint 35. Fernando expected to run the mile in the first 100 m and 12.3 s to sprint the second 100 m. How long does it take Anita to sprint the 200 m? 5.6 minutes. Because of an injury, he ran the mile in 6.3 minutes. How much slower than expected did Fernando run the mile? Use with Grade 4, Chapter 14, Lesson 9, pages 618–619. (460) NS 3.1; AF 1.2, 1.3; MR 2.2 Print This Page Name Print This 14–9 Page Use Properties to Add and Subtract R RETEACH You can use the Commutative, Associative, and Identity properties to add and subtract mentally. Look for compatible numbers. (1.3  4.2)  1.7 (4.2  1.3)  1.7 4.2  (1.3  1.7) 4.2  3.0 7.2 Look for zeros. Think: 1.3 and 1.7 are compatible. 5.35  0  5.35 Use the Commutative Property. 3.29  0  3.29 Use the Associative Property. Add the compatible numbers. Look for the same number. Find the sum. 0.85  0.85  0 16.5  0  16.5 Remember: Associative Property: When adding, the grouping of the numbers does not affect the sum. Commutative Property: When adding, the order of the numbers does not affect the sum. Identity Property: In addition, the sum of 0 and a number is the number. © McGraw-Hill School Division Use mental math to add or subtract. 1. 2.6  0.4 = 2. 4.75  0 = 3. 1.5  3.2  1.5 = 4. 2.7  2.7 = 5. 6.78  6 = 6. 4.7  0  5.3 = 7. 12.24  6.12 = 8. 10.10  5.01 = 9. 1.8  2.2  1.3 = 10. 3.3  3.3 = 11. 2.3  3.5 = 12. 8.9  2.9  8 = 13. 14.6  0  5.4 = 14. 4.44  4.44 = Use with Grade 4, Chapter 14, Lesson 9, pages 618–619. (461) NS 3.1; AF 1.2, 1.3; MR 2.2 Print This Page Name Print This 14–9 Page Use Properties to Add and Subtract E ENRICH Crack the Code Use the symbols below to write the top numbers in exercises 1–6. Use the code and properties to add or subtract the bottom number using mental math. Write the answers using numbers and the code symbols. Check your symbol answers with a friend. Use the code to write all the numbers in exercises 7–9 before you check by adding. 0 1 2 3 Example: 2.5  4 5 6 7 8 9 ←Think: 0.0 © McGraw-Hill School Division 2.5 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Which problem can you solve without using numbers? Use with Grade 4, Chapter 14, Lesson 9, pages 618–619. (462) NS 3.1; AF 1.2, 1.3; MR 2.2 Print This Page Name Print This Page 14–10 Part A WORKSHEET Problem Solving: Application Applying Adding and Subtracting Decimals Decision Making Record your data and notes. Route (List all stops and highways used.) Miles Traveled Costs Other Notes © McGraw-Hill School Division Your Decision What is your recommendation for the Lopez family? Explain. Use with Grade 4, Chapter 14, Lesson 10, pages 620–621. (463) MR 1.1, 2.2; NS 3.1 Print This Page Name Problem Solving: Application How would you conserve electricity? Print This Page 14–10 Part B WORKSHEET Math & Science Record data for your conservation plans in this chart. Plan Activity Time Saved Money Saved Plan 1 Plan 2 © McGraw-Hill School Division Plan 3 Use with Grade 4, Chapter 14, Lesson 10, pages 622–623. (464) NS 2.1; MR 1.1, 2.3, 3.3 Print This Page Name Print This Page 14–10 Part B WORKSHEET Problem Solving: Application Math & Science How would you conserve electricity? 1. Which of your three plans would you prefer to use? Explain your answer. 2. Which of your three plans might you actually use? Explain your answer. 3. Look at the plan you liked best. How much money would you save in a month? in a year? 4. Compare the advantages and disadvantages of the different ways to produce © McGraw-Hill School Division electricity. Think about costs, energy efficiency, and stress to the environment. Use with Grade 4, Chapter 14, Lesson 10, pages 622–623. (465) NS 2.1; MR 1.1, 2.3, 3.3