Math Worksheets

Chapter File Folders Teacher Tools Assessment Guide English Language Learner Handbook Math Center Cards Problemof the Day Quit Success on Standardized Tests Print This Page Name Explore How Big Is a Million? Solve. 1. How many 10-by-10 grids would 2. Print This 1–1 Page P PRACTICE 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? 8. How many thousands are in 1,000,000? © McGraw-Hill School Division 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 Explore How Big Is a Million? 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 1. What number is shown below? 10 hundreds Print This 1–1 Page R RETEACH Complete. Name each number in different ways. 2. 10,000 3. 100,000 4. 1,000,000 ten thousand thousands hundreds © McGraw-Hill School Division hundred thousand ten thousands thousands hundreds tens ones million hundred thousands ten thousands thousands hundreds tens 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? 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 Print This 1–1 Page E ENRICH 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 each store would need to sell in 1 day. © McGraw-Hill School Division 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 Place Value Through Millions Write the word name and the expanded form for each number. 1. 1,420,316 Print This 1–2 Page P PRACTICE 2. 2,672,400 3. 12,060,072 4. 785,004,012 Write the value of each underlined digit. 5. 842,753 7. 153,428,090 6. 6,782,141 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 11. five hundred eighty million, sixty-two thousand, seventeen © McGraw-Hill School Division 12. two hundred fifty-four million, seven thousand, five Algebra & Functions Write the missing number. 13. 42,865 ϭ 40,000 ϩ ϩ 800 ϩ 60 ϩ 5 ϩ 40 ϩ 3 14. 168,943 ϭ 100,000 ϩ 60,000 ϩ 8,000 ϩ 15. 888,888 ϭ 800,000 ϩ ϩ 8,000 ϩ 800 ϩ 80 ϩ 8 NS 1.1 Use with Grade 4, Chapter 1, Lesson 2, pages 4–7. (4) Print This Page Name Place Value Through Millions Numbers in the millions have three periods. Each period is separated by a comma. Print This 1–2 Page R RETEACH Millions Hundreds Tens Ones Thousands Hundreds Tens Ones Hundreds Ones Tens Ones 7 0 1 2 2 1 3 5 4 Expanded form: Standard form: Word name: Complete. 1. 824,124 = 700,000,000 ϩ 1,000,000 ϩ 200,000 ϩ 20,000 ϩ 1,000 ϩ 300 ϩ 50 ϩ 4 701,221,354 seven hundred one million, two hundred twenty-one thousand, three hundred fifty-four + 20,000 + 4,000 + + 20,000 + + 2,000,000 + 500,000 + Expanded Form 3,000,000 ϩ 200,000 ϩ 500 ϩ 20 2,000,000 ϩ 400,000 ϩ 50,000 ϩ 7,000 ϩ 800 ϩ 20 ϩ 1 30,000,000 ϩ 7,000,000 ϩ 800,000 ϩ 50,000 ϩ 2,000 ϩ 4 40,000,000 ϩ 9,000,000 ϩ 300,000 ϩ 50,000 ϩ 2,000 ϩ 6 + + + + + + + 10 + 2. 7,624,139 = 7,000,000 + 3. 42,521,012 = Standard Form Word Name 4. © McGraw-Hill School Division 5. 6. 7. Use with Grade 4, Chapter 1, Lesson 2, pages 4–7. (5) NS 1.1 Print This Page Name Place Value Through Millions 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? Print This 1–2 Page E ENRICH , , 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? , the ten thousands place? , , , 7. What is the least number with 9 in the millions place and 2 in 8. What is the greatest number with 7 in the hundred thousands © McGraw-Hill School Division 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 Compare and Order Numbers and Money Compare. Write >, <, or =. 1. 3,874 4. 14,624 7. $101.42 10. 150,420 13. 782,421 Print This 1–3 Page P PRACTICE 3,862 1,462 $126.41 2. 5,741 5. 42,542 8. 25,632 5,862 41,617 25,632 3. $78.24 6. 32,145 9. 89,000 $77.24 32,264 87,999 197,541 972,421 100,042 11. 434,121 782,342 14. 642,134 432,154 12. 187,654 642,134 15. 874,158 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 22. 324,621; 324,742; 325,697 © McGraw-Hill School Division 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 Thousands 4 4 Hundreds 8 8 Tens 7 9 Ones 2 2 Print This 1–3 Page R RETEACH same number of thousands same number of hundreds 4.002 $293. 4.45 822.2 Use with Grade 4.45 11. Write Ͼ.Print This Page Name Compare and Order Numbers and Money You can use a place-value chart to compare numbers. Ͻ. 832.117 7. So.89 8.872 and 4. or ϭ.97.234 Tens 3.300 8.239 3.89 56. 502. $319.892. $324.619 10.23 has more ten dollars than $306. So.23 $306.077 NS 1. 1. 3.97 and $319. 8. $285.515 5.216 Ones Thousands Hundreds © McGraw-Hill School Division Compare.23.916 510.216.585 $314. Compare 4.16 5. 2.872. 56. Chapter 1. 6. 5. Use the place-value chart to compare the numbers. Compare $306. Ͻ.117 51. Look for the first place where the digits are different.892 4.12 6.077 $21.558 6.872. Write Ͼ.281 9. or ϭ. $25. Hundred Dollars 3 3 Ten Dollars 0 1 One Dollars 6 9 Cents 97 23 same number of hundred dollars $319. Start at the left.504 4.97. 50.234 and 3.892 has more tens than 4. pages 8–11. Lesson 3. (8) . Compare 3. D. Chapter 1. In the year ending December 31. The area of Japan is 145.819 Maine coon cats registered in the United States.123 public libraries in the United States. 1997.2 . Then order the letters from least to greatest values in the boxes below.071 votes. Inc. there were 4.604 square miles. (9) NS 1. Inc. There were 54. I.216. Grant received © McGraw-Hill School Division 3. H.856 square miles. The area of the United States is 3. E. Lesson 3. C. Ulysses S. B.Print This Page Name Compare and Order Numbers and Money Greater Numbers Look at the value that each letter represents.770 square miles. In the 1868 United States Presidential election. The area of Mexico is 761. Print This 1–3 Page E ENRICH A. Use with Grade 4. pages 8–11.067 votes.618.470 beagles registered by the American Kennel Club.015. There were 54. Abraham Lincoln received 2. F. There are 9. G. In the 1864 United States Presidential election.773 poodles registered by the American Kennel Club. Which animal can grow to the greatest length? Use with Grade 4. A wolverine can be 36 inches long. 2. List the animals from least to greatest length. Write a 1 for the first step.3. A male moose weighs Print This 1–4 Page P PRACTICE Reading Skill 1.000 pounds. and so on. Read the problem. the male moose. Lesson 4. You need to find the order of the male elk. A male moose weighs 1. Make a plan for solving the problem. A wolverine can be 36 inches long. 1. and the male caribou from greatest to least weight. Read the problem. © McGraw-Hill School Division Check your answer.000 pounds. Identify what you need to find: Which animal can grow to the greatest length? Follow your plan to solve the problem. 3. A male caribou weighs 300 pounds. A male elk weighs 600 pounds. Which animal can grow to the greatest length? Identify what you know. A black-footed ferret can be 18 inches long. pages 12–13. 1. Order the animals by comparing their lengths two at a time.2 . List the animals from greatest to least weight. Write a number next to each step to show the order in which the steps are done. A black-footed ferret can be 18 inches long. Identify what you know: A male elk weighs 600 pounds. A mink can be 20 inches long. Then read each step in the problem-solving process. A mink can be 20 inches long. Follow your plan to solve the problem.Print This Page Name Problem Solving: Reading for Math Using the Four-Step Process Read the problem.1.4.2. Chapter 1. Make a plan for solving the problem. 2. What is the order of the three animals from greatest to least weight? Check your answer. What is the order of the three animals from greatest to least weight? 2. (10) MR 1. Order the animals by comparing their weights two at a time. Identify what you need to find. A male caribou weighs 300 pounds. 1. (11) .4. Top Dog Company walks 101 dogs per week.096 and 998. 3. Lesson 4. On which day did the most people go to Ocean World? 3. go to Ocean World? F Friday G Saturday H Sunday Lassie’s Dog Walking Service walks 68 dogs per week. On Sunday. A bottle-nosed dolphin can weigh up to 440 pounds. pages 12–13. On Friday. C Top Dog Company walks 68 dogs per week problem? F Compare the numbers of dogs walked two at a time. C Add 1.2 Use with Grade 4. and 998. B Add 660 and 1. G Compare 440 and 165. On Saturday. Which of these statements is true? Print This 1–4 Page P PRACTICE Math Skills Test Prep 2. Doggie Express walks 57 dogs per week. 998 people went to Ocean World.096. Which plan can you use to solve the A Lassie’s Dog Walking Service walks the most dogs per week.2. List the dog walking services in order from least dogs walked per week to most dogs walked per week. Which plan will help you solve the A A bottle-nosed dolphin cannot be as heavy as a common dolphin. © McGraw-Hill School Division 5.096 people went to Ocean World. B Doggie Express walks 57 dogs per week.1. G Find the difference between the number of dogs walked by Top Dog Company and the number walked by Lassie’s.Print This Page Name Problem Solving: Reading for Math Using the Four-Step Process Choose the correct answer. MR 1. A common dolphin can weigh up to 165 pounds. Which plan can you use to solve this 4. On which day did the most people problem? A Compare 660. C A bottle-nosed dolphin can weigh 440 pounds. 1. Chapter 1. H Subtract 165 from 440. Which kind of dolphin can be heavier? 1. 2. H Find the total number of dogs walked by the three services. 660 people went to Ocean World Animal Park.3.096. B A common dolphin can weigh 615 pounds. problem? F Add 440 and 165. Which statement is true? 6. 1. 2. 9. World make money? F Tuesday only G Wednesday only H Monday and Wednesday only 10. about 36.2 . On Wednesday. A killer whale can move 55 miles per hour. Ocean World had 691 customers. Who spots fewer birds? to aquariums and about 86.3. 2. 1. C Order the daily customer totals from greatest to least. On Monday. 424 students have cats. 13. Timothy earned $1. List the months in order from least number of dogs to greatest number of dogs. Timothy. 3. Which plan will help you solve the Print This 1–4 Page P PRACTICE Math Skills Test Prep 8. A striped dolphin can move 19 miles per hour. Chapter 1. 2. The pet shelter has 324 dogs in dogs. Nicole spots 51 14. Ocean World Animal Park needs 750 customers each day to make money.4. and Norah earned $650. Brandon earned $712. and Norah have pet care services.000. and 399 dogs in June. Dylan spots 48 birds. Lesson 4. pages 12–13.000 people went birds. List the animals in order from slowest to fastest. On which day or days did Ocean World make money? 7. (12) MR 1.000. Ocean World had 803 customers.000 people went to zoos. In 1997.Print This Page Name Problem Solving: Reading for Math Using the Four-Step Process Choose the correct answer. List the people in order from greatest amount earned to least amount earned. Which kind of pet is owned by the most students? April. On Tuesday. Did more people go to aquariums or to zoos? Use with Grade 4. A poll shows that 311 students have © McGraw-Hill School Division 12.110. Solve.1. Brandon. Ocean World had 911 customers. A marlin can move at a speed of 50 miles per hour. 11. B Compare each daily customer total to 750. On which day or days did Ocean problem? A Compare the daily customer totals two at a time.2. 411 dogs in May. 96 students have birds. Last year. and 38 students have a different pet. 124 60. Chapter 1.Print This Page Name Round Numbers and Money Round to the given place.Joe’s class bought a bird feeder for were 1. 923 to the nearest 2.653. To the nearest hundred.162 478. 380. 862 to the nearest 6. $57.789 to the ten cents nearest million nearest hundred thousand Algebra & Functions Find the rule.722 234.06 to the nearest ten thousand 14.3 .555 to the nearest hundred thousand 13.142 91. $73. $34. Rule: Input Output © McGraw-Hill School Division 57.96 to the nearest dollar 9.75. 61. 1. (13) NS 1. $0. $6.93 to the nearest Print This 1–5 Page P PRACTICE 3. Complete the table.47 to the nearest dollar 7. 7. 2. To the nearest dollar.000 64. how many sightings were there? $38.532 bluebird sightings on the island.256 to the nearest 11.502. pages 14–17. 8.49 to the nearest ten ten cents dollar 4. Lesson 5.The radio announcer said that there 18.553 to the nearest thousand ten cents hundred 10.357 to the nearest hundred 8.475 to the hundred 15. 16. what was the cost? Use with Grade 4. $46. 1.52 to the nearest 5.479 to the nearest 12.234 Problem Solving 17. 4. 60 19. pages 14–17. 1. Lesson 5. 42. Print This 1–5 Page R RETEACH 40.13 21. 7.50 $6.70 $6.20 $6. 45.39 24.00 $6. 41. $12. Chapter 1.000 13.000 46.30 $6.00 than $7. $12. 7. 46.000 is closer to 50. 49. 10.38 to the nearest dollar. $12. 47. $12. So. $6.000 41.000.3 . $12.000 47.450. Think: 46.550.289.80 $6.208 rounds up to 50.38 rounds down to $6.999 15.832.60 $6. $12. 7. $12.000 50.000 © McGraw-Hill School Division 11.203 Round to the nearest million.000 48.208 to the nearest ten thousand.512. 44.40 $6.300 12. $6. 43.000 42.45 20. 16.250 9. 45. $12.53 23.900 8.875 6. Think: $6.30 is closer to $6.000 49.25 17.62 18.875 3.009 5. 7.Print This Page Name Round Numbers and Money You can use a number line to help you round.987 2.010 14.00 Round $6.496 4.000 than 40.000 Round 46.90 $7.000. So.00. 7. Round to the nearest ten thousand.93 22. (14) NS 1. 42.000 45.362.000 44.59 Use with Grade 4.800 Round to the nearest dollar.800 7.000 43.10 $6. 7.00. $12. 000. you get 600. If you round me to the nearest ten thousand. Print This 1–5 Page E ENRICH If you round me to the nearest ten. you get 430. If you round me to the nearest 100. thousand. What number am I? 5. you get 50. you get 4. If you round me to the nearest hundred. you get 2. pages 14–17.000. ten thousand. The sum of my digits is 17.000. If you round me to the nearest thousand. My first two digits add up to 10.3 . The digit in my hundreds place is one more than 2.000. you get 3. The sum of my digits is 10. Lesson 5. Six of the digits are the same. you get 400. or million will give you the same number. (15) NS 1. The sum of my seven digits is 60. What number am I? Use with Grade 4. The sum of my digits is 8. What number am I? 3. Chapter 1.000. Three of my digits are the same. What number am I? 6. I am the same. What number am I? 2. If you round me to the nearest hundred. What number am I? 4. If you round me to the nearest thousand.600. hundred. My last three digits add up to 8. and round (to the nearest hundred) to 400. © McGraw-Hill School Division Rounding me to the nearest ten. Each of my six digits is the same.Print This Page Name Round Numbers and Money Mystery Numbers 1. If you read me forward or backward. Share it with others. How much did The Pet Palace make in 2000? Strategy: Strategy: 7.2. pages 20–21. 5. SDP 1. A pet store sold 137 bags of dog food called The Vet’s Choice. Mark cuts out letters to make a sign. Which letter does Mark need to The sign says. The Pet Palace increased this amount by $10.Print This Page Name Problem Solving: Strategy Make a Table Make a table. In 1999. Which pet had the most votes? 2. NS 1. Which bear weighs the least? Strategy: Use with Grade 4.000. MR 1. The Pet Palace made about $100. Chapter 1.3. 4. Lesson 6. 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 Print This 1–6 Page P PRACTICE Rebecca—bird Melanie—cat Traci—dog Noreen—fish Sylvia—cat 1. In 2000." How many different kinds of letters does Mark need to make? make the most of? How many of these letters does Mark have to make? Mixed Strategy Review Solve.000. 3. Adult Asiatic black bears weigh about 250 pounds. It sold 249 bags of a dog food called Fido’s Friend. Science Adult sun bears usually 8. Which pet had the least votes? 3. Create a problem you would make weigh from 60 to 100 pounds.1. Use any strategy. Use data from the table to solve problems 1 and 2. (16) a table to solve. 2. Adult grizzly bears weigh from 350 to 500 pounds. How many more bags of Fido’s Friend than The Vet’s Choice were sold? © McGraw-Hill School Division 6.3. "Get Pet Kittens for Free.2 . SDP 1. Choose a strategy. Step 2 Plan I I Make a plan.1. What do you know? • There are different varieties of .2. 2. (17) NS 1. 3. . Make a table to solve the problem. Lesson 6.Print This Page Name Problem Solving: Strategy Make a Table Page 21. and Angelfish tetras—black neon tetra goldfish—black moor angelfish—gold angel tetras—lemon tetra Step 1 goldfish—fan tail goldfish tetras—white skirt tetras—silver dollar angelfish—marble angel goldfish—lionhead tetras—black neon tetras angelfish—silver angel Read Be sure you understand the problem. and What do you need to find? • You need to know how many different varieties of . Chapter 1. I I I I I I I I 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 © McGraw-Hill School Division Use with Grade 4. Read carefully.3. Problem 2 Print This 1–6 Page R RETEACH Which type of fish has the greatest number of varieties? Different Varieties of Tetras. there are. A table can help you organize what you know. pages 20–21. and .3. Goldfish. .2 . MR 1. a lionhead goldfish. Write a number for each set of tallies.3. different kinds of angelfish. and Yumi each like one kind of dog. than either of the other 3 Tally of Different Varieties Number There are more varieties of two kinds of fish.Print This Page Name Problem Solving: Strategy Make a Table Step 3 Print This 1–6 Page R RETEACH Solve Carry out your plan. Of which type of fish does Jack have the least? 2. Type of Fish Tetras Goldfish Angelfish There are There are There are different kinds of tetras. The dog is either a terrier. SDP 1.2. a lemon tetra.2 . Tally the number of for each fish. MR 1. a gold angel angelfish. Who likes poodles? Use with Grade 4. Make a table to solve. (18) NS 1. a retriever. Brian does not like poodles or retrievers. Alex. different kinds of goldfish. Complete the table.3. pages 20–21.1. 3. Chapter 1. Alex does not like retrievers. Does your answer match the data given in the problem? Practice 1. Compare the numbers. Lesson 6. Step 4 Look Back © McGraw-Hill School Division Is the solution reasonable? Reread the problem. 2. He has a fan tail goldfish. and a black neon tetra. or a poodle. Brian. Jack lists the fish in his aquarium. Price: $2. Price: $0. Price: $3.0.86 11.45 9.25 Amount given: $5. 7. 4.00 10. 1. for a $3.67 Find the amount of change. Lowanda receives 1 quarter.00 Amount given: $10. Price: $0.00 © McGraw-Hill School Division Amount given: $10. $7.81 Amount given: $1. 2 dimes.09 12.62 6.89 5. 3. How much money is that? Use with Grade 4. pages 22–23.Print This Page Name Count Money and Make Change Write the amount of money shown. Andy gives the cashier $5. $0. (19) NS 1. 2.00 Problem Solving 13. Chapter 1.4 . Lesson 7. Print This 1–7 Page P PRACTICE 8 8 SCHOOL MONEY 8 8 8 8 SCHOOL MONEY 8 8 Tell which coins and bills make the amount.00 to pay 14. MR 2.00 Amount given: $10. Price: $7. How much change does he receive? and 1 nickel in change.00 Amount given: $5. $3.59 8. Price: $9.75 calendar. Someone gives you $5. You sell a pen for $2.50 $2. Amount given: $10. Find the amount of change. Print This 1–7 Page R RETEACH $2. Count up. Amount given: $6.00 $5. (20) NS 1. Chapter 1.49.Print This Page Name Count Money and Make Change To make change.00 © McGraw-Hill School Division 8 8 SCHOOL MONEY 8 8 $3.0.4 . 1. Use the fewest number of bills and coins possible.79 Cost Amount of change: Use with Grade 4. MR 2.00 $5.00 $4. start with the cost.49 Cost $2.34 Cost Amount of change: 2. pages 22–23. Lesson 7.75 $3.00 for the pen. Then count up to the amount given to you.51.00 Count the bills and coins to find the change: $2. 81 Clue: 10 coins Clue: 8 coins 5.00 $7. Lesson 7. MR 2.58 Clue: 6 coins Clue: 13 coins 3. but only two kinds Clue: 3 bills.Print This Page Name Count Money and Make Change Money Detective Use the clues to find which coins and bills are inside each bank. 8. $15.45 Clue: 19 coins. 3 coins Use with Grade 4. (21) NS 1. 4.73 $0. $0. 6.47 $0. $1.00 Clue: 2 bills.4 . 3 coins © McGraw-Hill School Division 7. Chapter 1. pages 22–23. 3 coins Clue: 5 bills. 1.0. 2.55 $23. Print This 1–7 Page E ENRICH $0. 12ЊF below zero 6. Lesson 8.500 feet. Go 3 floors down 8. minutes later. Ϫ 15 9 5 4 12 10 15 6 4 Ϫ 9 Ϫ Ϫ 8 28. 33. 0 34. 11. Ϫ 8 Ϫ Ϫ 11 35. Ϫ 8 10 24 13 Ϫ Ϫ 3 Ϫ 19. Ϫ 5 3 Ϫ 6 4 7 16. 11 © McGraw-Hill School Division Ϫ 11 32. Ϫ 12 0 Ϫ 22. 0 15. Deposit $50 4. Ϫ Ϫ 12 2 Ϫ Ϫ 21. 0 36. 0 20. Ϫ 6 1 2 10 Ϫ 4 12 7 Problem Solving 39.000 feet. 17 Ϫ 9 30. 29. Lose $4 3. 18.Print This Page Name Negative Numbers Write a positive or negative number to represent each situation. 1. 1 23. 6 24. Write Ͼ or Ͻ. An airplane descended 1. 7 26. it climbed 9. Take 8 steps back 9. 27. Write a number to represent each situation. Lose 10 pounds Print This 1–8 Page P PRACTICE Compare. Ϫ 4 3 2 0 Ϫ 14. pages 24–25. 37. Ϫ 11 3 Ϫ 31. 2 3 Ϫ 13. Gain 3 pounds 7. Earn $25 10. (22) NS 1. Write a number to represent each situation.8 . Use with Grade 4. 17. Chapter 1. Manuel deposited a check for $25 in 40. Ten his savings account. 52ЊF 2. 13 38. Ϫ 9 Ϫ 12. Then he withdrew $30. 12 25. You may use a number line to help. 300 feet above sea level 5. 21. 11. Ϫ 20 20 4 ϩ 18 Ϫ Ϫ Ϫ Ϫ Ϫ Ϫ Ϫ ϩ 20 ϩ 15 Ϫ Ϫ Ϫ Ϫ Ϫ ϩ 4 ϩ Ϫ 7 Ϫ 2 Ϫ Ϫ 22. so ϩ2 Ͼ Ϫ2. so 0 Ͼ 4. so Ϫ6 of ϩ4. so Ϫ2 1. Ϫ 9 8 2 9 Ϫ 15 2 12 8 10. 5. so Ϫ3 Ͼ Ϫ6. 2. so Ϫ4 of ϩ6. 20. negative numbers less than zero Ϫ Print This 1–8 Page R RETEACH positive numbers greater than zero 1 0 ϩ 6 Ϫ 5 Ϫ 4 Ϫ 3 Ϫ 2 Ϫ 1 ϩ 2 ϩ 3 ϩ 4 ϩ 5 ϩ 6 Numbers to the right are greater than numbers to the left. 4. Complete. 19. ϩ 2 is to the right of Ϫ2. 6. Ϫ ϩ Ϫ ϩ © McGraw-Hill School Division Compare. 0 Ϫ 10 NS 1. Chapter 1. Ϫ Ϫ Ϫ Ϫ 1. 18. Ϫ ϩ of Ϫ1. (23) . 6. 4. 14. 13. ϩ 14 12 6 7 ϩ Ϫ 14 21 8. Lesson 8. 15.Print This Page Name Negative Numbers You can use a number line to understand and compare positive and negative numbers. 1. ϩ 5 is to the right of ϩ3. 12. Write Ͼ or Ͻ. Ϫ 3 is to the right of Ϫ6. so ϩ1 of Ϫ6. You may use a number line to help. ϩ 13 25 10 8 ϩ ϩ 31 5 12 9. 7.8 Use with Grade 4. 16. 17. so ϩ5 Ͼ 1 is to the 5 is to the 4 is to the 6 is to the 2 is to the ϩ 3. 6. pages 24–25. Ϫ Ϫ 0 is to the right of 4. 3. so Ϫ5 of Ϫ1. One player announces “Mine is greater than (or ‘less than’ or ‘equal to’) yours. each player touches one of these cards. the player with the most cards wins. Chapter 1. they go to the original player. • To play.8 Use with Grade 4. • Each player writes five different negative and five different positive integers. They should use the integers from Ϫ10 to ϩ10.Print This Page Name Negative Numbers Are You Positive or Negative? Play with a partner. pages 24–25. one on each card. If the statement was correct. Print This 1–8 Page E ENRICH Ϫ 9 8 Ϫ Ϫ 2 7 © McGraw-Hill School Division 0 Ϫ 1 3 Ϫ 6 5 4 NS 1.” Both players turn over their card. You will need 10 blank cards for each player. If not. When all cards are collected. Each player mixes up their cards and spreads them out face down. that player gets both cards. Lesson 8. (24) . • Repeat touching cards and taking turns making the statements. Use with Grade 4. MR 1. Store Cost of 20 Pounds of Dog Food 1–9 Part A WORKSHEET Decision Making Print This Page Cost of Gas for Trip to Store Pet Supply Animal World Pet’s Place Discount Pet Food © McGraw-Hill School Division Your Decision What is your recommendation for Stacia? Explain. Answers may vary.2. Chapter 1.1.Print This Page Name Problem Solving: Application Applying Place Value Record your data. pages 26–27. 2. Lesson 9.3 . (25) NS 1. 2. Number of cats and dogs you know 7. Data for Student 1 Data for Student 2 1–9 Part B WORKSHEET Math & Science Print This Page Are the two sets of data the same or close to being the same? 1. Length of your arm from shoulder © McGraw-Hill School Division to wrist 8. Number of push-ups you can do in 30 seconds 4. Your favorite number 2. Lesson 9. pages 28–29.Print This Page Name Problem Solving: Application How do you compare with your partner? Record your data. Chapter 1.3 . MR 1. (26) NS 1.1.3. Number of times you breathe in one minute 10.2. 3. Number of cups of water you drank yesterday 6. Number of objects in your desk right now 5. Your age Use with Grade 4. How long you can stand on one foot 9. Number of hours you sleep each night 3. Did the numbers have to be exactly alike? Why or why not? 3. In which areas did you vary the least from your partner? © McGraw-Hill School Division 5.1.2. How many times were you and your partner the same? different? 1–9 Part B WORKSHEET Math & Science Print This Page 2. pages 28–29. Lesson 9. Chapter 1. (27) NS 1. In which areas did you vary the most from your partner? 4.3 .3. Explain how you decided whether you and your partner were the same.Print This Page Name Problem Solving: Application How do you compare with your partner? 1. 3. MR 1. Why is it good to have variation in nature? Use with Grade 4. 2. Chapter 2.1. 46 © McGraw-Hill School Division Problem Solving 13. 9. 14. 3. 6. How many coins does Meg have now? Use with Grade 4. 7. 10 n ϩ 6 ϭ 15 6 ϩ n ϭ 15 15 Ϫ n ϭ 6 15 Ϫ 6 ϭ n 6. 4. 9. Barb has 5 more coins than Ken. 5. 24. 34. 2 ϩ 9 ϭ n Ϫ 22 ϭ 5 27 Ϫ 5 ϭ n 8. pages 44–45. Lesson 1. 8. Meg has 13 coins in her collection. 5 . 8 2. 3.Print This Page Name Use Properties of Addition Complete the set of related number sentences. 4. 1.1 . 0. 46. 6. 22. 54 ϩ 0 ϭ Write the related number sentences for the set of numbers. How many coins does Barb have? Then she gives 7 coins to her cousin. 38 3 ϩ n ϭ 10 3ϩ7ϭn 22 ϩ n ϭ 27 5 ϩ 22 ϭ n 34 ϩ n ϭ 38 4 ϩ n ϭ 38 38 Ϫ n ϭ 34 n Ϫ 4 ϭ 34 nϪ3ϭ7 10 Ϫ n ϭ 3 7. 9 11. 5. 27 nϩ3ϭ8 8Ϫ5ϭn 8Ϫnϭ5 4. 10. 35 ϩ 4 ϭ Find the sum or difference. 14 3. Write the related number sentences. (28) NS 3. 11. 35 12. AF 1. 15 Print This 2–1 Page P PRACTICE 5ϩnϭ8 6ϩ8ϭn 8 ϩ n ϭ 14 14 Ϫ 6 ϭ n 14 Ϫ n ϭ 8 5. Ken has 6 coins in his collection. 2.1 . 17. 0. 9. 56 8. Lesson 1. 54 Use with Grade 4. Write the related number sentences. pages 44–45. (29) NS 3. 45. 56. Look at each model. 8 ϩ 3 ϭ n 4. 43 7. 5ϩ3ϭ8 3ϩ5ϭ8 8Ϫ3ϭ5 8Ϫ5ϭ3 You can also use the properties and the idea of related sentences with greater numbers.Print This Page Name Use Properties of Addition Every number sentence in a set of related number sentences uses the same numbers. Find the sum. Chapter 2. 26. The model below shows a set of related number sentences. 2 ϩ 7 ϭ n 5. AF 1. 1. 18 ϩ 0 ϭ n © McGraw-Hill School Division Write the related number sentences for the set of numbers. Write the related number sentences. 3. 6.1. Print This 2–1 Page R RETEACH } Commutative Property: 5 ϩ 3 ϭ 8 is the same as 3 ϩ 5 ϭ 8. 1. pages 44–45. Print This 2–1 Page E ENRICH MϩNϭM Nϭ BϭBϩ 2. 5.Print This Page Name Use Properties of Addition Properties and Rules Complete each number sentence.1 . DϩEϭF Use with Grade 4. Lesson 1. 1. AϩNϭB 10. A ϩ 3. Chapter 2. (30) NS 3. AF 1. © McGraw-Hill School Division ϩ0ϭW Write the related number sentences. 8. 9. Then write the property or rule you used. 6. ZϪ0ϭ ϩQϭQϩP 7. CϪDϭC Dϭ HϪHϭ ϩJϭJ 4. How much did the store make in all? copies of their first CD.000.000 ϭ © McGraw-Hill School Division 80 ϩ 90 ϭ n 800 ϩ 900 ϭ n 8.000 ϩ 500.000 ϭ n 6.000 ϩ 80.1 .000 ϩ 80.000 ϩ 30. The Green Hornets sold 800. They sold 500. 1. 8 ϩ 8 ϭ Print This 2–2 Page P PRACTICE n 2. How many CDs did the Green Hornets sell in all? Use with Grade 4.000 ϭ Problem Solving 13. 500 ϩ 400 ϭ 7.000 ϩ 9.000 ϩ 8.000 ϭ n 800. In January.000 ϭ 12. 5 ϩ 9 ϭ 70 ϩ 60 ϭ n 700 ϩ 600 ϭ n 7. 100.000 ϭ n 700.000 ϭ n 80. 3.000 ϩ 90. 5.000 CDs and tapes in December. Chapter 2. A music store made $50.000 ϭ 9.000 copies of their second CD. the store made $30.000 ϭ n 800.000 ϩ 60. pages 46–47. 600 ϩ 500 ϭ 11.000 ϭ n Add mentally.000 ϭ n 4.000 ϩ 900. 700 ϩ 800 ϭ 10.000 ϩ 600.000 ϩ 9. (31) NS 3.000 ϩ 9. 70. 7 ϩ 6 ϭ n 80 ϩ 80 ϭ n 800 ϩ 800 ϭ n 8.000 ϭ n 500. 8 ϩ 9 ϭ n n 50 ϩ 90 ϭ n 500 ϩ 900 ϭ n 5.000 ϭ n 50.000 ϩ 6.000 selling 14.000 ϭ n 80.000 ϩ 90.000 ϭ n 70.000 ϭ 8.000 ϭ n 3.1.000 ϩ 900. 800. Lesson 2.000 ϩ 900.Print This Page Name Addition Patterns Complete the pattern. MR 1. 30.000 ϩ 800. 800 ϩ 600 ϭ 5.000 ϭ n © McGraw-Hill School Division 50 ϩ 90 ϭ n 500 ϩ 900 ϭ n 5.000 ϭ 7.000 ϭ 12.1.200.000 ϭ n Add mentally. 5 ϩ 9 ϭ n 30 ϩ 80 ϭ n 300 ϩ 800 ϭ n 3.000 ϩ 700.000 50 ϩ 70 ϭ 120 50.000 ϭ 12.000 ϩ 7. Add the front digits. (32) 4.000 ϩ 90. pages 46–47. 5. 1.000 12.000 ϭ 120.000 ϭ 1.000 ϩ 7.000 ϭ n 30.200 5. 80.000 ϭ n 50.000 500 ϩ 700 ϭ 1.000 50.000 ϭ n 300.000 ϩ 80. Lesson 2.000 ϩ 800. 700.000 ϭ 8. MR 1. 80.000 120.000 ϩ 600.Print This Page Name Addition Patterns You can use addition facts and patterns to add multiples of ten mentally.000 Complete the pattern.000 ϭ 6. 3.000 Print This 2–2 Page R RETEACH 5. 9.1 .000 ϭ 11.000 1.000 ϩ 50. 900 ϩ 500 ϭ 9.000 ϩ 900. 5 ϩ 7 ϭ 12 5 ϩ7 12 50 ϩ 70 120 500 ϩ 700 1. Then write a zero to match each place value.000 ϩ 8.000 ϩ 70.000 ϩ 80. 3 ϩ 8 ϭ n 2.200.000 ϭ n 500.000 ϩ 90.200 500.000 ϩ 9.000 ϭ NS 3.000 ϩ 700. Chapter 2.000 500. 800.000 ϩ 7. 300 ϩ 700 ϭ Use with Grade 4.000 ϩ 700. 60.000 ϭ 10.000 ϩ 4.000 ϩ 70. 1 . Complete this Pascal’s Triangle. Row 1 Row 2 Row 3 Row 4 Row 5 Row 6 Row 7 1 1 1 1 1 3 6 1 2 3 1 1 1 1 1 Print This 2–2 Page E ENRICH 1 1 Now complete this Pascal’s Triangle.Print This Page Name Addition Patterns Pascal’s Triangle The triangle below is called Pascal’s Triangle. Chapter 2. Each row begins and ends with 200. Every other number is the sum of the two numbers above it. (33) NS 3. pages 46–47. Lesson 2. MR 1. Row 1 Row 2 Row 3 © McGraw-Hill School Division 200 200 200 200 200 200 200 600 1. Each row begins and ends with the number 1.1.200 400 600 200 200 200 200 200 200 Row 4 Row 5 Row 6 Row 7 Use with Grade 4. 802 ϩ 7. At the Lakeside School. 20. $8. $325 worth of play tickets ride the bus and 714 students walk or are driven to school. How much money was collected altogether? Use with Grade 4.18 2.38 $3. $7. 10. 6. Lesson 3. Chapter 2. 19.59 5.709 ϩ 3.345 ϩ 67.047 ϭ © McGraw-Hill School Division 22. 8.Print This Page Name Add Whole Numbers and Money Find each sum. Print This 2–3 Page P PRACTICE 688 ϩ 207 $2. 18.95 ϭ 26. 5.070 ϩ 879. (34) NS 3.278 4.687 3.608 ϩ 7. 9.43 43.82 ϩ $357. 574 ϩ 434 989 ϩ 624 $12.489 ϩ 87 ϩ 741 ϭ 25.872 ϩ 754 ϭ 24. 1. 13. 16.280 5.77 ϩ $6.316 ϩ 893 741.243 ϩ 85. 522 students 28.57 ϩ 7.672 ϩ 878 24.421.98 ϩ 0.72 ϩ 1. 782. 42. 7. 12.162 ϩ 115. $256. pages 48–51.603 ϭ Problem Solving 27. 17.177 ϩ 678.657.489 ϩ 2.462 ϩ 570.29 ϩ 45.66 ϭ 23.78 ϩ 1.824 ϩ 962 $78. 21.467 6.47 ϩ $83.184 $427. Last week.890 $3. 14.174 ϩ 327 12. 11.1 . How many students attend Lakeside School? and $729 worth of carnival tickets were sold. 15. 3. 757 ϩ 529 8.526 204.535 ϩ 6.32 183. 289 ϩ 764 14. pages 48–51.147 ϩ 3.41 7. 25. Step 1 Add the ones.421 2.625 99.68 9.717 12. 534 ϩ 394 8.487 20. O 7 9 6 H 1 Step 3 Add the hundreds.99 11.1 . $62.80 ϩ 2.21 Use with Grade 4.988 15. $7. 5.857 18. 1.726 19. Lesson 3. 399. $9.57 4. $4. 336 ϩ 574 3.032 ϩ 5.Print This Page Name Add Whole Numbers and Money Add 587 ϩ 269. Chapter 2. 71.408 ϩ 64. 1. $828 ϩ 16 6. 187 ϩ 219 7.245 ϩ 3. 8. H 5 ϩ2 T 1 Print This 2–3 Page R RETEACH Step 2 Add the tens. 6.99 ϩ 7.34 ϩ 3.784 4.38 ϩ 1. 327 ϩ 425 5. Regroup if necessary.511 17.29 © McGraw-Hill School Division 13.128 ϩ 3. $31. 692 ϩ 810 10. 413 ϩ 228 2. Regroup if necessary. O 7 9 6 H 1 T 1 T 1 O 7 9 6 8 6 5 ϩ2 8 6 5 5 ϩ2 8 8 6 5 7 ones ϩ 9 ones ϭ 16 ones 1 ten ϩ 8 tens ϩ 6 tens 1 hundred ϩ 5 hundreds ϩ ϭ 15 tens 2 hundreds ϭ 8 hundreds 16 ones ϭ 1 ten 6 ones 15 tens ϭ 1 hundred 5 tens Find each sum.326 ϩ 383 16.990 ϩ 437. Regroup if necessary. 87. (35) NS 3.15 ϩ 85. 238 ϩ 849 8. 96 ϩ 87 3. 289 ϩ 556 6.58 10. 874 ϩ 496 11.371. Regroup to the tens place.63 ϩ 8. 56 ϩ 35 2.Print This Page Name Add Whole Numbers and Money Hindu Addition The Hindu people of ancient India added numbers from the left and moved to the right. 589 ϩ 782 1261 37 589 ϩ 782 12 Use the Hindu method of addition to find the sum.97 Compare the Hindu method of addition to the method of addition you use.11 ϩ 9. Which method do you like best? Explain. 8 ϩ 8 ϭ 16. 589 ϩ 782 126 3 Print This 2–3 Page E ENRICH Last. Add the hundreds. 1. (36) NS 3. $6. Here is an example of Hindu addition. Regroup to the hundreds place.75 7.1 . Use with Grade 4. 538 ϩ 247 4. add the ones. $1. 766 ϩ 984 © McGraw-Hill School Division 9. The sum is 1. Chapter 2. pages 48–51. Show your work.87 ϩ 7. 322 ϩ 489 5. $9. Lesson 3. Next add the tens. 385 ϩ 496 12. $498 ϩ 21.511 ϭ Print This 2–4 Page P PRACTICE Algebra & Functions Find each missing number. Chapter 2. 48 ϩ 31 ϭ 7. $256 ϩ $222 ϭ 14. 730 ϩ 214 ϭ 12. How many cats and dogs are there in all? $316 on dog treats and $299 on cat treats. pages 52–53. b ϩ 61 ϭ 81 d ϩ 298 ϭ 598 h ϭ $243 19.137 r ϩ $750 ϭ $1. 255 ϩ 344 ϭ 10.487 ϩ 1. 4. 1. 1. 20. (37) NS 3.333 ϭ 16.173 ϭ 15.300 22.524 ϩ 3. $63 ϩ 24.Print This Page Name Use Mental Math to Add Add mentally. $725 ϩ m ϩ 837 ϭ 1. Lesson 4. 21 ϩ 64 ϭ 4. 891 ϩ 108 ϭ 13. 23. 26. There are 38 dogs and 24 cats at the 28.125 n ϭ 3.999 ϩ 1. 8.1 .1. $39 ϩ $24 ϭ 6.650 ϩ © McGraw-Hill School Division Problem Solving 27. 1. 35 ϩ 13 ϭ 5. 32 ϩ 45 ϭ 3. 595 ϩ 409 ϭ 9. e ϩ 657 ϭ 957 k ϭ $1. The pet show committee spends pet show. AF 1. How much does the committee spend on treats? Use with Grade 4.124 ϭ 2.500 25. 17. 298 ϩ 311 ϭ 8. 36 ϩ a ϭ 86 c ϭ $698 18. 2.295 ϩ 2. 238 ϩ 495 ϭ 11. 599 ϩ 109 ϭ 17. 298 ϩ 465 ϭ 14. 752 ϩ 247ϭ 15. 54 ϩ 17 ϭ 4. Compensation Use compensation when a number is close to a ten or a hundred. 627 ϭ 600 ϩ 20 ϩ 7 Then add each place separately. pages 52–53. Zig-zag Use the zig-zag method to add 356 ϩ 627. Subtract 3 from the other number: 254 Ϫ 3 ϭ 251. Lesson 4.Print This Page Name Use Mental Math to Add You can use these two strategies to add mentally. 356 ϩ 627 356 ϩ 600 956 956 ϩ 20 976 976 ϩ 7 983 Add mentally. 437 ϩ 128 ϭ 8. 697 ϩ 140 ϭ 10. $29 ϩ $56 ϭ © McGraw-Hill School Division 2. 202 ϩ 248 ϭ 5.1. 2. Take apart 627.097 ϭ NS 3. 425 ϩ 222 ϭ 21. (38) . 849 ϩ 52 ϭ 20. 253 ϩ 35 ϭ 19. $625 ϩ $330 ϭ 7. $6. 1.512 ϩ $950 ϭ Use with Grade 4. AF 1.398 ϩ 1. 499 ϩ 252 ϭ 9. $62 ϩ $78 ϭ 12. 62 ϩ 39 ϭ 3.377 ϩ 196 ϭ 24. 365 ϩ 113 ϭ 16. 3.343 ϭ 23. 197 → 200 ϩ 254 → ϩ 251 451 Print This 2–4 Page R RETEACH Add 3 to make 200: 197 ϩ 3 ϭ 200. 1. 723 ϩ 245 ϭ 22. Chapter 2. $316 ϩ $455 ϭ 6.783 ϩ 5. 232 ϩ 657 ϭ 18.1 11. $268 ϩ $441 ϭ 13. add 19 and 53. The sum is 72. Add each pair of numbers mentally.090 4. If the sum is 125.213 4. then shade the box with 125 in it. (39) NS 3.1.000 3. AF 1.090 115 149 595 270 110 199 174 805 39 399 915 238 573 857 1. Add 53 and 72. Lesson 4. Chapter 2.090 1.339 2. pages 52–53. or 1.Print This Page Name Use Mental Math to Add Countdown! Move from left to right. 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 10.000? the sum of the digits was greater than 9? © McGraw-Hill School Division How is mental math different from estimation? Use with Grade 4. Example: In row 1. Shade any box that is the sum of the previous two boxes. Shade the box with 72 in it. 100. What number do the boxes form? 2.277 1. 19 195 17 34 79 53 302 21 51 15 72 402 37 99 94 125 67 58 154 109 197 469 95 253 203 232 12 22 307 311 429 480 127 560 514 Print This 2–4 Page E ENRICH 661 1. Look at the shaded boxes.064 2.317 825 1.1 . 725 ϩ 321 19. 2.65 4.65 ϩ $7.122 ϩ 254. 621 ϩ 308 ϭ 10.621 ϭ 11. 863.152 ϩ 28.000 16.721 7.990 ϩ 405 5. 47. $0.95. The fifth-grade students make 229.081 ϩ 950 5.087 Print This 2–5 Page P PRACTICE Add.1.348 ϩ 2.188 ϩ 5. 900 300 895 ϩ 68 3. $4. Chapter 2. 8. 1. 49.839 Problem Solving 22.188 ϩ 5. 176 ϩ 335 14. 12. 3.487 ϩ 5.672 60.174 21. 243 ϩ 50 15.128 ϩ 328.522 ϩ 3.000 © McGraw-Hill School Division 20. Write Ͼ or Ͻ to make a true sentence. About how much will he spend? 268 posters about bicycle safety. $8.20 ϩ $8. (40) NS 2. The fourth-grade students make for $8. pages 54–55. 8.1. 4.489 18.125 ϭ Compare. 2. 500 400 13.1.000 4. Lesson 5.15 3. 4.000 6. Estimate to check that each answer is reasonable.5 .Print This Page Name Estimate Sums Estimate each sum. Julio wants to buy drawing paper 23. 22.50 and brushes for $19. 9.621 6.912 ϩ 2. About how many posters do the students make altogether? Use with Grade 4.32 ϩ $0. MR 2. 601. 478 ϩ 597 2. Show your work 1. 2.923 ϩ 289 251 ϩ 127 5.000 17.12 ϭ 9. 1.927 Estimate each sum. 896.95 ϩ $7.25 ↓ ↓ number to the nearest dollar.1.75 10. 5. 38.605 14. 143 ϩ 431 11.25 is about $13. $5. Show how you rounded.217 4.32 ϩ $0. 252 ϩ 49 is about 300.214 ϩ 642 6.455 ϩ 11.95 ϩ $7. $9.95 ϩ $7.995 ϩ 865.501 12.653 15.321 Use with Grade 4.629 ϩ 5. 2. 6.956 ϩ $7. 3. Chapter 2. Estimate 252 ϩ 49.00 ϭ $13. pages 54–55. 477. Round each number to the nearest ten.00 So. 2.90 ϩ $327.311 9. 1.357 ϩ 8. 5. $6.1.25.00 ϩ $7.5 . Add. To which place will you round each number? Circle the digits in that place. 27. $6.54 16. $38. Then estimate each sum. So.08 ϩ $12.827 ϩ 764 13. 252 ϩ 49 250 ϩ 50 250 ϩ 50 ϭ 300 Estimate $5.822 ϩ 2.723 ϩ 3.Print This Page Name Estimate Sums To estimate a sum.89 ϩ $5. $0. 1.48 3.00.714 ϩ 8. you can round each number. MR 2. Then add the rounded numbers.00 ϩ $7. (41) NS 2.00 Add. Lesson 5. 7. $46.29 2. 469 ϩ 563 © McGraw-Hill School Division 8. Print This 2–5 Page R RETEACH ↓ ↓ Round each $5. $7.321 5. 846 1. 45.Print This Page Name Estimate Sums Star Estimates There are five paths. Write your estimate in the box at the end of each path.582 381 714 © McGraw-Hill School Division 524 174 825 418.800 23.321 432 2. Print This 2–5 Page E ENRICH 3.100 810 126.700 Use with Grade 4. MR 2. 645 4. 2. pages 54–55.724 5.5 . (42) NS 2.670 41.1. Lesson 5. Then estimate the sum of the rounded numbers on each path of the star. 3. Each path has six numbers. Chapter 2. 30.672 152 172 429 44.600 874 Start 225 5. 129.600 447. Round each number to the nearest hundred.627 3.1.1. 47. 5.3. pages 56–57.2 .1. About how many tickets does the Comic Book Show sell? 5. 2. Lesson 6. and Melba has 812 cards.10. Nicki has a collection of 79 shells and 64 rocks.75. About how many stamps does Molly have? Use with Grade 4.000 baseball cards? 2. Chapter 2. James. Explain why you gave an estimate or an exact answer. Her quarters are worth $104. James has 870 cards.Print This Page Name Problem Solving: Reading for Math Estimate or Exact Answer Solve. 2. Her dimes are worth $75. 2. Her nickels are worth $27. 3. 3. The Comic Book Show sells 474 tickets on Friday and 396 tickets on Saturday.4. Print This 2–6 Page P PRACTICE Reading Skill Max has 569 cards.1. © McGraw-Hill School Division How many CDs does Eldon have? 6. 121 classical CDs. and Melba collect baseball cards. What is the total value of Kelly’s coin collection? 4. Max. Eldon has 98 rock CDs. Molly has 221 stamps from the United States and 395 stamps from other countries.50. and 25 folk music CDs. (43) MR 1. 1. 2. How many items are in her collection? 3. Do the three friends have more than 2. Kelly has a coin collection.1. 3.000 cards in all? © McGraw-Hill School Division 5. C Hiroshi has 97 football cards. Are there more than 500 cards in these two collections altogether? 1. Use with Grade 4. Which of the following statements is 6.000.1. G Estimate to tell if 429 ϩ 278 is greater than 1. 2. (44) MR 1. How many toy cars do they have problem? A Estimate the sum of 129 and 167.4. C Compare 129 and 167. in all? F 300 G 296 H 200 Hiroshi has 429 football cards. 2. Does Hiroshi have more than 1. problem? F Find the exact sum for 429 ϩ 278 ϩ 97. 2. H Estimate to tell if 429 ϩ 278 ϩ 97 is greater than 1. 2.1. 3. 278 baseball cards.000.1. B Add 129 and 167. Which plan can you use to solve the 4. you solve the problem? F 249 ϩ 329 Ͼ 500 G 329 Ϫ 249 Ͻ 500 H 500 Ϫ 249 Ͻ 500 Paco has 129 toy cars. pages 56–57.2 . Jenny has a collection of 249 football cards. Which of the following statements is Print This 2–6 Page P PRACTICE Math Skills Test Prep 2. and 97 hockey cards. C Jenny has 249 cards. How many toy cars do they have in all? 3. B Hiroshi has 429 cards in all. His brother has 167 toy cars. Lesson 6.5. 3.Print This Page Name Problem Solving: Reading for Math Estimate or Exact Answer Choose the correct answer. Ken has a collection of 329 football cards. Chapter 2. Which number sentence will help true? A Jenny has more cards than Ken. What do you have to do to solve this true? A Hiroshi has 278 baseball cards. B Ken has more than 500 cards. 3. Morris has a collection of United States and 458 stamps from other countries. 97 autographs from actors and actresses. Solve. Chelsea has 635 postcards from the the antique doll show during the three days? F 2. Evan has 4. On Sunday. 994 and 812 from least to greatest. 994. How many people came to see the antique doll show during the three days? 7.000 cards? 13. On Friday. About how many autographs does he have? 11. His sister has © McGraw-Hill School Division 63 concert posters. 812 people see the collection. will they have more than 9.335 G 2. On Saturday. (45) MR 1. pages 56–57. How many stamps does she have? 44 quarters. 9.3. Does she have more than 2. 2.4. Nina has 379 stamps from the 14.000 postcards? players.300 H 1. C Order 529. How many posters does Miles have? 5.523 10. and 456 postcards from Europe and Asia. 92 dimes.1. 291 postcards from Canada.Print This Page Name Problem Solving: Reading for Math Estimate or Exact Answer Choose the correct answer. 529 people see the museum’s collection of antique dolls. 2. 2. Gus has 65 autographs from sports United States.212 cards. 994. About how many coins does he have? Use with Grade 4.2 . and 812. and 54 posters from plays. 3. B Add 529. and 812. and 89 pennies. Lesson 6.1. Miles has 75 old movie posters. If they put their cards together. 2. Which plan can you use to solve the Print This 2–6 Page P PRACTICE Math Skills Test Prep 8.5.1. Chapter 2.349 cards. and 27 autographs from singers. 12. 994 people see the collection. How many people came to see problem? A Estimate the sum of 529. 000 ϭ 12. A video store rented 900.000 ϭ n 1. 15 Ϫ 8 ϭ n n 110 Ϫ 50 ϭ n 1.000 Ϫ 500. MR 1.000 Ϫ 8.000 ϭ 10.000 ϭ n 4.000 ϭ n 150.500.1.000 videos 14.000 Ϫ 50.600.000 ϭ n 110. How much does Ms.000 Ϫ 50.200.1 . $8.100 Ϫ 500 ϭ n 11.100. 1. Smith decides to make an offer that is $30.000 Ϫ 80. 140.000 Ϫ 800.000 Ϫ 700.Print This Page Name Subtraction Patterns Complete the pattern.000 Ϫ 8.000 ϭ n 1.000.000 Ϫ 80.600 Ϫ 700 ϭ n 16.000 ϭ n 6.200 Ϫ 600 ϭ 7.000 ϭ 9. How many more videos did it rent this year? Ms.500.000 ϭ n 120.000 ϭ © McGraw-Hill School Division 150 Ϫ 80 ϭ n 1. Lesson 7. Smith offer for the house? Use with Grade 4.000 ϭ Problem Solving 13. 160. 1. 600. (46) NS 3.000 Ϫ 5.000 Ϫ $9.200.000 Ϫ 500. This year the store rented 1.000 Ϫ 600. Chapter 2.000 ϭ n Subtract mentally. 1. The price for a house is $120.000 Ϫ 80. 11 Ϫ 5 ϭ 160 Ϫ 70 ϭ n 1.000 ϭ n 3.000 ϭ n 160.000 ϭ n 1.000 ϭ 8.000 Ϫ 7.500 Ϫ 800 ϭ n 15.000 Ϫ 70. pages 60–61.000 ϭ 11. $13.000 Ϫ $3.000 Ϫ 800.000 Ϫ 50. last year.000 less than the price.000 ϭ n 1. 70. 12 Ϫ 8 ϭ Print This 2–7 Page P PRACTICE n 2.200 Ϫ 800 ϭ n 12.000 videos. 16 Ϫ 7 ϭ n 120 Ϫ 80 ϭ n 1. 5. 000 ϭ Use with Grade 4.000 = n 110. 110.000 Ϫ 7. 11 Ϫ 8 ϭ n 2.000 Ϫ 900.000 Ϫ 500.000 ϩ 70. $1. 1.000 – 80.000 Ϫ 5.400.800. Chapter 2. Subtract the front digits.000 5. 14.000 Ϫ 40.000 ϭ 7.000 ϭ n 1.000 ϭ 5.000 Ϫ $900.000 ϭ 11. 1.000 ϭ n 1.100 Ϫ 800 ϭ n 11.000 ϩ 700. $16.000 120 Ϫ 70 ϭ 50 120.000 ϭ n 140.200 Ϫ 700 ϭ 500 1.000 Complete the pattern.000 ϭ n © McGraw-Hill School Division 140 Ϫ 50 ϭ n 1.200 Ϫ 500 ϭ 8.000 ϭ 50. pages 60–61.000 ϭ 12. 1. (47) NS 3.400 Ϫ 500 ϭ n 14. Then write a zero to match each place value. MR 1.000 1.200 Ϫ 700 500 12. Lesson 7.400 Ϫ 600 ϭ 5.000 ϭ 6.200.000 ϭ 10.000 Ϫ 80.000 500.000 ϭ n Subtract mentally.000 Ϫ 7.000 120. 12 Ϫ 7 ϭ 5 12 Ϫ 7 5 120 Ϫ 70 50 1.500 Ϫ $700 ϭ 9. 160. 1.000 Ϫ 50.000 1.000 Ϫ 700. 14 Ϫ 5 ϭ n 110 Ϫ 80 ϭ n 1.100.000 50. 120.000 ϭ 4.700.000.000 Ϫ 70.200.000 Ϫ 50.000 Ϫ 800.000 ϭ 500. $1.1 .000 Ϫ $7.000 Ϫ 8.Print This Page Name Subtraction Patterns You can use subtraction facts and patterns to subtract multiples of ten mentally.1. 3.000 Print This 2–7 Page R RETEACH 12.000 Ϫ 8. subtract the two corner numbers in each square and write the difference in between the numbers. MR 1. pages 60–61. (48) NS 3. Find the missing numbers.1 .Print This Page Name Subtraction Patterns Subtraction Squares (Diffy) Each subtraction square is made up of eight numbers.1. 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. Subtract until you reach the center of the square. Print This 2–7 Page E ENRICH 150 70 80 10 20 60 10 30 20 0 40 0 0 0 20 0 0 20 0 0 0 0 20 10 20 30 30 20 10 © McGraw-Hill School Division 90 40 50 2. Chapter 2. To find the missing numbers. Lesson 7. What happens in the center of the squares? 3. Use models to subtract 525 Ϫ 272. 5 Ϫ2 2 7 5 2 Subtract. Lesson 8. Chapter 2. 187 Ϫ 95 3.1 . 857 Ϫ 79 10. 813 Ϫ 75 ϭ 13. 923 Ϫ 707 6. Regroup 1 hundred as 10 tens. 711 Ϫ 380 8. ϫ ϫ 5 Ϫ2 2 7 5 2 Subtract the tens. 562 Ϫ 348 11. 227 Ϫ 138 12. 573 Ϫ 495 ϭ 15. 2. 263 Ϫ 88 ϭ Use with Grade 4. Print This 2–8 Page P PRACTICE Subtract the ones. 1. pages 62–63. 612 Ϫ 74 4. (49) NS 3.Print This Page Name Explore Subtracting Whole Numbers Subtract. 425 Ϫ 258 9. 356 Ϫ 127 5. 319 Ϫ 79 © McGraw-Hill School Division 7. 5 Ϫ2 2 7 5 2 Subtract the hundreds. 684 Ϫ 327 ϭ 14. Print This Page Name Explore Subtracting Whole Numbers Use models to subtract 322 Ϫ 145. Step 1 Model the greater number. You need to subtract 145, or 1 hundred 4 tens 5 ones. Print This 2–8 Page R RETEACH 322 Ϫ145 Step 2 Subtract the ones. Regroup a ten for 10 ones, if necessary. Step 3 Subtract the tens. Regroup a hundred for 10 tens, if necessary. Step 4 Subtract the hundreds. 1 12 Subtract 5 ones. 32 /2 / Ϫ145 7 2 11 12 3 /2 /2 / Ϫ145 77 Subtract 4 tens. 2 11 12 Subtract 1 hundred. 3 /2 /2 / Ϫ145 177 Subtract. Use or draw models to help you subtract. 1. © McGraw-Hill School Division 724 Ϫ 318 2. 916 Ϫ 108 3. 568 Ϫ 59 4. 428 Ϫ 247 5. 353 Ϫ 182 6. 964 Ϫ 281 7. 735 Ϫ 586 8. 327 Ϫ 299 9. 863 Ϫ 575 10. 651 Ϫ 93 11. 274 Ϫ 126 ϭ 12. 745 Ϫ 67 ϭ Use with Grade 4, Chapter 2, Lesson 8, pages 62–63. (50) NS 3.1 Print This Page Name Explore Subtracting Whole Numbers Crack the Code Find each difference. Match the code number beside each problem with the correct code letter. Problems 1. $3.63 Ϫ $1.77 2. $4.25 Ϫ $2.86 3. 181 Ϫ 92 4. 573 Ϫ 397 5. 426 Ϫ 326 6. 880 Ϫ 119 7. 625 Ϫ 317 8. 682 Ϫ594 9. 170 Ϫ 98 10. 590 Ϫ 399 11. 731 Ϫ 427 12. $9.05 Ϫ$7.89 13. $6.52 Ϫ $4.93 14. 464 Ϫ 387 15. 222 Ϫ 175 © McGraw-Hill School Division Print This 2–8 Page E ENRICH Code Numbers 6 4 9 13 14 5 2 12 7 15 11 3 16 8 1 10 Code Letters 761 ϭ S 88 ϭ A $1.39 ϭ U 176 ϭ T 304 ϭ C $1.59 ϭ N 89 ϭ V $1.86 ϭ E 308 ϭ M 100 ϭ I 77 ϭ N 191 ϭ O 47 ϭ A 138 ϭ A 72 ϭ O $1.16 ϭ O 16. 832 Ϫ 694 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 8 9 10 11 12 13 14 15 16 Use with Grade 4, Chapter 2, Lesson 8, pages 62–63. (51) NS 3.1 Print This Page Name Subtract Whole Numbers and Money Subtract. Check by adding. 1. Print This 2–9 Page P PRACTICE 757 Ϫ 28 $2.48 Ϫ 1.95 4,672 Ϫ 873 49,785 Ϫ 8,998 389,243 Ϫ 136,354 2. $582 Ϫ 492 2,345 Ϫ 1,658 3,523 Ϫ 2,846 98,142 Ϫ 617 $672,145 Ϫ 98,276 3. 693 Ϫ 516 $67.89 Ϫ 18.95 $33,572 Ϫ 13,689 $224.39 Ϫ 15.87 914,617 Ϫ 117,814 4. 851 Ϫ 569 $11,321 Ϫ 979 74,125 Ϫ 65,239 $4,561.71 Ϫ 291.68 $7,211.53 Ϫ 5,926.84 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 827 Ϫ 468 ϭ 23. 42,625 Ϫ 9,846 ϭ 25. $311.42 Ϫ $4.65 ϭ © McGraw-Hill School Division 22. $9.12 Ϫ $7.58 ϭ 24. 65,932 Ϫ 46,464 ϭ 26. $578,423 Ϫ $89,743 ϭ 28. $2,176.53 Ϫ $1,993.76 ϭ 27. 982,561 Ϫ 678,984 ϭ 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 Subtract Whole Numbers and Money Subtract 7,617 Ϫ 5,789. Step 1 Subtract the ones. Regroup if necessary. TH H T 0 Print This 2–9 Page R RETEACH Step 2 Subtract the tens. Regroup if necessary. TH H 5 O 17 T 10 0 / O 17 7 Ϫ5 6 7 1 / 8 7 / 9 8 7 Ϫ5 6 / 7 1 / 8 2 7 / 9 8 Step 3 Subtract the hundreds. Regroup if necessary. TH 6 Step 4 Subtract the thousands. T 10 0 / H 15 5 / O 17 TH 6 H 15 5 / T 10 0 / O 17 7 / Ϫ5 6 / 7 8 1 / 8 2 7 / 9 8 7 / Ϫ5 1 6 / 7 8 1 / 8 2 7 / 9 8 Use the same steps to subtract money. Subtract. Check by adding. 1. © McGraw-Hill School Division 577 Ϫ 385 2. 872 Ϫ 465 3. $6.21 Ϫ 4.43 4. 3,457 Ϫ 965 5. $2.49 Ϫ 0.98 6. 4,872 Ϫ 3,785 7. 7,501 Ϫ 6,874 8. 8,142 Ϫ 6,527 9. 12,435 Ϫ 8,679 10. $6,423 Ϫ 2,496 11. 24,652 Ϫ 9,788 12. $56,716 Ϫ 39,897 13. 347,072 Ϫ 59,687 14. 743,219 $6,192.48 15. Ϫ 1,671.39 Ϫ 19,733 Use with Grade 4, Chapter 2, Lesson 9, pages 64–65. (53) NS 3.1 Print This Page Name Subtract Whole Numbers and Money Sumerian Numbers Print This 2–9 Page E ENRICH 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 ϩ 600 ϩ 60 ϩ 10 ϩ 10 ϭ 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 Ϫ Ϫ125 2. 1,263 Ϫ Ϫ 626 3. 7,280 Ϫ Ϫ 4,861 8 © McGraw-Hill School Division 637 2,419 4. 1,821 Ϫ 1,205 5. 3,750 Ϫ Ϫ 3,650 6. 1,242 Ϫ 922 Ϫ Ϫ 616 100 320 Use with Grade 4, Chapter 2, Lesson 9, pages 64–65. (54) NS 3.1 Print This Page Name Regroup Across Zeros Subtract. Check by adding. 1. Print This 2–10 Page P PRACTICE 804 Ϫ 565 300 Ϫ 108 2,000 Ϫ 784 50,000 Ϫ 25,625 $900,000 Ϫ 321,229 2. 701 Ϫ 387 3,000 Ϫ 2,987 8,000 Ϫ 2,450 80,000 Ϫ 35,189 400,707 Ϫ 39,698 3. $500 Ϫ 244 9,000 Ϫ 5,431 $15,000 Ϫ 7,641 30,000 Ϫ 7,984 210,303 Ϫ 101,506 4. 600 Ϫ 58 4,050 Ϫ 2,542 70,700 Ϫ 8,633 600,003 Ϫ 25,178 575,000 Ϫ 89,342 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 602 Ϫ 423 ϭ 23. 3,400 Ϫ 1,762 ϭ 25. $20,800 Ϫ $13,972 ϭ © McGraw-Hill School Division 22. 800 Ϫ 68 ϭ 24. 6,000 Ϫ 672 ϭ 26. 70,000 Ϫ 52,087 ϭ 28. 307,000 Ϫ 198,621 ϭ 27. 160,000 Ϫ 149,999 ϭ 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 Regroup Across Zeros Subtract 500 Ϫ 185. Step 1 No ones. No tens. Regroup the hundreds. H 4 5 / Print This 2–10 Page R RETEACH Step 2 Regroup the tens. Step 3 Subtract the ones, the tens, and then the hundreds. O 10 T 10 0 / O H 4 T 9 10 / H 4 T 9 10 / O 10 5 / Ϫ1 0 / 8 0 5 5 / Ϫ1 0 / 8 0 / 5 5 / Ϫ1 3 0 / 8 1 0 / 5 5 5 hundreds ϭ 4 hundreds 10 tens There are not enough ones to subtract 9 ones. Subtract. Check by adding. 1. 10 tens ϭ 9 tens 10 ones 10 ones Ϫ 5 ones ϭ 5 ones 9 tens Ϫ 8 tens ϭ 1 ten 4 hundreds Ϫ 1 hundred ϭ 3 hundreds 602 Ϫ 314 2. 700 Ϫ 203 3. $900 Ϫ 306 4. 800 Ϫ 523 5. 304 Ϫ 150 6. $4,000 Ϫ 1,527 7. 2,005 Ϫ 1,083 8. 3,000 Ϫ 2,225 9. 5,000 Ϫ 259 10. 6,000 Ϫ 1,326 © McGraw-Hill School Division 11. 68,000 Ϫ 11,770 12. 80,000 13. 74,800 Ϫ 5,287 Ϫ 27,862 14. $40,050 Ϫ 32,037 15. 45,000 Ϫ 2,374 16. 300,077 Ϫ 124,364 ϭ 18. 107,006 Ϫ 84,119 ϭ 20. 60,000 Ϫ 29,730 ϭ 17. $200,008 Ϫ $187,053 ϭ 19. 906,004 Ϫ 205,457 ϭ 21. $500,600 Ϫ $50,250 ϭ Use with Grade 4, Chapter 2, Lesson 10, pages 66–67. (56) NS 3.1 Print This Page Name Regroup Across Zeros Missing Digits Find the missing digits. 1. Print This 2–10 Page E ENRICH 8 Ϫ 7 0 1 5 7 2. 5, Ϫ 2, 0 3 , 7 8 3 2 7 3. 9 Ϫ 2 8 6 7 3 4. 3 Ϫ 1 0 7 8 9 9 5. 2, Ϫ 1, 9 0 8 2 3 1 6. 5, Ϫ 4, 1 6 0 5 4 8 5 7. 6, Ϫ 3, 0 8 , 2 4 0 4 7 7 8. 6 Ϫ 3 3 7 6 1 9. 5, Ϫ 3, 2, 0 5 2 8 8 3 10. 7 Ϫ 2 0 6 4 11. 2 2 Ϫ 3 0 8 1 12. 6 6 7, Ϫ 3, 3 0 , 2 8 1 0 5 5 13. © McGraw-Hill School Division 9 Ϫ 3 6 7 8 9 14. 6, Ϫ , 3 5 5 2 2 7 9 15. , 0 Ϫ 4, 8 , 1 7 8 1 4 16. 5 Ϫ 2 5 7 0 7 17. 0 Ϫ 2 3 3 0 3 18. 7 , Ϫ , 2 5, 7 1 3 4 6 Use with Grade 4, Chapter 2, Lesson 10, pages 66–67. (57) NS 3.1 Print This Page Name Problem Solving: Strategy Write a Number Sentence Write a number sentence to solve. 1. Meg buys candle-making supplies for Print This 2–11 Page P PRACTICE 2. Sally has finished 86 squares in her $37. She has $25 left. How much money did Meg have before she bought the supplies? quilt. The quilt will have 100 squares. How many squares does Sally still have to make? 3. Eric sells a painting for $125. He sells 4. Noah has saved $42. How much a sculpture for $390. How much money does Eric earn in all? 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 6. Tom makes letters for a sign that collects another 16 shells. How many shells does he have now? says “Arts and Crafts Fair.” Which letter does Mark need to make the most of? Strategy: Strategy: 7. Social Studies During the 1800s, © McGraw-Hill School Division 8. Create a problem which you could 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? 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 buttons left.1 . Since you know the original total and the number left.1. you can write a subtraction sentence. (59) NS 3. AF 1.1. What do you need to find? • You need to find how many . What do you know? • Ms. Problem 2 Print This 2–11 Page R RETEACH Ms. MR 1. Green had 29 buttons to sew on dolls. Green had • She has buttons to sew on dolls. How many buttons has she already sewn on? Step 1 Read Be sure you understand the problem. Read carefully. Step 2 Plan I Make a plan. Lesson 11. I I I I I © McGraw-Hill School Division I I I I 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 You can write a number sentence to solve the problem. pages 68–69. She has 14 buttons left.1. Choose a strategy. Use with Grade 4. 2.Print This Page Name Problem Solving: Strategy Write a Number Sentence Page 69. Chapter 2. Lesson 11. How much change does Keshawn get back? 2. He pays with a hundred-dollar bill. buttons already sewn on She has already sewn on Step 4 Look Back Is the solution reasonable? Reread the problem. Melanie sells a model sailing ship and a model airplane for a total of $40. Keshawn spends $45 on glass and copper molding. Write a subtration sentence to represent the situation. • You know Ms.1.95. How much money does Melanie receive for the airplane? Use with Grade 4.49 for the ship. She receives $23. Ϫ ϭ number of buttons she had buttons left buttons. 29 Ϫ n ϭ 14 number of buttons buttons left buttons she had already sewn on Then use a related sentence to solve.1.Print This Page Name Problem Solving: Strategy Write a Number Sentence Step 3 Carry out your plan. Chapter 2.1. MR 1. Green had • You know she has Print This 2–11 Page R RETEACH Solve buttons to sew on dolls. AF 1. buttons left. 2. (60) NS 3.1 . Does your answer make sense? Did you answer the question? How can you check your answer? What other stategies could you use to solve the problem? Yes Yes No No © McGraw-Hill School Division Practice 1. pages 68–69. Ashley buys 259 water-bottle holders from the shop. AF 2.1 . 782 Ϫ 203 ϭ 17. 1.1. (61) NS 3. 823 Ϫ 27. 64 Ϫ 37 ϭ 11. © McGraw-Hill School Division 25. a ϭ 548 21.Print This Page Name Subtract Using Mental Math Subtract mentally. 450 Ϫ 29. 92 Ϫ 28 ϭ 9. $273 Ϫ $58 ϭ 13. 31. 95 Ϫ 37ϭ 3. pages 70–71. 578 Ϫ 465 ϭ Print This 2–12 Page P PRACTICE Algebra & Functions Find each missing number. Lesson 12. $704 Ϫ $589 ϭ 15.456 Problem Solving 30. How many water-bottle holders does the store have left? Use with Grade 4. 53 Ϫ 19 ϭ 6. 99 Ϫ 19 ϭ 7. 745 Ϫ 597 ϭ 16. 81 Ϫ 36 ϭ 5. Josh buys a wooden horse for $4. k Ϫ 599 ϭ 301 n ϭ 200 28. 998 Ϫ 145 ϭ 2.00. 775 Ϫ r Ϫ 300 ϭ 1. 613 Ϫ 309 ϭ 18. 950 Ϫ 26. 46 Ϫ 7 ϭ 4. How much change should Josh receive? holders in stock. 394 Ϫ 86 ϭ 14. 555 Ϫ 299 ϭ 19.89. A bicycle shop has 309 water-bottle He gives the cashier $5. b Ϫ 60 ϭ 340 d Ϫ 235 ϭ 665 h ϭ 123 m ϭ 100 c Ϫ 412 ϭ 388 e ϭ 400 24. 23. Chapter 2. 20. 74 Ϫ 38 ϭ 10. 648 Ϫ 22. 687 Ϫ 48 ϭ 12. $78 Ϫ $49 ϭ 8. 86 Ϫ 24 ϭ 8. 482 Ϫ 204 ϭ 15. pages 70–71. Compensation Use compensation when one number is close to a ten or a hundred. 648 Ϫ 305ϭ NS 3. 888 Ϫ 277 ϭ 12.1. 196 Ϫ 49 ϭ 9. Take apart 28. 350 Ϫ 198 ϭ 22. 28 ϭ 20 ϩ 8 Then subtract each place separately. 613 Ϫ 307 ϭ 16. $428 Ϫ $117 ϭ 14. Add 2 to the other number: 95 ϩ 2 ϭ 97. 505 Ϫ 301 ϭ 20. $253 Ϫ $42ϭ 7. 26 Ϫ 7 ϭ 4. $58 Ϫ $17 ϭ © McGraw-Hill School Division 2. Chapter 2. 519 Ϫ 404 ϭ 19. 94 Ϫ 38 ϭ 3. 657 Ϫ 312ϭ Use with Grade 4. 79 Ϫ 31 ϭ 6. $535 Ϫ $122 ϭ 21. 245 Ϫ 197 ϭ 13. Subtract 3 from 103 to make 100: 103 Ϫ 3 ϭ 100. 395 Ϫ 91 ϭ 11. 84 Ϫ 32 ϭ 5. $755 Ϫ $402 ϭ 18. 95 Ϫ 28 103 Ϫ 45 97 → → Ϫ 30 67 Add 2 to 28 to make 30: 28 ϩ 2 ϭ 30. 95 Ϫ 28 95 Ϫ 20 75 75 Ϫ 8 67 Subtract mentally. Lesson 12. 354 Ϫ 99 ϭ 17. Print This 2–12 Page R RETEACH → 100 → Ϫ 42 58 Zig-zag Use the zig-zag method to subtract 95 Ϫ 28. Add or subtract the same number from both numbers.1 .Print This Page Name Subtract Using Mental Math You can use these two strategies to subtract mentally. Subtract 3 from 45: 45 Ϫ 3 ϭ 42. (62) 10. 1. AF 2. (63) NS 3. AF 2. Lesson 12. 596 Ϫ 111 C. 879 Ϫ 65 E. 192 Ϫ 95 © McGraw-Hill School Division A. Chapter 2. 383 Ϫ 99 K. Down.1.253Ϫ599 M. 626 Ϫ 197 B. 281 Ϫ 28 G.Print This Page Name Subtract Using Mental Math Crossnumber Puzzle Subtract mentally to complete the crossnumber puzzle. 448 Ϫ 203 O. 360 Ϫ 308 D. 591 Ϫ 76 I. 950 Ϫ 113 J. 194 Ϫ 162 N. What method did you use to subtract mentally? Use with Grade 4. 228 Ϫ 199 H. 1. 635 Ϫ 179 N. 765 Ϫ 723 K. 237Ϫ 105 F. 662 Ϫ 25 Look at N. pages 70–71.1 . A B E C F D Print This 2–12 Page E ENRICH 4 2 8 5 2 5 1 3 8 1 3 4 G 9 7 K H L 2 I M 8 3 7 J 4 2 6 5 8 5 4 5 N 2 9 4 O 6 3 Down 7 Across A. 686 Ϫ 28 L. 000 20.000 $367. 174. 6.25 4.645 20. 2.472 5. Lesson 13.79 Ϫ 31.88 Ϫ $0. 13.026 Ϫ 529. 2.887 10.000 938 Ϫ 452 1.1.99 for Science Monthly sold last year. Show your work.000 17.008 Ϫ 117. About how many more were sold this year? an ad in the Science Monthly. 835 Ϫ 487 7. pages 72–73. 8.95 Ϫ $7.5 .29 for an ad in the Allentown News. $300. 242.421 Print This 2–13 Page P PRACTICE Subtract.20 Ϫ $59.000 14. 914. The Hoop Store spends $129. $13. 65. (64) NS 2. About how much more does the store spend on advertising in the Science Monthly than in the Allentown News? Use with Grade 4. $81.Print This Page Name Estimate Differences Estimate each difference.074 Ϫ 15. The store spends $19.835 Ϫ 1. Estimate to check that each answer is reasonable.174 © McGraw-Hill School Division 18. 48. 3.003 Ϫ 49.1.425 Ϫ 3.00 2.584 ϭ Compare. 1. 600 7. 654. 15. Chapter 2.35 ϭ 12. 6. 8.632 copies were sold.173 Ϫ 2.45 10. Write Ͼ or Ͻ to make a true sentence.921 Ϫ 18.535 19. There were 787. 787.053 Ϫ 7. 4.329 Ϫ 957 16. 467 Ϫ 215 2. This year.345 Ϫ 16. 42. MR 2.589 15.620 11.897 copies of the 22.592 Ϫ 961 Problem Solving 21. $0.55 8.487 3.984 Ϫ 322 9.1.000 4. 00 Ϫ $5. $0.393 Ϫ 8.721 Estimate each difference. 3.00 So. 5. Then subtract the rounded numbers.378 12. 809.98 Ϫ $4. Chapter 2. 232.48 Ϫ $3. $12. 1. Show how you rounded. 486 Ϫ 27 490 Ϫ 30 490 Ϫ 30 ϭ 460 Estimate $6. 947 Ϫ 349 11.59 is about $2.00 Ϫ $5. 425. MR 2.10 Ϫ $85.1.522 Ϫ 1. 529 Ϫ 158 9.59.1.98 Ϫ $4.00 Subtract. Round each number to the nearest ten.523 15.78 Ϫ $0.750 NS 2. 53. $14.241 Ϫ 678 14. © McGraw-Hill School Division 7.900 Use with Grade 4. 3.98 Ϫ $4.088 16. 486 Ϫ 27 is about 460.842 Ϫ 799 4.425 Ϫ 20. Lesson 13.98 13.59 ↓ ↓ to the nearest dollar $7. pages 72–73. Subtract.500 Ϫ 83. (65) 8. $7. $6. $683 Ϫ $475 10. To which place will you round each number? Circle the digits in that place. Estimate 486 Ϫ 27.35 2. 72.Print This Page Name Estimate Differences To estimate a difference.741 6.25 5. $589. So.95 Ϫ $8.00 ϭ $2.00.745 Ϫ 47.765 Ϫ 528.1.29 3.5 . you can round each number. Print This 2–13 Page R RETEACH ↓ ↓ Round each number $6.697 Ϫ 289. 52. 2. Then estimate each difference. 7. 000 C.000 7. 40.16 Ϫ $1.1. 0 B. 42. 100 C.124 Ϫ 31.1.617 Ϫ 85.742 Ϫ 6.000 C. 40. 892.381 A. 4. 700 6. 526 Ϫ 481 A. 3. 500 8.000 B. 4. 2. 500 B.Print This Page Name Estimate Differences A-Mazing Differences Estimate each difference. $50. $8.692 Ϫ 3. 874 Ϫ 215 A. 2. Circle the correct answer. 20. 9. 30.766 A.000 C. 500 C.1.874 Ϫ 16. 20. MR 2. 1. $5. 2.364 A. $30.000 3. 961 Ϫ 472 A. $7. $72. 2.00 10.71 A.59 Ϫ $24.00 B.00 B. 400 C.5 2A 3B 12 Use with Grade 4.600 A. 1. 200 9. pages 72–73. 729 Ϫ346 A.000 B. 1.000 12.000 C.000 B.000 Print This 2–13 Page E ENRICH 4.000 6B ar 6C t 7A 5A St 5B 6A 8A 1A 4B 5C 9B 7B 1C 4A © McGraw-Hill School Division 1B 4C A 10 C 2B 10 3C 8B 11 B 11 A 11 C 2C 3A A 12 C Fi NS 2. 700.000 B. 300 B.000 C. $40. 5. Chapter 2.000 B. Use your answers to find the path through the maze. 3.000 B. 600 5.346 A. 3. 600 C. $6. Lesson 13.00 11. 800.000 C.00 C. 400 B. 900.000 2.422 A.971 Ϫ 2. (66) 12 B ni sh 10 B 8C 7C 7A 9C . 3. 30. 69.00 C.92 A. Lesson 14. (67) MR 1. Chapter 2. Burgers-to-Go Ruby’s Healthy Diner 2–14 Part A WORKSHEET Decision Making Print This Page Carnival Lunch Menu © McGraw-Hill School Division Your Decision Where do you think The Outdoor Club should eat? Explain.1.Print This Page Name Problem Solving: Application Applying Addition and Subtraction Record your data. NS 3. Use with Grade 4.1 . pages 74–75. MR 1. Lesson 14.1.2. Material used as blocker 2–14 Part B WORKSHEET Math & Science Print This Page 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 Magnet with paper © McGraw-Hill School Division Magnet with foil Magnet with tape Use with Grade 4. pages 76–77.1 . (68) NS 1. Chapter 2.1.Print This Page Name Problem Solving: Application Which materials block a magnet? Record your data. 3. 3. What are some other materials that you think would be good blockers? Explain. (69) NS 1. MR 1. Explain the results of your activity in terms of shielding.1. 3. Chapter 2.Print This Page Name Problem Solving: Application Which materials block a magnet? 1. Put the three materials in order from best blocker to worst. pages 76–77.1 .1. What are some other materials that you think would be bad blockers? Explain. 3. What is the difference between the number of paper clips a magnet 2–14 Part B WORKSHEET Math & Science Print This Page can hold with no blocker and the number of paper clips a magnet can hold with each of the different blockers you used? 2. Lesson 14. 3. © McGraw-Hill School Division 5.2. Use with Grade 4. 4. pages 92–95. Ben swims underwater for 30 at the dentist. minutes. 2. Write seconds. 120 minutes = 1 10. You are in school for about 6 6. .Print This Page Name Tell Time Write the time in two ways. 2.3 . © McGraw-Hill School Division hours 9. Chapter 3. Jerry walks to the store in 15 7. 15 minutes = 13. Print This 3–1 Page P PRACTICE 9 48 Choose the most reasonable units of time. seconds = 3 minutes hour minutes 11. . Minutes Seconds 1 60 2 120 3 4 5 Use with Grade 4. or hours. Debbie spends 20 5. minutes = 2 1 2 hours 1 minutes = 1 4 hours Algebra & Functions Describe and complete the conversion patterns. 3. (70) MR 1. Lesson 1. Tell how much time. 2 hour = 12. 1. 4. Minutes Hours 60 1 120 2 180 240 300 15. .1. 8. 14. 5.3 . pages 92–95. (71) MR 1. 1.Print This Page Name Tell Time You can read time in different ways. Print This 3–1 Page R RETEACH 5 40 Read: five-forty Read: forty minutes after five Write: 5:40 Write the time in as many different ways as you can. 2. 3. Read: twenty minutes before six or twenty minutes to six 4.1. 4 15 3 20 2 50 © McGraw-Hill School Division 7. 9. 6. 8. Lesson 1. Chapter 3. 2. Use with Grade 4. 1. Use with Grade 4. 5 :45 Time: 5 :30 Pattern: Decrease by 11 12 1 2 10 3 9 4 8 7 6 5 5 :15 hour. (72) MR 1.3 . 2.Print This Page Name Tell Time Patterns in Time The times shown on the clocks are in a pattern. 11 12 1 2 10 3 9 4 8 7 6 5 Time: 4. 11 12 1 2 10 3 9 4 8 7 6 5 Time: Pattern: Increase by hour. 11 12 1 2 10 3 9 4 8 7 6 5 3. Pattern: Increase by hour. Pattern: Increase by hour. Lesson 1. pages 92–95. 3 :10 Time: 3 :00 Pattern: Decrease by 11 12 1 2 10 3 9 4 8 7 6 5 2 :50 hour. 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 Print This 3–1 Page E ENRICH Time: 2. What time would the next clock show? What is the pattern? 1. 11 12 1 2 10 3 9 4 8 7 6 5 © McGraw-Hill School Division 5. Chapter 3. M. End: 2:20 P. End: 8:00 A. 7. 5:16 A. 12.M.M.M. Begin: 11:05 P. The Big Beach bus leaves the city at She gets to karate class 35 minutes later. 2. Lisa leaves her house at 8:45 A. Begin: 3:40 P. 4.M. 15. (73) MR 1. 2:45 P. What time will it be in 1 hour 20 minutes? 10.M.M.1. End: 1:00 A. 6. Begin: 2:25 A.M.M.M.M. Print This 3–2 Page P PRACTICE 3.M.M. 18.M.M.M. hours minutes before minutes after 7:00 P. 9.3 . End: 5:40 A. Lesson 2.M.M. 9:58 A. Chapter 3. Begin: 1:15 A. How long is the trip to the beach? Use with Grade 4.M. 8.M. is © McGraw-Hill School Division minutes after 5:00 A.M. End: 12:00 A. Begin: 12:00 P. 11.M. minutes before 3:00 P. Begin: 10:35 P. is 16. A. End: 1:55 A. End: 1:50 A. 2. End: 2:10 P. Begin: 5:45 A.M.M. 13. 7:22 P.M.M. Begin: 8:10 P.M. The bus arrives at the beach at 8:25 P. pages 96–97.M. Begin: 9:30 A. At what time does Lisa get to karate class? 6:40 P.M. is Problem Solving 17. 5.Print This Page Name Elapsed Time How much time has passed? 1. 8 50 Algebra & Functions Write the missing numbers. is 14. End: 12:15 P. Print This 3–2 Page R RETEACH Then count the number of minutes. Begin End 6. Follow these steps to find how much time has elapsed from 8:20 A. From 8:20 to 11:20 is 3 hours. Chapter 3. pages 96–97. Begin End 6 00 10 30 2 15 2 35 Use with Grade 4. to 11:35 A. (74) MR 1. First count the number of hours. 2. Lesson 2.1. From 11:20 to 11:35 is 15 minutes. How much time has passed? 1.Print This Page Name Elapsed Time Elapsed time is the amount of time that passes from the start to the end of an action. Begin End 3. Begin End 4. So. Begin End 12 15 © McGraw-Hill School Division 3 15 5.3 .M. 3 hours 15 minutes have passed. Begin End 2.M. How did you adjust for the time zones in your answers? Use with Grade 4.Print This Page Name Elapsed Time Flying Time Print This 3–2 Page E ENRICH Use the time zone map to answer each question. If a plane leaves Los Angeles at 8:00 A. Remember to include the time zone. ET 6:57 P. pages 96–97. The flight between Dallas and Miami takes 2 hours 41 minutes. CT 9:10 A.1. ET Arrive Dallas 5. for example.M. Show your answer in local time.M.M. The flight lasted for 5 hours 40 minutes. 7:00 A. At what time did it depart from Seattle? 4. (75) MR 1. Lesson 2. at what time will it arrive in New York City? 2. Pacific Time 11 12 1 2 10 3 9 4 8 7 6 5 Mountain Time 11 12 1 2 10 3 9 4 8 7 6 5 Central Time 11 12 1 2 10 3 9 4 8 7 6 5 Eastern Time 11 12 1 2 10 3 9 4 8 7 6 5 Seattle New York City Los Angeles Phoenix Atlanta Dallas Miami 1.3 . It takes about 5 hours to fly from Los Angeles to New York City. It takes 4 hours 30 minutes for a plane to fly from Atlanta to Phoenix. A plane flew from Seattle to Atlanta. Central Time. If a plane departs from Atlanta at 10:00 A.. CT Arrive Miami Depart Miami 2:30 P. CT 11:20 A..M.M. at what time will it arrive in Phoenix? 3.M.M. Complete the flight schedule below.M.M. Chapter 3.M. 2. ET 4:45 P. © McGraw-Hill School Division Depart Dallas 7:00 A. It arrived in Atlanta at 1:05 A. (76) MR 1. On which day of the week is Thursday in July? Independence Day? 3. Pat saw the dentist on July 25. For how many weeks will he visit? another appointment 10 days later. Lesson 3. What is the date of the fourth 2. Justin is moving to a new town on 6. Jason has a violin lesson every August 1. Nick will leave on August 30. how long is soccer camp? 5. 2. How many lessons will he have in July and August? 8. On which date will Cindy return? © McGraw-Hill School Division through the following Saturday. pages 98–99. On which date is Pat’s appointment? Use with Grade 4. The movers are coming 4 days before that. He has 7. Cindy will return from vacation on 4. Print This 3–3 Page P PRACTICE July 2000 S M T W T F S 1 2 9 16 23 30 3 10 17 24 31 4 Independence Day! August 2000 S M T 1 6 13 20 27 7 14 21 28 8 15 22 29 W 2 Nick arrives! T 3 10 17 24 31 F 4 11 18 25 S 5 12 19 26 5 12 19 26 6 13 20 27 7 14 21 28 8 15 22 29 9 16 23 30 11 18 25 Football practice begins! 1. On which date will the movers arrive? Wednesday.3 .1.Print This Page Name Calendar Use the calendars for July and August for exercises 1–8. Chapter 3. If soccer camp runs from July 7 the Monday after Nick arrives. Chapter 3. On which day of the week is Flag Day? 6.Print This Page Name Calendar You can use a calendar to find elapsed time.3 . How long is camp? © McGraw-Hill School Division 1 to June 5? 5. The last day of school is June 7. It is 6 days from May 8 to May 14. How many weeks are there from May June 30. On which date will he return? birthday is 5 days before that.1. Sports camp runs from June 19 through 4. How many days is it until Mother’s Day? Count on from May 8 to May 14. Tom’s Monday after Flag Day. 2. Which date is that? 7. Print This 3–3 Page R RETEACH May 2000 S M 1 7 14 Mother’s Day June 2000 F 5 12 19 26 S 6 13 20 27 4 11 18 Father’s Day T 2 9 16 23 30 W 3 10 17 24 31 T 4 11 18 25 S M T W T 1 F 2 9 16 23 30 S 3 10 17 24 31 8 15 22 29 5 12 19 26 6 13 20 27 7 14 Flag Day 8 15 22 29 21 28 21 28 25 Use the calendars above for exercises 1–8. Suppose today is May 8. (77) MR 1. pages 98–99. Memorial Day is celebrated on the last Monday in May. How long is it from Mother’s Day Father’s Day? to the following Sunday? 3. When is Tom’s birthday? Use with Grade 4. 1. Lesson 3. How long is it from Flag Day to 2. Dave will return from vacation on the 8. 2. On which date will basketball practice begin? Which is the latest date on which she can buy her sneakers? third Friday in December. Before she begins speed training. she must do endurance runs for 4 weeks. Which is the latest date on which they should start practicing? second Saturday in June.3 . They plan to spend four Saturdays practicing. Which is the latest date on which he should make his plane reservations? 3. To train. John plans to go on a skiing trip the on the first Monday in September. Which is the latest date on which she should begin training? Use with Grade 4. pages 98–99. Holly wants to run her best race the May 15. George's team has its first game on © McGraw-Hill School Division 4. Lesson 3. Jamie will start basketball practice 2. He wants to make the plane reservations 4 weeks before buying the ticket. she wants to do speed workouts for 5 weeks. She plans to buy sneakers at least two weeks before practice begins.1. Chapter 3.Print This Page Name Calendar Calendar Calculations Use the calendar to solve the problems. Then they will spend a week practicing every day after school. (78) MR 1. January February March April May Print This 3–3 Page E ENRICH 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 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 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. He must buy his ticket 14 days in advance of the flight. 2. pages 100–101. How many miles did the greatest number of students run? 3. How many more members ran 4 miles a day than ran 1 mile a day? 6. Chapter 3.Print This Page Name Line Plots 1.1 . What statement can you make about the data in your line plot? Use with Grade 4. How many members ran 6 miles a day? 4. Complete the tally table and line plot for the following data. Print This 3–4 Page P PRACTICE 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 1 2 3 4 5 6 1 2 3 4 5 6 Tally Total Number of Miles Run Each Day by Members of The Fleet-Footed Club Use the line plot to answer the questions. 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. Lesson 4. How many members are in the club? © McGraw-Hill School Division Use the data below to make a tally table and line plot on a separate sheet of paper. How many members ran 4 miles or more a day? 5. (79) SDP 1. ↓ ↓ X X X X X 8 3 words had 6 letters. less than 3 letters? 6. Lesson 4. Number of Letters in Words in a Story Number of Letters in Words 1 2 3 4 5 © McGraw-Hill School Division Tally Total Number of Words 2 Number of Letters in Words in a Story 2 words had 7 words had 1 letter. more than 3 letters? 2. How many letters did the greatest number of words have? Use with Grade 4. To compare the data. Example: For the first number. How many words had: 1. Chapter 3. pages 100–101. The data is shown below. ↓ X X X 6 X X 1 2 3 4 X X 5 6 7 8 Use the line plot. 8 letters? 5. In the line plot. make a tally mark in the table. 3 letters? 4. 2 letters? 7 8 3. you can make a line plot. (80) SDP 1.Print This Page Name Line Plots Marcia counted the number of letters in each word in a story. 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 Print This 3–4 Page R RETEACH 7 2 You can organize the data in a tally table. 5 letters. Cross out the 3 in the data above.1 . Complete the tally table and the line plot. 3. use an X to stand for each word in the story. Then record and cross out the remaining 3s. How many students were surveyed? 2.Print This Page Name Line Plots Mystery Plot Use the clues below to complete the line plot. pages 100–101. • 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 9 books a month is twice as many as the number of the students who read 6 books a month. Chapter 3. (81) SDP 1.1 . 1. 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. Lesson 4. © McGraw-Hill School Division • 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 10 books a month is half the number who read 7 books a month. Use the line plot to answer the questions. Print This 3–4 Page E ENRICH Number of Books Read in September by Students in Fourth Grade 5 6 7 8 9 10 Clues • There are 4 students who read 5 books a month and 3 times as many who read 7 books a month. median. Find the range. $9. 35. and mode Print This 3–5 Page P PRACTICE from the line plot. 20. 78. 17. 100. 4. 95. Range: Median: Mode: 2. 80. 1. 40. Use data from the line plot for exercises 1–3. 5. 30. pages 102–103. 30. 5 5. $13.1. 88 9. 8. 19. 8. 40 6. Lesson 5. 42. 23. 92. What does the mode tell you about Number of Aluminum Cans Collected in March X X X X X X X X X X this data? X X 3. 7. 35. $13 Use with Grade 4. 8. 9. 29. Chapter 3. 90. Median and Mode The third-grade class at Blue Hill School collects and recycles aluminum cans. 25. 85. $15. 35. 100. 6. 1. The line plot shows how many cans the students collected in March. (82) SDP 1. 21. 50 8.Print This Page Name Range.2 . 50. 60. $23. Data © McGraw-Hill School Division Order Data from Least to Greatest Range Median Mode 4. 25 7. 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 24 25 26 27 28 29 30 31 32 this data? Complete the table. 100. so the middle X is the 15th X. 83 – 0 = List in order from least to greatest: © McGraw-Hill School Division . and mode. . 3. 0.Print This Page Name Range. . Use the line plot to help you find the range. Lesson 5. median.1. 1. The 15th X in the line plot is above 10. 5. Data: 56. median. 34. . . (83) . SDP 1. . and mode. Then find the range. 88. . 91. 96. 1. . Print This 3–5 Page R RETEACH 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 Order the data from least to greatest. . Range: 96 – Median: Mode: = 3. Median and Mode You can analyze data using the range. 8 List in order from least to greatest: . . 56. so the median is 10. and mode. 4. median. Range: Median: Mode: 2. .2 . . Range: the difference between the greatest and least numbers Range: 25 Ϫ 5 ϭ 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. 96. 3. 92 List in order from least to greatest: Range: Median: Mode: Use with Grade 4. There are 29 Xs. Chapter 3. Data: 6. Mode: the number that occurs most often The greatest number of Xs is above 10. . Data: 83. so 10 is the mode. 72. . pages 102–103. 1. Use with Grade 4. Lesson 5. and mode of the group's scores. Lee's math class is divided into three groups. Use the data for each group to find the missing scores. median.1. Chapter 3. Explain how you found each missing test score.1.Print This Page Name Range. and Mode The Case of the Missing Math Tests Ms. Each group found the range. Group 3’s Test Scores Range Median 16 92 92 Sam Beth Students’ Scores for Group 3 Jamal 92 88 86 Sally Bill Rita 92 96 82 92 © McGraw-Hill School Division Mode Susan Mario 4. pages 102–103. Print This 3–5 Page E ENRICH Group 1’s Test Scores Range Median Mode 18 88 94 Students’ Scores for Group 1 Megan Stephanie Gregory Brian 80 92 84 86 Joe Chris Alison Nancy 90 76 94 2.2 . Group 2’s Test Scores Range Median Mode 18 91 94 Students’ Scores for Group 2 Jason Steven Melissa Serena 82 94 98 Ann Karen Leroy Carl 88 94 90 80 3. (84) SDP 1. Median. and arrives in Philadelphia at 1:43 P. A train from New York City arrives in Washington. 3. Noah Providence on May 6th. at Atlanta to Dallas. How long is the train trip? bought a ticket for a flight that leaves on September 20th. 2.M.3 .M. What was the round-trip fare the last time Marion flew? 5:45 A. Marion and her daughter fly from 4.1. This is $20 more than a ticket on Flight 20. Cross out any extra information. and arrives in Philadelphia at 8:00 A. 3.M. On Tuesday. The train arrives in Providence at 3:54 P. 3. D. and arrives in Philadelphia at 10:54 P. Kendra wants to fly from Atlanta to 6.. The fare for Marion’s daughter is the same.M.609. Chapter 3. This fare costs $50 more than the fare the last time Marion flew.M. 1.. How much more expensive is a round-trip coach ticket on Flight 98 than on Flight 54? Use with Grade 4. A round-trip coach ticket on Flight 98 from New York City to San Francisco costs $438. pages 104–105.3. The round-trip fare for Marion is $349. September 7.4.1. Flight 17 leaves Atlanta at 11:39 A. Then solve or tell what information you need to solve the problem. The ticket cost $329. A coach ticket on Flight 17 is $109.2. Flight 20 leaves Atlanta at 8:40 P. A round-trip coach ticket on Flight © McGraw-Hill School Division Philadelphia. A train leaves Washington. On what day of the week is Noah’s flight? 3. A round-trip first-class ticket on Flight 54 costs $1.M. Which flight is shorter? How much shorter is it? 54 from New York City to San Francisco costs $399. Fiona is taking a train from Boston to Print This 3–6 Page P PRACTICE Reading Skill 2. at 8:10 A.Print This Page Name Problem Solving: Reading for Math Identify Extra and Missing Information Circle the question that you need to answer.C. Which train ride takes more time? 5.M.M. (85) MR 1. Lesson 6. 2. D.C. .M. and arrives in Phoenix at 4:30 P. 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. Which extra information is not 4. the next day. G the time that Flight 81 arrives in Phoenix C Flight 62 is sold out. arrives in Phoenix at 3:45 P.3 . 2.Print This Page Name Problem Solving: Reading for Math Identify Extra and Missing Information Choose the correct answer.2. How long does the train ride take? 5. Which of the following statements 2. 3.1.M. 3. Chapter 3.M.. Lesson 6.M. The train arrives at the first stop at 5:21 P. the second stop at 5:46 P. (86) MR 1. 2.M. It arrives in Houston at 11:50 A.M. F the time that Flight 81 leaves Salt Lake City B Flight 62 arrives in Phoenix after Flight 81 does. J the time that Flight 62 arrives in Salt Lake City An express train leaves Grand Terminal at 5:05 P.1. Print This 3–6 Page P PRACTICE Math Skills Test Prep © McGraw-Hill School Division Flight 81 leaves Salt Lake City at 2:55 P. Flight 62 from Salt Lake City. which is sold out.M.M. 3. What important information is is false? missing? A Flight 81 takes less than 2 hours.3. 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. November 24.4.M. on Wednesday. H the time that Flight 62 leaves Salt D Flight 81 arrives in Phoenix before Lake City 5:00 P. Which extra information is not 6. pages 104–105.M. How long is the train ride? 3. and the last stop at 6:04 P. Which flight is faster? 1. A train leaves Rocky Mount. 3. A round-trip first-class ticket from St. 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 8.1. Samantha takes a train to New York It makes its first stop at 6:30 P.M. flight from Miami to Atlanta. C The nonstop flight takes less than 3 hours. at 2:45 P. What information do you still need is false? A Ty catches a 12:00 noon flight.M.M. flight from Miami arrives in Atlanta H the time the 7:25 A. 3. Louis to San Diego costs $1. Lesson 6. 9. (87) MR 1. to solve the problem? F the time the 12:00 noon flight from Atlanta arrives in Cincinnati G the time the 9:00 A.600.M. The Howards buy 3 tickets. pages 104–105. and its second stop at 6:55 P. The train arrives in New York at 7:59 A.M. and in Richmond.4. VA. 2. That flight leaves Atlanta at 12:00 noon. B Ty catches a 9:00 A. The train arrives in Petersburg. A round-trip coach ticket costs $359. VA.M.M. Then Ty takes a flight from Atlanta to Cincinnati.M. 3.M. at Solve.M. 12. D Ty’s trip to Cincinnati takes 3 hours. Print This 3–6 Page P PRACTICE Math Skills Test Prep Ty wants to take a nonstop flight that leaves Miami at 7:25 A. 2. flight. How much time does Samantha’s ride take? Use with Grade 4. She catches the train at 7:25 A..Print This Page Name Problem Solving: Reading for Math Identify Extra and Missing Information Choose the correct answer. flight from Miami arrives in Cincinnati J the time the 7:25 A. and arrives in Cincinnati at 9:55 A.3. at 3:22 P.M.M. How much do they spend? 1:16 P.1. Identify extra or missing information in each problem. How long is the trip from Rocky Mount to Richmond? © McGraw-Hill School Division 11.M.M. but the flight is sold out.M. he takes a 9:00 A. Instead.M.3 . flight from Miami arrives in Atlanta 10. The train stops in Newark at 7:41 A. When will the bus arrive at its third stop? City. Chapter 3.2. NC. A bus leaves the terminal at 6:10 P. Share it with others. Lesson 7. She spends 45 minutes at the mall.10.1. $2.75 on a snack. Nick spent $21. Strategy: Use with Grade 4. Mr.50 on a theater ticket 4. 1. It takes Sandy 35 minutes to walk for a movie that starts at 7:45 P. How much money did Nick start with? on tolls. When should Bill leave home? from school to the mall.1.M. How much money did she start with? Mixed Strategy Review Solve.3 . Barry makes letters for a sign that 6.4. Chapter 3. He spends reads “Free Field Trip Sign-Up Sheet.50 on a meal. When did she leave school? 3.2. 5. About how many calories would you burn if you walked 2 miles? solved by working backward. Sandy leaves the mall at 4:20 P. Health Walking a mile burns about 8. He has $14. Carlson has $424. How much money does Mr. 3.Print This Page Name Problem Solving: Strategy Work Backward Work backward to solve. Carlson have left? Strategy: Strategy: © McGraw-Hill School Division 7.3. 3. pages 108–109.” Which letter does Mark need to make the most of? $29 on gasoline. It will take him about 20 minutes to walk to the theater. Sally spends $16.25 left. 2.M. Use any strategy. 3.50 on gas. (88) MR 1. Create a problem which can be 110 calories. 2. She has $32.25 and $12. and $2. Bill wants to arrive 15 minutes early Print This 3–7 Page P PRACTICE 2. Start at the time of the show. Use with Grade 4.4. What is the latest time she can order? Step 1 Read Be sure you understand the problem.Print This Page Name Problem Solving: Strategy Work Backward Page 109. Then work backward to find the time that Mindy needs to order. minutes to order and . Problem 1 Print This 3–7 Page R RETEACH Mindy wants to eat before the 7:40 P. 3. (89) MR 1. pages 108–109.3 . She needs about 45 minutes to order and eat her dinner. 2. What do you know? • Mindy needs about eat her dinner. • She wants to eat before What do you need to find? • You need to find the latest time that Mindy .1. 3. 3.1. 2. Choose a strategy. Lesson 7.M. Read carefully. Step 2 Plan I Make a plan.2. Chapter 3. I I I © McGraw-Hill School Division I I I I I I 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 You can work backward to solve the problem. show.3. 2. Paul plays basketball for 30 minutes and Frisbee for 15 minutes. Step 4 Look Back Is the solution reasonable? Reread the problem. Move backward 45 minutes. Then he walks home. Before she can watch TV.3 .M. pages 108–109.? What other strategies could you use to solve the problem? © McGraw-Hill School Division Practice 1.3.M. 3. Move forward 45 minutes.M. • She wants to finish eating by Start at 7:40 P. Lesson 7.4.The walk takes 20 minutes. Laurel wants to watch a show that begins at 8:30 A.M. If Paul gets home at 2:30 P. Chapter 3.. Work forward to check your answer. (90) MR 1.Print This Page Name Problem Solving: Strategy Work Backward Step 3 Print This 3–7 Page R RETEACH Solve Carry out your plan. At what time does Laurel have to start practicing? 2.2. The latest time that Mindy can order is . she has to practice piano for 1 hour 15 minutes. • Mindy needs about eat her dinner. 3. Did you end at 7:40 P. 3.M. minutes to order and .1. at what time did he start playing basketball? Use with Grade 4. Start with your answer. 2. Think: Mindy wants to finish eating by 7:40 P. She needs to order 45 minutes before that time.1. pages 110–111. How many students took part in the survey? Use with Grade 4. (91) SDP 1.Print This Page Name Explore Pictographs 1. 2.1. Chapter 3. Then use the table to complete the pictograph. © McGraw-Hill School Division Use the table to make a pictograph on a separate piece of paper. What key would you use if 80 people were surveyed? Explain. Complete the table. Which item do people like the most? 3.3 . Then answer each question. How many more people like their computers than their televisions? 4. 6. Print This 3–8 Page P PRACTICE Which Modern Invention Do You Like the Most? Invention Computer CD Player Car Television Tally Total Which Modern Invention Do You Like the Most? Computer CD Player Car Television Key: Each stands for people Use the pictograph for exercises 2–5. Lesson 8. How many people were surveyed? 5. 1. Favorite Lunches Lunch Pizza Hamburgers Spaghetti Chicken Tally 7. How many more students like pizza more than spaghetti? 8. So.3 Fruit Apples Pears Oranges Plums Tally Apples Pears Use with Grade 4.Print This Page Name Explore Pictographs Evan and Jenny surveyed students to find out whether their favorite color is red. pages 110–111. 1. Favorite Colors Red Blue Yellow Here is how to make a pictograph of the data.1. half of a picture will represent 1 student. You can use 1 picture to represent 2 students. blue. Answer the questions to help you. Step 1: Write a title. stands for 1 student. How many people chose apples? How many faces will you draw? How many faces will you draw? Favorite Fruit © McGraw-Hill School Division Favorite Fruit Total 9 5 10 4 Oranges Plums Key: Each Key: Each stands for 2 people. stands for 1 person. (92) . Step 2: Choose a picture to show the data. This is the data they collected. How many people chose oranges? 2. SDP 1. Red Blue Yellow Key: Each Print This 3–8 Page R RETEACH 10 11 6 Favorite Colors stands for 2 students. Use the picture to make a key. List the categories. Lesson 1. or yellow. Chapter 3. Step 3: Use the key to draw pictures to show Key: Each the data for each category. Use the data in the table to complete the pictograph. 1. Print This 3–8 Page E ENRICH © McGraw-Hill School Division Clues • Sarah has 5 fewer stamps from other countries than stamps of famous people. she would have an amount equal to the number of bird stamps. 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 Key: Each stands for 2 stamps. Chapter 3. pages 110–111. • If Sarah had 6 more flower stamps. • Sarah has 1 more than twice as many bird stamps as stamps of famous events.1. • Sarah has 3 more stamps of famous landmarks than stamps from other countries. (93) SDP 1. • Sarah has twice as many stamps of famous events as stamps from other countries. Would you use 1 stamp to stand for 8 stamps in the key? Why or why not? Use with Grade 4.3 .Print This Page Name Explore Pictographs Stamp Collecting Use the clues below to complete the pictograph. 1. Lesson 8. 1. Chapter 3. How many teenagers chose rock and roll? 2. 1.3 . Lesson 9. Which type of music was chosen about the same number of times by adults and teenagers? 3. Then use it to complete the bar graph and answer exercises 1–4. Which type of music do adults like the most? 4. (94) SDP 1. Did more adults or teenagers choose jazz as their favorite music? Use with Grade 4. Favorite Types of Music Adults Type of Music Country Classical Jazz Rap Rock and roll Favorite Types of Music Print This 3–9 Page P PRACTICE Teenagers Total Tally Marks Total Tally Marks 16 Number of People 14 12 10 8 6 4 2 0 Country © McGraw-Hill School Division Classical Adults Jazz Rap Teenagers Rock and Roll 1. pages 112–115.Print This Page Name Bar Graphs Complete the table below. Remember to include different headings for both sets of data. A single-bar graph presents one set of data. Lesson 9. A double-bar graph presents two sets of data. Chapter 3. How many more boys than © McGraw-Hill School Division 4. 1. 1. and select a scale just as you would for a single-bar graph.Print This Page Name Bar Graphs You can use single-bar graphs or double-bar graphs to show data. Hawaii. Did more people choose France. or Greece as their favorite vacation spot? 20 18 16 14 12 10 8 6 4 2 0 Hawaii Favorite Vacation Spots Greece Florida France Australia 3. When you create a double-bar graph. What is the favorite vacation spot? How many people chose it? Number of People 2.3 . you need to make a key to represent each set of data. Print This 3–9 Page R RETEACH Use the graphs to answer the questions. Which vacation spot shows the greatest difference between boys and girls? Number of People girls chose Hawaii as their favorite vacation spot? 10 9 8 7 6 5 4 3 2 1 0 Hawaii Favorite Vacation Spots Greece Boys Florida France Girls Australia Use with Grade 4. (95) SDP 1. Write a title. pages 112–115.1. headings for the vertical and horizontal sides. Is the graph misleading? Explain. The bar for Auto World is twice as Print This 3–9 Page E ENRICH high as the bar for Bayside Auto Plaza. Feb. What is the actual difference in the earnings of the two stores? 3.Print This Page Name Bar Graphs Misleading Graphs The bar graph shows the earnings of Bayside Auto Plaza and Auto World. Chapter 3.000 $120.3 © McGraw-Hill School Division Jan. Dec.000 Bayside Auto Plaza Auto World Number of Cars Sold Number of Cars Sold A car salesperson made Graphs A and B to show the number of cars she sold in one year. Which graph do you think the salesperson showed her boss? Tell why.1. pages 112–115. .000 $130.000 150.– Dec. Use with Grade 4.– March April– June 0 Oct. Oct. SDP 1. Does this mean that Auto World earns twice as much as Bayside Auto Plaza? Earnings of Car Sales $150.000 $140. 1. Lesson 9. Sept. (96) July– Sept. March April May June July Aug. Do both bar graphs show the same data? Months 5.000 2. Nov. 1. Month 4. Car Sales—Graph A Car Sales—Graph B 100 50 80 40 30 20 10 0 60 40 20 Jan. 0 130. (3. jail 11. © McGraw-Hill School Division 14.2. mall 2. What ordered pair names this location? between the city hall and the court house. library 3. 8) 19. video arcade Print This 3–10 Page P PRACTICE Name the place at each location. 10. 2. 9) 9. 2) 16.Print This Page Name Coordinate Graphing Give the ordered pair for each place on the grid. 1. A parking garage is being built 3 blocks down from the pet store. (4. Chapter 3. 2. What ordered pair names the garage’s location? Use with Grade 4. (1. Lesson 10. A drive-in diner is being built 15. (7. (9. movie theater 12. 11) 17. park 4. police station 13. 5) 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 7. (97) MG 2. (8. 1) 8. (4. grocery store 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 Name the place at each location. (8.3 . 6. pages 116–117. 9) 18. 8) Give the ordered pair for each place on the grid. school 5.1. 8) MG 2. Lesson 10. then up 3. The ordered pair is (8. (5. Go up 1.3 . Where is the Space Ride located? Start at 0. 2). the first number tells you how far to go to the right. (4. (2. 2. Chapter 3. The second number tells you how far to go up. Go right 4. © McGraw-Hill School Division 4. 4) Use with Grade 4. Go right 6. 1) ← ordered pair Which ride do you find? 0 0 1 2 3 4 5 6 7 10 9 8 7 6 5 4 3 2 1 Log Ride Swings Tidal Force Sky Ride Print This 3–10 Page R RETEACH Ferris Wheel Carousel Paddle Boats Roller Coaster Shells Space Ride Scrambler Tea Cups 8 9 10 Complete. 2. Use the grid above. 8) 7. 4).2. then up 8. 5. (5. (8. 6) 10. Use the grid above to tell which is at each location. You can write the location of the Space Ride as the ordered pair (1. Start at 0. and then go up 2. pages 116–117. Go right 8. Start at 0. 3) 8. Try this. What is here? ). then up 7. In an ordered pair. then up 4. 3. Go right 2. The ordered pair is What is here? . The ordered pair is What is here? . Start at 0. (1. Go right 5. (98) 6. 1. 2. 6) 9. (6. The ordered pair is ( What is here? . Start at 0. Go right 1.1.Print This Page Name Coordinate Graphing The grid shows the location of rides at an amusement park. 9) 20 19 18 17 16 15 14 13 12 11 10 9 8 © McGraw-Hill School Division 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 MG 2. 13) 16. 10) 11. (3. (0. 0) 7. 17) 13. (3.1. 7) 6.Print This Page Name Coordinate Graphing Find the Hidden Picture Locate each ordered pair on the grid below. 2.2. (99) . (11. (9. (17. 20) 15. 1.3 Use with Grade 4. (10. (11. (20. Chapter 3. 7) 8. (7. Label it with the exercise number. (9. 2. 13) 14. pages 116–117. 10) Print This 3–10 Page E ENRICH 4. (13. Lesson 10. 3) 5. 11) 3. (10. 9) 10. 17) 2. (17. 3) 9. Then connect the dots in order. (13. 11) 12. (7. 600 $1. Toy Sales at Toy City Month July August September October November December Amount $1. pages 118–119.500 $2.400 $1. What is the difference in sales 6. In which two months were sales the same? dollar amount of toys sold at Toy City? © McGraw-Hill School Division 3. 1. Chapter 3.600 $2.1. Dec.700 $3. (100) SDP 1. Oct.200 $2.000 0 Print This 3–11 Page P PRACTICE Toys Sold at Toy City July Aug.000 $1.200 Amount $3.800 $2.600 worth of toys? between the highest and lowest points on the graph Use with Grade 4. During which month did sales 4.800 $1. During which month did sales increase the most? decrease? 5. Month Use the line graph to answer the questions.200 $1. Sept.1. Nov.Print This Page Name Explore Line Graphs Use the table to complete the line graph.000 $2. Lesson 11. In how many months did Toy City sell more than $1.400 $2.700 $1.000 $1.200 $3.700 $2. In which month was the greatest 2.3 . How many more ice-cream cones 4. You can also show this information in a line graph. How many ice-cream cones were number of ice-cream cones sold? sold in July? 3. Sept. Show the data from the table in the line graph. 1. The table below shows the number of ice-cream cones sold over a year at the Ice-Cream Cottage. 1. Nov. Between which two months did the were sold in July than in December? greatest decrease in sales take place? Use with Grade 4. 650 cones were sold. pages 118–119.1. Dec.3 . Print This 3–11 Page R RETEACH Ice-Cream Cones Sold Month July August September October November December Number 800 900 700 650 350 100 Number of Cones Sold Ice-Cream Cone Sales 900 800 700 600 500 400 300 200 100 0 July Aug. • In October. © McGraw-Hill School Division Use the line graph to answer the questions. Draw a dot across from 650 on the graph’s scale (650 is half way between 600 and 700). In which month was the greatest 2. Oct. Month • Draw a dot for each of the other month’s number of sales. Lesson 11. (101) SDP 1.Print This Page Name Explore Line Graphs A line graph shows change over a period of time. Chapter 3. Chapter 3.Print This Page Name Explore Line Graphs Population Trends Use the clues to complete the line graph.3 .400 1.300 1.600 1.900 1.100 0 Print This 3–11 Page E ENRICH Number of People 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Year Write the years during which each event most likely happened.200 2.200 1. • There were 1. Lesson 11.100 2.700 1. the population began growing again. People moved to Foxwood for jobs. 1. • The number of people decreased by 200 in 1970 and 100 in 1980. The town's toy factory closed.000 1.600 people living in Foxwood in 1960. • The population in 1990 was 200 more than in 1980.1. (102) Years between between between and and and SDP 1. © McGraw-Hill School Division Event For the first time in 30 years. Many people lost their jobs. A computer factory opened. • The population was the same in 1940 as it was in 1930. pages 118–119. Use with Grade 4. • In 1950.800 1. Population Changes in Foxwood 2. the number of people increased by 200.500 1. Clues • Foxwood had 200 more people in 1930 than it did in 1920. 1.1 . 2. 2. 2. Chapter 3. 3.3. Use with Grade 4. Activity Starting Time of Activity 3–12 Part A WORKSHEET Decision Making Print This Page Ending Time of Activity Your Decision © McGraw-Hill School Division Which activities did you choose for the Sequoia Nature Club? Explain your choices. Make a schedule. (103) MR 1. Lesson 12.6.Print This Page Name Problem Solving: Application Applying Time and Data Show how the Sequoia Nature Club can spend its time.4. pages 120–121. pages 122–123. Lesson 12. 1.Print This Page Name Problem Solving: Application Does practice make perfect? Record your data.1. Use with Grade 4. 3.2. Describe what happened to the time you needed as you repeated the puzzle over and over. Attempt 1 2 3 4 5 6 7 8 9 10 3–12 Part B WORKSHEET Math & Science Print This Page Time Needed to Complete the Puzzle © McGraw-Hill School Division 1.3. (104) NS 1. MR 2. Chapter 3.2 .3. SDP 1. 3. Explain how you used your short.2. What happened to the line on the graph after you mastered the puzzle? © McGraw-Hill School Division 5. Chapter 3. How many times did you have to work the puzzle until you 3–12 Part B WORKSHEET Math & Science Print This Page mastered it? 3.Print This Page Name Problem Solving: Application Does practice make perfect? 2.and long-term memory to learn the puzzle. Use with Grade 4. Make a line graph. Lesson 12.2 .1. 1. What happened to your time after you mastered the puzzle? 4. 3. pages 122–123. (105) NS 1.3. comparing puzzle number and time. MR 2. SDP 1. 9 ϫ 3 ϭ Algebra & Functions Find the missing number. 6 ϫ8 16. Find each product. 9 ϫ 8 ϭ 24. 2 ϫ (n ϫ 5) ϭ 30 31. (106) AF 1. 7 ϫ5 11. How many pennies does Sheila have? Use with Grade 4.Print This Page Name The Meaning of Multiplication Write a multiplication sentence for each model. 3 ϫ 3 ϭ 25. How many hours does he practice in 7 days? rows with 6 pennies in each row. 8 ϫ 6 ϭ 18. 7 ϫ7 7. 3 ϫ 6 ϭ 19. 9 ϫ 6 ϭ 23. 3 ϫ5 8. 6 ϫ 7 ϭ 26. 8 ϫ7 13. Print This 4–1 Page P PRACTICE 3. © McGraw-Hill School Division 29. pages 138–139. 6 ϫ6 6. 8 ϫ 8 ϭ 21.1 . 1 ϫ 9 ϭ 20. Chapter 4. 2 ϫ 6 ϭ 22. (3 ϫ r) ϫ 8 ϭ 72 Problem Solving 33. 5. 2. 7 ϫ3 9. 4 ϫ8 17. (2 ϫ v) ϫ 6 ϭ 48 30. Jason practices his violin 2 hours 34. 5 ϫ8 12. 9 ϫ5 15. 4. 1. Sheila arranges her pennies in 9 every day. Lesson 1. 6 ϫ0 10. (j ϫ 7) ϫ 4 ϭ 56 32. 2 ϫ 3 ϭ 27. 4 ϫ6 14. 6 ϫ 9 ϭ 28. pages 138–139. Chapter 4. Find each product. 5 ϫ 5 ϭ 17. 8 ϫ 3 ϭ 12. Lesson 1. © McGraw-Hill School Division 4.Print This Page Name The Meaning of Multiplication The numbers you multiply are the factors. 5 ϫ 9 ϭ 13. 6 ϫ 2 ϭ Use with Grade 4. 2 ϫ 5 ϭ 14. First factor: number of rows Second factor: number in each row 5 6 Print This 4–1 Page R RETEACH 6 ←factor 6 ϩ 6 ϩ 6 ϩ 6 ϩ 6 ϭ 30 You can write 5 ϫ 6 ϭ 30 or ϫ 5 ←factor ↑ ↑ ↑ 30 ←product factor factor product Complete the table. 9 ϫ 3 ϭ 16. 3 ϫ5 9. 4 ϫ3 5. 5 ϫ0 8. 6 ϫ4 7. 3.1 . 6 ϫ5 10. Number of Rows 1. Number in Number Multiplication Each Row in All Sentence 2. (107) AF 1. 4 ϫ 7 ϭ 11. 5 ϫ 3 ϭ 15. The answer is the product. 7 ϫ3 6. Print This 4–1 Page E ENRICH List the numbers you count. The factors of 6 are 1. Then list the factors. Count the number of squares in each column and row. 1. Chapter 4. draw as many rectangles as you can that contain 6 squares. Products. 24 © McGraw-Hill School Division Use with Grade 4.Print This Page Name The Meaning of Multiplication Factors. (108) AF 1. and 6. Lesson 1. 18 4. Those are the factors. and Rectangles To show all the facts with a product of 6. 3. 6ϫ1ϭ6 1ϫ6ϭ6 3ϫ2ϭ6 2ϫ3ϭ6 Draw as many rectangles as you can to show different facts for each product. 20 2. 2. pages 138–139.1 . 12 3. Tanya has 9 pencils in each package. Then use the Commutative Property to write a different multiplication sentence. 5 ϫ 2 ϭ Print This 4–2 Page P PRACTICE 4. 3 ϫ 9 ϭ 11. Chapter 4.Print This Page Name Properties of Multiplication Find the product. 7 22. 7 ϫ 4 ϭ 10. 9 ϫ 4 ϭ 5. 2 ϫ 3 ϭ 9.1 . 8 ϫ 7 ϭ 3. 8 26. 4 ϫ 5 ϭ Write ϩ or ϫ to make a true sentence. pages 140–141. (109) AF 1. 9 ϫ 8 ϭ 2. 29. MR 1. 9 23. 4 25. 9 24. 5 ϫ 8 ϭ 13. 9 ϫ 7 ϭ 12. 6 ϫ 9 ϭ 8. 9 ϫ 2 ϭ 7. 6 19. 9 © McGraw-Hill School Division 6 ϭ 36 7 ϭ 14 3ϭ9 2ϭ6 3 3 17. Lesson 2. 3 21. 5 ϫ 0 ϭ 14. How many seedlings does Joe plant? She has 6 packages. 6 27. 1 ϫ 8 ϭ 15. 1.1. 16. 6 1ϭ9 0ϭ9 7ϭ5 7ϭ9 3 4 18. 4 9 ϭ 27 9 ϭ 81 4 ϭ 12 4ϭ8 2 8 Problem Solving 28. 8 20. 3 ϫ 4 ϭ 6. How many pencils does Tanya have in all? Use with Grade 4. Joe plants pine seedlings in 7 rows. He puts 6 seedlings in each row. Chapter 4. 7.1. Then use the Commutative Property to write another sentence. 5 ϫ 1 ϭ 10. Print This 4–2 Page R RETEACH 4ϫ2ϭ8 Identity Property The product of 1 and any number is that number. 5 ϫ 7 ϭ 3. pages 140–141. 1 ϫ 9 ϭ Use with Grade 4. Lesson 2. 1 ϫ 4 ϭ 6ϫ 6. 1 ϫ 8 ϭ 8. MR 1. 3ϫ1ϭ3 Think: 4 rows of 0 counters. (110) AF 1. 2 ϫ 8 ϭ Multiply. 1. 6 ϫ 0 ϭ 11. 3 ϫ 9 ϭ 2. 0 ϫ 5 ϭ ϭ 4. 0 ϫ 7 ϭ 9. 4ϫ0ϭ0 1ϫ6ϭ6 Think: 0 rows of 7 counters. 4 ϫ 6 ϭ 9ϫ © McGraw-Hill School Division ϭ 27 ϫ5ϭ 5. Tell which property you used. 2ϫ4ϭ8 Zero Property The product of any number and zero is zero.1 . 0ϫ7ϭ0 Find each product. 0 ϫ 4 ϭ 12.Print This Page Name Properties of Multiplication Commutative Property The order of the factors does not change the answer. Print This Page Name Properties of Multiplication Crack the Code! What number does each symbol in the table below stand for? Use the Commutative. ϫ9ϭ0 5ϫ ϭ0 4. ϩ ϩ ϭ0ϩ5 ϭ 10 8. Write the number next to the symbol in the code key. Lesson 2. Chapter 4. 6 ϫ ϭ2ϫ6 ϭ 10 7ϩ 5ϫ 3.1 . (111) AF 1. ϫ ϫ ϭ8 ϭ © McGraw-Hill School Division 7.1. what other multiplication fact do you know? Use with Grade 4. If you know that ϫ ϭ . MR 1. Identity. 6 ϫ ϭ ϭ 6ϩ 5. ϩ ϩ ϭ4 ϭ6 9. 6 ϫ ϭ6 ϭ8 2. 9 ϫ ϭ ϫ ϭ9 6. ϭ ϭ ϭ ϭ Print This 4–2 Page E ENRICH ϭ ϭ ϭ ϭ ϭ ϭ 1. pages 140–141. and Zero properties of multiplication to help you find out. Four parents are needed on each of 8 cars in each row. 3. pages 142–145. Algebra & Functions Find the answer.1 . 9 ϫ 4 ϭ 17. 3 ϫ 3 ϭ 10. 33. If ᭪ ϭ 3. 2 ϫ 4 ϭ 19. How many cars are parked? 9 committees. 4. 31. 8 ϫ 3 ϭ 20. 4 ϫ3 4 ϫ4 4 ϫ6 5 ϫ6 2 ϫ3 6 ϫ8 21. Chapter 4. 5 ϫ 4 ϭ 12. 2 ϫ2 2 ϫ0 2 ϫ5 3 ϫ6 7 ϫ6 6 ϫ6 4 ϫ8 6 ϫ2 3 ϫ9 24. 35. then how much is ‫?ف ف ف ف ف‬ Problem Solving 40. then how much is ᭝ 39. 29. 32. 8 ϫ 2 ϭ 9. 27. 34. If ‫ ف‬ϭ 4. 9 ϫ 6 ϭ 11.Print This Page Name Multiply by 2. 5. 5 ϫ 3 ϭ 14. 7 ϫ 4 ϭ 7. How many parents are needed? Use with Grade 4. 6 ϫ 4 ϭ 16. 5 ϫ 2 ϭ 15. 30. Cars are parked in 2 rows. 26. 9 ϫ6 1 ϫ6 4 ϫ7 25. 2. and 6 Write the multiplication sentence. 1 ϫ 6 ϭ 8. 36. Print This 4–3 Page P PRACTICE Multiply. 1. (112) NS 4. 37. There are 41. If ᭝ ϭ 6. 6 ϫ 3 ϭ 18. Lesson 3. 6. 4 ϫ 2 ϭ 22. 3. 28. 4. then how much is ᭪ © McGraw-Hill School Division ᭪ ᭝ ᭪ ᭝ ᭪? ᭝ ᭝? 38. 6 ϫ 7 ϭ 23. 0 ϫ 6 ϭ 13. 2 4 6 8 10 12 14 16 ᭺᭺ ᭺᭺ ᭺᭺ ᭺᭺ ᭺᭺ ᭺᭺ ᭺᭺ ᭺᭺ 2 ϫ 8 ϭ 16 Find 7 ϫ 3. 21 ᭺᭺᭺ These are multiples of 3. Find 2 ϫ 8. Double a fact to multiply by 6. Double a fact to multiply by 4. You can double a fact you know to multiply by 4 and 6. 7 ϫ 6 ϭ (7 ϫ ) ϩ (7 ϫ ϩ 12.Print This Page Name Multiply by 2. 9 ϫ 3 ϭ 4. 1. 6 ϫ 3 ϭ © McGraw-Hill School Division 2. pages 142–145. 9 ϫ 2 ϭ 8. Use the models above to help you. Think: Skip count by 2s eight times. 6 ϫ 2 ϭ 6. 3 ϫ 7 ϭ Double a fact to find the answer. 3.1 . 6 ϫ 8 ϭ (3 ϫ 8) ϩ (3 ϫ )ϭ ϭ )ϭ ϭ 10. Chapter 4. 3 6 9 12 15 18 ᭺᭺᭺ ᭺᭺᭺ ᭺᭺᭺ ᭺᭺᭺ ᭺᭺᭺ ᭺᭺᭺ 7 ϫ 3 ϭ 21 Print This 4–3 Page R RETEACH These are multiples of 2. and 6 You can skip count to multiply by 2 and 3. 3 ϫ 8 ϭ 3. 4 ϫ 5 ϭ (2 ϫ 5) ϩ (2 ϫ 5) ↓ ↓ 10 ϩ 10 ϭ 20 ••••• ••••• ••••• ϭ ••••• ••••• ϩ ••••• ••••• ••••• 6 ϫ 5 ϭ (3 ϫ 5) ϩ (3 ϫ 5) ↓ ↓ 15 ϩ 15 ϭ 30 ••••• ••••• ••••• ••••• ••••• ϭ ••••• ••••• ϩ ••••• ••••• ••••• ••••• ••••• Skip count to find the answer. 2 ϫ 7 ϭ 5. 4. 2 ϫ 8 ϭ 7. You can use counters to help you. Think: Skip count by 3s seven times. (113) NS 4. Lesson 3. 4 ϫ 7 ϭ (2 ϫ ) ϩ (2 ϫ ϩ )ϭ ϭ )ϭ ϭ ϩ 11. 9. 8 ϫ 4 ϭ (8 ϫ ) ϩ (8 ϫ ϩ Use with Grade 4. pages 142–145. 3 18 8 3 12 12 6. 2 8 6 7 8 24 42 9. (114) NS 4. 21 4 2 3 8 9 5 18 13. Complete the triangles. 3. 14 6 6 36 14. Explain how you found the answer to the triangle in exercise 3. 3 6 6 6 3 9 7. 2. 4. The number on the bottom right is the product of the middle right and the top number.1 . Use with Grade 4. Chapter 4. 24 12. 18 2 32 3 6 7 5 7 4 8 16 11. 30 10. 4. 3. 5 5 20 16. Lesson 3. 4. The top number must be a 2. 9 36 10 48 4 15 6 3 2 9 2 4 1 3 4 4 16 7 4 24 3 6 12 28 54 17. or 6. the number on the bottom left is the product of the middle left and the top number.Print This Page Name Multiply by 2. 3. 4 1 6 8. and 6 Triangle Math In each triangle. © McGraw-Hill School Division 9 27 15. 1. Print This 4–3 Page E ENRICH 2 1 2 5. 49. 40. 38. 5 ϫ3 5 ϫ5 5 ϫ0 6 ϫ5 10 ϫ 8 10 ϫ 6 10 ϫ 0 9 ϫ5 29. 40 Problem Solving 53. 2 ϫ 10 ϭ 22. 5 ϫ 8 ϭ 6. 5 ϫ 4 ϭ 5. 45. 30 51. 1 ϫ 5 ϭ 8. 36. (115) NS 3. 35 52. 4 ϫ 5 ϭ 18. © McGraw-Hill School Division Tell whether the number is a multiple of 2. 18 50. Gene has 5 boxes of crayons with 54. 33. 37. 2 ϫ 5 ϭ 17. 0 ϫ 5 ϭ 9. 9 ϫ 5 ϭ 19. 6 ϫ 5 ϭ 14. 35. 48. 10 ϫ 5 5 ϫ4 5 ϫ7 3 ϫ5 31.2 . pages 146–147. 5. Jan places 5 rows of 8 stars in a 10 crayons in each box. 10 ϫ 6 ϭ 25. 44. How many stars does she use? Use with Grade 4. 32. 1. 6 ϫ 10 ϭ 7. 42. Lesson 4. 8 ϫ 10 ϭ 20. or 10. 34. 9 ϫ 10 ϭ 21. 3 ϫ 5 ϭ 13. 46. 41. 4 ϫ 10 ϭ 12.Print This Page Name Multiply by 5 and 10 Multiply. 5 ϫ 5 ϭ 24. 7 ϫ 10 ϭ 5 ϫ6 10 ϫ 9 10 ϫ 7 10 ϫ 1 26. 0 ϫ 10 ϭ 3. 47. 5 ϫ 10 ϭ 15. 5 ϫ2 10 ϫ 4 10 ϫ 2 8 ϫ5 30. 3 ϫ 10 ϭ 10. How many crayons does Gene have? rectangle to make a design. 7 ϫ 5 ϭ 11. 10 ϫ 3 5 ϫ1 5 ϫ8 5 ϫ9 27. Chapter 4. 1 ϫ 10 ϭ 16. 43. 8 ϫ 5 ϭ 23. 2. 39. 5 ϫ 2 ϭ 28. Print This 4–4 Page P PRACTICE 4. 9 ϫ 5 ϭ 11. 5 ϫ 5 ϭ 10 ϫ 8 5 ϫ8 17. 7 ϫ 10 ϭ 14. Find 7 ϫ 5 Think: Skip count by 5s four times. 2 ϫ 10 ϭ 16. 3. Think: Skip count by 10s three times. 10 ϫ 5 10 ϫ 9 19. 6 ϫ 5 ϭ 10. Chapter 4. Print This 4–4 Page R RETEACH five 5 ten 10 fifteen 15 twenty 20 twenty-five 25 thirty 30 thirty-five 35 7 ϫ 5 ϭ 35 You can skip count using dimes to multiply by ten. 5 ϫ 10 ϭ 9. 7 ϫ 5 ϭ 13. 5. ten 10 twenty 20 thirty 30 forty 40 fifty 50 sixty 60 seventy 70 eighty 80 8 ϫ 10 ϭ 80 Skip count to find the answer. 2. 6 ϫ 10 ϭ 12. 3 ϫ 10 ϭ 8. 4. (116) NS 3. 2 ϫ 5 ϭ 15. Lesson 4. 10 ϫ 4 Use with Grade 4. 6. 5 ϫ9 20. pages 146–147. 6ϫ5ϭ © McGraw-Hill School Division 5 ϫ 10 ϭ Multiply.2 . 1. You can use nickels and dimes to help you. Find 8 ϫ 10. 4 ϫ 5 ϭ 7.Print This Page Name Multiply by 5 and 10 You can skip count using nickels to multiply by 5. 1 ϫ 10 ϭ 18. Lesson 4. 5ϫ © McGraw-Hill School Division 10 9 30 45 75 Sum 5ϫ 10 10 40 50 90 Sum 5ϫ 10 ϫ 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. Each multiplication sentence must have a 5 or a 10 as one of its factors.Print This Page Name Multiply by 5 and 10 True Sums Write multiplication sentences to make each sum true. 2 ϫ Print This 4–4 Page E ENRICH Product 2.2 . 5ϫ 10 ϫ 3 15 10 100 115 Sum 8ϫ 6 10 30 80 110 Sum 4ϫ 10 ϫ 5 9 20 90 110 Sum Product 7. (117) NS 3. Product 9. 3 ϫ Product 11. 10 ϫ Product 3. 5 ϫ Product 8. 5 ϫ 5ϫ 7 10 35 50 85 Sum 9ϫ 10 ϫ 5 8 45 80 125 Sum 5ϫ 1 10 5 50 55 Sum Product 10. Chapter 4. 5 ϫ Product 6. Product 5. pages 146–147. 7 ϫ 5ϫ 10 4 20 20 40 Sum 5ϫ 1 2 10 10 20 Sum 8ϫ 10 5 70 40 110 Sum Product 4. 4 ϫ Product 12. Product 1. Rule: 0 0 40. 8 ϫ 7 ϭ 10. 4. 3 ϫ 8 ϭ 9. 36. 0 ϫ 7 ϭ 19. Nathan puts 6 cards on each of 8 42. 6 ϫ 9 ϭ 14. 29. 38. Print This 4–5 Page P PRACTICE 4. 39. 3. 8 ϫ 9 ϭ 24. 33. 7 ϫ9 9 ϫ6 8 ϫ6 27. 1 ϫ 8 ϭ 7. 37. 9 ϫ8 7 ϫ1 7 ϫ3 9 ϫ3 6 ϫ7 8 ϫ3 8 ϫ0 9 ϫ1 7 ϫ5 26.1 . 34.2. 9 ϫ 9 ϭ 8. Lesson 5. 5 ϫ 7 ϭ 5. 7 ϫ 8 ϭ 15. How many students are in the marching band? Use with Grade 4. 31. 2. Then complete the table. 32. (118) NS 3. and 9 Multiply. Algebra & Functions Find the rule. 35. 1. 5 ϫ9 8 ϫ8 8 ϫ4 7 ϫ2 2 ϫ8 9 ϫ2 23. 30. 6 ϫ 8 ϭ 21. 2 ϫ 9 ϭ 18. How many cards does he put in the album? 9 students in each row. 3 ϫ 7 ϭ 13. A marching band has 5 rows with 1 8 2 16 3 24 4 5 6 pages in an album. 7 ϫ 7 ϭ 16. 5 ϫ 8 ϭ 17. 8. 4 ϫ 7 ϭ 22. 2 ϫ 8 ϭ 12. 4 ϫ 8 ϭ 25. Chapter 4. 1 ϫ 9 ϭ 20. © McGraw-Hill School Division 1 9 2 18 3 27 4 5 6 Rule: 0 0 Problem Solving 41. 4 ϫ 9 ϭ 11. pages 148–149. 28. 9 ϫ 7 ϭ 6.Print This Page Name Multiply by 7. 9 ϫ 7 ϭ 8. Add to a known fact to multiply by 7. 7 ϫ 4 ϭ 14. 3 ϫ 8 ϭ 13. 7 ϫ 5 ϭ 4. (119) NS 3. 8 ϫ 6 ϭ 5. 9 ϫ 2 ϭ 16. and 9 You can use known facts to multiply by 7. 7 ϫ 7 ϭ 9. Double 4 ϫ 7. Find 7 ϫ 6. 8 ϫ 8 ϭ 7. 60 Ϫ 6 is the same as 6 ϫ 9. 10 ϫ 9 20. 10 ϫ 7 24. 1. pages 148–149. 8. 5 ϫ8 22. Print This 4–5 Page R RETEACH Double a fact to multiply by 8. 4 ϫ6 21.Print This Page Name Multiply by 7. Lesson 5. 4 ϫ8 19. Find 6 ϫ 9. (4 ϫ 7) ϩ (4 ϫ 7) Think: Think: ↓ 35 ϩ 7 is the same as 7 ϫ 6. 8. You know 6 ϫ 10 ϭ 60. 9 ϫ 9 ϭ © McGraw-Hill School Division 6 ϫ 9 ϭ 54 8 ϫ 7 ϭ 56 2. 9 ϫ 8 ϭ 6. Find 8 ϫ 7. 3.1 . 8 ϫ 10 ϭ 12. 6 ϫ7 18.2. 5 ϫ9 8 ϫ9 15. 7 ϫ 9 ϭ 11. 10. You know 7 ϫ 5 ϭ 35. Chapter 4. and 9. Subtract from a known fact to multiply by 9. 4 ϫ7 3 ϫ9 17. ↓ 28 ϩ 28 ϭ 56 35 ϩ 7 ϭ 42 60 Ϫ 6 ϭ 54 7 ϫ 6 ϭ 42 Multiply. 4. 4 ϫ9 23. 9 ϫ8 Use with Grade 4. 8. Eq uip Bo me x nt Ball bounced in puddle. pages 148–149. • Pick a card from A and a card from B. move forward two spaces. and 9 Multiplication Game Play with a partner. Find the product of the two numbers. Field Markers Start Use with Grade 4.1 . If the product is correct. Take turns. The first player to get to the field wins. Cut out the game markers. ce s. (120) NS 3. If the product is wrong. 4. • Have your partner check the product. The other puts the baseball on START. Ball is Lost in Woods.Print This Page Name Multiply by 7. Go back 3 spaces. Go back to Start. One player puts the glove on START. Chapter 4. You will need: Print This 4–5 Page E ENRICH Two sets of number cards. Each set contains number cards from 0 through 10. © McGraw-Hill School Division glo Dro v p Go e in ped 3s b m pa ack ud. Label one set A and the other set B. Go to equipment box. move back one space.2. Puddle Woods Tripped over feet. Lesson 5. She gives away 7 flower stickers. Ben buys 9 packs of dinosaur stickers.2 . James collects model cars. Melanie has a collection of 242 stamps.4. Wendy has 10 flower stickers. she buys 19 more stamps. Print This 4–6 Page P PRACTICE Reading Skill 1. 2. 2. Georgia puts coins in an album. He has 48 model cars. How many stamps does Melanie have now? 5. pages 150–151. How many coins can Georgia put in the album? 2.1.3. Who has more dolls? How many more does she have? 3. Tell how you chose the operation. How many stickers does Ben buy? 4. Each page has slots for 8 coins. (121) MR 1. Chapter 4.Print This Page Name Problem Solving: Reading for Math Choose an Operation Solve. Lesson 6. Dina has 37 international dolls. How many flower stickers does Wendy have left? Use with Grade 4. On his birthday. There are 6 stickers in each pack. Maxine has 26 international dolls. There are 8 pages in the album. How many model cars does James have in all? © McGraw-Hill School Division 6. At a stamp convention. James gets 7 more cars. 3. 2 . Juan has 24 stickers.Print This Page Name Problem Solving: Reading for Math Choose an Operation Choose the correct answer. There are 7 flags in each row. Juan buys 6 packs of stickers. Which of the following can you use is true? A B C D Juan has 4 packs of stickers. he buys 3 silver dollars. Juan has 10 stickers. What do you have to do to solve 4. (122) F G H J 21 flags 10 flags 4 flags 3 flags MR 1. to solve the problem? F G H J 6ϩ4 6Ϫ4 6ϫ4 6Ϭ4 Warren has 9 silver dollars. Each pack has 4 stickers. How many flags are there? 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. Juan has 24 packs of stickers. At a coin show.1. Which of the following statements Print This 4–6 Page P PRACTICE Math Skills Test Prep 2. How many stickers does Juan buy in all? 1. Lesson 6. She puts the flags in her bookcase in 3 rows.4. 2. How many silver dollars does Warren have now? 3. 2. What do you have to do to solve 6.3. Chapter 4. 3. How many silver dollars does this problem? 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 Warren have? F G H J 3 silver dollars 6 silver dollars 12 silver dollars 27 silver dollars © McGraw-Hill School Division Nadia collects souvenir flags. pages 150–151. How many flags does Nadia have? 5. Lesson 6. How many kites does Morris have now? 11. How many more baseball cards does Janell have than Lou? © McGraw-Hill School Division There are 4 football cards in each pack. Brian displays his trophies in his 14. Kevin buys 7 packs of football cards. He buys 4 more gets $8 for each poster. has 397 baseball cards. How many football cards does Kevin buy? 13.Print This Page Name Problem Solving: Reading for Math Choose an Operation Choose the correct answer. What operation could you use to Print This 4–6 Page P PRACTICE Math Skills Test Prep 8. 2. There are 6 trophies in each row. Morris has 16 kites. 3. How many movie posters do Selena solve this problem? A addition B subtraction C multiplication D division and her brother have in all? F 16 G 26 H 68 J 78 Solve. Her brother has 26 movie posters. How many trophies does Brian have? a photo album.1.3. How many movie posters do they have in all? 7. He puts his trophies in 3 rows. She 10.4.2 . How much money does Lois receive? kites. Barbara puts photos of France in bedroom. (123) MR 1. 9. 2. pages 150–151. Chapter 4. How many more photos can she put in the album? Use with Grade 4. Lois sells 10 rock-star posters. Lou 12. Janell has 472 baseball cards. Barbara has 78 photos. Selena has 42 movie posters. The photo album can hold 94 photos. 1. 9 ϩ 7 2ϫ7 4ϫ4 15. 4. 9 ϫ 8 ϭ 5. (124) . 12 ϫ 7 10 ϫ 10 9. What is the pattern of odd and even 12. Chapter 4. 2. or ϭ. 1. pages 152–153. MR 1. What is the pattern of odd and even numbers in the 3 row or 3 column? numbers in the 4 row or 4 column? Compare.1 Use with Grade 4. 12 ϫ 9 © McGraw-Hill School Division 11. 11 ϫ 11 ϭ 8.2. 4 ϫ 8 18. 15 Ϫ 7 17. 11 ϫ 7 10. 12 Ϫ 4 25 ϩ 4 2ϫ3 NS 4. 9 ϫ 7 3ϫ3 6 ϫ 11 14. Write Ͼ. Ͻ. 13. ϫ 0 1 2 3 4 5 6 7 8 9 10 11 12 22 24 55 84 88 99 7 16 32 54 0 0 0 1 2 3 8 15 2 4 9 20 30 36 40 50 4 12 21 27 8 1 2 3 4 5 6 7 8 9 10 Print This 4–7 Page P PRACTICE 11 12 36 60 66 77 96 108 72 121 132 120 144 Use the table to multiply. 6 ϩ 3 16.Print This Page Name Multiplication Table and Patterns Complete the table. Lesson 7. 4. 3 ϫ 12 ϭ 6. 4 ϫ 12 ϭ 12 ϫ 8 12 ϫ 12 7. 3. 9 ϫ 12 14. 10 ϫ 5 ϭ 8. 7. 6 ϫ 7 ϭ 16. 7 ϫ 7 ϭ © McGraw-Hill School Division 2. 8 ϫ 11 9 ϫ8 17. 11 ϫ 12 20. 8 ϫ8 21. 3 ϫ 8 ϭ 11. 1. 12 ϫ 12 23. Chapter 4. ϫ 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 Print This 4–7 Page R RETEACH 11 0 11 22 33 44 55 66 77 88 99 12 0 12 24 36 48 60 72 84 96 108 120 132 144 100 110 110 121 120 132 Multiply. (125) NS 4.1. 8 ϫ 4 ϭ 6. 9 ϫ 9 ϭ 3. So. 4. You can use the multiplication table to help you. pages 152–153. 9 ϫ7 22. draw arrows to show where the 8 row and the 9 column meet in the table. 9 ϫ 11 ϭ 9. 11 ϫ 3 24. The 8 row and the 9 column meet at 72.2. 6 ϫ 8 ϭ 4. 11 ϫ 7 19. 4 ϫ 9 ϭ 12. 8 ϫ 12 ϭ 5. 7 ϫ 12 ϭ 13. 11 ϫ 11 Use with Grade 4. 8 ϫ7 15.Print This Page Name Multiplication Table and Patterns To find 8 ϫ 9. MR 1.1 . 12 ϫ 10 18. Lesson 7. 8 ϫ 9 ϭ 72. 7 ϫ 4 ϭ 10. ϫ 12 24 3 9 28 56 7 21 0 0 0 0 8 16 2 6 5. ϫ 15 21 42 35 0 18 Use with Grade 4. MR 1. Print This 4–7 Page E ENRICH ϫ 10 12 14 15 18 21 20 24 28 2. ϫ 42 18 30 14 6 10 28 12 20 3.2. 4.1. ϫ 56 16 16 24 28 18 36 6 8. pages 152–153. ϫ 36 6 12 30 42 7 14 35 54 9 18 45 24 4 8 20 4. ϫ 72 28 27 7 6 24 6 2 6.1 . Lesson 7.Print This Page Name Multiplication Table and Patterns Twisted Tables Complete each multiplication table. ϫ 63 72 18 0 9 42 21 40 © McGraw-Hill School Division 7. Chapter 4. (126) NS 4. Fill in the missing factors. 1. The school gives each basketball 35. (9 ϫ 3) ϫ 0 ϭ 12. 1. How many outs are there in a game? Use with Grade 4. (2 ϫ 2) ϫ 2 ϭ 11. 5 ϫ (3 ϫ 3) ϭ 19. Lesson 8. pages 156–157. (5 ϫ 2) ϫ 4 ϭ 10. (3 ϫ 3) ϫ 3 ϭ Print This 4–8 Page P PRACTICE 3. Chapter 4. 28.Print This Page Name Multiply Three Numbers Multiply. 2 ϫ (7 ϫ 2) ϭ 16. 5 ϫ 6 ϭ 5 ϫ (3 ϫ 33. (7 ϫ 2) ϫ 4 ϭ 27. 4 ϫ (8 ϫ 1) ϭ 20. Each shirt costs $8. 4 ϫ (4 ϫ 2) ϭ 8. 2 ϫ (4 ϫ 3) ϭ 2. 3 ϫ (2 ϫ 8) ϭ 5. (7 ϫ 2) ϫ 2 ϭ Complete the multiplication sentence. 9 ϫ (2 ϫ 3) ϭ 22. (8 ϫ 1) ϫ 9 ϭ 23. 5 ϫ 4 ϭ 30. 9 ϫ (3 ϫ 3) ϭ 26. (127) AF 1. 5 ϫ (3 ϫ 2) ϭ 24. (6 ϫ 2) ϫ 2 ϭ 15. ϫ (3 ϫ 5) ϭ 9 ϫ 5 Problem Solving 34.3 . 4 ϫ 4 ϫ 2 ϭ (2 ϫ 32. (8 ϫ 4) ϫ 2 ϭ 17. What is the total cost of shirts for 6 players? each of the 2 teams gets 3 outs per inning. (8 ϫ 2) ϫ 3 ϭ 13. (8 ϫ 3) ϫ 0 ϭ 25. In a baseball game of 9 innings. player 2 shirts. (9 ϫ 3) ϫ © McGraw-Hill School Division ϫ5 ϭ 27 29. ( ϫ 8) ϫ 7 ϭ 0 ) ) ϫ (4 ϫ 2) 31. (2 ϫ 5) ϫ 4 ϭ 4. 7 ϫ (2 ϫ 3) ϭ 21. 7 ϫ (3 ϫ 3) ϭ 14. 6 ϫ (3 ϫ 2) ϭ 7. 7 ϫ (2 ϫ 5) ϭ 9. (9 ϫ 2) ϫ 4 ϭ 18. (4 ϫ 2) ϫ 3 ϭ 6. 5 ϫ (3 ϫ 2) Use the Associative Property to regroup the numbers. Think: 5 sixes Multiply. (7 ϫ 1) ϫ 3 ϭ 10. (2 ϫ 6) ϫ 3 (5 ϫ 5ϫ( 5ϫ )ϫ4 ϫ ) 3ϫ( ( ϫ ϫ4 ϫ ) (6 ϫ 6ϫ( 6ϫ )ϫ3 ϫ ) )ϫ4 4. (3 ϫ 3) ϫ 3 ϭ 15. (5 ϫ 2) ϫ 3 ϭ 9. 9 ϫ (2 ϫ 3) ϭ 14. (9 ϫ 2) ϫ 2 ϭ 18. 2 ϫ (2 ϫ 3) ϭ © McGraw-Hill School Division 5. pages 156–157. Think: 3 twos Print This 4–8 Page R RETEACH 5 ϫ 6 ϭ 30 Multiply again. (4 ϫ 8) ϫ 1 ϭ 11.Print This Page Name Multiply Three Numbers Find: (3 ϫ 5) ϫ 2 Think: 3 ϫ 2 is a known fact.3 . (2 ϫ 5) ϫ 4 2. (5 ϫ 4) ϫ 2 ϭ 13. 3 ϫ (3 ϫ 5) ϭ 17. 5 ϫ (4 ϫ 3) ϭ 7. (2 ϫ 7) ϫ 3 ϭ 6. Chapter 4. Lesson 8. 3 ϫ (3 ϫ 2) ϭ 12. (9 ϫ 6) ϫ 1 ϭ Use with Grade 4. (128) AF 1. 1. (5 ϫ 3) ϫ 2 Use the Commutative Property to change the order. 5ϫ6 Multiply inside the parentheses first. (2 ϫ 4) ϫ 3 ϭ 8. (8 ϫ 2) ϫ 4 ϭ 16. 3 ϫ (4 ϫ 3) 3. Look across. up. Can you find all 26 combinations? Print This 4–8 Page E ENRICH 4 4 5 6 7 © McGraw-Hill School Division 3 9 2 6 4 2 4 2 3 6 9 2 2 2 2 7 4 8 3 4 4 6 3 3 7 6 8 6 4 2 8 4 8 3 2 9 2 Choose one of these numbers: 24.Print This Page Name Multiply Three Numbers The Search for 48 Circle each combination of numbers that has a product of 48. Make your own number search and give it to a friend to solve. 64. or 72. and diagonally. You can multiply up to four numbers. (129) AF 1. pages 156–157. down. Be sure to keep a copy with the solution! Use with Grade 4. 36. Lesson 8.3 . Chapter 4. 1 . 9 63 31. 9 36 34. How 37. 7 21 22. 42 Ϭ 7 ϭ 19. 27 Ϭ 3 ϭ 11. 8 64 35. 3 21 21. How many groups can 24 people make? Use with Grade 4. 5 45 26. 9 54 29. 7 56 27. 8 56 © McGraw-Hill School Division 15 Ϭ 3 ϭ 16 Ϭ 4 ϭ 5. 1. 18 Ϭ 3 ϭ 14. 9 45 32. 8 Ϭ 4 ϭ 10. 18 Ϭ 9 2. 15 Ϭ 5 ϭ 9. MR 1. 4 24 8 3 9 6 6 6 4 9 20. Chapter 4. 3 18 24.Print This Page Name Relate Multiplication and Division Facts Write a related multiplication fact and complete the division sentence. 8 24 28. It takes 4 horses to pull a coach. 48 Ϭ 6 ϭ 16. Groups of 6 visitors can take tours of many coaches can 20 horses pull? an old western town. 16 Ϭ 4 Print This 4–9 Page P PRACTICE 9ϫ ϭ 18 3ϫ ϭ 15 4ϫ ϭ 16 18 Ϭ 9 ϭ Divide. 15 Ϭ 3 3. 7 63 Problem Solving 36. 5 25 25. (130) NS 3. 28 Ϭ 7 ϭ 13. 4 36 7 9 7 9 3 8 5 9 18. 4. 9 81 33.2. 6 54 6. 14 Ϭ 2 ϭ 12. 18 Ϭ 2 ϭ 8. 6 Ϭ 2 ϭ 7. 3 9 5 3 8 7 30. Lesson 9. 63 Ϭ 7 ϭ 15. pages 160–161. 2 16 23. 35 Ϭ 7 ϭ 17. 21 Ϭ 7 12 Ϭ 3 ϭ 6. 28 Ϭ 4 7. 1. pages 160–161. Lesson 9. 12 Ϭ 3 6ϫ ϭ 18 8ϫ ϭ 16 4ϫ ϭ 12 18 Ϭ 6 ϭ 4. Chapter 4. (131) NS 3. 27 Ϭ 9 24 Ϭ 6 ϭ 9. 18 Ϭ 6 2. 20 Ϭ 5 16 Ϭ 8 ϭ 5.1 . Think: How many groups of 5 are in 15? Print This 4–9 Page R RETEACH 5 ϫ ? ϭ 15 → 5 ϫ 3 ϭ 15 There are 3 groups of 5 in 15. 24 Ϭ 6 20 Ϭ 5 ϭ © McGraw-Hill School Division 21 Ϭ 7 ϭ 8. 30 Ϭ 5 30 Ϭ 5 ϭ 27 Ϭ 9 ϭ 28 Ϭ 4 ϭ Use with Grade 4. 16 Ϭ 8 3. MR 1.Print This Page Name Relate Multiplication and Division Facts Find 15 Ϭ 5. So.2. 15 Ϭ 5 ϭ 3. Write a related multiplication fact and complete the division sentence. if you placed the letter B in the top left square. Then add to find the value of each word. pages 160–161.Print This Page Name Relate Multiplication and Division Facts Word Puzzle Use the letters in the table below to complete the word puzzle. complete the multiplication or division to find the value of each letter you used. Words have to connect as they do in a crossword puzzle. you would get 5 for that square (25 Ϭ 5 ϭ 5). Lesson 9. add the values of all four words. • You cannot move the vowels in the puzzle.2. Letter Values Letter A B D E F G J Rules • Use each letter in the table only once. • Try to get the highest score you can. For example.1 Use with Grade 4. To find your score. Finally. MR 1. Chapter 4. (132) . Value 10 ϫ 3 ϭ ? 25 Ϭ 5 ϭ ? 12 Ϭ 6 ϭ ? 3ϫ6ϭ? 4ϫ5ϭ? 36 Ϭ 4 ϭ ? 10 ϫ 4 ϭ ? Letter L N O S T U Y Print This 4–9 Page E ENRICH Value 45 Ϭ 5 ϭ ? 4ϫ9ϭ? 30 Ϭ 3 ϭ ? 5ϫ5ϭ? 6ϫ7ϭ? 42 Ϭ 7 ϭ ? 54 Ϭ 6 ϭ ? © McGraw-Hill School Division J E T O G U A N NS 3. 1. pages 162–163. Yoki has 20 posters of science-fiction movies. which tables should the club use? How many of these tables will be needed? soda. Square tables seat 4 people and round tables seat 5 people.M. Chapter 4. A small box will hold 6 bottles and a large box will hold 8 bottles. Create a problem which you could Robert 45 minutes to get there. She puts an equal number of these posters on each of 4 walls. Dinner starts at 6:00 P. She cuts 3-foot by 1-foot rectangles from it. If the club wants full tables. he wants to stop at the library for 30 minutes. Art For posters. How can the club arrange the rest of the trophies so that each smaller case has an equal number of trophies? Mixed Strategy Review Solve.Print This Page Name Problem Solving: Strategy Act It Out Use act it out to solve. There are 6 smaller cases. Nancy has a piece of poster paper that is 9 feet by 2 feet. (133) NS 3. The Sailing Club puts 12 of its 48 42 shells. How many posters does she make? Strategy: 7. What time does Robert need to leave to get to the dinner on time? act out to solve. How many posters does Yoki put on each wall? © McGraw-Hill School Division 6. How many rows does Courtney make? trophies in a large display case.1 . It will take Strategy: 8. Lesson 10. She arranges the shells in rows of 6. Courtney is making a display of 4. 5. The Rare Book Club invites its Print This 4–10 Page P PRACTICE 2.2. Share it with others. Strategy: Use with Grade 4. Which box should Len use if he wants to put an equal number of bottles in each box? How many boxes will he need? 3. Len delivers 16 bottles of juice and 25 members to a dinner. MR 1. On his way. Use any strategy. Draw a rectangle that represents the piece of fabric. Read • Meg is going to cut the placemats from a piece of fabric that is by . Problem 2 Print This 4–10 Page R RETEACH For placemats. Use with Grade 4. Chapter 4. How many placemats can she cut from one piece of fabric? Step 1 Be sure you understand the problem. Make rectangles that represent the placemats.Print This Page Name Problem Solving: Strategy Act It Out Page 163. What do you know? • The placemats are by . so draw a rectangle that is 4 centimeters by 3 centimeters to represent the piece of fabric. MR 1.1 . (134) NS 3. I I © McGraw-Hill School Division I I I I I I I 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 To solve the problem. you can act it out using models. What do you need to find? • You need to find how many . Lesson 10. The fabric is 4 feet wide and 3 feet long. pages 162–163. Step 2 Plan I Make a plan.2. Since the placemats are 2 feet by 1 foot. Choose a strategy. Meg is going to cut 2-foot by 1-foot rectangles from a piece of fabric with a starry background. cut out rectangles that are 2 centimeters by 1 centimeter. A rectangle that is 4 feet by 3 feet would be very large. Read carefully. . . MR 1. How many name tags can Randy cut from the piece of poster paper? 2.Print This Page Name Problem Solving: Strategy Act It Out Step 3 Print This 4–10 Page R RETEACH Solve Carry out your plan. Each name tag will be 3 inches by 4 inches. He has small boxes that will each hold 6 train cars. Lesson 10. He has large boxes that will each hold 8 train cars. Fill the large rectangle with small rectangles. Ted has 54 model train cars. The large rectangle represents Each small rectangle represents Meg can cut Step 4 placemats from the piece of fabric. Does your answer make sense? Did you answer the question? Yes Yes No No What other stategies could you use to solve the problem? © McGraw-Hill School Division Practice 1. Look Back Is the solution reasonable? Reread the problem. pages 162–163. 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? Use with Grade 4.1 . Randy wants to cut name tags from a piece of poster paper. Chapter 4. (135) NS 3. The poster paper is 18 inches by 24 inches.2. 4 24 26. pages 164–167. 6 42 3. 48 Ϭ 6 ϭ 13. 1. 49 Ϭ 7 ϭ 14. 54 Ϭ 6 ϭ 8.2 . There are 42 tomato plants in rows of 37. Each tomato plant has the same number of tomatoes. 90 Ϭ 10 ϭ 19. 10 80 32. 32 Ϭ 4 ϭ 6. 3. 2. Rule: 0 7 1 2 3 4 5 6 © McGraw-Hill School Division 0 Problem Solving 36. 7 14 27. 7 63 2.1. 27 Ϭ 3 ϭ 15. 12 72 30. 121 Ϭ 11 ϭ 20. 11 99 33. 30 Ϭ 5 ϭ 16. 144 Ϭ 12 ϭ 22. Chapter 4. 24 Ϭ 3 ϭ 5. 36 Ϭ 4 ϭ 17. 9 63 6 7 8 2 9 9 23. 40 Ϭ 8 ϭ 12. How many tomatoes are on each plant? Use with Grade 4. Rule: 0 0 9 1 2 3 4 5 6 35.4. Lesson 11. There are 45 tomatoes on 5 tomato 6 plants in each row. 64 Ϭ 8 ϭ 10. 35 Ϭ 5 ϭ 7. 34. 12 108 Algebra & Functions Find the rule.2. 81 Ϭ 9 ϭ 11. 72 Ϭ 9 ϭ 18. MR 1. 56 Ϭ 7 ϭ 9. Then complete the table. 3 18 25. (136) NS 3. How many rows of tomato plants are there? plants. 5 45 Print This 4–11 Page P PRACTICE 9 9 6 6 7 7 21. 8 72 2 9 9 29. 12 Ϭ 2 ϭ 4. 8 16 28. 2 18 24.Print This Page Name Divide by 2 Through 12 Divide. 11 77 31. 2 18 © McGraw-Hill School Division 5. 6 54 25. 7 42 6.2. 30 Ϭ 5 ϭ 24 Ϭ 8 ϭ 16 Ϭ 4 ϭ Divide. 21 Ϭ 3 ϭ 8.Print This Page Name Divide by 2 Through 12 Find 48 Ϭ 6. 12 Ϭ 2 ϭ 7. Chapter 4. 9 45 9 3 3 9 6 3 12 5 3 8 9 16. 10 30 22. 32 Ϭ 8 ϭ 13. 12 36 24. 3 36 18. pages 164–167. 14 Ϭ 7 ϭ 10. 1. MR 1. 24 Ϭ 6 ϭ 11. 10 80 27. 48 Ϭ 6 ϭ 8. 5 40 21. (137) NS 3. 20 Ϭ 5 ϭ 9. Draw models if you wish. 2. 11 99 9 9 8 2 26. 2. So. 4 36 17. 18 Ϭ 3 ϭ 14.4. 16 Ϭ 2 ϭ 12. 11 33 23. Think: How many groups of 6 are in 48? Print This 4–11 Page R RETEACH 6 ϫ ? ϭ 48 → 6 ϫ 8 ϭ 48 There are 8 groups of 6 in 48. Lesson 11. 3. Complete the division sentence. 4. 9 81 20. 5 15 19.1. 28 Ϭ 4 ϭ 15. 3. 12 24 Use with Grade 4.2 . move to that circle. Rules • Place your game pieces at the START positions on the 50-yard line. Lesson 11. You’ll need a number cube and 2 two-color counters to use as game pieces. • Keep rolling the number cubes until one of you scores a touchdown.Print This Page Name Divide by 2 Through 12 Win the Division Play this division football game with a partner.2. 2. Chapter 4. MR 1. • If the number in the circle on the next 10-yard line can be evenly divided by the divisor.2 .4. 3.1. pages 164–167. • Take turns rolling the number cubes. 42 Print This 4–11 Page E ENRICH 16 TOUCHDOWN! G 28 10 20 15 36 12 Start Start 24 © McGraw-Hill School Division 30 40 50 40 18 30 20 10 10 G 30 54 TOUCHDOWN! 35 Use with Grade 4. (138) NS 3. Add the number cubes to get a divisor. Each player can only move in the direction of the arrow. 54 17. 8 ϫ 9 ϭ m 8 ϫ r ϭ 32 32 Ϭ 8 ϭ s 32 Ϭ t ϭ 8 Find the missing factor. 5. 27 12. 9 ϫ 5 ϭ a 3. h ϫ 7 ϭ 56 56 Ϭ 7 ϭ h y ϭ 63 63 Ϭ 9 ϭ y 6.Print This Page Name Fact Families Complete each fact family. What patterns do you see? 18. 8. 4. 4 Ϭ 4 ϭ 8Ϭ8ϭ 9Ϭ9ϭ 6Ϭ6ϭ 19. 6. 9. 6. 9. Lesson 12. 42 13. Chapter 4. 9 ϫ w ϭ 54 54 Ϭ 9 ϭ w 8. 9. 5. 20 16. AF 1.2. 3. MR 1. 4 ϫ 8 ϭ Print This 4–12 Page P PRACTICE q 2. 4. 5. 7. 5 ϫ 5 ϫ b ϭ 45 45 Ϭ 5 ϭ c 45 Ϭ d ϭ 5 8 ϫ n ϭ 72 72 Ϭ 8 ϭ o 72 Ϭ p ϭ 8 k ϭ 30 30 Ϭ 5 ϭ k 5. 45 © McGraw-Hill School Division Divide. pages 168–171. 8. 9 ϫ 9.1 . 5.1. 0 Ϭ 7 ϭ 0Ϭ8ϭ 0Ϭ1ϭ 0Ϭ5ϭ Use with Grade 4. 9. 10. Write a multiplication and division fact family for each group of numbers. 72 14. 7. 1. 35 15. 40 11. (139) NS 3. 9 ϫ g ϭ 72 72 Ϭ 9 ϭ g d ϫ 8 ϭ 48 48 Ϭ 8 ϭ d 7. 7. Every sentence in a fact family uses the same numbers. Print This 4–12 Page R RETEACH Fact Family 5 ϫ 2 ϭ 10 2 ϫ 5 ϭ 10 10 Ϭ 5 ϭ 2 10 Ϭ 2 ϭ 5 3 ϫ 5 ϭ 15 5ϫ 15 Ϭ ϭ ϭ 15 Ϭ 5 ϭ 9ϫ ϫ ϭ ϭ Ϭ4ϭ Ϭ [9] ϭ Write the fact family for each set of numbers. 3 ϫ n ϭ 27 27 Ϭ 3 ϭ n nϭ Use with Grade 4. 5 ϫ n ϭ 30 30 Ϭ 5 ϭ n nϭ 8. 6.1 . n ϫ 8 ϭ 64 64 Ϭ 8 ϭ n nϭ 10. AF 1. pages 168–171.Print This Page Name Fact Families Multiplication and division sentences that are related make up a fact family. 9 © McGraw-Hill School Division Find the missing numbers. Fact Family 3 ϫ 4 ϭ 12 4 ϫ 3 ϭ 12 12 Ϭ 3 ϭ 4 12 Ϭ 4 ϭ 3 Complete each fact family. (140) NS 3. 1. 7. 6. MR 1. 5 6. 24 4. n ϫ 7 ϭ 56 56 Ϭ 7 ϭ n nϭ 9.1. 2. Lesson 12. Chapter 4. 3. 4.2. 35. 7. 54. 3. 21 5. 1. AF 1. pages 168–171. 8ϫ 6 ϭ 48 Ϭ 4 ϭ 12 ϫ4ϭ 48 Ϭ6ϭ 8 4.2. (141) NS 3. 66 Ϭ 11 ϭ 6 ϫ 5 ϭ 30 Ϭ 6 ϭ 5 ϫ9ϭ 45 5. Print This 4–12 Page E ENRICH 1. 5 ϫ 12 ϭ 60 Ϭ 10 ϭ6ϫ9ϭ 54 Ϭ6ϭ 9 © McGraw-Hill School Division 6. 24 Ϭ 6 ϭ 4 ϫ6ϭ 24 Ϭ3ϭ 8 ϫ5ϭ 40 2.Print This Page Name Fact Families Chain Reaction Write the missing numbers to complete each chain. 9ϫ8ϭ 72 Ϭ 12 ϭ 6 Ϭ6ϭ 1 ϫ0ϭ 0 3. Chapter 4. MR 1. Lesson 12. 81Ϭ 9 ϭ9Ϭ3ϭ 3 ϫ3ϭ 9 ϫ9ϭ 81 7.1 . 45 Ϭ 9 ϭ 5 ϫ 9 ϭ 45 Ϭ 5 ϭ 9 ϫ3ϭ 27 Use with Grade 4. pages 174–175.Print This Page Name Problem Solving: Application Applying Multiplication and Division Record your data. MR 1.1. 3. Chapter 4. Storage Unit Capacity: Number of trophies or medals per unit Number of Units Used 4–13 Part A WORKSHEET Decision Making Print This Page Total Cost Shelf Frame (small or large) © McGraw-Hill School Division Your Decision What is your recommendation for Lily? Explain. Use with Grade 4. 1. (142) NS 3. Lesson 13.3.1.2 . 2. Lesson 13. (143) NS 3.Print This Page Name Problem Solving: Application Ramp races: How does height affect distance? Record your data. MR 1. pages 176–177. 1 book 2 books 3 books © McGraw-Hill School Division 4 books 5 books Use with Grade 4. 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. Chapter 4. Ramp height Distance traveled 4–13 Part B WORKSHEET Math & Science Print This Page Use division.4.1.3 . 3 . Lesson 13. Use with Grade 4. Do your calculations in the table and then list your answers here. and 5-book ramps than it did for the 1-book ramp. Round to the nearest whole number. Explain the activity in terms of speed. If the pattern continues. Use division to calculate how many times farther the crayon traveled for the 2-. On which ramp did the crayon travel the farthest? On which ramp 4–13 Part B WORKSHEET Math & Science Print This Page did the crayon travel the shortest distance? 2. pages 176–177. Do you see a pattern? Describe it. © McGraw-Hill School Division 5. 2. 3-.Print This Page Name Problem Solving: Application Ramp races: How does height affect distance? 1. MR 1. Chapter 4. 3. 4-. 4.4.1. (144) NS 3. how far will a crayon travel if released from a 10-book ramp? a 20-book ramp? Explain how you made these estimates. 5 ϫ 600 ϭ 18.000 5 ϫ 8. 90 ϫ6 8. 5. (145) NS 3. How many sheets are in 7 reams? Use with Grade 4. 80 ϫ6 4. 700 ϫ 9 11. 3. © McGraw-Hill School Division 25. 9 ϫ 600 ϭ 20. Use mental math. A ream of paper is 500 sheets of many stamps are in 9 rolls? paper. 90 ϫ 5 ϭ 16.000 ϫ 6 13. 2. How 29. 800 ϫ 6 10.000 ϭ Find each missing number. 22. 700 ϫ 8 ϭ 19. 6 ϫ c ϫ 8 ϭ 72. 3 ϫ 26. 8 ϫ 4. pages 192–193. 2. Lesson 1. 4 ϫ 90 ϭ 17. 40 ϫ5 6. 400 ϫ 5 9. 3. 2 ϫ c ϭ 180 cϭ 27.2 . a ϫ 5 ϭ 300 aϭ a ϭ 900 23. Stamps are sold in rolls of 100. 1. 700 ϫ 4 ϭ 21. 70 ϫ8 5.000 ϫ 8 ϭ 14. Chapter 5.000 ϫ 7 ϭ 15. 5 ϫ 8 ϭ e 5 ϫ c ϭ 400 g ϫ 800 ϭ 4. 3 ϫ 2 ϭ Print This 5–1 Page P PRACTICE a 3 ϫ b ϭ 60 c ϫ 200 ϭ 600 3 ϫ 2.000 ϭ d aϭ bϭ cϭ dϭ 2.Print This Page Name Patterns of Multiplication Complete.000 cϭ aϭ Problem Solving bϭ 28.600 24.000 ϫ 4 12.000 ϭ h eϭ fϭ gϭ hϭ Multiply. 60 ϫ7 7. b ϫ 4 ϭ 320 aϭ b ϭ 3. (146) . 4 ϫ 5 ϭ 3 ϫ 30 ϭ 3 ϫ 300 ϭ 3 ϫ 3.000 ϭ NS 3. 8 ϫ 400 ϭ 24. 6 ϫ 800 ϭ 21. 5 ϫ 6. 8 ϫ 5. 70 ϫ4 7. 4. 9 ϫ 60 ϭ 17. 8 ϫ 200 ϭ 19. 3. Chapter 5. 1. 3 ϫ 3 ϭ 2 ϫ 4 tens ϭ 8 tens 2 ϫ 40 ϭ 80 2 ϫ 4 hundreds ϭ 8 hundreds 2 ϫ 400 ϭ 800 2.000 ϭ 4 ϫ 50 ϭ 4 ϫ 500 ϭ 4 ϫ 5. pages 192–193. 3 ϫ 4. 5 ϫ 900 ϭ 22. © McGraw-Hill School Division 200 ϫ 8 10. 6 ϫ 600 ϭ 23. 6 ϫ 3 ϭ 3. 6 ϫ 30 ϭ 6 ϫ 300 ϭ 6 ϫ 3. 60 ϫ7 8. 8 ϫ 800 ϭ 20.000 ϫ 8 12. Use mental math. 9 ϫ 700 ϭ 25. 6 ϫ 50 ϭ 18. 4 ϫ 600 ϭ 26. 90 ϫ4 6.Print This Page Name Patterns of Multiplication Using basic facts and patterns can help you multiply mentally. Print This 5–1 Page R RETEACH 2 ϫ 4 ones ϭ 8 ones 2ϫ4ϭ8 Complete the pattern.000 ϭ Multiply. Lesson 1.000 ϭ 15.000 ϫ 3 13.000 ϭ 27. 7 ϫ 2.000 ϫ 8 14. 500 ϫ 7 11. 800 ϫ 9 9.000 ϭ 16. 6.000 ϭ 70 ϫ8 5.000 ϭ 28. 7.2 Use with Grade 4. 4 ϫ 4. 23. 11. 13. When Columbus discovered America. pages 192–193. 2. 16. 22.800 21. 1.000 3. 7 ϫ ϫ 9 ϭ 1. 10.000 8. 6 ϫ ϭ 350 ϫ 8 ϭ 400 ϫ 6 ϭ 3. Write the letter in the blank above the same exercise number. 24. 5. where did he first stand? 20. 4. 6 ϫ 22. 4 ϫ 7. 1. 7 ϫ 20 E 30 N 40 B 50 A 80 M 200 300 400 500 800 2. © McGraw-Hill School Division Where was the Declaration of Independence signed? 6. 9 ϫ 20. (147) NS 3.000 ϭ 1. 16. 3 ϫ 13. 6 ϫ 17. 14.800 ϫ 5 ϭ 1.000 3. 15. 7 ϫ 14. 8.000 ϫ 5 ϭ 100 ϭ 180 ϭ 210 ϭ 18. Use with Grade 4. 12. 60 ϫ 5.000 4. 7 ϫ 10.200 ϭ 3.000 18. Solve the riddles. 9. 23. 9. Then find the letter in the table that matches that number. 21.000 T S H O I F W U K Y What did Paul Revere say at the end of his ride? 7.000 ϭ 21.400 ϫ 7 ϭ 2. 15. Lesson 1.000 5. 12. 4. 11. 17. ϫ 8 ϭ 4.2 . 8.000 ϫ 6 ϭ 1.400 ϭ 480 6. 18. 19.100 2. 9 ϫ 24.000 ϭ 4. 19.000 ϭ 1.200 ϫ 6 ϭ 240 ϫ 3 ϭ 600 ϭ 2. Print This 5–1 Page E ENRICH ϫ 5 ϭ 100 ϭ 2. Chapter 5.Print This Page Name Patterns of Multiplication History Riddles Find each missing number. 6 ϫ ϭ 24. 3. 2 . 77 ϫ7 14. 84 ϫ4 21. 76 ϫ7 22. Multiply 4 ϫ 15. 7 ϫ 22 ϭ 29. 5 ϫ 26 ϭ © McGraw-Hill School Division 23. 56 ϫ7 11. 66 ϫ6 13. 2. 19 ϫ8 19. 59 ϫ4 16. pages 194–195. Each layer has 24 oranges. 76 ϫ6 9. 98 ϫ5 8. 62 ϫ2 3. 94 ϫ3 15. Chapter 5. Lesson 2.Print This Page Name Explore Multiplying 2-Digit Numbers by1-Digit Numbers 1. crate. How many members are in the band? Use with Grade 4. 67 ϫ5 20. 38 ϫ4 4. 35 ϫ 4 ϭ 24. Print This 5–2 Page P PRACTICE Find each product. 91 ϫ3 5. 99 ϫ 3 ϭ 25. 9 ϫ 49 ϭ 30. 78 ϫ6 7. Band members march in 24 rows. 48 ϫ8 12. Katy arranges oranges in 5 layers in a 32. 24 ϫ7 18. Draw squares to multiply. How many oranges does she put in the crate? There are 8 members in each row. 37 ϫ 8 ϭ 26. 24 ϫ9 10. 38 ϫ 4 ϭ 28. 44 ϫ9 17. 45 ϫ 6 ϭ 27. 46 ϫ5 6. 8 ϫ 67 ϭ Problem Solving 31. (148) NS 3. Print This Page Name Explore Multiplying 2-Digit Numbers by 1-Digit Numbers Find 5 ϫ 21. 22 ϫ 6 ϭ 22. 1. 4 ϫ 18 ϭ 4 dots 18 dots 24 dots 2. Lesson 2. 37 ϫ4 10. 46 ϫ3 9. 20 ϫ 6 ϭ 24. 13 ϫ9 7. Find the total number of dots. 4 ϫ 17 ϭ 21. Chapter 5. 19 ϫ6 4. 33 ϫ4 14. 3. 18 ϫ9 18. You can draw an array to multiply. 21 ϫ5 15. 5 dots 5 ϫ 21 ϭ 105 Print This 5–2 Page R RETEACH 21 dots Draw an array to multiply. 24 ϫ5 5. 5 ϫ 31 ϭ 25. 58 ϫ5 11. 5 ϫ 24 ϭ 5 dots Find each product. 30 ϫ6 17. 4 ϫ 50 ϭ 20. 18 ϫ3 16. 25 ϫ8 6. 23 ϫ 6 © McGraw-Hill School Division 13. 3 ϫ 13 ϭ 19. pages 194–195. 12 ϫ9 8. 26 ϫ 4 ϭ 26. 5 ϫ 15 ϭ NS 3. (149) . 7 ϫ 14 ϭ 23. 28 ϫ 7 12.2 Use with Grade 4. Lesson 2. Use the abacus to find each product. 4 ϫ 212 ϭ 6. Show the answer by drawing the beads you moved down. 3 ϫ 31 ϭ H T O H T O H T O © McGraw-Hill School Division 4. pages 194–195. 1. 3 ϫ 304 ϭ H T O H T O H T O Use with Grade 4. multiply 3 tens by 3. Move 9 beads to the bottom of the tens column to show 3 ϫ 3 tens ϭ 9 tens. Move 6 beads to the bottom of the ones column to show 3 ϫ 2 ϭ 6. Chapter 5. Cross out the beads you moved down from the top. Count the beads in each column.Print This Page Name Explore Multiplying 2-Digit Numbers by1-Digit Numbers The Abacus The abacus is a computing tool that is thousands of years old. first multiply 2 ones by 3. 2 ϫ 34 ϭ 3.2 . 4 ϫ 22 ϭ 2. 5 ϫ 43 ϭ 5. (150) NS 3. so 3 ϫ 32 ϭ 96. H T O Next. To multiply 3 ϫ 32 using a Russian abacus. H Print This 5–2 Page E ENRICH T O There are 9 tens 6 ones. 74 ϫ5 11. Multiply 82 by 3. 77 ϫ7 18.Print This Page Name Multiply 2-Digit Numbers by 1-Digit Numbers Multiply. Lesson 3. 66 ϫ8 15. 44 ϫ5 3. Multiply 45 by 5. Chapter 5. 38 ϫ8 20. 3. 88 ϫ4 10. 2 ϫ 98 ϭ 28. 97 ϫ2 14. Multiply 37 by 6. Multiply 56 by 7. Multiply 63 by 8. pages 196–199. 33. 1. 85 ϫ4 12. 32. Problem Solving 36. Print This 5–3 Page P PRACTICE 73 ϫ3 2. 65 ϫ5 7. 6 ϫ 39 ϭ 27. 4 ϫ 52 ϭ 30.2. 63 ϫ 7 ϭ 23. 77 ϫ6 13. 55 ϫ 5 ϭ 24. 18 ϫ9 19. 84 ϫ 6 ϭ 29. How many tiles are in the rectangle? 17 books in each stack. 94 ϫ3 16. (151) NS 3. 31 ϫ7 4. 8 ϫ 47 ϭ 26. 75 ϫ 6 ϭ 25. 68 ϫ8 5.3 . 96 ϫ3 9. 44 ϫ4 17. Multiply 78 by 4. 35. Books are stacked in 3 stacks with 13 tiles high. 34. 32 ϫ9 6. A rectangle is 5 tiles wide by 37. 29 ϫ 9 ϭ 31. © McGraw-Hill School Division 22. 99 ϫ6 21. How many books are in the stacks? Use with Grade 4. 33 ϫ6 8. 44 ϫ3 3. 5 ϫ 83 ϭ 12. Step 1 Multiply the ones. 9 ϫ 52 ϭ 14. Lesson 3. 64 ϫ6 8. 68 ϫ 3 ϭ 16. 78 ϫ3 9. 2 ϫ 88 ϭ 13. 72 ϫ 7 ϭ 15. 52 ϫ7 5. Show 4 groups of 26. 23 ϫ5 2. 92 ϫ5 11. Find 4 ϫ 26. Complete to find the product.Print This Page Name Multiply 2-Digit Numbers by 1-Digit Numbers You can multiply using models or pencil and paper. (152) . 45 ϫ9 © McGraw-Hill School Division 6. 48 ϫ 6 ϭ NS 3. 4 ϫ 2 tens ϭ 8 tens Step 3 Add. You may use models to help you.3 Use with Grade 4. 3. pages 196–199. 86 ϫ4 10. 1. 31 ϫ8 4. Chapter 5. 4 ϫ 6 ones ϭ 24 ones Print This 5–3 Page R RETEACH You can record this way: 26 ϫ4 24 26 ϫ4 24 ϩ 80 26 ϫ4 24 ϩ 80 104 Step 2 Multiply the tens. 45 ϫ5 7.2. Multiply 7 ϫ 8. Write 7 on the right.3 . Start at the right. 5 ϫ 34 ϭ 3. 7 ϫ 79 ϭ 3 7 6 8 3 7 8 9 2 2 4 9 5 6 6 5 4 8 0 2 4 4 5 4 9 5 6 3 3 7 Use with Grade 4. Write 56 in the first box. Write 28 in the second box. Multiply 7 ϫ 48. Chapter 5. 1. pages 196–199. 8 ϫ 63 ϭ 6. 3. Regroup as you would in any addition problem.2. Print This 5–3 Page E ENRICH Multiply 7 ϫ 4. 2 ϫ 27 ϭ 2. 4 ϫ 56 ϭ 2 7 3 2 4 5 5 6 1 4 5 4. Lesson 3. (153) NS 3. Write 48 over the top boxes. 4 2 5 8 3 6 8 48 7 ϫ 7 336 6 4 8 7 4 5 8 7 6 3 Use lattice multiplication to find the products.Print This Page Name Multiply 2-Digit Numbers by 1-Digit Numbers Lattice Multiplication You can use lattice multiplication to multiply. Add on the diagonals. 8 ϫ 37 ϭ 4 4 1 1 5 7 2 0 0 2 2 0 2 2 4 4 4 © McGraw-Hill School Division 5. 7 ϫ 1.3 . 612 ϫ 9 ϭ 14. 41 ϫ 6 20. 4 ϫ 305 ϭ 11.2. 7 ϫ $46 ϭ 6. 8 ϫ 3. 4 ϫ 712 6 ϫ 523 36. 85 ϫ 6 ϭ 7. 1. 5 ϫ 423 © McGraw-Hill School Division Estimate. Chapter 5. About how much does it cost for 6 kits? miles a day. 6 ϫ 105 1 ϫ 49 89 ϫ 2 68 ϫ 4 31.723 ϫ 4 ϭ 3. 3 ϫ $2. 488 ϫ 3 26. 4.4. 5 ϫ 784 ϭ 13.307 ϫ 5 28. Each kit costs $39.118 ϭ 22. 5 ϫ 21 ϭ 4. The volunteer ambulance group 39. 3. 6 ϫ 556 ϭ Print This 5–4 Page P PRACTICE 15. 2. 2 ϫ 36 32. 255 ϫ 4 25. 97 ϫ 1 35. An ambulance travels about 386 orders 6 first aid kits. 96 ϫ 3 33. 2 ϫ $298 ϭ 10. pages 200–201. 3 ϫ 666 Problem Solving 38.596 ϫ 6 Algebra & Functions 29. 5 ϫ $7. 3 ϫ 39 ϭ 5. 563 ϫ 5 27. About how many miles does it travel in a week? Use with Grade 4. 2. 31 ϫ9 24.Print This Page Name Estimate Products Estimate each product. 396 ϫ 4 2 ϫ 366 37. Write Ͼ or Ͻ. 30.987 ϭ 16. Lesson 4. 2 ϫ 1.126 ϭ 17. 17 ϫ 9 ϭ 8. 478 ϫ 6 ϭ 12. (154) NS 1. 7.905 ϭ 18. 81 ϫ 3 ϭ 9. 3. 28 ϫ 7 21.495 ϭ 19. 6 ϫ 28 5 ϫ 41 106 ϫ 9 3 ϫ 412 4 ϫ 209 34. 96 ϫ 2 17 ϫ8 23. 623 ϫ 8 32. 8 ϫ 287 is about 2. 2.409 31. 7. 1. 5 ϫ 2. 9 ϫ 18 8. Estimate 8 ϫ 287. 2. (155) NS 1. 8 ϫ 300 ϭ 2. 6 ϫ 36 6. $66 ϫ 4 17 ϫ5 17. 3 ϫ 71 9.Print This Page Name Estimate Products You can round to estimate products. Print This 5–4 Page R RETEACH ↓ 8 ϫ 287 8 ϫ 300 ↓ 287 200 210 220 230 240 250 260 270 280 290 300 Multiply using the rounded number Estimate each product.522 ϫ 9 Use with Grade 4. 4. Round 287 to the nearest hundred. 845 ϫ 2 23. $637 ϫ 4 22. 2 ϫ 74 4. Lesson 4.4.987 13. Round the greater factor to its greatest place and multiply using patterns. 4 ϫ 378 12.524 ϫ 8 26. 8.400.905 16. 51 ϫ6 18.047 ϫ 3 25. 3. 5. $7. 498 ϫ 9 21. 3 ϫ 198 10. 7 ϫ $2. 2 ϫ $405 11.809 ϫ 6 24. 8 ϫ 2. Chapter 5.537 ϫ 4 29. © McGraw-Hill School Division $454 ϫ 7 19. $2. $6. 31 ϫ2 58 ϫ3 15.400 So. pages 200–201.3 .126 14. 6 ϫ $58 7.107 ϫ 6 27. $6.088 ϫ 2 30. ϫ 7 3.2. 3.596 ϫ 4 28. 3 ϫ 42 5. 512 ϫ 8 20. 3. 762 ϫ 7 Z. 79 ϫ 9 U. 76 ϫ 8 A.000 L. Circle the letter of the answer. 9 ϫ 430 12.400 I. 839 ϫ 8 J. Chapter 5. 782 ϫ 9 Print This 5–4 Page E ENRICH 3. 52 ϫ 3 4.000 17.200 A. 2. 849 ϫ 4 O.097 ϫ 7 Write the circled letters above each exercise number to answer the question.500 E.700 T. 4. 4. 7 ϫ 68 8. 352 ϫ 8 16. 889 ϫ 4 13.181 ϫ 3 M. 4. Target Number: 2. 3 ϫ 849 10. Target Number: 4. Target Number: 2. Target Number: 25. 7 ϫ 62 U. 899 ϫ 8 2.4. 4.Print This Page Name Estimate Products Target Practice Estimate to find the factors whose product is closer to the target number. 57 ϫ 3 T.000 © McGraw-Hill School Division Q. Target Number: 150 S. Target Number: 180 D. Target Number: 6. Target Number: 630 T.2.898 ϫ 3 15. 83 ϫ 6 7.000 18. pages 200–201. “I lift my lamp beside the golden door!” Who am I? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 NS 1. Target Number: 6. Target Number: 560 O. 711 ϫ 9 B.899 ϫ 5 T. Target Number: 7. 72 ϫ 8 9. Target Number: 160 H. 7.175 ϫ 5 R. 3 ϫ 61 6. Target Number: 540 S. 3. 9 ϫ 490 F.400 E. 3 ϫ 67 E. 37 ϫ 4 I.600 E. (156) . Target Number: 5. 3. Lesson 4. 72 ϫ 9 11.825 ϫ 4 U.600 N. 1. Target Number: 420 T. Target Number: 35. 770 ϫ 8 F. 88 ϫ 6 T. Target Number: 3. 303 ϫ 8 F. 680 ϫ 8 14.239 ϫ 4 Y. 2. Target Number: 32. 3 ϫ 879 U. 32 ϫ 4 5.3 Use with Grade 4. 7. On Wednesday. A total of 184 people are taking a desert hike. The park rangers have 3 boxes of fact books.1. (157) MR 1.4. Print This 5–5 Page P PRACTICE Reading Skill Each student will get a nature guide fact book.2 . Are there enough fact books so each student can get a book? 2. pages 202–203. Each hiking group © McGraw-Hill School Division can have up to 36 people. These books come in boxes of 32. Chapter 5. The Nolans want to use a campsite for 4 nights. 2. Are there enough hike leaders and helpers so that all of the people can go on a hike? Use with Grade 4. 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. Lesson 5. They have $80 set aside for using a campsite.Print This Page Name Problem Solving: Reading for Math Use an Overestimate or Underestimate Form a conclusion about whether you would use an overestimate or an underestimate. Then solve each problem. a group of 98 students will visit the national forest. 1. There are enough hike leaders and helpers to lead 6 groups. The park charges $16 per day to use a campsite. 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. Have the Nolans set aside enough money? Should you use an overestimate or an underestimate to solve this problem? Explain. 3. Have the Nolans set aside enough money? 3. Are there enough pamphlets for a day of river tours? 5. © McGraw-Hill School Division There are 7 river tours per day. Chapter 5. A group of 120 is visiting the forest.2 . Lesson 5.Print This Page Name Problem Solving: Reading for Math Use an Overestimate or Underestimate Choose the correct answer. B Each bus can hold 48 students.1. H overestimate the number of tables. to hold 148 students. Each bus can hold 48 students. The tour leaders have 400 pamphlets. G overestimate the number of students the buses can hold. Are there enough tables so that all 120 people can eat in the cafeteria at once? 3. to seat 120 people. Which statement is true? Print This 5–5 Page P PRACTICE Math Skills Test Prep 2. How would you use estimation to 6. To make sure that 3 buses are enough A There are 48 students going on a trip to the desert. G underestimate the number of tables. Each river tour has room for 48 people. The cafeteria in the national forest visitors’ center has 23 tables. Which statement is not true? 4. 2. pages 202–203. C Each table can seat 6 people. 3. Each person on the river tour receives a pamphlet. The school has 3 buses. B The cafeteria has 23 tables. you should F underestimate the number of students the buses can hold. To make sure there are enough tables A Each table can seat 23 people. Should a fourth bus be ordered for the trip? 1. (158) solve the problem? F 7 ϫ 40 ϭ 280 G 6 ϫ 50 ϭ 300 H 7 ϫ 50 ϭ 350 MR 1. There are 146 students going on a trip to the desert. C Three buses can hold exactly 150 students. Each table seats 6 people.4. you should F overestimate the number of seats. Which estimate would you use 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. H underestimate the number of students going on the trip. 1. Will $650 be enough to rent an SUV for a 7-day trip through the desert? Use with Grade 4. 2. How would you use estimation to Print This 5–5 Page P PRACTICE Math Skills Test Prep 8. Nick sets aside $150 to pay for the motel. The motel in the national park costs 14. Are there enough boats to take 76 people on a tour? each. There are 5 groups of 25 students has room for 24 people. pages 202–203. Phyllis takes 118 photos of the © McGraw-Hill School Division wildlife guides. Is this enough money to pay for 5 nights? vehicle (SUV) for one day. The rangers need 200 pamphlets. Which estimate would you use to solve this problem? A overestimate the amount made on each book B underestimate the amount made on each book C underestimate the number of books Solve.75 on each book it sells. Each boat solve the problem? F $9 x 50 = $450 G $8 x 50 = $400 H $8 x 40 = $320 10. Do they have enough T-shirts to give a T-shirt to each student? 11. The forest rangers have 5 boxes of 12. Lesson 5. 3. If the committee sells 50 books. Chapter 5. The rangers have 150 forest T-shirts. (159) MR 1.Print This Page Name Problem Solving: Reading for Math Use an Overestimate or Underestimate Choose the correct answer. The river tour has 4 boats. The committee makes $8.2 . It costs $89 to rent a sport utility $39 per night. 9. Should they order another box? desert. Each box contains 36 pamphlets. Can all the photos fit in the album? 13.4. She buys a photo album with 24 pages. The Wildlife Committee is selling books to raise $400. will that be enough to raise $400? 7. Each page can hold 6 photos. 1. pages 206–209. 907 ϫ 5 3. A company buys 8 computers.Print This Page Name Multiply Greater Numbers Multiply. 10.091 ϭ 15. Maria made 9 trips between 20. Multiply 3. Each New York City and Los Angeles. How much does the company spend on the 8 computers? Use with Grade 4. 5 ϫ 19.901 ϫ 2 6.786 ϭ 12.369 ϭ 11. 6 ϫ 2. 368 ϫ 9 4. $38. 8 ϫ 12.245.967 ϭ 16.096 by 9.072 ϫ 8 8. Input Output 3 4 5 © McGraw-Hill School Division Problem Solving 19.2.999 ϫ 7 7. 2. 3. How much did the 9 trips cost? computer costs $2.88 ϫ 4 9. Print This 5–6 Page P PRACTICE 693 ϫ 4 2.687 by 8. Chapter 5. 8. Each trip cost $498. (160) NS 3.3 . Check for reasonableness. Multiply 1. Algebra & Functions Complete the table. 9 ϫ $1. $601 ϫ 3 5. 17. Input Output 12 48 1 37 15 60 2 74 18 21 24 18. Lesson 6.288 ϭ 14. 7ϫ 5. 1. 3 ϫ 4.964 ϭ 13. 530 10.862 ϫ 9 9. © McGraw-Hill School Division Print This 5–6 Page R RETEACH You can record this way: 1 357 ϫ 2 4 11 357 ϫ 2 14 11 357 ϫ 2 714 234 ϫ 5 2.Print This Page Name Multiply Greater Numbers You can use models to help you multiply greater numbers. 9. 2 ϫ 5 tens ϭ 10 tens Add the tens. 357 ϫ 4 4.62 ϫ 6 5. Chapter 5. (161) NS 3. Step 1 Multiply the ones.681 ϫ 2 11.548 ϫ 2 6.452 ϫ 5 Use with Grade 4. ϫ 4 2. $6. Lesson 6. Check for reasonableness. 14 ones ϭ 1 ten 4 ones Step 2 Multiply the tens.781 ϫ 8 8.275 ϫ 6 12. $1.164 ϫ 7 7. Show 2 groups of 357. 6 hundreds ϩ 1 hundred ϭ 7 hundreds Multiply. 4. 10 tens ϩ 1 ten ϭ 11 tens Step 3 Multiply the hundreds. 2. 2 ϫ 3 hundreds ϭ 6 hundreds Add the hundreds. 3.3 . $4.2. 1. 146 ϫ 3 3. pages 206–209. $7. Find 2 ϫ 357. 3. 2 ϫ 7 ones ϭ 14 ones Regroup. 450 3 24. 4.472 Use with Grade 4.564 13.6 ϫ 7. $1. 6. 2 ϫ 3 735 14. 25 9 5 16. 3 ϫ 138 7. 3 1 ϫ 1.3 . 2 56 19.3 3.3 9 82. Lesson 6.0 ϫ $5. 46 ϫ . ϫ 1 4 5 0 6.400 © McGraw-Hill School Division 17. 3. ϫ 7 76 . 1. 74. 9 8 5 18.38 ϫ 31 .666 12.6 7 5 22. 4 ϫ 32 0. Print This 5–6 Page E ENRICH 3 ϫ 8 184 2. Chapter 5. 1 ϫ 7 98 3. 4. 29. 4 64 15. . 4 ϫ 6 744 1 10. ϫ 5 . ϫ 3 2. 3 ϫ 111 ϫ 3 174 5. ϫ 7.184 21. ϫ 75 23. ϫ 7 434 9.06 7 9 20. pages 206–209. (162) NS 3. Write them in the boxes.2. 2 ϫ 416 8. 8. $3 ϫ $1 . 3 ϫ 7 1.Print This Page Name Multiply Greater Numbers Deducing Digits Find the missing digits. 1 ϫ 4 770 11. In one desert area. She puts 3 chestnuts in the first row. The fourth tree has 81 rings. 1. Describe the pattern. 5. 6. Social Studies Colorado’s state © McGraw-Hill School Division He has one photo album with 8 pages and another with 12 pages. The first tree has 3 annual rings. The third tree has 27 rings. Annie makes an arrangement of Print This 5–7 Page P PRACTICE 2. The next year he counts 9 nests.Print This Page Name Problem Solving: Strategy Find a Pattern Use find a pattern to solve. (163) NS 3. If the pattern continues. Connecticut’s state parks cover 176. One year he counts 4 nests. Which album should he use? parks cover 347. 3. and 9 chestnuts in the third row. Nick took 40 photos of the desert. how many annual rings does the fourth tree have? block. The fourth year he counts 19 nests. the rabbit chestnuts.2. The second tree has 9 rings.000 acres. Rangers examine trees that fell 4.1. and 200 the next year. Chapter 5.2 . Share it with others. How many chestnuts will be in the fourth row? population is estimated at 25 in one year. Nick wants to put the same number of photos on each page. 2. pages 210–211. 3. Create a problem for which you would find a pattern to solve. Then estimate the rabbit population for the fifth year. 6 chestnuts in the second row. How many more acres do state parks cover in Colorado than in Connecticut? Strategy: Strategy: 7.000 acres. Stan counts robins’ nests on his during a storm.4. If the pattern continues. Use any strategy. 50 the next year. The third year Stan counts 14 nests. Lesson 7. MR 1. 100 the third year. Describe the pattern. how many nests will he count in the fifth year? Mixed Strategy Review Solve. Use with Grade 4. 4.2 . 2. and four cells divide into What do you need to find? • You need to find how many . pages 210–211. cells. Continue the pattern to find the number of cells after the 7th cell division. Problem 1 Print This 5–7 Page R RETEACH As a plant cell grows. Use with Grade 4. (164) NS 3. four into eight. What do you know? • One cell divides into cells. and 3rd cell divisions. How many cells will there be after seven divisions? Step 1 Read Be sure you understand the problem. Lesson 7. Describe the pattern. 2nd. Step 2 Plan I I Make a plan. Two cells divide into four cells.Print This Page Name Problem Solving: Strategy Find a Pattern Page 211. and so on. Choose a strategy. 3. Read carefully. 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 I I I © McGraw-Hill School Division I I I I I 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 Find the pattern in the number of cells after the 1st. one cell divides into two cells. MR 1.1. Chapter 5.2. two cells divide into cells. Finding a pattern will help you solve the problem. 2 . $12. If the pattern continues. and 3rd cell divisions. there will be cells after the 7th cell division.000.000. If the pattern continues. What pattern do you see? Continue the pattern to complete the chart. Lesson 7. how many miles will she hike the fourth day? goals of $3. Kate hikes 2 miles the first day. Did you find a pattern and continue it? Yes No What other strategies could you use to solve the problem? © McGraw-Hill School Division Practice 1. $6. You know the number of cells after the 1st.Print This Page Name Problem Solving: Strategy Find a Pattern Step 3 Print This 5–7 Page R RETEACH Solve Carry out your plan. 2nd.000 for its first four fund drives.1. If the pattern continues. and 8 miles the third day. 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. Chapter 5. pages 210–211. 2.2. The Support-Our-Forests Fund has 5 miles the second day. what will the goal be for the fifth fund drive? Use with Grade 4. 2nd. Step 4 Look Back Is the solution reasonable? Reread the problem. (165) NS 3. and $24. MR 1.000. 3.4. 2. another number. Then graph the function. y ϭ 4x x 0 y 7. 3 4 5 x y 1 8 2 9 r s 1 8 2 16 3 4 5 3.Print This Page Name Functions and Graphs Complete each table. 6 7 8 c d 4 8 5 11 m n 1 10 2 12 3 4 5 Complete each table. One number is 8 greater than 2 times another number. pages 212–215. Roger runs 7 miles more each week Print This 5–8 Page P PRACTICE 2. Liz swims 2 more than 2 times as Jana does.5. peppers than another plant. Lesson 8. (166) AF 1. Chapter 5. many laps as Sunny does. Each of 4 people orders a $8. 1. Stella works 4 times as many hours as 6. lunch. SDP 2. How much do the 4 lunches cost? Write and solve an equation.1 . Then write an equation. 1. One plant produces 8 times more than another boy.1. 5. 2 3 4 a ϭ 2b ϩ 2 b 0 1 a 2 4 2 3 4 0 s ϭ 2r Ϫ 2 r 1 0 2 2 3 4 5 n ϭ 3t ϩ 1 t n 1 4 2 7 3 4 5 © McGraw-Hill School Division s Problem Solving 9. How much do the toys cost? Write and solve an equation.95 10. Use with Grade 4. One number is 4 less than 3 times 4. 1 4 8. Ben buys 3 toys that cost $3 each. 3. The values in the table form ordered pairs. One number is 2 greater than 2.Print This Page Name Functions and Graphs The numbers in a function table relate to one another to form a pattern. SDP 2. number. 1. Write the ordered pairs. One number is 1 greater than 2 times a number. 5) (3. Then write an equation. 11) You can graph these ordered pairs Complete each table.y ϭ 2x ϩ 2 x y 0 0 1 2 2 3 4 x y 0 2 1 4 2 3 4 Use with Grade 4. Think: Multiply x by 4 to get y. Print This 5–8 Page R RETEACH x y 1 3 2 5 3 7 4 9 5 11 3 4 5 Think: How can I find the value of y? xϭ 1 2 Equation ϭ 2x ϩ 1 ↓ ↓ 3 2x ϩ 1 ↓ ↓ 5 2x ϩ 1 ↓ ↓ 7 2x ϩ 1 ↓ ↓ 9 2x ϩ 1 ↓ ↓ yϭ 11 In each case. 9) (5. Think: Add 2 to x to get y. 5 x y © McGraw-Hill School Division 1 3 2 4 3 4 x y 1 4 2 8 3 4 5 Complete each table. 1. One number is 4 times another another number.1. Lesson 8. Then graph the function. Chapter 5. pages 212–215. multiply by 2 and add 1. 7) (4. 3) (2.1 .5. y) (1. (167) AF 1. x 1 2 3 4 5 y 3 5 7 9 11 (x.y ϭ 2x 4. find the points on the grid. 1) (6.1. SDP 2. 2) (0. 6) (7. 7) (2. 2) (9. 8) (4. 5) (3. Print This 5–8 Page E ENRICH (1. Lesson 8. Chapter 5. 8) (0. 0) (1. Then write the letter for each point on the lines. 8) (0. 1. Use with Grade 4. 6) (4.Print This Page Name Functions and Graphs When Are Houses Like Books? To answer this riddle.1 . 6) (6. 0) (7. 2) and (6. pages 212–215. 4) (7. name two other points that would make a square. 3) (7. (168) AF 1. 1) (3. 5) (0. 6) (6. 5) 12 11 10 9 8 7 6 5 4 3 © McGraw-Hill School Division H A E S Y W V O T 0 1 2 3 4 5 6 7 8 9 10 11 12 I 2 1 R N If you are given the points (2.5. 2). one dinner.3.1. Chapter 5. 3.2.2. MR 1.1 .Print This Page Name Problem Solving: Application Analyze and Make Decisions Record your data. one lunch. Item Name Cost of Item per Unit Number of Units Total Cost of Item 5–9 Part A WORKSHEET Decision Making Print This Page Total Cost of Meal or Snack Breakfast Items Lunch Items Dinner Items Snack Items © McGraw-Hill School Division Your Decision What is your recommendation for the menus (one breakfast. 2. (169) NS 1. and snacks)? Use with Grade 4. Lesson 9. pages 216–217. 3. (170) NS 1. 3. Lesson 9. Chapter 5. 3. MR 1.3 . Place You Use Water Number of Times Amount of Water a Day You Use This for Each Use Source of Water 5–9 Part B WORKSHEET Math & Science Print This Page Total Amount of Water © McGraw-Hill School Division Use with Grade 4. pages 218–219.2.Print This Page Name Problem Solving: Application How much water do you use each day? Record your data.2.1. 3 .1. 3. (171) NS 1. © McGraw-Hill School Division 5. Use with Grade 4. Chapter 5. How much water is being used by your whole class each day? 4. Work Space 3. pages 218–219.2.2. If a cup of water costs $0. Give some other examples of renewable and nonrenewable resources. how much money do you spend on water each day? Show your work. 3. How much water do you use each day? 5–9 Part B WORKSHEET Math & Science Print This Page 2.10. Lesson 9.Print This Page Name Problem Solving: Application How much water do you use each day? 1. Is clean water a renewable or nonrenewable resource? Explain. MR 1. 30 ϫ 6.800 400 ϫ t ϭ 12.000 © McGraw-Hill School Division Find each missing number.000 ϫ 90 ϭ 23.000 ϫ 70 ϭ 16. 40 ϫ 800 ϭ 20.000 nails in each carton.Print This Page Name Patterns of Multiplication Complete.000 sϭ tϭ rϭ 28.000 ϭ Algebra & Functions 24. 50 ϫ 5. How many hinges does the store have? Use with Grade 4.000 26.000 ϭ 5. 6. 1. 29. 700 ϫ 40 ϭ 4. 400 ϫ 30 ϭ 11.100 30. (172) NS 3. 80 ϫ 800 ϭ 8. jϭ bϭ qϭ 25. There are 4. w ϫ 3 ϭ 21 70 ϫ 3 ϭ x wϭ xϭ yϭ zϭ 60 ϫ t ϭ 480 60 ϫ 80 ϭ u 60 ϫ 800 ϭ v y ϫ 30 ϭ 2.000 ϭ 21.000 ϭ 14. How many nails does the store have? Handy Hardware has 500 boxes of hinges. 50 ϫ 40 ϭ 10.000 ϫ 30 ϭ 15.100 70 ϫ 300 ϭ z Multiply. 27. 6 ϫ 8 ϭ Print This 6-1 Page P PRACTICE s sϭ tϭ uϭ vϭ 2.000 ϫ 80 ϭ 19. 30 ϫ 200 ϭ 9. 90 ϫ 70 ϭ 13. p ϫ 600 ϭ 30.000 n ϫ 300 ϭ 6. 900 ϫ 60 ϭ 17.2 . pages 234–235. nails. 20 ϫ 500 ϭ 22. Each box has 90 hinges. 7. 600 ϫ 50 ϭ 12. 80 ϫ 5. ABC Hardware has 50 cartons of 33. 20 ϫ 60 ϭ 7. 20 ϫ 4.000 ϭ 18. Chapter 6. Use mental math. 3. 80 ϫ 2. 31.000 p ϭ r ϫ 800 ϭ 40. 60 ϫ 70 ϭ 6. s ϫ 70 ϭ 2. Lesson 1. 30 ϫ j ϭ 9. 60 ϫ b ϭ 24. 9. 90 ϫ q ϭ 8. 3.000 n ϭ Problem Solving 32. 2.000 ϭ Multiply. 300 ϫ 9 ϭ 17. 5 ϫ 6 ϭ 70 ϫ 20 ϭ 70 ϫ 200 ϭ 70 ϫ 2. 4. 70 ϫ 7. Lesson 1. Chapter 6. (173) . 30 ϫ 60 ϭ 9.000 ϫ 90 ϭ 21.000 1 zero 2 zeros 3 zeros 40 ϫ 5.2 Use with Grade 4. pages 234–235.000 1 zero 1 zero 2 zeros 40 ϫ 500 ϭ 20.000 ϭ 20. 2 ϫ 3 ϭ 6 basic fact 20 ϫ 30 ϭ 600 1 zero 1 zero 2 zeros 20 ϫ 300 ϭ 6. 30 ϫ 8. 30 ϫ 600 ϭ 10.000 1 zero 3 zeros 4 zeros 40 ϫ 30 ϭ 40 ϫ 300 ϭ 40 ϫ 3.000 ϭ 5.000 ϭ 60. 4 ϫ 9 ϭ 11.000 ϫ 60 ϭ 7. © McGraw-Hill School Division 80 ϫ 50 ϭ 80 ϫ 500 ϭ 80 ϫ 5. 80 ϫ 30 ϭ 14. 4 ϫ 3 ϭ 2.000 ϭ 200.000ϭ NS 3.Print This Page Name Patterns of Multiplication You can use basic facts and patterns to help you multiply.000 ϭ 4. Use mental math. 40 ϫ 90 ϭ 12. 1. 7 ϫ 2 ϭ Print This 6–1 Page R RETEACH 4 ϫ 5 ϭ 20 basic fact 40 ϫ 50 ϭ 2.000 1 zero 3 zeros 4 zeros Complete the pattern. 7. 20 ϫ 50 ϭ 16.000 ϫ 50 ϭ 22. 3 ϫ 6 ϭ 8. 8 ϫ 5 ϭ 50 ϫ 60 ϭ 50 ϫ 600 ϭ 50 ϫ 6. 700 ϫ 30 ϭ 15.000 ϭ 6.000 1 zero 2 zeros 3 zeros 20 ϫ 3.000 ϭ 3. 90 ϫ 8. 40 ϫ 900 ϭ 13. 80 ϫ 600 ϭ 18. 70 ϫ 800 ϭ 19. 3. 4. 70 ϫ 90. 6. Use with Grade 4. 4. Print This 6–1 Page E ENRICH 1 2 3 4 5 6 Across 1. Each answer is a product of two factors. 2. (174) NS 3. Lesson 1. pages 234–235.2 . 6. 5.Print This Page Name Patterns of Multiplication Clueless Puzzle This puzzle has all the answers. Make up clues for each answer. 5. 3. 80 ϫ 8.000 2. but no clues. Chapter 6.000 © McGraw-Hill School Division Down 1. Print This Page Name Explore Multiplying by 2-Digit Numbers Multiply. 49 ϫ 30 26. 19 ϫ 27 25. 17 ϫ 25 9. 17 ϫ 17 23. 3. Lesson 2. 1. 48 ϫ 20 11. How many students ride the buses? Use with Grade 4. 12 ϫ 46 19. 26 ϫ 21 ϭ 32. 32 ϫ 18 17. 38 ϫ 27 12. 46 ϫ 14 8. The art teacher wants to decorate 39. 63 ϫ 15 ϭ © McGraw-Hill School Division 27. Print This 6–2 Page P PRACTICE 36 ϫ 12 2. 30 ϫ 13 ϭ 30. 15 ϫ 23 ϭ 29. 26 ϫ 34 16. 36 ϫ 36 20. There are 35 buses waiting for each classroom with 28 balloons.3 . How many balloons does he need for 18 classrooms? students after school. 25 ϫ 25 ϭ 35. (175) NS 3. 16 ϫ 40 22. 32 ϫ 15 13. 28 ϫ 44 21. 47 ϫ 34 7. 23 ϫ 22 5. 37 ϫ 26 24. Each bus carries 45 students. 49 ϫ 13 6. 14 ϫ 22 ϭ 31. 45 ϫ 25 14. pages 236–237. 30 ϫ 24 ϭ 33. 14 ϫ 15 15. 13 ϫ 13 ϭ 37. 45 ϫ 35 10. 31 ϫ 25 18. Chapter 6. 38 ϫ 14 4. 32 ϫ 20 ϭ 28. 27 ϫ 41 3. 42 ϫ 17 ϭ 34. 70 ϫ 14 ϭ Problem Solving 38.2. 50 ϫ 23 ϭ 36. 2. 18 ϫ 41 9. 42 ϫ 33 6. © McGraw-Hill School Division 3. Think: 12 ϭ 10 ϩ 2 19 ϫ 12 38 ϩ 190 228 Print This 6–2 Page R RETEACH 19 2 2 ϫ19 10 ϫ19 10 38 ϩ 190 ϭ 228 Find each product. 49 ϫ 27 7. pages 236–237. 41 ϫ 32 ϭ 15.3 Use with Grade 4. 45 ϫ 28 12. 35 ϫ 26 5. (176) . Chapter 6. Draw an array diagram to help you. 24 ϫ 52 11. 1. 14 ϫ 15 ϭ 2. 27 ϫ 27 13.Print This Page Name Explore Multiplying by 2-Digit Numbers An array can help you multiply. 32 ϫ 21 ϭ 14. 3. 32 ϫ 18 8. 11 ϫ 19 ϭ Multiply. Find 12 ϫ 19. 26 ϫ 17 ϭ NS 3. Lesson 2. 28 ϫ 14 4. 23 ϫ 17 10. Here is a way to use Napier’s Bones to multiply 49 ϫ 37. INDEX Add diagonally to find the product. pages 236–237. 57 ϫ 34 ϭ 4. (177) . 32 ϫ 33 ϭ 7. Remember to carry. Place the strips headed 4 and 9 next to each other. 39 ϫ 68 ϭ 2. 75 ϫ 38 ϭ 3. 1. John Napier invented a simple calculator that multiplied by adding. Use them to find each product. 94 ϫ 65 ϭ 8. 85 ϫ 29 ϭ 6. INDEX 4 8 1 2 1 6 2 0 2 4 2 8 3 2 3 6 9 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 1 2 2 8 9 2 7 6 3 1 3 7 4 1 2 2 8 9 2 7 6 3 1 3 7 37 ϫ 49 Cut out the ten strips of Napier’s Bones below.3 Use with Grade 4. 56 ϫ 48 ϭ 9. Start at the bottom with the ones. INDEX Print This 6–2 Page E ENRICH Fold the strips so that the rows headed 3 and 7 on the index are next to each other.Print This Page Name Explore Multiplying by 2-Digit Numbers Napier’s Bones In the seventeenth century. 89 ϫ 21 ϭ Napier’s Bones INDEX © McGraw-Hill School Division 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 0 5 0 5 0 5 0 5 1 1 2 2 2 3 3 8 2 6 0 4 8 2 6 1 1 1 2 2 2 6 9 2 5 8 1 4 7 1 1 1 1 1 4 6 8 0 2 4 6 8 2 3 4 5 6 7 8 9 NS 3.2. 61 ϫ 76 ϭ 5. Chapter 6. 3. Lesson 2. It became known as Napier’s Bones. Place the index beside the two strips. How much will 30 chairs cost? Problem Solving 41.3 .967 ϫ 10 20. 87 ϫ 10 5. 207 ϫ 60 9.075 ϫ 80 21. 80 ϫ 1. 42. 40 ϫ 608 ϭ 28.226 ϫ 20 14.002 ϫ n ϭ 70. Lesson 3.185 ϭ 32. 1. 135 ϫ 50 8. 56 ϫ m ϭ 1.549 ϭ Algebra & Functions 33. 861 ϫ b ϭ 77.375 ϫ 20 17. 91 ϫ 20 4.160 qϭ mϭ nϭ cϭ 35.490 39. 6. 2.108 ϭ 63.038 ϫ 40 13.116 ϭ 31. 39 ϫ 80 ϭ 25.510 ϫ 60 15.345. 36.240 s ϭ Classroom chairs cost $39.503 ϫ 50 16. 4. Print This 6–3 Page P PRACTICE 26 ϫ 40 2. 99 ϫ a ϭ 7. 17 ϫ 80 7. 399 ϫ 50 10.680 38. 1. 23 ϫ 90 6. 3. 712 ϫ 30ϭ 30. 67 ϫ 20 ϭ 26. (178) NS 3.009 ϫ 40 18. jϭ aϭ bϭ 34. 50 ϫ 5.920 37.Print This Page Name Multiply by Multiples of 10 Multiply. 325 ϫ 60 ϭ 27. A computer costs $2. 2.140 40. 10 ϫ 3. 999 ϫ 10 ϭ 29. 51 ϫ 30 ϭ 24. 47 ϫ 30 3. 1.2. Chapter 6.090 ϭ 22. 90 ϫ 4. 34 ϫ j ϭ 680 © McGraw-Hill School Division Find the missing number. pages 238–239. 2. How much will 20 computers cost? Use with Grade 4. 3. 9. 5. 498 ϫ 70 12.490 ϫ 70 19.111 ϫ 70 ϭ 23. 2. q ϫ 72 ϭ 2. 756 ϫ 30 11. 898 ϫ c ϭ 53.880 s ϫ 2. 2. 20 ϫ 39 ϭ NS 3. 10 ϫ 39 ϭ 16. 40 ϫ 18 ϭ 18. 10 ϫ 28 2. Lesson 3. Chapter 6. © McGraw-Hill School Division ) ϫ (60 ϩ ϫ ϭ ) ( ϫ ) ϩ( ϩ ) ϫ ϭ ) 34 ϫ 40 6. 35 ϫ 20 12. pages 238–239.Print This Page Name Multiply by Multiples of 1 0 An expanded form can help you multiply. 57 ϫ 60 15. 5. 19 ϫ 30 13. (179) . 18 ϫ 50 10. 80 ϫ 27 4. 50 ϫ 64 ϫ (20 ϩ ( ϫ )ϩ( ϩ Multiply. Think: 37 ϭ 30 ϩ 7 20 ϫ (30 ϩ 7) (20 ϫ 30)ϩ (20 ϫ 7) 6 0 0 ϩ 1 4 0 ϭ 740 37 ϫ 20 740 Print This 6–3 Page R RETEACH Complete to find each product. 30 ϫ 32 ϭ 20. 22 ϫ 10 14. Find 20 ϫ 37.3 Use with Grade 4. 30 ϫ 33 10 ϫ ( ( ϩ 8) ϫ 20) ϩ ( ϩ ϫ 8) ϭ ( ϫ( ϫ ϩ 3) ) ϩ( ϩ ϫ ϭ ) 3. 43 ϫ 10 9. 1. 27 ϫ 30 7. 38 ϫ 40 8. 3. 16 ϫ 30 ϭ 17. 28 ϫ 30 ϭ 19. 24 ϫ 80 11. 0 0 0 2. 1 2 0 2 5 ϫ 8 0 7 4. 19. 8 4 0 5 8 4 ϫ 0 3 5. 6 2 0 9 1 ϫ 9 0 8 2. Print This 6–3 Page E ENRICH 7 4 ϫ 1 7 4 0 9 ϫ 9 0 6. 7. 8 8 0 5 6 ϫ 9 0 5 0. 9. 6 4 0 2 1 1 ϫ 0 1 0. 4 9 0 4 6 ϫ 0 1. 6. 1. 7 6 0 9 5 3. 16. 20. 17. 6 2 ϫ 0 3. 25. Use with Grade 4. 0 8 0 6 7 ϫ 3 0 2 0. 2 0 0 7 6 8 5. 4 4 0 6 3 6 ϫ 0 5 7. 5 5 0 4 6 ϫ 7 0 5 2. 2 5 0 4 ϫ 5 0 3 9. 2 4 0 7 1 6 ϫ 0 6 4. 0 4 0 3 ϫ 6 0 3 3. 22.Print This Page Name Multiply by Multiples of 10 Missing Digits Find each missing digit. Chapter 6. 14. 28. 3 ϫ 5 0 1. 7 8 0 8 3 ϫ 4 0 3 3. 8 ϫ 3 0 2. 6 5 0 4 ϫ 7 0 6. 5 6 0 5 ϫ 2 0 1 8. pages 238–239. 10. 7 2 0 8 1 ϫ 0 1. 11. © McGraw-Hill School Division 21.3 . 5 0 0 5 4 ϫ 4 0 2 1. 4 9 0 5 ϫ 7 0 4 7. 27. Lesson 3. 2 4 0 4. 13. 8. 3. 2 2 0 1 4 ϫ 8 0 2 5.2. (180) NS 3. 6 3 0 6 ϫ 8 0 6 6. 1 9 0 7 8 ϫ 8 0 3 8. 15. 26. 5 8 0 7 2 1 ϫ 0 2 1. 24. 18. 2 1 0 4 8 ϫ 8 0 3 8. 23. 12. Burke’s Bluff Beach sells 25 guest passes in one day. A group of travelers rents 5 boats for 8 hours each. 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. Each student pays a total of $50 for the classes for the season. 2. 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. (181) MR 1. Boats cost Print This 6–4 Page P PRACTICE Reading Skill $12 an hour to rent.Print This Page Name Problem Solving: Reading for Math Solve Multistep Problems Circle the hidden question that can help you solve the problem. A swimming instructor has 4 classes with 8 students in each class. Estimate the total number of guest passes that beaches will sell in 3 days.2 . Chapter 6. Condor Cove Beach sells 2 times as many guest passes that same day. 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. 3. 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? Solution: © McGraw-Hill School Division 4. Lesson 4. Then solve the problem. 1. Miguel rents his boat for 3 hours per day for 12 days. pages 240–241. Miguel charges $30 per hour to take people on his boat.4.2. (182) . 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. Estimate the number of fish the girls will catch if they fish for 3 hours. They rent a boat for $24 per hour.Print This Page Name Problem Solving: Reading for Math Solve Multistep Problems Choose the correct answer. C Olive’s sister catches 3 times as many fish as Olive does. 3 buses of students go to Ocean Land. One “hidden question” you must is true? A Olive and her sister catch 9 fish. Her sister catches 3 times as many fish. Which of the following statements Print This 6–4 Page P PRACTICE Math Skills Test Prep 2. They use the boat and the equipment for 7 hours. 2. One “hidden question” you must is true? A Lana and Ken pay $40 per hour to rent a boat. Which of the following statements 6. Each bus has 44 students. 3. pages 240–241. Which question do you have to answer 4. 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.320 G $440 H $10 Olive catches 3 fish in 1 hour.2 Use with Grade 4. Each student spends $10 on admission and a special show. B Olive’s sister catches 3 fish. Lana and Ken rent 2 sets of scuba equipment for $16 an hour each. B Lana and Ken pay $168 to rent the boat. Lesson 4. How much money do the students 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? © McGraw-Hill School Division spend altogether? F $1.4. How much money do the students spend altogether? 3.2. C Lana and Ken rent the boat and equipment for 16 hours. Chapter 6. 5. 1. A fishing guide charges $25 per diving classes each day. During one week. Altogether. The Beach Shack rents out 12 umbrellas for 5 hours each. Which question do you have to Print This 6–4 Page P PRACTICE Math Skills Test Prep 8.2 .M. Amanda rents a canoe and a life 14. to 5:00 P. He works 6 hours per day for 5 days. (183) MR 1. Chapter 6. A group of 20 people goes to the aquarium and takes the tour. to 1:00 P. 9. A canoe costs $12 per hour.Print This Page Name Problem Solving: Reading for Math Solve Multistep Problems Choose the correct answer. The aquarium charges $12 admission © McGraw-Hill School Division rented for a total of 16 hours each. to 4:45 P. Jenny rented a rowboat from preserver from 2:00 P. Lesson 4.M. how much is paid for these rentals? and $6 for a tour. How much does Amanda spend? 10:45 A. The rental cost is $25 per hour. 2.M. A life preserver costs $2 per hour. For how many minutes did she rent the boat? Use with Grade 4. After lunch. pages 240–241. How much money does the group spend? 13. The Diving Club offers 4 beginning Shack make? F $30 G $72 H $360 10.M. How many people can take classes in 30 days? hour. How much money does the guide earn? 11. How much money does The Beach 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? C How many umbrellas does The Beach Shack have? Solve. How much money does The Beach Shack make? 7. 3.M. Umbrellas cost $6 per hour. she rented another rowboat from 1:45 P.4. Each class has room for 6 people.2.M. 5 sailboats are 12. Chapter 6. How many bales do they eat in 31 days? Use with Grade 4. 79 ϫ 73 12. 88 ϫ 62 ϭ Algebra & Functions Find each product. 68 ϫ 24 15. pages 242–245. 77 ϫ 22 9.2. (80 ϩ 1) ϫ (40 ϩ 2) ϭ p 29. (50 ϩ 6) ϫ (70 ϩ 3) = r 30. 73 ϫ 51 3. 26. $46 ϫ 35 7. (60 ϩ 4) ϫ (20 ϩ 9) = v 25. 28 ϫ 19 ϭ 18. 94 ϫ 61 13. Horses on a ranch eat 28 bales 18 boards in each section. 18 ϫ 92 ϭ 17.18 ϭ 24.Print This Page Name Multiply by 2-Digit Numbers Find each product 1. 59 ϫ 47 8. (184) NS 3. (90 ϩ 5) ϫ (10 ϩ 1) ϭ q © McGraw-Hill School Division 28. (40 ϩ 3) ϫ (80 ϩ 4) ϭ b 31. (20 ϩ 8) ϫ (70 ϩ 7) ϭ s Problem Solving 33. $0. Print This 6-5 Page P PRACTICE 26 ϫ 35 2. 86 ϫ 43 ϭ 21. A fence has 28 sections with 34.63 ϫ 58 14. How many boards are in the fence? of hay each day. 74 ϫ 33 ϭ 22. Lesson 5. 77 ϫ 94 ϭ 20. 48 ϫ 26 ϭ 23. 44 ϫ 46 11. $0. 55 ϫ 15 10. 31 ϫ $0.56 ϫ 83 5. 29 ϫ 19 6. 27 ϫ 34 ϭ 19. 51 ϫ 34 16. 3.3 . (60 ϩ 6) ϫ (50 ϩ 5) ϭ c 32. (30 ϩ 7) ϫ (10 ϩ 8) ϭ n 27. 44 ϫ 87 4. 72 ϫ 53 14. (185) NS 3. 59 ϫ 31 12. 23 ϫ 39 7.3 . Find each product.39 ϫ 66 ϭ Use with Grade 4. Regroup if necessary. 3. 96 ϫ 35 ϭ 16. 67 ϫ 29 11. O TH H T 2 3 Step 3 Add the products. $31 ϫ 28 13. $15 ϫ 42 6. TH H T O 3. $0. $0. 85 ϫ 43 ϭ 15. TH H T 2 3 O O ϫ ϩ 1 2 4 7 5 7 5 ϫ ϩ 1 1 0 2 4 7 0 5 7 5 0 ϫ ϩ 1 1 1 0 1 2 4 7 0 7 5 7 5 0 5 Complete. Lesson 5. H T O 2.2.Print This Page Name Multiply by 2-Digit Numbers You can use a place-value chart to help you multiply 2-digit numbers. Multiply 47 ϫ 25. TH H T 3 Print This 6–5 Page R RETEACH Step 2 Multiply by the tens.27 ϫ 51 8. 38 ϫ 26 9. 1. Chapter 6. TH H T O ϫ 1 4 6 0 ϩ 5 5 5 0 ϫ ϩ 2 5 3 8 2 6 2 7 4 0 ϫ ϩ 5 3 5 9 7 1 9 3 7 0 4. pages 242–245. Step 1 Multiply by the ones. 46 ϫ 44 10. © McGraw-Hill School Division 16 ϫ 23 5. 17. 11 ϫ 31 11 ϫ 53 10. 14. 16. 3 ϫ 11 ϭ 6. 7 ϫ 11 ϭ 3. © McGraw-Hill School Division 11 ϫ 41 18. 1. 4 ϫ 11 ϭ 7.2. 2 ϫ 11 ϭ 5. 8 ϫ 11 ϭ Print This 6–5 Page E ENRICH 4. 11 ϫ 22 19. 11 ϫ 38 20. Chapter 6. 11 ϫ 16 21. 11 ϫ 32 11 ϫ 62 11. 55 ϫ 11 ϭ 24. 6 ϫ 11 ϭ 2. 3. 9 ϫ 11 ϭ What pattern do you see? Multiply 11 by a 2-digit number. What pattern do you see? Use the pattern to find these products. Lesson 5. (186) NS 3. 9. 11 ϫ 34 11 ϫ 18 13. 11 ϫ 33 11 ϫ 27 12. 64 ϫ 11 ϭ 22. pages 242–245.Print This Page Name Multiply by 2-Digit Numbers Patterns for Eleven Multiply 11 by a 1-digit number.3 . 44 ϫ 11 ϭ 23. 5 ϫ 11 ϭ 8. 15. 72 ϫ 11 ϭ Use with Grade 4. 3 . 8. 9. 13. 12.000 37 ϫ 58 21. 10. 37 ϫ 196 19. Print This 6–6 Page P PRACTICE 49 ϫ 59 41 ϫ 52 98 ϫ 402 61 ϫ $216 81 ϫ 350 85 ϫ 1. 42 ϫ 84 20. 28. 98 ϫ 27 18. The price of a bus ticket is $58. About how much will tickets for a group of 62 passengers cost? About how much will tickets cost for a group of 25 people? Use with Grade 4. 16.000 8. Algebra & Functions 15. 6. 498 ϫ 16 © McGraw-Hill School Division Estimate to compare.907 3. Write Ͼ or Ͻ. (187) NS 3. 26 ϫ 42 Problem Solving 27. 55 ϫ 65 18 ϫ 29 71 ϫ 874 42 ϫ 605 23 ϫ 999 71 ϫ 2.000 10.000 34 ϫ 21 8.302 2. 1. 3. 224 ϫ 41 26. 4. 14.000 42. 11. 5.000 59 ϫ 68 17. 15 ϫ 47 3.Print This Page Name Estimate Products Estimate each product. 59 ϫ 689 24.200 24. pages 246–247.118 ϭ 29 ϫ 7. Chapter 6. 49 ϫ 188 25. 34 ϫ 82 3. 589 ϫ 36 23. 21 ϫ 423 22. Lesson 6.000 100. 7.211 19 ϫ 6. An airline ticket costs $375.2.000 8. 69 ϫ 19 7. 85 ϫ 263 10. 19 ϫ 315 9.3 . 23 ϫ 51 6. 2. Chapter 6. 1. 48 ϫ 1. 12 ϫ 9. 54 ϫ 19 $29 ϫ 32 788 ϫ 51 Estimate each product. Lesson 6. 76 ϫ 6. pages 246–247. (188) NS 3.698 14.419 15. 72 ϫ 803 © McGraw-Hill School Division 11. 57 ϫ $5.000 2 zeros ϫ 1 zero 3 zeros Estimate each product by rounding. 55 ϫ 4. 26 ϫ $72 8. 42 ϫ 59 40 ϫ 60 2.2. 227 ϫ 74 200 ϫ 70 14.Print This Page Name Estimate Products You can round to estimate products.228 13. 92 ϫ 2.400 1 zero ϫ 1 zero 2 zeros Print This 6–6 Page R RETEACH Estimate 74 ϫ 229.568 Use with Grade 4.830 17. 3. Round each number to its greatest place. 4.056 12.058 16. 92 ϫ 1. 3. Then multiply using patterns with zeros Estimate 42 ϫ 59. 37 ϫ 49 5. Print This Page Name Estimate Products Estimation Maze Estimate to find your way out of the maze. First. Then.888 52.2. in order.910 34 ϫ 90 6. estimate to find and go through the boxes in which the answers are: 3.822 2. Lesson 6. pages 246–247.3 .416 57 ϫ 14 36. Start in that box. What message do you find? ’ ! Use with Grade 4.344 M 87 ϫ 84 O 178 ϫ 95 H 706 ϫ 48 819 ϫ 64 E 157 ϫ 39 39 ϫ 98 P 67 ϫ 34 U 196 ϫ 77 F 616 ϫ 59 R C T O W E Write the letters from the boxes you go through in order. estimate to find the box in which the answer could be 858. (189) NS 3.092 42 ϫ 19 33.278 16.308 78 ϫ 11 I 26 ϫ 34 B 172 ϫ 24 R 953 ϫ 48 © McGraw-Hill School Division Print This 6–6 Page E ENRICH 3. 3. Chapter 6.123 15.060 7. 3. 7. 279 ϫ 64 6. 908 ϫ 43 3.85 15. 714 ϫ 36 5.118 19. pages 250–253. 36 ϫ 19. 46. 9. ϫ 27 92.95 ϫ 18 21. make the greatest and least product possible by multiplying by a 2-digit number. Check that each answer is reasonable 1.Print This Page Name Multiply Greater Numbers Multiply.2.306 ϫ 31 20. 6. 5.26 ϫ 98 8.3 . 305 ϫ 77 9.016 ϫ 25 11. How many pencils are there in 50 boxes? Use with Grade 4. 1 26. 71 ϫ 23. 2. 53 ϫ 36.618 ϫ 91 16. (190) NS 3. 26 ϫ $591. 7. 309 ϫ 32 7.401 ϭ Algebra & Functions Given each set of digits. Print This 6–7 Page P PRACTICE 653 ϫ 27 2.219 ϭ 23. $1. $123. 9. A box holds 250 ping pong balls. 4.007 ϫ 75 14. 21. Pencils are packaged with 144 pencils How many ping pong balls can be packaged in 85 boxes? in a box. $50.148 ϫ 16 12.962 ϭ 22. Lesson 7.35 ϫ 72 17.09 ϫ 31 13. © McGraw-Hill School Division 25. 2.084 ϫ 43 10. 412 ϫ 65 4. 0 Problem Solving 27. Use each digit one time. Chapter 6.05 ϭ 24. 2. 28.107 ϫ 42 18. $82. ϫ 74 6. $39. Ones Print This 6–7 Page R RETEACH Step 2 Multiply by the tens.000 ϭ 90.188.95 ϭ 10. 85 ϫ $116. Chapter 6. 3. 52 ϫ 19. the answer is reasonable. Estimate: 30 ϫ 3. Ones 2. Thousands Ones Step 3 Add the products.69 ϫ 18 5.450 is close to the estimate of 90. Multiply 25 ϫ 3.Print This Page Name Multiply by Greater Numbers You can use a place-value chart to multiply greater numbers.098 ϫ 66 8.000. 8. Lesson 7. Thousands 1. Regroup if necessary. pages 250–253.000 Step 1 Multiply by the ones. Thousands Ones H T O H T O H T O H T O 1 1 4 H T O H T O 1 3 1 4 3 4 3 ϫ 3 1 7 8 2 5 1 5 8 9 0 ϫ 3 1 7 8 2 5 1 5 8 9 0 ϫ 3 1 7 8 2 5 1 5 8 9 0 ϩ ϩ 6 3 5 6 0 ϩ 6 3 5 6 0 7 9 4 5 0 Since 79.484 ϫ 72 ϭ 9. Multiply.2. Regroup if necessary. 518 ϫ 49 6. 6. Thousands Ones H T O H T O H T O H T O H T O H T O 2 ϫ © McGraw-Hill School Division 1 4 5 7 2 5 ϫ 1 2 9 3 1 8 ϫ 2 0 0 6 1 3 ϩ ϩ ϩ 4.735 ϫ 37 7. Thousands Ones 3. 4. Thousands 1.3 . (191) NS 3.071ϭ Use with Grade 4. $3. ϫ 14 ← 1 ϩ 4 ϭ 5 20. Draw an X next to any incorrect product.214 ϫ 88 193.216 7. Chapter 6. Use the method shown above to check each problem.896 2.090 3. 4.455 ϫ 76 707. 1. (192) .456 to the sum you got in Step 2. 7 ϫ5 35 3 ϩ5 8 Step 3 Compare the sum you got from adding the digits in the product for 14 ϫ 1.410 12.432 ϫ 37 311.456 4. 9.456. 1ϩ6ϭ7 1ϩ7ϭ8 Print This 6–7 Page E ENRICH Step 2 Multiply the two numbers you got from adding the factors. 1. 689 ϫ 24 16. 8.456 9. Step 1 Add the digits in each number. 7. 3.580 NS 3.832 8. 3.984 11.Print This Page Name Multiply Greater Numbers Quick Check Here is a quick way to check the product for 14 ϫ 1.498 ϫ 45 337.3 Use with Grade 4.213 6.418 ϫ 92 314.384 ← 2 ϩ 0 ϩ 3 ϩ 8 ϩ 4 ϭ 17.480 10. 815 ϫ 32 26.2. so the product 20.456 ← 1 ϩ 4 ϩ 5 ϩ 6 ϭ 16. 496 ϫ 71 35. 742 ϫ 68 50. 314 ϫ 57 17. Lesson 7.536 © McGraw-Hill School Division 5.372 ϫ 15 65. 8 ϭ 8.384 is correct. Then add the digits in the product. Add again if the sum has two digits. 537 ϫ 49 26. 2. pages 250–253. Then find the correct product. Lesson 8. 3.1. pages 254–255. MR 2.3. It takes 15 minutes for Elliot to travel from his home to the beach. Chapter 6.M. A beach sells 1. Which type of boat generated the most income? least income? 3.200 passes in 1999. Use data from the graph to solve problems 1 and 2. Which type of boat generated the Print This 6–8 Page P PRACTICE Income from Boat Rentals $1.2 .100 passes in 2000.000 passes in 1998. Suppose you make a pictograph in which each symbol stands for 200 passes. Boat Rentals at Lake Willow in July and August Type of Boat Sailboats Rowboats Paddle boats Canoes 1. Create a problem for which you would make a graph to solve.300 $1. How many symbols would you make for each year? © McGraw-Hill School Division Mixed Strategy Review Solve. Use any strategy. What time did Elliot leave home to go to the beach? 6. 5. (193) SDP 1. How many symbols would you make for each year? data in problem 3 in which each symbol stands for 100 passes. Suppose you make a graph for the 1.000 2. 4. Share it with others.100 $800 $1.Print This Page Name Problem Solving: Strategy Make a Graph Make a graph for the data in the table. Time Elliot returns from the beach at 4:30 P. Strategy: Use with Grade 4. 2. He spent 2 hours at the beach. and 1.4. 3.Print This Page Name Problem Solving: Strategy Make a Graph Page 255. WA Seal Beach. Lesson 8. Read carefully. Make a bar graph to solve the problem. What do you need to find? • You need to find .2 . Choose a strategy. CA Atlantic City.775 1.375 Step 1 Read Be sure you understand the problem. Step 2 Plan I Make a plan. (194) SDP 1. TX Wenatchee.1.675 1. What do you know? • You know how many . © McGraw-Hill School Division I I I I I I I I I 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 A graph can help you compare data quickly.4. Use with Grade 4. pages 254–255. NJ Malibu. 2. Problem 2 Print This 6–8 Page R RETEACH Which contest had the most people? The least? Sandcastle Building Contests Location Port Aransas.525 1.250 1. 3. MR 2. Chapter 6. CA Number of People 1. 200 1. Make a bar graph. 2. NJ Malibu.4. In which year did the Lakefront Swim Club have the most members? the least members? Use with Grade 4. has the least people. and 550 members in 2000. 600 members in 1990. 250 members in 1980. Make a graph that displays this data.3. 3. 2.1. MR 2.700 1.800 Location Number of People The contest at: has the most people.500 1. CA 100 200 300 400 500 600 700 800 900 1.300 1. (195) SDP 1. Sandcastle Building Contest Port Aransas.100 1. Chapter 6.400 1. 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. Step 4 Look Back © McGraw-Hill School Division Is the solution reasonable? Reread the problem.000 1.600 1. WA Seal Beach. Lesson 8. pages 254–255.TK Wenatchee. The Lakefront Swim Club had 400 members in 1970.Print This Page Name Problem Solving: Strategy Make a Graph Step 3 Print This 6–8 Page R RETEACH Solve Carry out your plan.2 . CA Atlantic City. 52 ϫ 11 ϭ 17. 44 ϫ 22 ϭ 10.520 Problem Solving 33. 55 ϫ 18 ϭ 7. 22 ϫ 55 ϭ Print This 6–9 Page P PRACTICE Algebra & Functions 31. 25 ϫ 50 ϭ 13.2. 35 ϫ 21 ϭ 29. 24 ϫ 40 ϭ 15. There are 21 teams. 30 ϫ 26 ϭ 14.850 130 4. 16 ϫ 21 ϭ 25. Rule: Multiply by 35. 35 ϫ 22 ϭ 19. Each bus carries 35 students. 90 ϫ 9 ϭ 12. 40 ϫ 21 ϭ 5. 65 ϫ 40 ϭ 23.550 32. 1. How many students in all are helping clean the park? 34. Chapter 6. 48 ϫ 40 ϭ 24. Lesson 9. 60 ϫ 14 ϭ 8. (196) NS 3.Print This Page Name Multiply Using Mental Math Multiply. Teams of 16 students are helping clean the park. pages 256–257. 44 ϫ 15 ϭ 16. 15 ϫ 16 ϭ 18. 30 ϫ 19 ϭ 22. 50 ϫ 14 ϭ 28. 61 ϫ 30 ϭ 20. Complete each table. 80 ϫ 51 ϭ 11. How many students are going on the field trip? Use with Grade 4.470 110 3. 70 ϫ 31 ϭ 9.200 100 1. 20 ϫ 48 ϭ 21.085 42 1. 25 ϫ 28 ϭ 26. 90 ϫ 42 ϭ 3. © McGraw-Hill School Division Rule: Multiply by 16. Use mental math.600 220 3. Input Output 20 700 31 1. Input Output 15 240 25 400 75 1. 70 ϫ 49 ϭ 30. 12 ϫ 30 ϭ 4. 34 ϫ 11 ϭ 6. Students are going on a field trip in 20 buses. 59 ϫ 61 ϭ 27. 3.3 . 11 ϫ 62 ϭ 2. 15 ϫ 28 ϭ 9. 59 ϫ 71 ϭ 16. 35 ϫ 40 ϭ (35 ϫ ) ϫ (40 Ϭ ϭ ) 2. 35 ϫ 90 ϭ 25. pages 256–257. 25 ϫ 25 ϭ 26.Print This Page Name Multiply Using Mental Math You can multiply using mental math. 53 ϫ 11 ϭ 20. 36 ϫ 40 ϭ 12. 50 ϫ 23 ϭ 13. 11 ϫ 37 ϭ 29. Lesson 9. 80 ϫ 61 ϭ 22. 70 ϫ 18 ϭ 15. Chapter 6. 25 ϫ 16 ϭ (25 ϫ 10) ϩ (25 ϫ 6) 250 ϩ 150 ϭ 400 Multiply mentally. 22 ϫ 30 ϭ ( ϫ 30) ϩ ( ϩ ϭ ϫ 30) ϭ ϭ Multiply. Use mental math. 65 ϫ 16 ϭ 24. Use compensation. 5. 1. 26 ϫ 23 ϭ 28. 11 ϫ 72 ϭ 10. 20 ϫ 45 ϭ 8.2. Then add. 3. 60 ϫ 73 ϭ 18. 62 ϫ 10 ϭ 6. 25 ϫ 16 ϭ (25 ϫ 2) ϫ (16 Ϭ 2) 50 ϫ 8 ϭ 400 Print This 6–9 Page R RETEACH Compatible Numbers Break apart one number and multiply. Use compatible numbers. 32 ϫ 26 ϭ 21. 75 ϫ 30 ϭ 31. 75 ϫ 20 ϭ 11. 60 ϫ 25 ϭ (60 Ϭ ϭ ϫ ) ϫ (25 ϫ ϭ ) ϭ ϫ Multiply mentally. 80 ϫ 18 ϭ 27. 70 ϫ 19 ϭ 23. 99 ϫ 10 ϭ 17. Compensation Multiply one factor by a number. 45 ϫ 36 ϭ 19. (197) NS 3. 25 ϫ 45 ϭ 7. 55 ϫ 27 ϭ 30.3 . 50 ϫ 88 ϭ © McGraw-Hill School Division Use with Grade 4. 15 ϫ 16 ϭ ( ϫ 16) ϩ (5 ϫ ϩ ϭ ) 4. 44 ϫ 25 ϭ 14. 3. Divide another factor by the same number. Lesson 9. 18 33 24 © McGraw-Hill School Division 16 ϫ 14 40 300 22 Use with Grade 4. Chapter 6. 3. The person with the greater number of points wins. 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. • Write each of these numbers on an index card: 12 15 18 25 30 35 50 10 index cards Print This 6–9 Page E ENRICH 60 200 400 • Mix up the cards and then place them facedown between you and your partner.2. Repeat the activity until all the cards have been drawn. The first person to complete the circle with correct answers scores 1 point. • Erase the number in the center. (198) NS 3.Print This Page Name Multiply Using Mental Math Circle Race You will need: Play with a partner.3 . Draw a card. pages 256–257. Lesson 10. (199) NS 1.1. Sailboats Rowboats Paddle boats 6–10 Part A WORKSHEET Decision Making Print This Page Canoes © McGraw-Hill School Division Your Decision Which boat or boats will the family rent? How long will they ride? Explain. 3.2.3. MR 1. pages 258–259. Use with Grade 4. Chapter 6.Print This Page Name Problem Solving: Application Applying Multiplication Record your data.3 . 2. Chapter 6.1. Time Each minute Estimate 6–10 Part B WORKSHEET Math & Science Print This Page Actual Heart Beats Each hour Each day Each year Show how you estimated the number of heart beats in each hour.Print This Page Name Problem Solving: Application How many times does your heart beat each day? Record your data in the table below.3. pages 260–261.2. Lesson 10. (200) NS 3. each day. and each year. Each hour Each day Each year © McGraw-Hill School Division Use with Grade 4.3 . 3. MR 1. 3. 1.000.2. (201) NS 3. Tamara’s heart beats 60 times each minute. What was the range of heartbeats? What number was most common? 3. Round the number of beats for a day to the nearest 10. Explain how exercise can reduce the number of times your heart beats each day.3. How many more times does Marty’s heart beat each day? Show your work. minute. © McGraw-Hill School Division 5. 2. Chapter 6. Make a bar graph to display the data 4.3 . Lesson 10. 3. Use with Grade 4. 3. pages 260–261.Print This Page Name Problem Solving: Application How many times does your heart beat each day? 1. Marty’s heart beats 70 times each from the class. MR 1. Why would it be difficult to count the number of heart beats in a 6–10 Part B WORKSHEET Math & Science Print This Page day? Explain how math made your job easier. Collect the data for the whole class. How many aquariums of fish are there? Use with Grade 4. 5 3. 5 250 50 $70 6.000 19.600 400 18.800 Ϭ 6 ϭ Divide. $3. 9 3. 40.200 700 14.200 20. There are 150 students in 3 buses.800 15.500 Ϭ 34.200 Ϭ 8 ϭ 30. 3 620 350 Ϭ 5 ϭ 3. 2 160 60 700 11. Each aquarium has 40 fish.2 .600 Ϭ 7 ϭ 22. 3 1. 16 Ϭ 4 ϭ Print This 7–1 Page P PRACTICE 480 Ϭ 6 ϭ 4. 200 Ϭ © McGraw-Hill School Division ϭ 50 Ϭ 6 ϭ 40 Ϭ 4 ϭ 600 33.2.000 21. 3. 3 $270 13.600 Ϭ 4 ϭ 206 R2 80 800 $600 5.4. 9 7.600 Ϭ 4 ϭ Algebra & Functions Write the missing number. Lesson 1. 2 8. $240 Ϭ 3 ϭ 24.200 16. (202) NS 3. 32. 5. A pet shop has 160 fish in bus carries the same number of students.Print This Page Name Division Patterns Complete.000 Ϭ 5 ϭ Problem Solving 41. $450 Ϭ 5 ϭ 26. 3. ϭ 40 ϭ 500 37. 1.500 Ϭ 5 ϭ 160 Ϭ 4 ϭ 1. 4 240 7. 1.800 600 4. 7 $4.500 8. 810 Ϭ 9 ϭ 25. 630 Ϭ ϭ 90 Ϭ 8 ϭ 80 35.200 Ϭ 8 ϭ 17. 630 Ϭ 7 ϭ 27. 6 $420 10. 120 Ϭ 2 ϭ 23. 4. 450 Ϭ 5 ϭ 36. pages 276–277. Each 42. 7 560 80 $90 9. $7. 4 2. MR 3. How many students are on each bus? aquariums. 6 $4.800 Ϭ 8 ϭ 31.000 Ϭ 6 ϭ 29. 35 Ϭ 5 ϭ 3. 3. 200 Ϭ 39. Chapter 7. 4. 48 Ϭ 6 ϭ 2. 8 560 70 $700 12. 38. 540 Ϭ 9 ϭ 28. 3. 700 Ϭ 7 ϭ 14.000 Ϭ 5 ϭ 4. Lesson 1. Think: The basic fact is 12 Ϭ 3 ϭ 4. 30 Ϭ 6 ϭ 320 Ϭ 4 ϭ 3. Count the zeros.2. Chapter 7.2 .Print This Page Name Division Patterns You can divide mentally by using basic division facts and looking for a pattern. 540 Ϭ 9 ϭ 16. 3.400 Ϭ 2 ϭ 17. 48 Ϭ 8 ϭ 480 Ϭ 8 ϭ 4.400 Ϭ 8 ϭ 10. 180 Ϭ 2 ϭ 1 2.800 Ϭ 8 ϭ 9.4. 32 Ϭ 4 ϭ 200 Ϭ 5 ϭ 2. 360 Ϭ 6 ϭ 15.200 Ϭ 7 ϭ 640 Ϭ 8 ϭ 6. 12 Ϭ 3 ϭ 4 120 Ϭ 3 ϭ 40 1. 4. 360 Ϭ 4 ϭ 13. 2.900 Ϭ 7 ϭ Use with Grade 4. 45 Ϭ 9 ϭ 350 Ϭ 5 ϭ 3.200 Ϭ 4 ϭ 5.000 Ϭ 8 ϭ 500 no zeros 1 zero 2 zeros 150 Ϭ 3 ϭ 1. 64 Ϭ 8 ϭ 7. Divide. 1. MR 3. 15 Ϭ 3 ϭ 2.500 Ϭ 9 ϭ 8. 40 Ϭ 8 ϭ 5 400 Ϭ 8 ϭ 50 4.200 Ϭ 3 ϭ 400 Complete. (203) → → → → → → no extra zeros 1 extra zero 2 extra zeros NS 3. 35 Ϭ 5 ϭ 300 Ϭ 6 ϭ 3. pages 276–277.500 Ϭ 3 ϭ 3. 1.700 Ϭ 9 ϭ 11. 4. 20 Ϭ 5 ϭ Print This 7–1 Page R RETEACH Think: The basic fact is 40 Ϭ 8 ϭ 5.500 Ϭ 5 ϭ © McGraw-Hill School Division 450 Ϭ 9 ϭ 4.000 Ϭ 6 ϭ 6. Print This Page Name Division Patterns Geography Riddles Find each missing number. 120 Ϭ 2 ϭ 21.600 90 8 What country is always cold? 4. 5. Solve the riddles by placing the letter from each exercise in the blank above the matching answer number. 320 Ϭ 10. 8. MR 3. 720 Ϭ 9 ϭ 17. 20. 240 Ϭ Ϭ 2 ϭ 800 Ϭ 4 ϭ 30 ϭ 80 Ϭ 9 ϭ 90 Ϭ 3 ϭ 700 E ϭ 400 ϭ 700 ϭ 600 ϭ 80 14. 2. Ϭ 9 ϭ 40 U A N A I E R I N R O H S S L 4. 150 Ϭ 3 ϭ 19. 810 Ϭ 9 ϭ What state reminds you of part of a lion? © McGraw-Hill School Division 20 4 3 120 420 What city likes to wander? 2 6 50 900 Which people are always in a hurry? 810 360 60 7 3.4.000 5 80 9 2. 140 Ϭ 7 ϭ 3. Print This 7–1 Page E ENRICH M ϭ 700 ϭ 700 2. 1. 5. 6.100 Use with Grade 4. Lesson 1. 12.400 Ϭ 15.500 Ϭ 7.600 Ϭ 13.800 Ϭ 11. 3. I M S C ϭ 400 Ϭ 7 ϭ 60 E Ϭ 8 ϭ 400 Ϭ 5 ϭ 800 22.2. 4. (204) NS 3.200 Ϭ 5. 800 Ϭ 18. 9.2 . 3.2001.700 Ϭ 3 ϭ 16. 2. pages 276–277. Chapter 7. 7. pages 278–279. 6 78 13 27 R1 14. 8 29 3 R5 9. If 59 ping pong balls are packed. 5 66 13 R1 14 20. Books are packed in boxes of 9. 6 99 16. Lesson 2. 6. 2. 2 55 18. Find each quotient. how many full boxes will there be? How many ping pong balls will be left over? Use with Grade 4. 67 Ϭ 6 ϭ Problem Solving 28. 58 Ϭ 4 ϭ 27. 4 51 12 R3 16 R3 12. 73 Ϭ 5 ϭ 26. Print This 7–2 Page P PRACTICE 4. 88 Ϭ 3 ϭ © McGraw-Hill School Division 21. 1. 29. 9 33 3 R6 11. 4 37 9 R1 10. 3. Chapter 7. (205) NS 3. 77 Ϭ 7 ϭ 13. 7 98 17. 5. 62 Ϭ 9 ϭ 23.4 . 6 20 3 R2 8. 59 Ϭ 7 ϭ 24. 41 Ϭ 9 ϭ 22. how many full boxes will there be? How many books will be left over? of 6. 43 Ϭ 2 ϭ 25. 3.Print This Page Name Explore Division Write a division sentence for each model. 2 99 19. You may draw place-value models.2. 7 83 11 R6 49 R1 15. Ping pong balls are packed in boxes If 67 books are packed. You can divide the 26 ones into 3 groups of 8 with 2 left over. Print This 7–2 Page R RETEACH Divide. 2. Place 2 tens in each of 3 groups. Regroup the 2 tens that are left as 20 ones. 82 Ϭ 5 ϭ 6.Print This Page Name Explore Division You can use models to help you divide. 49 Ϭ 4 ϭ Divide. You can divide 86 cubes into 3 groups of 28 with 2 left over. 25 Ϭ 2 ϭ 9. Show 86. © McGraw-Hill School Division 37 Ϭ 2 ϭ 4. Lesson 2. 58 Ϭ 4 ϭ 3. 86 Ϭ 3 ϭ 28 R2. 5. Chapter 7. You may use models to help you. pages 278–279. 1. 3. 78 Ϭ 9 ϭ NS 3. 42 Ϭ 4 ϭ 10. (206) . So.4 Use with Grade 4. 48 Ϭ 4 ϭ 68 Ϭ 3 ϭ 7. 43 Ϭ 2 ϭ 8. Divide 86 Ϭ 3.2. 3. 4. 9 if the sum of its digits is divisible by 9. 4. © McGraw-Hill School Division 3. 6 if it is divisible by both 2 and 3.Print This Page Name Explore Division Remainder Rules Print This 7–2 Page E ENRICH 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. Lesson 2. pages 278–279. Which divisions will have remainders? Which divisions will not have remainders? Prove your answers. 5. or 8. 1. 10 if the ones digit is 0.2. Think about dividing a 3-digit number by each of the following 1-digit numbers: 2. 7. will there be a remainder? How do you know? Divide to prove your answers. 2. 6.4 . Chapter 7. 5 if the ones digit is 0 or 5. (207) NS 3. 8. 9. 3 if the sum of its digits is divisible by 3. 2. If you divide 315 by 5. If you divide 691 by any 1-digit number. 3. Use with Grade 4. will there be a remainder? How do you know? Divide to prove your answer. 6. 467 Ϭ 2 ϭ 26. 7 779 23. 506 Ϭ 7 ϭ 111 R2 21. Lesson 3. 8 231 $135 28 R7 3. 5 $675 6. 3 391 130 R1 $0. 1. 6 $6.2. 593 Ϭ 4 ϭ 27. She plants 8 pine seedlings in each row. 6 377 19. The tickets will be divided equally among 9 classes.72 $1. 7 785 8.68 11. Divide 909 by 8. c Ϭ 4 ϭ 168 d ϭ 195 32. b Ϭ 8 ϭ 116 x ϭ 44 34.065 Ϭ n ϭ 213 31. (208) NS 3. Algebra & Functions Find each missing number. Divide 726 by 7. How many rows are there? How many seedlings are left? the circus. 29. 4 $2. pages 280–283. 3. How many tickets will each class get? Use with Grade 4. 5 557 7. Morgan is planting 906 pine seedlings 40. 2 723 361 R1 62 R5 119 R3 $37 16. (700 + y) Ϭ 7 ϭ 106 38.880 tickets to in rows. 690 Ϭ m ϭ 345 33. 8 745 17. 585 Ϭ 35. 5 457 112 R1 124 R3 91 R2 93 R1 5. t Ϭ 9 ϭ 111 © McGraw-Hill School Division 36. 7 836 9. Divide 834 by 5. 215 Ϭ 3 ϭ 24.Print This Page Name Divide 3-Digit Numbers Divide.67 4. The school bought 2.12 311 R2 13. 3 935 15. 1. 756 Ϭ (r + 3) ϭ 126 Problem Solving 39. 4 398 10. 30. 7 903 129 14. 367 Ϭ 5 ϭ 25.4 . (250 + 14) Ϭ 37. 298 Ϭ 6 ϭ 28. 22. Check your work. 8 995 12. Chapter 7. 9 999 111 18. 8 $296 20. 2 698 Print This 7–3 Page P PRACTICE 349 111 R2 99 R2 2. 2 2 8 36 8 4 Ϫ6 Ϫ Ϫ 2. There aren’t enough hundreds. Lesson 3. Check your answer: 53 ϫ 8 ϩ 1 ϭ 425 Complete. 680 Ϭ 5 ϭ 14. 3 745 248 R1 9. Think: 4 Ϭ 8. 745 Ϭ 3 ϭ 13. 53 R1 8 425 Ϫ40 25 Ϫ24 Multiply: 8 ϫ 3 ϭ 24 1 Subtract: 25 Ϫ 24 ϭ 1 The remainder is 1. 1 4 3 R 57 1 7 Ϫ5 Ϫ 2 3. 3 866 288 R2 12. Bring down the ones. 662 Ϭ 5 ϭ 15. Chapter 7. 4 573 143 R1 5. Bring down the tens. Divide the tens. 5 764 152 R4 94 R8 7.2. pages 280–283. (209) NS 3. 5 8 425 Ϫ40 Multiply: 8 ϫ 5 ϭ 40 2 Subtract: 42 Ϫ 40 ϭ 2 Print This 7–3 Page R RETEACH Step 3 Divide the ones. © McGraw-Hill School Division 4. 7 973 139 10. 7 293 41 R6 8. 3. 927 Ϭ 4 ϭ 17. 571 Ϭ 6 ϭ Use with Grade 4.Print This Page Name Divide 3-Digit Numbers Divide 8 425 . Divide the ones. 571 Ϭ 8 ϭ 16. 8 9 76 2 4 Ϫ5 6 Ϫ R 1 8 6 2 4 2 4 0 2 1 2 0 1 7 Ϫ 1 5 2 6 4 6 3 1 Find each quotient. Step 1 Divide the hundreds. 5 349 69 R4 6. 1.4 . 8 425 Step 2 Divide the tens. 9 854 11. Write the remainder as part of the quotient. Use short division to divide. 9 624 69 R3 15. 8 944 118 17. Write the difference in front of the digit in the tens place. 8 8 6513 Think: 8 ϫ 8 ϭ 64. 8 653 Think: 8 ϫ 1 ϭ 8. (210) . 2 342 Divide the tens. 6 443 10. Here is how it works.4 Use with Grade 4. 3 761 253 R2 3.Print This Page Name Divide 3-Digit Numbers Short Division Short division is a quick way to divide. 7 918 131 R1 73 R5 61 R4 61 R4 7. Step 1 Step 2 Step 3 Print This 7–3 Page E ENRICH Divide the hundreds. Multiply and subtract mentally. 1. Multiply and subtract mentally. Divide the ones. 6 432 11. pages 280–283. Divide 6 892 . 1 6 8292 Think: 6 ϫ 1 ϭ 6 8Ϫ6ϭ2 Divide 8 653 . 6 791 131 R5 NS 3. Chapter 7. 8 1R5 8 6513 Think: 8 ϫ 1 ϭ 8. Step 1 Divide the tens. not enough hundreds. 3. 8 894 8. Write the difference in front of the digit in the ones place. 8 492 16. 4 623 155 R3 4. Multiply and subtract mentally. 1 4 8 R4 6 82952 Think: 6 ϫ 8 ϭ 48 52 Ϫ 48 ϭ 4 Step 2 Step 3 Divide the hundreds. 9 867 9. 14 6 82952 Think: 6 ϫ 4 ϭ 24 29 Ϫ 24 ϭ 5 Divide the ones. 7 365 12. Lesson 3. 5 823 © McGraw-Hill School Division 164 R3 111 R6 72 65 R2 5. 171 2. 9 862 95 R7 18. 6 942 157 96 R3 52 R1 6. 65 Ϫ 64 ϭ 1. 13 Ϫ 8 ϭ 5. 7 431 13. 5 327 14.2. 818 Ϭ 2 ϭ Problem Solving 40. 920 Ϭ 9 ϭ 37. 8 812 15. 823 Ϭ 4 ϭ 28.09 101 R4 70 R1 9 918 12. 2 419 6. $1. 4 839 8. 6 657 23. Lesson 4. 206 R2 2. 10 R8 106 R7 3 211 19.63 11. A family of 4 spent $824 during their vacation. 965 Ϭ 6 ϭ 25. 2 819 16. 845 Ϭ 6 ϭ 33. 102 5 549 13. 920 Ϭ 3 ϭ 31. 704 Ϭ 5 ϭ 29. 540 Ϭ 2 ϭ 36. 10 R2 4. pages 284–285. how much is that a month? 41.Print This Page Name Zeros in the Quotient Divide. If divided evenly. If divided evenly. Jenna earns $636 in 6 months by babysitting. Check your answer. 209 R3 6 $630 9. 9 98 18. 5 544 21.2. 3. 954 Ϭ 5 ϭ Find only those quotients that are greater than 200.4 . 619 Ϭ 3 ϭ 38. 4 827 20. 992 Ϭ 3 ϭ © McGraw-Hill School Division 35. 981 Ϭ 2 ϭ 30. $1. Print This 7–4 Page P PRACTICE 3 620 5. $105 109 R4 103 R2 8 $8.56 10. 305 R2 50 R6 2 981 4 835 208 R3 7 727 103 R6 8 406 27. 109 R3 3 917 24. 209 R1 3. 7 748 14. 409 R1 206 R3 6 620 17. 9 92 7. (211) NS 3. 34.07 106 R6 7 $7. 916 Ϭ 7 ϭ 32. 747 Ϭ 4 ϭ 39. Chapter 7. 885 Ϭ 8 ϭ 26. how much is that per person? Use with Grade 4. 108 R4 490 R1 8 855 22. 1. Lesson 4. There are not enough tens to divide. Think: 3 ϫ 2 ϭ 600 The first digit is in the hundreds place. (212) NS 3. Write 02 a 0 in the quotient. 912 Ϭ 9 ϭ 15. 7 765 109 R2 $70 8. © McGraw-Hill School Division 4. Chapter 7. 662 Ϭ 3 ϭ 17. 2 361 180 R1 10. 20 3 629 There are not enough Ϫ6 tens to divide. 209 R2 3 629 Ϫ6 029 Ϫ27 Multiply: 3 ϫ 9 ϭ 27 2 Subtract: 29 Ϫ 27 ϭ 2 Check your answer: 209 ϫ 3 ϩ 2 ϭ 629 Complete.4 . 452 Ϭ 5 ϭ 16. 965 Ϭ 6 ϭ 13. 1 0 7 66 4 2 Ϫ6 Ϫ 3. 1.Print This Page Name Zeros in the Quotient Divide 3 629 . 3. Bring down the tens. 2 0 71 4 3 Ϫ1 4 R 3 2 6 2 4 2 4 2 4 2 0 105 R1 209 R1 3 Divide. 734 Ϭ 7 ϭ 12.2. 4 438 109 R2 6. 4 $816 $204 5. 3 316 7. 905 Ϭ 3 ϭ Use with Grade 4. 2 615 307 R1 9. 3 0 8 R 39 2 6 Ϫ9 Ϫ 2 2. Bring down the ones. Follow the steps below. Compare: 0 Ͻ 4 Print This 7–4 Page R RETEACH Step 3 Divide the ones. 3 $210 14. 3 628 11. 2 3 629 Multiply: 3 ϫ 2 ϭ 6 Ϫ6 Subtract: 6 Ϫ 6 ϭ 0 0 Compare: 0 Ͻ 6 Step 2 Divide the tens. Divide the ones. Step 1 Divide the hundreds. pages 284–285. Trade 2 tens for 20 ones. 4 363 90 R3 12. (213) NS 3. give yourself 1 point. 390 R1 2 781 105 R3 4 423 120 R5 6 725 109 5 545 3. Divisors: 1. 3 211 70 R1 14. 2. Chapter 7. 18. Then complete the exercises. Lesson 4.Print This Page Name Zeros in the Quotient Pick a Winner Pick divisors from the list below to create 20 division exercises. If you do not have a zero in the quotient. 6. 7 775 7. If you have a zero in the quotient. 302 3 906 20. 3. pages 284–285. 403 2 806 Total Points Earned: 21. 9 Print This 7–4 Page E ENRICH 1.2. 7. 11. © McGraw-Hill School Division When will you get a quotient with a zero in the tens place? Give an example. 3. 4. 1 170 9. 8 875 109 R3 10. 7 354 16. Use with Grade 4. 5 101 R4 509 5. 103 R1 6 619 201R6 9 1. give yourself 2 points. Think about dividing a 3-digit number by a 1-digit number. 40 R3 8 323 19.815 50 R4 6. 20 R4 5 104 17.4 . 5. 302 2 604 110 R5 2. 13. 106 R4 8 852 170 4. 2 321 160 R1 15. 8. 8. 3. Each friend earns Explain your thinking: © McGraw-Hill School Division more than less than 4. They will ride in vans that can hold 6 students.1. There will be 12 13 vans. she will have $ 0 $4 $8 left. The school needs There are 7 15 16 tables.Print This Page Name Problem Solving: Reading for Math Interpret the Remainders Circle the correct word(s) or number(s) to make each statement true. Demming has $92. There are 124 people at the Howard School Sports Dinner.1. They each do the same amount of work. 2. 7 or 8 people at each table. MR 1. students in each van. Explain your thinking: 2.4.4. Chapter 7. Lesson 5.2 . Demming buys the greatest possible number of T-shirts.6. They sit at tables that have 8 seats each. Demming can buy 11 11 2 1 Print This 7–5 Page P PRACTICE Reading Skill 12 T-shirts. The Art Club sells T-shirts for $8. Ms. $30. pages 286–287. There are 5 5 or 6 Explain your thinking: Use with Grade 4. Manny and two friends are paid $100 for setting up a new computer in the school’s math lab. There are 75 students going to the art museum. 2. Manny earns more than the same as his friends. 1. Ms. Explain your thinking: 3. (214) NS 3. If Ms. 3. There are 94 people who volunteer to clean the park. How many groups of 4 can they make? 1. B Use only the remainder. They will form as many groups of 4 as possible. C The computer club has $80 to buy disks. to solve this problem? F Add 1 to the quotient. 3. How do you interpret the remainder is false? A Each box of disks costs $7. How many boxes will the to solve this problem? A Use only the quotient. A box of disks costs $7. (215) NS 3.1.6. C There are 94 volunteers.4. Lesson 5. B Everyone can be in a group of 4.1. The baseballs come in boxes of 6. 3. to solve this problem? F Use only the quotient. How many boxes will the league need? 3. 2. H Use only the remainder. Chapter 7. pages 286–287. league need? F 41 boxes G 42 boxes H 43 boxes The Computer Club has $80 to buy disks. How many boxes of disks can the club buy? 5. How do you interpret the remainder 4. B All of the money will be spent. Use with Grade 4. MR 1. G Use only the quotient. Which of the following statements Print This 7–5 Page P PRACTICE Math Skills Test Prep 2. C Add 1 to the quotient. The after-school baseball league wants to buy 250 baseballs. There is no sales tax.4. G Use only the remainder H Add 1 to the quotient. Which of the following statements © McGraw-Hill School Division 6.Print This Page Name Problem Solving: Reading for Math Interpret the Remainders Choose the correct answer. 2. How do you interpret the remainder is true? A They will make 4 groups.2 . How many boxes should she open? Use with Grade 4.Print This Page Name Problem Solving: Reading for Math Interpret the Remainders Choose the correct answer.1. How many shirts does the club need to sell to raise $75? 7.6. They travel to the science fair in cars that can hold 5 members each.1.4. How many cars are needed? rows of 6 seats each. How many 7-ounce cups can they pour? 11. There are 64 members in the Science © McGraw-Hill School Division 14. Each song played by a DJ is 16. 2. How many rows of seats are needed? 13. How many songs does he play in a music set that is 30 minutes long? sunglasses to 50 people at a party. how much money will be left over? The seats are arranged in rows of 8. Chapter 7. They will start at the front row and fill as many rows as they can. C Use only the remainder. The Hockey Club buys 128 ounces of Club. How many shirts does the club need to solve this problem? A Add 1 to the quotient. 3. There are 83 students. If the club buys as many paint sets as it can. pages 286–287. B Use only the quotient. Paint sets cost $6. 3. (216) NS 3. How many students will be in the last row? 15. The Art Club makes $4 on each T-shirt it sells.4. Lesson 5. The Art Club has 12. The DJ’s assistant distributes neon 4 minutes long. How many teams of 5 can they make? juice. There are 6 glasses in a box. $93.2 . They will sit in Club. There are 132 students at a meeting. Solve. There are 72 students in the Hockey to sell to raise $75? F 3 shirts G 18 shirts H 19 shirts 10. 2. 9. MR 1. How do you interpret the remainder Print This 7–5 Page P PRACTICE Math Skills Test Prep 8. 300 7 2. 481 Ϭ 7 26.4 . 50 3 159 6.011 13. 1. 2.904 Ϭ 7 34. 2.000 3 5. 309 Ϭ 5 25. 555 Ϭ 6 22. Choose compatible numbers. 381 Ϭ 8 21.2. pages 288–289.124 14. 4. Print This 7–6 Page P PRACTICE 20 2 43 2. 65 Ϭ 3 18. (217) NS 3.105 15. 1.714 Ϭ 2 32. 70 2 131 8. 40 5 209 11. 281 Ϭ 3 27. 80 8 650 10. 90 9 831 12.186 Ϭ 4 33.000 9 46. 640 Ϭ 7 23. 349 Ϭ 4 28. 90 6 521 4. 22 Ϭ 3 17. 800 4 3.124 Ϭ 6 © McGraw-Hill School Division 30. It took him 9 days. 40 4 171 7. Lesson 6.Print This Page Name Estimate Quotients Estimate. 1. 98 Ϭ 5 20. 500 6 3.912 Ϭ 9 31.999 19.711 Ϭ 8 Problem Solving 35. If she goes 3 times a month. about how many miles is each round trip? 173 miles to Austin. 4. 468 Ϭ 9 24. Jeff went on a bike trip of month to San Francisco for business. 2. Marta travels a total of 850 miles every 36. 30 9 286 9. 20 4 71 3. 412 Ϭ 5 29. 3. Chapter 7. 5. About how many miles did he travel each day? Use with Grade 4.896 16. 70 7 501 5. 122 Ϭ 4 © McGraw-Hill School Division a. 351 Ϭ 4 is about 90. 280 Ϭ 9 ϭ b. 3. Chapter 7. Estimate 299 Ϭ 5 Division fact: 27 Ϭ 3 ϭ Estimate: 270 Ϭ 3 ϭ 4. Estimate 562 Ϭ 6. Circle the letter of the division sentence with the compatible number. 272 Ϭ 9 10. Estimate 279 Ϭ 3. 480 Ϭ 9 ϭ b. 2. 450 Ϭ 9 ϭ 8. Estimate 351 Ϭ 4.Print This Page Name Estimate Quotients Compatible numbers are numbers you can divide easily. Then complete the division. Estimate 319 Ϭ 4. Think: What basic division fact is close to 43 Ϭ 7? 42 Ϭ 7 ϭ 6 420 Ϭ 7 ϭ 60 So. Division fact: Estimate: Division fact: Estimate: Estimate. 1. 360 Ϭ 7 ϭ a. 100 Ϭ 4 ϭ b. Division fact: Estimate: 5. pages 288–289 (218) NS 3. 290 Ϭ 5 ϭ b. Estimate 430 Ϭ 9. 120 Ϭ 4 ϭ a. Print This 7–6 Page R RETEACH Estimate 435 Ϭ 7. You can use compatible numbers to estimate quotients.4 . 349 Ϭ 7 9. Division fact: Estimate: 6. 453 Ϭ 9 Use with Grade 4. 435 Ϭ 7 is about 60. Think: What basic division fact is close to 35 Ϭ 4? 36 Ϭ 4 ϭ 9 360 Ϭ 4 ϭ 90 So. Lesson 6.2. 270 Ϭ 9 ϭ a. Complete. Division fact: 45 Ϭ 9 ϭ Estimate: 450 Ϭ 9 ϭ 3. 350 Ϭ 7ϭ b. 292 Ϭ 5 11. 7. 300 Ϭ 5 ϭ a. Estimate 631 Ϭ 8. 4 85 12. 9 98 8 725 5 5. D 2. 14. H 11.620 13. 7. Print This 7–6 Page E ENRICH 7 428 4. 4 316 6. 3. Rearrange the circled letters to spell the name of the Treasure State.999 9.140 7. 8 3. Then cross out the letters above quotients with two digits. 5 5.165 8.546 10. I 9. B 3. N 90 T © McGraw-Hill School Division M 8.100 600 3. 200 600 1. O 1.100 5. 6 3. Use with Grade 4. 2 196 11. Show how to estimate 605 Ϭ 3. 5. Lesson 6. 15. Chapter 7. 3 605 5.2. Write the estimated quotient beside each exercise number below.000 20 80 1.000 100 200 90 720 3. Write the estimated quotient. (219) NS 3.4 . Circle the letters above quotients with three or more digits.Print This Page Name Estimate Quotients The Treasure State Rewrite each exercise using compatible numbers. N 4.000 5. 1. 60 420 900 8. A 6.500 9 8. The first one is done for you. P 12.600 10 90 2. A 10. 80 320 500 4. pages 288–289. Divide 1. 3.411 9 $7.083 peppers.949 Ϭ 7 3.647 Ϭ 4 ϭ 11.464 for 9 new bicycles.049 Ϭ 7 ϭ 17.598 Ϭ 5 ϭ 15.121 8 3. How many jars can the club make? Use with Grade 4.299 9.448 6 5. 19.418 Ϭ 6 22.350 Ϭ 5 ϭ 18.644 Ϭ 2 1. $1.028 431 3. 1. Lesson 7. If each bicycle costs the same amount. The mountain bike club wants to 24. Chapter 7. 9.306 R3 901 R5 4.227 7. 1.732 by 9. Write Ͼ or Ͻ. 1.409 Ϭ 2 ϭ 12. 3 6. Divide $4.456 Ϭ 8 ϭ 13.814 Ϭ 7 2. 4 5. 1.027 R2 $811 7 2. Divide 5. $6. 2. 5.083 8. 20. Check your answer. $4.598 Ϭ 4 © McGraw-Hill School Division Problem Solving 23. 3. 2. 4.568 Ϭ 6 ϭ 14.4 .2.435 5. Each jar of hot sauce contains 3 peppers.526 by 3.487 303 2. The Let’s Grow club makes and sells raise $4. 3.Print This Page Name Divide 4-Digit Numbers Divide. 2 $8. pages 290–293. Compare. (220) NS 3. how much does each bicycle cost? hot sauce. The club grows 1.032 by 8. 5. Print This 7–7 Page P PRACTICE 5 7.841 Ϭ 2 ϭ 16. 10.056 6.932 Ϭ3 21. 1. © McGraw-Hill School Division 1 5 1 4 1 6 Ϫ 1 6 0 3 Ϫ 2 1 7. 3.009 R1 2 5. Write 5 in the quotient above the 1. 5 4 9 Ϫ1 5 Ϫ Ϫ R 1 2. 1.055 1. 5_ _ 6 3. Lesson 7. 4 7 8 1 2 9. 5 3. pages 290–293.Print This Page Name Divide 4-Digit Numbers When you divide 4-digit numbers. $656 3 1. 5 6 3 Ϫ8 Ϫ R 1 4 3 1 9 1 8 1 3 6 3 6 0 5 Ϫ 4 1 3 Ϫ 1 2 1 6.558 R1 9 9. 7.671 Ϭ 8 ϭ 14.159 R3 6 6. begin by deciding where to place the first digit in the quotient.986 9.117 2. 5 1 6 3 1. $6.4 .818 1. (221) NS 3.393 Ϭ 4 ϭ 13. Chapter 7. 6 5 3 Ϫ4 Ϫ R 1 3.087 Ϭ 5 ϭ 15. 1 9 1 3 4 7.275 1.154 Ϭ 6.090 R8 12. 1. 712 R2 4 $2. Complete.154 Print This 7–7 Page R RETEACH You can see the quotient will have 3 digits. 694 R2 5. 7 4.2.624 10. Divide 3. Divide. Divide 31 by 6. Think: You cannot divide 3 by 6. 457 R2 8 9. 3.426 Ϭ 3 ϭ Use with Grade 4.472 8. 4.373 11. 947 868 R3 285 R7 606 R5 5 5. • Place your marker on START.2.219 Print This 7–7 Page E ENRICH 203 R1 965 R3 8 6.632 8 5. 3.4 . Solve one of the exercises below.774 4 4.619 9 8. Then move your marker the same number of spaces as the remainder. (222) NS 3. Lesson 7.287 9 7.723 430 R3 © McGraw-Hill School Division T AR ST EN D Use with Grade 4. 6 1.829 1.165 R4 863 R7 985 904 R3 7 4. pages 290–293.804 967 R2 6 3.640 1.895 5 2.339 1. Chapter 7.337 1.697 674 R1 349 R3 6 7.863 8 2.748 3 2. Take turns.674 709 R2 6 3.757 1.259 4 2. • The winner is the first player to reach END.574 653 R3 4 3.377 R1 5 5.Print This Page Name Divide 4-Digit Numbers Greatest Remainder Game Play with a partner.151 R2 5 3.084 R3 451 R4 921 R4 665 R5 6 5.995 7 9.222 R5 877 R1 4 3.038 607 R3 4 1.641 7 6.293 5 1. 505 3.168 2.480 Ϭ n ϭ $5. $19.333 11. 9 27.832 19. 54.615 R4 12.220 R7 6.384 $15. 19.988 26. 3 $19.2.147 7.316 R1 13.073 R1 10. 2 14.748 people sat in the stadium. Print This 7–8 Page P PRACTICE 5 65. Each banner cost $6. A total of 17.697 Ϭ 6 ϭ 14.079 4.328 Ϭ 4 ϭ 15.998 5.986 Ϭ 8 ϭ Algebra & Functions Find each missing number. 7 45. The King School raised $75.213 9.4 . How many banners did the school sell? Use with Grade 4. 6 31.288 by games in its sports stadium for 3 days. pages 294–295. 6 $90. How many seats does the stadium have? selling Junior Olympic banners. 73.Print This Page Name Divide 5-Digit Numbers Divide.356 Ϭ r ϭ 11.620 Ϭ 5 ϭ 17. The King School held Junior Olympic 23.425 $6. 2 53. (223) NS 3.296 20. 16. Check your answer. 37.183 Ϭ 2 ϭ 18.056 R1 9. 1.840 13. 44. 8 33.089 Problem Solving © McGraw-Hill School Division 22. 71. $26. Each day. every seat in the stadium was full. Chapter 7.131 6.475 8.895 Ϭ 9 ϭ 16.447 R2 7. 3.064 5.767 4. 4 76.208 3. 41.990 21. Lesson 8.994 4. 5 23.910 Ϭ v ϭ 7. 7 65. Chapter 7. 4.834 Divide.472 Ϭ 8 ϭ 6 44.445 Use with Grade 4.738 5 31.084 5.273 8.Print This Page Name Divide 5-Digit Numbers Divide 19. 2 $26. Step 1: Decide where to place the first digit in the quotient. 4.958 R2 4 19.042 9.4 . Divide 19 by 4. 4.222 Ϭ 3 ϭ 13. 3. 2. 74. 7. 1. pages 294–295. © McGraw-Hill School Division 3 94.958 ϫ 4 ϭ 19.275 Ϭ 8 ϭ 11. 15. 39.834 Ϫ 16 38 Ϫ36 23 Ϫ 20 34 Ϫ 32 2 Step 3: Check your work.619 10. Lesson 8. Write 4 in the quotient above the 9.856 7 23. 5 68. $33. Step 2: Divide. Think: You cannot divide 1 by 4.834 Ϭ 4.2.217 Ϭ 3 ϭ 14. 19. (224) NS 3. $45.832 ϩ 2 ϭ 19.021 Ϭ 9 ϭ 12. 3. Print This 7–8 Page R RETEACH The quotient will have 4 digits. 4 52.832.391 6. 19.496 Ϭ 4 ϭ 9 82. 98. 41. 47. 11. 59. 85. 43.4 . 24. 92. 39. 25. 3. 58. 62. 40. 82.037 Ϭ 9 ϭ 1. 8. 10. 49. 48. 13. 72. 74. 75. 20. 80. 56. 100. 6. 38. 29. 88. 91.338 Ϭ 5 ϭ 54. 46. 55. 54. 9. 61. 3.150 Ϭ 4 ϭ 6. 47. 42. 4. 69. 27. 83. 22. 31.829 Ϭ 3 ϭ Print This 7–8 Page E ENRICH Down 1. 77. 5. 65. 44. 34. Lesson 8. 66. 17. Then create and solve your own Across and Down clues. 99. (225) NS 3. 17. 33. 86. 63. 76. 52. 28.Print This Page Name Divide 5-Digit Numbers Crossnumber Puzzle Divide to complete the crossnumber puzzle. 23. 21. 15. 37. 20.393 Ϭ 7 ϭ 4. 70. 84. 97. 57. 71. Chapter 7. © McGraw-Hill School Division 2. 36. 43. 7.2. 87.351 Ϭ 6 ϭ 31. 68. 16. 79. 60. 67. 78. 65. pages 294–295. 90. 51. 93. 35. 73. 81. 45. 32. 18. 64. 95. 12. 94. 89. 19. 53. Use with Grade 4. 14. 96. 26. 37. Across 1. 50. 30. 4 feet for $2. 6 pints for $7.50 9 inches for $78. 1.91 Print This 7–9 Page P PRACTICE 4 ounces for $14. What is the unit price for a 2-pound 5 feet for $2.2.90 Better buy: 4.31 Better buy: 6. 3.40 4 yards for $199. What is the unit price for a 5-pound © McGraw-Hill School Division bag of wild bird seed? 11.7 5 12. 5 inches for $48. 3 gallons for $59.00 Better buy: Solve. 9.2. pages 298–299.44 9 pints for $14. 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 $3.4 5 9-pou nd ba g for $15. MR 3.80 2.08 6 quarts for $315.Print This Page Name Find the Better Buy Find each unit price.96 for 5-pou nd ba g for $9. 3. (226) NS 3.80 Better buy: 7.00 Better buy: 3.14 7 pounds for $19. Chapter 7.3 . 2 quarts for $99.4.21 Better buy: 8.92 5 gallons for $94. Lesson 9. Which bag of wild bird seed is the best buy? Use with Grade 4. 2 ounces for $6.53 Better buy: 5. Use the ad to answer exercises 9–12. 3 yards for $157. 4 pounds for $10.10 Better buy: bag of wild bird seed? 10. Compare to find the better buy. $0.35 So. Compare to find the better buy.4.98 unit price: 3. Find the better buy: a 6-ounce jar of pickles for $1.92.2.35 8 $2.69 4 pints for $4.25 Better buy: 4. $0. Find each unit price.00 unit price: Better buy: 2. 6 quarts for $55. Print This 7–9 Page R RETEACH Step 2 Compare the unit prices.80. 1. 5 feet for $46.80 Ϫ24 40 Ϫ 40 0 Think: Write the dollar sign and the decimal point in the quotient.96 © McGraw-Hill School Division 5 gallons for $6. 3 cups for $11.32 Ͻ $0.38 8 cups for $31. Divide the price by the number of ounces.92 Ϫ18 12 Ϫ 12 0 $0.60 Better buy: 5. the 6-ounce jar of pickles is the better buy.52 Better buy: Use with Grade 4.62 5 gallons of paint for $75. 4 yards for $12. pages 298–299. Chapter 7. You can find the better buy by comparing the unit price of each size. 3 gallons of paint for $43. 3 gallons for $3. Step 1 Find the unit prices.01 Better buy: NS 3.32 6 $1.72 6 yards for $20. MR 3. or an 8-ounce jar of pickles for $2.2. (227) 9 quarts for $80.22 7 feet for $63.Print This Page Name Find the Better Buy Products often come in different sizes. 2 pints for $2.35 Better buy: 7. 3. Lesson 9. 3.70 Better buy: 6.3 . Find the unit price for each item in the Food Barn ad. The Food Barn placed the ad below in the newspaper. the Food Barn and Best Foods.36/pound $1.4. Print This 7–9 Page E ENRICH Food Barn s Weekend Specials! Greek olives $2. are across the street from each other. Chapter 7.74 Ju ice Ju ice $0. MR 3.3 .79/box T UNA T UNA pa Dog Food T UNA NEW! Fresh pasta $3. a 7-ounce jar of Greek olives. Lesson 9. 3. for example. pages 298–299.2.62/can $0.88 for a 8-pound bag $6.65/ounce Dog food $10.Print This Page Name Find the Better Buy Beat This Price! Two grocery stores. 3.60 for a O lives 4-ounce jar Cheddar cheese $34. Best Foods—Our Prices Are Always Lower! Item/Amount © McGraw-Hill School Division Our Price oz pounds boxes pounds cans inches Our Unit Price Greek olives: Cheddar cheese: Cranberry juice: Dog food: Tuna: Fresh pasta: Use with Grade 4.35/inch Best Foods says its prices are lower than the Food Barn’s prices.15 for 9 inches st a $1.75 for a 5-pound wheel Six-pack of cranberry juice boxes $4. but different amounts.95/pound Three cans of tuna $4.86 $0. (228) NS 3.2. Then create an ad for Best Foods. Use the same items. When should Sally leave? solved by using the guess-and-check strategy.4. It will take her about 20 minutes to walk from school to the job. Use any strategy. The case has more than 7 shelves. 5. She has 3 more flags to draw. (229) NS 3. Strategy: Use with Grade 4. 2. How many of each kind of pack does Jamal buy? auditorium.4. There are 36 students in an in packs of 5 or 8. 4 cards are left. and 10 in the fourth row. 7 in the third row. Social Studies Each of the 50 1 photo in the first row. How many shelves does the case have? How many dolls does each shelf hold? equally from a deck of 52 cards. 3. how many photos will Warren put in the fifth row? © McGraw-Hill School Division states in the United States has a state flag. Warren is making a display. A group of friends choose cards case. If the pattern continues. Teri is putting 57 dolls in a display Print This 7–10 Page P PRACTICE 2. Create a problem which can be for her job.1. MR 1. There are more than 6 friends. She puts the same number on each shelf and has 3 dolls left.3.M. 1. 2. Stickers come 4. She starts work at 4:15 P. 3. How many flags has Evelyn drawn? Strategy: 7. There are twice as many girls as boys. Evelyn wants to make a drawing of each state flag. How many friends are there? How many cards does each friend have? 3. Jamal buys 59 stickers. How many girls are there? How many boys are there? Mixed Strategy Review Solve. Share it with others. 4 photos in the second row. Lesson 10. pages 300–301. He puts 6. Chapter 7.Print This Page Name Problem Solving: Strategy Guess and Check Use the guess-and-check strategy to solve.1.2 . Sally wants to arrive 20 minutes early Strategy: 8. After they have chosen. Print This Page Name Problem Solving: Strategy Guess and Check Page 301. How many inches of sand will she pour? Step 1 Read Be sure you understand the problem. of red sand than Step 2 Plan I I Make a plan. I I I I I I I I 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 List the information you know. inches of sand. What do you need to find? • You need to find how many . check. 3.1. 2. © McGraw-Hill School Division Use with Grade 4.4. Choose a strategy. 3. Check your guess. Lesson 10. Problem 2 Print This 7–10 Page R RETEACH Jenny is making sand art. Chapter 7. 2. Guess. Revise the guess and try again if it is wrong. and revise until you find the answer that makes sense. (230) NS 3. What do you know? • A bottle holds • There will be blue sand.1. Read carefully. pages 300–301. A bottle holds 8 inches of sand. Jenny wants to have 2 inches more of red sand than blue sand.2 . Use what you know to make a guess. MR 1.4. Guess how many inches of each color sand can be used to make a total of 8 inches.3. Lesson 10. 2. Guess Start with two numbers that have a sum of 8.1. Erica bought 9 pens. You know that the bottle holds You know that Jenny wants to have inches of sand than inches of sand. There are inches of blue sand more inches of red sand. Each pen costs either $2 or $3. 3.Print This Page Name Problem Solving: Strategy Guess and Check Step 3 Print This 7–10 Page R RETEACH Solve Carry out your plan. how many $2 and $3 pens did Erica buy? Use with Grade 4. There are more than 5 friends.1. Check 6 + 2 = 8 inches of red sand.3.4. MR 1. Does your answer make all of the statements true? Practice 1.4. How many friends are there? How many stickers does each friend get? 2. Try 6 and 2.2 . (231) NS 3. There are inches of blue sand more inches of red sand. A group of friends share 30 stickers equally. Does that answer fit the problem? Revise 5 + 3 = 8 inches of red sand. with 3 stickers left over. Chapter 7. more sand. 3. 2. pages 300–301. If the total cost was $23. Does that answer fit the problem? Step 4 Look Back © McGraw-Hill School Division Is the solution reasonable? Reread the problem. 9 6. 15. 9. 10. 6. 1. 2 © McGraw-Hill School Division Problem Solving 19. 24. 6. Chapter 7. 9. 3. 5. 6. 20. 9.4. 7. 25 16. (232) NS 3. 5. 4. 3. 20. 0 10. She scored the following numbers of points in 5 games: 20. 15. 10. 1. 8. 7. 8 7. 5. 3. The students in Homeroom 101 20. What was the mean number of labels brought in each day? tournament this week. 1. 30 13. 2. 2. 1. 6. 1. 4. 2 Mean: Mean: Mean: Find the mean. 8 12. 9. 6. Alison played in a basketball collected soup labels this week. 4. 9. 6. and 18. 6. 20. 1. 9 17. and 5. 7. Lesson 11. 6.2 . 12. 36 15. 4. 15. 1. 3. 6. What was her average point total? Use with Grade 4. 6 8. 8. 8. 9. 4 Print This 7–11 Page P PRACTICE 3. 2. 3. The number of labels brought in to class each day were 8. 4. 1. 20. 4. 8. 3 9. SDP 1. 4. 5. 2. 9. 17. 2. 12. 10. 30. 9. 2. 7 11. 2 14. 15. 10. 2. You may use connecting cubes. 9. 2 18. 10. 6. Redraw the cubes so that the rows are all the same length. 1. 5 2. 8. 10. 5.Print This Page Name Explore Finding the Mean Use the connecting cubes to find the mean. 9. 5. pages 302–303. 3. 30 5. 9. 5. 5. 0. 5. 20. 6 7. 10. 4 10. You should have 16 cubes connected together. You may draw cubes to help you. 10. 20 3. and 6 is 4. 5. 40. 3. pages 302–303. Find the mean. 6 11. 4. 4. 10 8. 2. 3. 9. 7. 3 2.2 . 1 4. and 6 using connecting cubes. 6. Chapter 7. 9 9. 8. 3. 2. Here is how to find the mean of 2. 3. 7 5. 10. You should have 4 cubes in each group. 5. Lesson 11. Connect cubes to represent each number. 2. 8. 5. 5. (233) NS 3. 6. the mean of 2. 5. SDP 1. 8. 3. 4. Print This 7–11 Page R RETEACH Connect the cubes into one long row.4. 3. 7. 3. 5. © McGraw-Hill School Division 1. 2 6. Divide the cubes into 4 equal groups. 12. 0. 5. 10. 5. 5 Use with Grade 4.Print This Page Name Explore Finding the Mean 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. 11. 2. 15. So. 5. 1. 2. or mean. you should have an average temperature of 68°F. from 1961 to 1990. Chapter 7.Print This Page Name Explore Finding the Mean January in Los Angeles In Los Angeles. January Sunday 1 Monday 2 Tuesday 3 70° 8 9 10 11 12 73° 15 63° 22 23 24 25 26 27 28 16 17 18 19 20 21 13 14 Wednesday Thursday 4 5 Friday 6 Saturday 7 29 © McGraw-Hill School Division 30 31 68° 2. Complete the calendar by writing different temperatures for the days. the average. (234) NS 3. Lesson 11. SDP 1. Imagine that the average high temperature for the month below is 68°F. When you add the temperatures and divide by 31. Explain how you chose the temperatures. Print This 7–11 Page E ENRICH 1. California. high temperature in January was 68° Fahrenheit.2 . pages 302–303.4. Use with Grade 4. $506 7. 7. 10. 8. 120. 38. 90 9. 67. 40. 20. 80. 11. SDP 1. 54. 116. and 151 pizzas. 4. Number of books Emily read each 14. 630 13. 9. Number of miles a pilot flew each day: 6. 7. 11. 3. $446. 781 Print This 7–12 Page P PRACTICE 8. 140 © McGraw-Hill School Division campers each week: 24. 11. 482. 4. 665. 9. 14.Print This Page Name Find the Mean Find the mean. 80. $48. 90. 910. 6. 33. 40. (235) NS 3. 9 11. $120. What is the average number of pizzas sold each day? Use with Grade 4. Number of rolls of film used each day 10. 18. $308. Number of gallons of gas used to take class pictures: 6. 1. 760. 18. 208. 13. 590. Lesson 12. 64. month: 2. 20. Number of minutes Jason practiced 2. 12 day: 980. Number of miles Dorothy ran each 12. 1. $77 5. 5 3. Pizza She traded 42. 619. pages 304–305. What is the mean number of cards she trades on a Saturday? Guy sold 97. 100. Number of boxes of cereal eaten by each shelf: 60. 85. 8. 115. From Thursday through Sunday. 72. 40.2 . 26. 6. 70. Number of bottles of juice on 16. 13 Problem Solving 17. 1. 823. 60 15. Kathy trades baseball cards. 66. 5. 8. 11.4. and 40 cards the last three Saturdays. 18. Number of miles traveled each day: violin this week: 30. 85. 4 each day: 8. 1. 14 4. Chapter 7. 2. 3. 62. 88 6. 125. 6. $25. Height of six boys in inches: 60. 80. 15 6. Chapter 7. 709. 14. Print This 7–12 Page R RETEACH You can use connecting cubes to help you record the steps for finding a mean. 2 5. 7. 16. 15. Step 2 Divide the cubes into 4 equal groups. Number of miles Lance bicycled each 35.4. 7. 54 day: 74. 842. 6. SDP 1. 6. 20 7. and 4 is 5. 69. 5 © McGraw-Hill School Division 2. 12. 3. pages 304–305. 21. 12. Number of hawks the ranger saw 10. 21. 12. 10. 5 4 20 So. 661. 4. 3. Connect the cubes into one long row. 16. 13. 6. 27 4. 3. the mean of 7. 15.Print This Page Name Find the Mean Find the mean of 7. and 4. 12. So. 19. Weight of five dogs in pounds: 42. Lesson 12. and 4 is 5. You should have 5 cubes in each group. 1. 9. the mean of 7. 8. 8. Using Connecting Cubes Step 1 Build each number with connecting cubes. Number of cars that used the parking each day: 19. Find the mean. 13 garage each day: 563. 7 6 3 ϩ4 20 Step 2 Divide the sum by the number of addends. 5. 4. 3. 22. 13. You should have 20 cubes connected together. 57 9. 12. 805 NS 3. 13. (236) . 38.2 Use with Grade 4. 11 3. Using Pencil and Paper Step 1 Add the numbers. The scorecards below show the scores for the first five frames. SDP 1.2 . (237) NS 3.4. Chapter 7. Team A Jason 12 Deanna 21 Serena 6 4 22 9 4 Total: Print This 7–12 Page E ENRICH eric 6 13 10 7 8 50 5 18 16 5 Total: 19 30 15 10 Total: Total: Mean: 45 Mean: 65 10 Mean: 13 Total Score: Annie 12 13 9 10 16 5 12 11 12 80 9 Mean: 16 Team A’s Team B Steven Mean Score per Person: Chris 16 18 Lindsey 20 9 10 12 Total: Total: 17 18 15 15 © McGraw-Hill School Division Total: 60 Mean: 10 Total: Mean: 50 65 10 Mean: 13 Mean: Mean Score per Person: 85 17 12 Team B’s Total Score: Use with Grade 4. Then fill in the team’s total score and mean score.Print This Page Name Find the Mean Missing Pins The computer at the bowling alley is down. pages 304–305. so teams have to keep track of their scores on cards. Lesson 12. A cat with muddy paws ran across the cards. or rounds. Complete the scorecards by writing the correct numbers in the paw prints. 1 . Lesson 13. 2.3. or car to the aquarium? Explain. Cost Bus 7–13 Part A WORKSHEET Decision Making Print This Page Advantages and Disadvantages Train Car © McGraw-Hill School Division Your Decision What is your recommendation for the club? Should they take a bus. (238) NS 3. Chapter 7. 3.Print This Page Name Problem Solving: Application Applying Division Record your data and notes.4. Use with Grade 4. pages 306–307.1. train. MR 1. 3. Paper Clip Eraser © McGraw-Hill School Division Use with Grade 4. Record your data in the table below.2.2 . Show how you found the mean or average distance for each object. Lesson 13.1. pages 308–309.Print This Page Name Problem Solving: Application Do light or heavy objects fly farther? Safety: Wear goggles to protect your eyes and work away from other people. 2. 3. (239) NS 1. MR 1. SDP 1. Distance Traveled Object Paper Clip Eraser 1 2 3 4 5 7–13 Part B WORKSHEET Math & Science Print This Page Mean 1.2. Chapter 7. 2. 3. Which object traveled farther? How do you know? 7–13 Part B WORKSHEET Math & Science Print This Page 3.2 . SDP 1.2. Lesson 13. Explain the results of the activity in terms of gravity. 2. pages 308–309. (240) NS 1. In your own words. Chapter 7.3. © McGraw-Hill School Division 5. Show your work. Use division to decide how many times farther one object traveled than the other.Print This Page Name Problem Solving: Application Do light or heavy objects fly farther? 2. Work Space 4. MR 1. explain what gravity is. Use with Grade 4.1. 80 560. 16.000 Ϭ 80 ϭ 15. 18 Ϭ b ϭ 6 Print This 8–1 Page P PRACTICE 360 Ϭ 90 ϭ n 3.000 Ϭ 90 ϭ n Divide. 36 Ϭ 9 ϭ n 2.600 Ϭ 90 ϭ n 36. d Ϭ 70 ϭ 7 b ϭ 400 24.700 Ϭ 90 ϭ 16. 4.000 Ϭ 90 ϭ n 360. 18. 640 Ϭ 80 ϭ s 6. t Ϭ 60 ϭ 70 26. 7.800 Ϭ 30 ϭ b 18. 28.000 Ϭ 80 ϭ s b Ϭ 30 ϭ 6 1. If 6. 40.000 90 450.000 Ϭ 50 ϭ Problem Solving 28. 3. 45.000 10.000 Ϭ 80 ϭ s 640.000 11. 22.000 Ϭ 27. 2 5. 140 Ϭ © McGraw-Hill School Division aϭ2 23.000 Ϭ 20 ϭ 17.000 Ϭ 30 ϭ b 60 120 8. 810 Ϭ 90 ϭ 20.200 Ϭ 20 ϭ 18.000 12. 3.000 Ϭ 30 ϭ b 180.2 . A box of 400 stickers is to be divided 29. How many stickers will each student receive? among 90 libraries. how many books will each library get? Use with Grade 4. 2. 500 $50 7.Print This Page Name Division Patterns Complete. 1.300 books are divided equally equally among 80 students. 150 Ϭ 30 ϭ 14. pages 324–325.000 $300 40 $2. (241) NS 3. 42. 40 2. 70 35. Chapter 8.800 9.400 Ϭ 80 ϭ s 64.000 Ϭ 70 ϭ 21. 1. 70 6. Lesson 1. Use mental math. 56.000 Ϭ 50 ϭ Algebra & Functions Find each missing number.000 10 $400 $40 70 $21.000 Ϭ 60 ϭ x y 25.000 5.600 Ϭ 40 ϭ 13.000 Ϭ 70 ϭ 19. 64 Ϭ 8 ϭ s 3. 60 Ϭ 20 ϭ 3 → 600 Ϭ 20 ϭ 30 → 6. 4. 40 Ϭ 8 ϭ Use with Grade 4.300 Ϭ 90 ϭ 63.Print This Page Name Division Patterns To divide mentally. 30 Ϭ 5 ϭ 630 Ϭ 90 ϭ 6.200 Ϭ 40 ϭ 12.2 . Then count and subtract zeros. 900 Ϭ 30 ϭ 10.800 Ϭ 30 ϭ 13.000 Ϭ 20 ϭ 300 → 1 zero Ϫ 1 zero ϭ 0 zeros 2 zeros Ϫ 1 zero ϭ 1 zero 3 zeros Ϫ 1 zero ϭ 2 zeros Print This 8–1 Page R RETEACH The basic fact is 20 Ϭ 4 ϭ 5. you can use basic division facts and look for a pattern. (242) NS 3. pages 324–325. Chapter 8.000 Ϭ 80 ϭ 5. 420 Ϭ 60 ϭ 15. 1. 18 Ϭ 3 ϭ 11.000 Ϭ 50 ϭ 30. 90 Ϭ 30 ϭ 9. 400 Ϭ 80 ϭ 7. 4. Lesson 1. 12 Ϭ 4 ϭ 240 Ϭ 30 ϭ 2.000 Ϭ 40 ϭ 50 → 2 extra zeros – 1 zero ϭ 1 zero 20.000 Ϭ 40 ϭ 4.400 Ϭ 30 ϭ 24.000 Ϭ 90 ϭ © McGraw-Hill School Division 300 Ϭ 50 ϭ 3. Find the basic division fact. 200 Ϭ 40 ϭ 5 → 1 extra zero – 1 zero ϭ 0 zeros 2.000 Ϭ 40 ϭ 500 → 3 extra zeros – 1 zero ϭ 2 zeros Complete the pattern. 9 Ϭ 3 ϭ 8. 24 Ϭ 3 ϭ 2. Count and subtract the zeros.000 Ϭ 30 ϭ 3. 42 Ϭ 6 ϭ 14. The basic fact is 6 Ϭ 2 ϭ 3. 180 Ϭ 30 ϭ 12. This will tell you how many zeros the quotient will have.200 Ϭ 60 ϭ 16. 1.000 Ϭ 50 ϭ 6. 63 Ϭ 9 ϭ 120 Ϭ 40 ϭ 1. 000 9. Then use the remaining two answers to write the next division sentence. 60 c. b. 50 a.000 c.000 a. 3. 10. 5. a. pages 324–325. 900 c. 50 b.200 Ϭ 80 = Print This 8–1 Page E ENRICH a.000 b. (243) NS 3. a. 54. a. 50 a. a. 4. 40 a. 90 12. 500 c. © McGraw-Hill School Division b.000 c. b. 90 5. 900. Chapter 8. 8. 100. 4. 100.800 c. 90 c. 80 c. b. 80 4.000 11.000 b. 800 c. 50 13. 70 10.500 6. 1.200 3. 70 7. 4. 60 c.200 b. 2. 81. 40 b.000 Ϭ 10 = 800 2. a.2 .000 c.000 c.Print This Page Name Division Patterns Move Along Circle the correct answer for each exercise. 10. 4. 10 b. Look at exercise 12.000 a. 900 b. b. Repeat until you finish the page. 3. Lesson 1. 80 8. How did you decide how many zeros were in the quotient? Use with Grade 4. 20 a. 156 Ϭ 18 ϭ 13 87 9. 230 Ϭ 19 ϭ 15. 143 Ϭ 30 ϭ 121 Ϭ 14 ϭ Divide. 4. 8 R13 16 293 © McGraw-Hill School Division 18 R5 17 235 13 R14 19 258 13 R11 25 441 17 R16 13.2 . 14 125 12. The dividend is 280. 282 Ϭ 18 ϭ 14.Print This Page Name Explore Dividing by 2-Digit Numbers Divide. The divisor is 23. You may use place-value models. 6 R9 6. Print This 8–2 Page P PRACTICE 130 Ϭ 10 ϭ 3. pages 326–327. 134 Ϭ 14 ϭ 17. 1. 12 93 11. 269 Ϭ 24 ϭ Problem Solving 19. Chapter 8. What are the quotient and remainder? What are the quotient and remainder? Use with Grade 4. 115 Ϭ 15 ϭ 18. The divisor is 12. 135 Ϭ 16 ϭ 16. 9 R2 7. 20. The dividend is 160. 7 R9 8. 2. (244) NS 3. 5. Lesson 2. 15 137 10. Chapter 8. So. 214 Ϭ 12 ϭ 4. 285 Ϭ 14 ϭ 5. 268 Ϭ 11 ϭ 9. 163 Ϭ 13 ϭ 2. Divide. Print This 8–2 Page R RETEACH Exchange tens for ones so you can keep grouping 1 ten and 2 ones. 158 Ϭ 10 ϭ 3. You may use place-value models to help you. You can make 12 equal groups of 12 with 4 ones remaining.2 . Find 148 Ϭ 12. Lesson 2. 148 Ϭ 12 ϭ 12 R4. pages 326–327.Print This Page Name Explore Dividing by 2-Digit Numbers You can use estimation and models to help you divide. Show 148 using place-value models. 352 Ϭ 16 ϭ 6. Think: How many groups of 12 are there in 148? Exchange 1 hundred for 10 tens. 183 Ϭ 17 ϭ 8. Divide the tens. Make as many groups of 12 as you can. 385 Ϭ 15 ϭ 7. © McGraw-Hill School Division 1. 376 Ϭ 18 ϭ Use with Grade 4. (245) NS 3. 1 2 3 4 5 6 7 8 9 10 20 50 60 70 90 100 Using these symbols. pages 326–327.946 is shown as .Print This Page Name Explore Dividing by 2-Digit Numbers Stick Division Print This 8–2 Page E ENRICH What if we used a number system that used symbols instead of numerals? In this Chinese system. Chapter 8. 3. (246) NS 3. 21 8. 5. 2.946 426 → Use the number system above to create four division exercises where the divisor is a 2-digit number. 1. Lesson 2. Use with Grade 4.2 . 21 is shown as Example: and 8. Is it easier or harder to divide using the number system above? Explain. Then exchange exercises with a partner and find the quotient using symbols. © McGraw-Hill School Division 4. numbers are written using the symbols shown. 40 81 22. 2 R3 1 R9 1 R9 10 76 24. 87 Ϭ 10 ϭ 9. 88 Ϭ 20 ϭ 8. 27 Ϭ 30. 67 Ϭ 30 ϭ 15. 71 Ϭ 30 ϭ 11. 52 Ϭ 10 ϭ 14. 40 49 27. 30 63 23. 2. 74 Ϭ 20 ϭ 13. 20 95 25. 75 Ϭ 10 ϭ 5. Lesson 3. 62 Ϭ 40 ϭ 17. How many packages will there be? How many pencils will be left over? tennis balls in boxes. 97 Ϭ 20 ϭ 12. 1. 2 R1 1 R24 2 R4 19. Sam needs to put 76 pencils in 35. 71 Ϭ © McGraw-Hill School Division m ϭ 2 R7 a ϭ 1 R13 y ϭ 3 R11 29. 90 Ϭ k ϭ 1 R21 p ϭ 3 R14 r ϭ 2 R10 Problem Solving 34. 63 Ϭ 32. 51 Ϭ 20 ϭ 6. 51 Ϭ 31. How many boxes will Kenya fill? How many cans will she have left over? Use with Grade 4.Print This Page Name 8–3 Page Divide 2-Digit Numbers by Multiples of 10 Print P This PRACTICE Divide. 60 84 26. 74 Ϭ 33. Each package should have 10 pencils. (247) NS 3. 3 R1 7 R6 9 R6 50 78 21. 28. 93 Ϭ 40 ϭ 10. 10 96 30 59 20 44 50 59 Algebra & Functions Find the missing number. Chapter 8. 91 Ϭ 10 ϭ 16. 1 R28 4 R15 1 R29 18. pages 328–329. 94 Ϭ 30 ϭ 7. Kenya needs to put 84 cans of packages. 82 Ϭ 20 ϭ 4. 3.2 . Each box should have 20 cans. 94 Ϭ 40 ϭ 20 61 20. Then make as many groups of 20 as you can. 63 Ϭ 30 ϭ 4. 76 Ϭ 10 ϭ 12. 74 Ϭ 10 ϭ 8. 48 Ϭ 20 ϭ 7. 27 Ϭ 10 ϭ 2. 88 Ϭ 40 ϭ 5. 71 Ϭ 20 ϭ 18.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. 81 Ϭ 20 ϭ 11. Divide. Chapter 8. 85 Ϭ 30 ϭ 10. 93 Ϭ 30 ϭ 9. Find 74 Ϭ 20. You can use place-value models.2 . pages 328–329. Lesson 3. Think: How many groups of 20 are in 74? Using Pencil and Paper Step 1: Divide 74 by 20. 59 Ϭ 30 ϭ © McGraw-Hill School Division Use with Grade 4. Write the remainder in the quotient. Think: 60 Ϭ 20 ϭ 3. 74 Ϭ 20 ϭ 17. 1. 55 Ϭ 10 ϭ 6. 3 R14 20 74 Ϫ 60 14 You can make 3 equal groups of 20 with 14 remaining. 63 Ϭ 50 ϭ 14. Using Models Show 74 using place-value models. 84 Ϭ 60 ϭ 15. 90 Ϭ 40 ϭ 16. 3 20 74 Ϫ 60 Step 2: Subtract. (248) NS 3. 59 Ϭ 50 ϭ 3. 51 Ϭ 30 ϭ 13. Chapter 8.Print This Page Name Divide 2-Digit Numbers by Multiples of 10 Winning Start • Label the faces of a number cube 20. the starting position. Start 72 Print This 8–3 Page E ENRICH 85 97 100 115 120 260 138 253 149 250 © McGraw-Hill School Division 150 235 164 226 219 205 197 186 173 Use with Grade 4. and 70. Lesson 3. 50. 40. Divide the number your marker is on by the number tossed.2 . After passing "Start". Find the whole number quotient. pages 328–329. The winner is the person who lands directly on "Start". you may move forward or backward. • Continue moving forward until you have gone around the board once. (249) NS 3. Move forward that number of spaces. 60. Take turns tossing the number cube. 30. • Place a marker on 72. 900 Ϭ 84 ϭ 18. 8. 44 530 11.000 ϩ 160) Ϭ 46 ϭ 32. Print This 8–4 Page P PRACTICE 22 952 5. Chapter 8. $0. 29.700 ϩ 53) Ϭ 37 ϭ w v n c 30. 14 R4 13 R9 81 891 9.76 Ϭ 64 ϭ 26. 895 Ϭ 24 ϭ 19. Lesson 4. 814 Ϭ 36 ϭ 23.18 88 6. (1. 4. pages 330–333.621 71 62 $55.59 Ϭ 43 ϭ 28.600 ϩ 240) Ϭ 83 ϭ d x 31. 43 R6 2. (250) NS 3. 1. 26 1. 25 R9 17 R3 3.500 ϩ 80) Ϭ (11 ϫ 5) ϭ Problem Solving 35. 54 760 8. 83 93 8. (2. Mr. 75 R4 96 R1 17 $11.11 12 R2 4. (1.39 14.818 16.930 Ϭ 92 ϭ Algebra & Functions Solve. 7.467 Ϭ 24 ϭ 25. 907 Ϭ 31 ϭ 20.67 39 2.08 Ϭ 59 ϭ 22. Tallo’s class made 234 ribbons for 36. (1. 367 Ϭ 14 ϭ 21. Each student made the same number of ribbons. 66 $7. There are 25 students in the class. 531 Ϭ 45 ϭ 24.780 Ϭ 77 ϭ 27. (1. 11 29 496 10. 1. $48. How many tickets will each student need to sell? Use with Grade 4. There are 18 students in the class. $0. Mrs. How many ribbons did each student make? 200 tickets to the Winter Sports Fair.Print This Page Name Divide by 2-Digit Divisors Divide.2 . 75 984 12.89 46 3.900 ϩ 100) Ϭ 29 ϭ 33. Willow’s class wants to sell the Sports Fair. 31 784 6.929 51 3.381 15.26 7.300 ϩ 70) Ϭ (12 ϫ 4) ϭ © McGraw-Hill School Division 34. (1.518 74 R6 17. 61 R2 $0. $7. $37.954 13. 135 Ϭ 14 ϭ 7. 6 R15 25 165 Ϫ 150 15 ← 165 Ϫ 150 ϭ 15 © McGraw-Hill School Division Divide. 212 Ϭ 24 ϭ 2. You can use place-value models. 1. Chapter 8. 166 Ϭ 13 ϭ Use with Grade 4. Step 3: Subtract. Print This 8–4 Page R RETEACH Using Pencil and Paper Step 1: Divide. 164 Ϭ 12 ϭ 4. Lesson 4. Exchange tens for ones. Step 2: Multiply.2 . 318 Ϭ 21 ϭ 6. 372 Ϭ 23 ϭ 8. 435 Ϭ 16 ϭ 3.Print This Page Name Divide by 2-Digit Divisors You can use models to help you understand dividing by 2-digit numbers. Write the remainder in the quotient. 243 Ϭ 17 ϭ 9. 174 Ϭ 18 ϭ 5. You can make 6 equal groups of 25 with 15 remaining. Using Models Use place-value models to show 165. Think: 180 Ϭ 30 ϭ 6 6 25 165 Exchange the one hundred for 10 tens. Find 165 Ϭ 25. (251) NS 3. pages 330–333. 6 25 165 Ϫ 150 ← 6 ϫ 25 ϭ 150 Then make as many groups of 25 as you can. 8. If you divide either 74 or 214 by me. If you divide either 131 or 154 by me. If you divide either 175 or 204 by me. If you divide either 68 or 134 by me. the remainder is 1. Use with Grade 4. (252) NS 3. I am a number between 20 and 30. © McGraw-Hill School Division 11.Print This Page Name Divide by 2-Digit Divisors What Number Am I? Solve. 3. 14. I am a number between 30 and 40. 13. the remainder is 1. 9. 10. I am a number between 20 and 30. Chapter 8. pages 330–333. 4. the remainder is 1. I am a number between 10 and 20. I am a number between 10 and 20. If you divide either 147 or 255 by me. If you divide either 45 or 56 by me. I am a number between 10 and 20. the remainder is 16. I am a number between 10 and 20. If you divide either 221 or 265 by me. I am a number between 20 and 30. 7. If you divide either 110 or 144 by me. the remainder is 4. If you divide either 61 or 73 by me. 6. If you divide either 69 or 88 by me. I am a number between 30 and 40. the remainder is 1. the remainder is 8. the remainder is 1. If you divide either 107 or 128 by me. If you divide either 76 or 126 by me. the remainder is 2.2 . If you divide either 295 or 322 by me. the remainder is 2. the remainder is 25. 12. I am a number between 20 and 30. What number am I? 1. I am a number between 40 and 50. the remainder is 2. I am a number between 20 and 30. I am a number between 20 and 30. If you divide either 74 or 110 by me. Print This 8–4 Page E ENRICH 2. Lesson 4. the remainder is 12. I am a number between 10 and 20. the remainder is 3. 5. 806 Ϭ 56 15. 2. 396 Ϭ 21 © McGraw-Hill School Division 914 Ϭ 31 2.106 Ϭ 82 Problem Solving 28.585 6. 49 1. 53 2. 16 789 5.612 19.100 Ϭ 82 556 Ϭ 71 2. 1.806 Ϭ 38 11. 32 8.732 17.947 Ϭ 38 26.Print This Page Name Estimate Quotients Estimate the quotient.116 miles in 6 hours. Choose compatible numbers.256 9. 46 miles per hour. 68 34. 17 211 3. 1.300 Ϭ 21 27. Lesson 5.210 Ϭ 48 16.920 8. 2.512 20.912 10.280 7. 41 1. 72 6. pages 334–335. 7.011 Ϭ 48 6.903 Ϭ 86 12. 63 546 18. 18 586 Print This 8–5 Page P PRACTICE 4. About how many hours did she drive? About how many miles per hour did it fly? Use with Grade 4. 3.2 . Write Ͼ or Ͻ.709 Algebra & Functions Estimate to compare. A jet flew 3. 61 3.113 Ϭ 31 13. Karen drove 283 miles at a speed of 29. 21 1. (253) NS 3. Chapter 8.700 Ϭ 71 24. 2. 492 Ϭ 68 25. 7. 86 1. 19 389 2. 1. 22.160 Ϭ 93 14.206 Ϭ 91 23.300 Ϭ 13 4. 5. 78 4.106 21. 1. 3.123 Ϭ 64 12. Division fact: 27 Ϭ 3 ϭ Estimate: 2. 2. Estimate 3. Estimate 2.482 Ϭ 33 6.726 Ϭ 72. 2. 3.463 Ϭ 73. Print This 8–5 Page R RETEACH Division fact: 18 Ϭ 3 ϭ Estimate: 1. 2.952 Ϭ 79.700 Ϭ 30 ϭ 4. You can use compatible numbers to estimate quotients. 1.500 Ϭ 70 ϭ 50 So.587 Ϭ 53 11. Estimate 3.512 Ϭ 78 7. Lesson 5. 7.Print This Page Name Estimate Quotients Compatible numbers are numbers you can divide easily. 3. 3.789 Ϭ 27 15.512 Ϭ 42 © McGraw-Hill School Division 10.432 Ϭ 92 Use with Grade 4.800 Ϭ 30 ϭ 3.463 Ϭ 73 Think: A basic fact that is close is 35 Ϭ 7. 2. (254) NS 3.880 Ϭ 29.797 Ϭ 43 16.463 Ϭ 73 is about 50. 3. pages 334–335.207 Ϭ 68 9. 6. 5. Estimate 5.712 Ϭ 32 14. 4. 1.132 Ϭ 71 13.785 Ϭ 31. Complete. 1.2 . Estimate 1.164 Ϭ 89 8. 2. Division fact: Estimate: Division fact: Estimate: Use compatible numbers to estimate each quotient. 6. Chapter 8. 72 H P . 82 75 92 is about 40.370 Ϭ A © McGraw-Hill School Division 47 is about 300. (255) NS 3. 24 Print This 8–5 Page E ENRICH 33 51 is about 80. 72 52 92 84 33 59 63 33 24 33 42 Explain how you estimated the divisors.880 Ϭ 74 59 is about 500.Print This Page Name Estimate Quotients Box Estimation Choose the best estimate from each box to complete the sentence. 42 28 is about 400. 44 38 is about 40. 72 91 D. 34. 7 84 25. 32 44 E. 42 2. 81 64 is about 500. 31 52 2.277 Ϭ P. pages 334–335. Chapter 8. Who was the first American in space? A.790 Ϭ D L R B. 29. 68 58 12.575 Ϭ N.841 Ϭ E N S S. 63 53 48 is about 70. 27 71 4.356 Ϭ L. JR. 24 64 3. 15. Use the code to answer the question.2 .430 Ϭ H.250 Ϭ R. Lesson 5. Then write the answer next to the letter of the box to make a code. Use with Grade 4. 68 52 is about 600. 56 476 17. (256) NS 3.Print This Page Name Adjust the Quotient Divide. pages 336–337. 88 339 20. 84 626 10. 1. 44 371 21. 13 $92. no 29. 25 $93.95 11 $99.00. 75 295 14. 7 R11 2 R44 8 R74 8 R28 8 R19 5 R77 2. How much should he save each month? Use with Grade 4. 26 189 6.50 © McGraw-Hill School Division $5. 14 $60.15 no 27. 65 247 23. 16 $98. no 28.40 30. 63 238 12. 92 546 19. Print This 8–6 Page P PRACTICE 34 249 5. 81 482 22 186 45 395 36 299 Algebra & Functions Divide only those with quotients between $5. 69 507 18. 92 810 13. 8 R21 4 R34 5 R35 5 R86 3 R52 8 R35 4. 8 R39 3 R49 7 R11 3 R75 4 R56 8 R11 51 146 9. Chapter 8. will she meet her goal? 12 months.75 32. 25.25 $7.11 15 $56. Jason wants to save $180 in 30 days.76 Problem Solving 33. 24 129 22.12 $7. 79 350 11.2 . 57 284 24. $6.15 26. 7 R7 7 R38 3 R70 7 R24 5 R9 8 R10 3. 56 469 7. 39 230 15. If she walks 7 miles every day.25 no 12 $93.00 and $8.90 31. 25 186 16. 41 367 8. Lesson 6. Candy wants to walk 220 miles in 34. 18 $94. 61 120 8. 293 Ϭ 44 ϭ 11. Chapter 8. Step 1: Estimate: 120 Ϭ 40 ϭ 3 Step 2: Use your estimate to divide. 208 Ϭ 25 ϭ Use with Grade 4. Lesson 6. You cannot subtract. Multiply to check the answer. Step 3: Adjust your estimate and divide. 29 148 7. 7 R1 8 R1 3. 43 ϫ2 86 ϩ 39 125 2 R39 43 125 Ϫ 86 ← Multiply: 2 ϫ 43 ϭ 86 39 Subtract: 125 Ϫ 86 ϭ 39 Compare: 39 Ͻ 43 Divide. 24 110 5.Print This Page Name Adjust the Quotient When you divide.2 . 173 Ϭ 19 ϭ 10. Then you must adjust the quotient. 4 R14 6 R8 2. Divide 125 Ϭ 43. © McGraw-Hill School Division 1. 1 R59 1 R61 57 350 16 129 37 223 63 124 9. 5 R3 6 R1 4. sometimes your first estimate is too high or too low. pages 336–337. (257) NS 3. Check your answer. The estimate of 3 is too high. 27 190 6. 3 43 125 Ϫ 129 ← Multiply: 3 ϫ 43 ϭ 129 3 43 125 Print This 8–6 Page R RETEACH Compare: 129 Ͼ 125. Print This Page Name Adjust the Quotient Hi Lo Estimate each quotient. If your estimate was too high.25 Too High Down Too Low Up 5. 88 530 6 R2 $2. Too High Left Too Low Right 6. Bernard hummingbird swordfish Maple greyhound parakeet Use with Grade 4." Use the circled answers to complete the maze below.13 91 $25. circle "Too High.56 48 343 7 R7 26 184 7 R2 Too High Down Too Low Up Too High Right Too Low Left Too High Up Too Low Down Too High Left Too Low Right What is the fastest fish.2 . the biggest dog. Lesson 6. $3. 31 247 7 R30 4. the tallest tree. 1. Too High Down Too Low Up 7. (258) dolphin oak Great Dane sparrow NS 3. 65 595 9 R10 3. Write your estimate. Print This 8–6 Page E ENRICH 73 290 3 R71 2. Move one space in the direction given next to each circled answer. Chapter 8. and the smallest bird? To find out. Then divide. " If your estimate was too low.25 21 $68. Start © McGraw-Hill School Division sailfish redwood St. pages 336–337. Too High Left Too Low Right 8. circle "Too Low. begin at Start. 1.4. How many trophies can they buy? Should you overestimate or underestimate to solve this problem? Explain. 2. They share 7 softballs. How many packages of Frisbees can the club buy? 3. A group of 118 people have signed up for the 5-kilometer run. The Flying Disk Club has saved $90 to buy Disks for its members. Then solve the problem. The tournament organizers have $60 budgeted for trophies. Lesson 7. What is the least number of students who can share a softball? Use with Grade 4. © McGraw-Hill School Division How many trophies can they buy? 4. (259) MR 1. Chapter 8. Each person will receive a special cap. Caps are sold in boxes of 36.1. A group of 24 students is playing catch. What is the least number of students who can share each softball? Should you overestimate or underestimate to solve this problem? Explain. A package of 2 Disks costs $8. 2. How many packages of Disks can the club buy? Should you overestimate or underestimate to solve this problem? Explain.2 .5. How many boxes are needed? Should you overestimate or underestimate to solve this problem? Explain.Print This Page Name Problem Solving: Reading for Math Use an Overestimate or Underestimate Print This 8–7 Page P PRACTICE Reading Skill Form a conclusion about whether you would overestimate or underestimate. 2. How many boxes are needed? 2. 3.1. pages 338–339. 3. Trophies cost $9 each.1. There are 95 volunteers working at the marathon. 2. A box contains 24 water bottles. J underestimate the number of flags per student. H underestimate the number of boxes needed. Lesson 7. D Four water bottles are needed. you should: F underestimate the number of volunteers. D The flags are on 6-foot poles. How many boxes are needed? 1.Print This Page Name Problem Solving: Reading for Math Use an Overestimate or Underestimate Choose the correct answer. © McGraw-Hill School Division who will share a flag. you should: F overestimate the number of students per flag. C There are 21 flags. To find the greatest number of students important to solving the problem? A There are 44 students carrying flags. Each color guard will help carry flags.5. there are 44 color guards. bottles for the volunteers. 2. C There are 95 water bottles.1. Chapter 8. H overestimate the number of flags and underestimate the number of students. B Each color guard will help carry a flag.1. B A box contains 24 water bottles.1. Which of the following is not 4. To be sure there are enough water is true? A There are not enough water bottles for the volunteers. Each volunteer will get a water bottle. 3. There are 21 flags on 6-foot poles. 3. G overestimate the number of volunteers and underestimate the number of boxes needed. Which of the following statements Print This 8–7 Page P PRACTICE Math Skills Test Prep 2. 2. (260) MR 1. J overestimate the number of boxes needed. G underestimate the number of students per flag.4.2 . Use with Grade 4. At the game. What is the greatest number of students that will have to share a flag? 3. pages 338–339. 2.1. you: A use 63 feet for the length of the fabric. B round down the length of the fabric to 50 feet. D use 6 feet for the length of each banner. C round up the length of each banner to 10 feet. Is this enough to buy 4 packs of pennants? Explain. Chapter 8. Each shirt costs $18.1. Underestimate the number of ribbons he can make. Mark wants to buy baseball shirts of Night Dinner. (261) MR 1. 2. Mark has $62. How many shirts can he buy? Explain. Each blue ribbon will be 8 inches long. 12. Sports Committee has $185 to spend on medals. What is the greatest number of people that can sit at a table? Explain. How many boxes can the committee buy? Explain. 9.2 . There are 46 students in the soccer club. 5. pages 338–339. The Maryanne has $30. The soccer club makes 100 cups of fruit drink. 2. Use with Grade 4. Underestimate the number of 9-foot banners that can be made from the fabric. Is there enough fruit drink for each student to have 2 cups? Explain. Solve. A box of gold medals costs $56. 3. To underestimate the number of Print This 8–7 Page P PRACTICE Math Skills Test Prep 6. Travis is making first-place ribbons for Sports Day.5. How many 9-foot banners can be banners that can be made. 3. There are 33 tables.4. different teams. 11.Print This Page Name Problem Solving: Reading for Math Use an Overestimate or Underestimate Choose the correct answer. There are 152 people at the Sports © McGraw-Hill School Division 10. made from the fabric? F 5 G 6 H 7 J 8 8. The sports committee buys a piece of fabric that is 60 feet long. A pack of 3 pennants costs $8.1. Lesson 7. He has 111 inches of blue ribbon. 7. 1. The material will be cut into banners that are 5 feet long. If Liam uses sections of fencing that are 12 feet long. How many banners can be made? balls in stock. the third row has 10. There are 115 students who want to backyard. Use it to solve the problem. Lesson 8. pages 342–343. How many sneakers will be in the fifth row? Strategy: © McGraw-Hill School Division Strategy: 7. Tina also has 4 smaller display cases. One bus can carry 26 students.Print This Page Name Problem Solving: Strategy Choose a Strategy Choose a strategy. How can she arrange the baseballs in the smaller cases so that each smaller case has an equal number of baseballs? 6. How many buses will be needed? Mixed Strategy Review Solve. Create a problem which you could photos and 369 individual photos. the second row has 6 sneakers. Art Tina makes a display of 36 autographed baseballs. Liam is building a fence around his 4. The golf balls are packed in tubes of 6. 5. Use any strategy. How many photos does it sell in all? solve by drawing a diagram or by writing a division sentence. How many tubes of golf balls does the store have? 3. The backyard is 24 feet wide and 60 feet long. The Sports Committee buys 30 yards Print This 8–8 Page P PRACTICE 2.2. The Stadium Store sells 450 team 8. how many sections will he need? go to the basketball tournament. Chapter 8. Francine uses a pattern to make a window display for a sneaker store. The first row has 2 sneakers. and the fourth row has 14. Share it with others. Strategy: Use with Grade 4. She puts 12 baseballs in a large display case. (262) NS 3. MR 2. The Sand Trap Golf Shop has 132 golf of material.4 . What do you know? • The total distance is yards. (263) NS 3. Lesson 8. you can also write a number sentence. Find the number of feet in 20 yards. Read carefully. Count by 3s to see how many cones Camille will use if they are placed 3 feet apart. Plan I I Make a plan. To find the answer. .Print This Page Name Problem Solving: Strategy Choose a Strategy Page 343. I © McGraw-Hill School Division I I I I I 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 To find the answer.4 . MR 2. How many cones will she use? Step 1 Read Be sure you understand the problem. Problem 1 Print This 8–8 Page R RETEACH Camille wants to practice sharper turns. All the cones are the same distance apart. She uses the same 20-yard distance in the driveway and begins at the starting line. Chapter 8. pages 342–343. This time she places the cones 3 feet apart. • Camille will start at the starting line and place cones feet apart. you may draw a diagram. Choose a strategy. What do you need to find? • You need to find the number of feet in • You need to find how many Step 2 yards. Use division to find how many cones Camille will use. Use with Grade 4. Show a distance that is that many feet long.2. Lesson 8. He divides the stickers among 3 friends. There will be 5 rows of stands. How many stickers does each friend get? Use with Grade 4.2. feet. Camille will use a total of cones. (264) NS 3. Camille will use a total of Step 4 Ϭ cones ϭ Look Back Is the solution reasonable? Reread the problem. MR 2. The parks department builds stands next to a baseball field. The distance is feet. How many 10-foot long boards will they need to build the stands? 2. Each row will be 20 feet long. There are 24 stickers in each pack.Print This Page Name Problem Solving: Strategy Choose a Strategy Step 3 Carry out your plan. Write a number sentence. Count by 3s to see how many cones Camille will use. 0 3 6 9 Print This 8–8 Page R RETEACH Solve 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 Count. Show a 60-foot distance.4 . © McGraw-Hill School Division Practice 1. pages 342–343. How many feet are in 20 yards? 1 yard ϭ 3 feet 20 ϫ 3 ϭ 60 Draw a diagram. There will be 1 cone every Write a division sentence. Ed has 4 packs of sports stickers. Chapter 8. Does your answer make sense? Yes No Which method do you prefer? Explain. 2 ϫ 8 Ϭ 4 ϭ 25. 2 ϫ 6 ϩ 4 ϫ 3 ϭ 27. 10 Ϭ 5 ϫ 2 10. He finds 18 more photos.3 . Each page holds 12 photos. 12 Ϫ 3 ϩ 9 ϭ 22. 2 ϫ 8 ϩ 7 2. Lesson 9. 31. (2 ϩ 9) ϫ (7 Ϫ 3) ϭ © McGraw-Hill School Division 14. 24 Ϭ 2 Ϫ 8 ϭ 18. 8 Ϭ (2 ϩ 2) 7. 7 Ϫ 8 Ϭ 2 11. (12 Ϫ 4) Ϭ 2 12. Chapter 8.Print This Page Name Order of Operations Write which operation should be done first. Write an expression and simplify to find her final cost. (4 ϩ 6) Ϭ 5 ϭ 21. 13. 2 ϫ 9 ϩ 10 Ϭ 5 ϫ (3 ϩ 2) ϭ Problem Solving 30. (2 ϩ 6) ϫ 7 ϭ 19.50 off coupon. 10 Ϭ 2 Ϫ 1 ϭ 16. Write an expression and simplify to find how many pages Steven will fill. 9 Ϫ 6 Ϭ 2 ϭ 17. 9 ϩ 2 Ϫ 6 Simplify. 3 ϩ 2 ϫ 7 ϭ 15. 20 Ϫ 5 ϫ 4 ϭ 26. Use order of operations. 1 ϩ 3 ϫ 5 9. (265) AF 1. 9 Ϫ 2 ϩ 3 5. Tamara buys 6 apples for $0. (3 ϩ 2) ϫ 9 6. 20 Ϭ 5 Ϭ 2 ϭ 23. pages 344–345. Steven has 126 photos to put in an She has a $0. Use with Grade 4.40 each. 12 Ϫ 12 Ϭ 3 ϭ 20. album. 1. 20 Ϭ 2 ϫ 3 Ϫ 6 ϭ 28. 4 ϩ (14 Ϫ 6) ϫ 2 ϩ 5 ϭ 29. 2 ϩ 3 ϫ 9 Print This 8–9 Page P PRACTICE 3. 4 ϩ 10 Ϭ 2 4. 6 Ϭ 2 Ϫ 1 8. 18 Ϭ 9 ϫ 6 ϭ 24. 14 Ϫ 10 ϩ 2 ϭ Use with Grade 4. (1 ϩ 5) ϫ 4 ϭ 19. 7Ϫ2 5 Which operation should you do first? 1. 28 Ϭ 4 Ϫ 2 7Ϫ2 Step 3: Print This 8–9 Page R RETEACH Add and subtract from left to right. 12 Ϭ (2 ϩ 2) Simplify. 8 Ϫ 4 ϫ 2 9. 3 ϫ (2 ϩ 5) ϭ 12. 8 Ϭ 2 Ϫ 2 ϭ 16.Print This Page Name Order of Operations Always use the order of operations to simplify expressions. pages 344–345. 4 ϩ 2 ϫ 5 ϭ 15. 8 Ϫ 8 Ϭ 4 ϭ 20. 6 ϫ (8 Ϫ 5) 8. 10 Ϫ 8 Ϭ 4 ϭ 17. Use the order of operations. Lesson 9. Simplify (20 ϩ 8) Ϭ 4 Ϫ 2.3 . 14 Ϭ 7 ϩ 2 ϭ 13.12 Ϭ 3 Ϫ 2 ϭ 18. Chapter 8. The rules for the order in which you should perform operations are given below. 9 ϩ (6 Ϫ 2) ϭ © McGraw-Hill School Division 11. 8 ϩ 2 Ϫ 4 7. 2 ϫ 8 Ϭ 4 4. 10. 9 ϩ 3 ϫ 2 6. (266) AF 1. 16 Ϭ 4 Ϭ 2 ϭ 14. (3 ϩ 7) Ϭ 2 5. (5 ϩ 5) Ϭ 2 ϭ 21. (20 ϩ 8) Ϭ 4 Ϫ 2 28 Ϭ 4 Ϫ 2 Step 2: Multiply and divide from left to right. 12 ϩ 4 Ϭ 2 2. Step 1: Do the operations in parentheses first. 4 ϩ (10 Ϫ 2) 3. Print This Page Name Order of Operations Order Counts Rewrite each number sentence. Put in parentheses to make each number sentence true. 40 ÷ 10 – 2 = 5 12. 1. 10 – 6 ÷ 4 = 1 10. 3 + 40 ÷ 8 x 5 = 4 9. 16 – 6 + 2 = 8 © McGraw-Hill School Division Print This 8–9 Page E ENRICH In your own words describe the rules for the order of operations. 6 ÷ 9 – 8 = 6 4. 3 ϩ 8 ϫ 2 Ϫ 1 ϭ 21 2. (267) AF 1. 4 x 5 – 2 = 12 11. Chapter 8. 6 + 2 x 7 = 56 14. 6 x 5 + 9 ÷ 3 = 28 7. 22 – 3 x 5 + 2 = 1 5. Lesson 9. 18 ÷ 2 + 1 + 1 = 7 6. pages 344–345.3 . 20 + 8 ÷ 4 = 7 13. Use with Grade 4. 5 x 16 + 14 + 6÷ 2 = 153 3. 5 x 10 + 1 ÷ 11 = 5 8. Chapter 8. (268) NS 1.2. MR 1. Use with Grade 4. pages 346–347. Lesson 10.4.Print This Page Name Problem Solving: Application Applying Multiplication Record your data.3. 3.2. 3. 2.4 . 3. Cost to the club Profit per bar for the club at a sale price of $1 8–10 Part A WORKSHEET Decision Making Print This Page Sales needed to reach goal for $110 in profits Home-made hiker bars Boxed hiker bars Your Decision © McGraw-Hill School Division What is your recommendation for the hiking club? Explain.1. 1. (269) NS 1. MR 1. 3. Did you do more sit-ups before or after lunch? 2. pages 348–349.3 . © McGraw-Hill School Division Work Space Use with Grade 4.3.4. Lesson 10. How many more sit-ups did you do? Show your work. Chapter 8. Record your data. Number of Sit-ups Student Before Lunch 8–10 Part B WORKSHEET Math & Science Print This Page After Lunch 1. 2.Print This Page Name Problem Solving: Application Does eating improve performance? Safety: Wait at least 30 minutes after eating before doing vigorous exercise.2. 3. Print This Page Name Problem Solving: Application Does eating improve performance? 3. 2.4.3 .2.1. Explain the activity in terms of energy conversion. Lesson 10. Use with Grade 4. Chapter 8. pages 348–349. In what ways could you improve this activity? © McGraw-Hill School Division 6. Work Space 4. Can you conclude that the food from lunch gave you more energy? Why or why not? 5. (270) NS 1. How many times more sit-ups did you do? Round to the nearest 8–10 Part B WORKSHEET Math & Science Print This Page whole number.3. MR 1. Show your work. 3. 3. 3 ft B. 3 in. it is 12 4 in. length of a football field Problem Solving 15. 10 ft B. 1. A. width of the classroom 4. 4 ft B. height of a cat 11. 2 ft B. 1 yd A. 3 yd C. What does it measure to the nearest inch? Use with Grade 4. 2. height of a desk 3. Lesson 1. 100 ft B. 4 in. 4 yd B. 100 mi 14. A. 4 ft A. 4 yd C. height of a refrigerator 13. distance you go in a stride Print This 9–1 Page P PRACTICE Circle the letter of the correct estimate. About how long would it take her to walk 5 miles? notebook. 2 mi A. 10 yd C. length of a pencil 2. length of a worm 12. distance you can ride your bike 7. 6. 100 yd C. Jane can walk a mile in about 16. (271) MR 1. length of a book 5. A. 1 ft C. height of a tree 10. length of a crayon © McGraw-Hill School Division A. 2 mi C. 2 ft A. 1 mi B. 2 yd C. height of a fourth-grader 9. 2 yd B. 40 mi A. 40 ft C. C. Marta measures the length of her 15 minutes. 10 in. To the nearest quarter 3 inch. 40 yd B. pages 364–365. length of a car 8.3 . Tell what unit and tool you use.Print This Page Name Explore Customary Length Estimate and then measure. 4 in.1. Chapter 9. A. Lesson 1.1.) is used to measure short lengths in the customary system.) 1 yard (yd) ϭ 3 feet (ft) 1 mile (mi) ϭ 1.760 yards (yd) 1 mile (mi) ϭ 5. 2. 3. B. length of a person’s foot 6. 6 ft C.Print This Page Name Explore Customary Length An inch (in. length of a bed Use with Grade 4. 8 yd C. pages 364–365. The foot (ft) and yard (yd) are used to measure larger units in the customary system. 6 in. Chapter 9. (272) A. © McGraw-Hill School Division 4.3 .280 feet (ft) 31 4 in. Circle the letter of the correct estimate. 6 yd MR 1. 5. 2. 8 in. 1. Measure to the nearest 1 4 inch. 8 ft B. You can use a ruler to measure in inches. 1 yd 1 ft Use an inch ruler to measure each object. 0 1 2 3 Print This 9–1 Page R RETEACH Customary Units of Length 1 foot (ft) ϭ 12 inches (in. length of your notebook 4.1. Then estimate. thickness of your math book 3. 2. your friend’s height 8. or cubit as the appropriate unit of measure. width of your desk 2. pages 364–365. span. Chapter 9. height of the classroom 6. hands.Print This Page Name Explore Customary Length Early Measurements In early times. and arms. distances were measured using fingers. length of a car 7. 1. diameter of an apple 5. (273) MR 1. What is an advantage of this system? What is a disadvantage? 10. digit span Print This 9–1 Page E ENRICH cubit digit: the width of a finger span: the width of a stretched hand cubit: the distance from fingertip to elbow Choose digit.3 . Lesson 1. length of your foot © McGraw-Hill School Division 9. What kinds of distance would be difficult to measure using this system of measurement? Use with Grade 4. 3 . 2 fl oz B. four potatoes 8. a pencil 10. 2.1. 500 T 16. A. 6 c B. 3 T C. pages 366–369. © McGraw-Hill School Division A. a large pot 3. a cereal bowl 4. A. 5 gal 12. 1 c B. an apple 7. Kyle pours 3 oz of cereal into his bowl. 1 pt C. 5 pt C. (274) MR 1. 11. Estimate and then measure the weight of each object. 6. two envelopes 9. A box of Krispy Krunch cereal holds 20 oz. Circle the letter of the correct estimate. Order the objects above from least to greatest capacity. 2 c C. How much cereal is left in the box? 18. Order the objects above from least to greatest weight. A. A. A. Sarah buys a 48 fl oz bottle of apple juice. 3 oz B. How many cups of juice can she pour from the bottle? Use with Grade 4. 1 qt 13. 5 c B. 3 lb Problem Solving 17. 500 oz B. Lesson 2. a milk carton Print This 9–2 Page P PRACTICE 5. Chapter 9.Print This Page Name Customary Capacity and Weight Estimate and then measure the capacity of each object. 1. 6 gal 14. 6 qt C. 2 pt 15. 500 lb C. a water glass 2. 1 2 T C. Pour water into empty milk cartons to model the equivalent units of capacity shown below. 1. weight of a fourth grader 3. Customary Units of Weight 16 ounces (oz) ϭ 1 pound (lb) 2. 25 gal B. 25 qt A. 1 2 T A. 2. pages 366–369. 5 oz A.1. 5 qt B. amount of water in a bathtub 4. Lesson 2. 25 pt C. 2 lb B. 50 gal C.Print This Page Name Customary Capacity and Weight Capacity is the measure of dry or liquid volume of a container. 100 lb B. © McGraw-Hill School Division A book weighs about 1 pound.000 pounds (lb) ϭ 1 ton (T) A card and envelope weigh about 1 ounce. 500 c Use with Grade 4.3 . Chapter 9. 5 T C. 20 oz B. (275) MR 1. Print This 9–2 Page R RETEACH Customary Units of Capacity 8 fluid ounces (fl oz) ϭ 1 cup (c) 2 cups (c) ϭ 1 pint (pt) 2 pints (pt) ϭ 1 quart (qt) 4 quarts (qt) ϭ 1 gallon (gal) 2 cups ϭ 1 pint (c) (pt) 2 pints ϭ 1 quart (pt) (qt) 4 quarts ϭ 1 gallon (qt) (gal) Weight is the measure that tells how heavy an object is. weight of a refrigerator 5. weight of an apple 2. Circle the letter of the correct estimate. 60 lb C. 100 oz A. amount of water in a pail A. 1 is 4 mile long. The train was 125 yd long. A gallon of paint is enough to paint a large wall. © McGraw-Hill School Division The subway sandwich was 12 yd long. In an hour. 2. The pitcher holds 3 qt of lemonade. The punch bowl holds 24 cups of punch. A light bulb weighs 2 ounces.780 miles. A sneaker weighs 40 oz. pages 366–369. A banana is 9 inches long. Chapter 9.545 lb. A football field A frog can jump 475 feet. Jen held her breath for 63 seconds. The climbing rope to the tree fort was 37 inches long. an airplane flew 1. The newborn baby drank 7 oz of milk. A goldfish bowl holds 18 cups of water.525 ft. (276) MR 1. A TV commercial lasts about 600 seconds.Print This Page Name Customary Capacity and Weight Reasonable Measure Maze Shade each box that contains a reasonable measure. An automobile might weigh 2.3 . The kitten drank an ounce of milk. It took about 3 yards of fabric to make a cape. A girl’s braid was 3 yards long.1. A bathtub holds 18 pints of water. Beth ran a distance of 10. A dog can jump 17 yards. A living room is 6 yards long. The movie lasted 107 minutes. Pat rode his bike 12 mph. Lesson 2. You could walk a mile in 20 seconds. Start How did you decide if running a distance of 10. A song is about 3 minutes long. A horse weighs 827 oz. The diving pool was 4 yd deep. Print This 9–2 Page E ENRICH Finish A pizza weighs 144 oz. The gate is 40 inches high. Your smile is 1 yard wide. The shaded boxes will form a path from start to finish.525 feet was reasonable? Use with Grade 4. Ounces 31. 48 oz ϭ yd ft c yd lb fl oz pt yd gal ft qt T 18. 12 pt ϭ 16. 1 lb 10 oz ϭ 25. How much is that per person? Use with Grade 4. 1. 10 ft ϭ in. 1 gal 2 pt ϭ lb 26.3 . Amy cuts a piece of ribbon 60 in. 8 qt ϭ 10. Yards Feet Inches 1 9 72 30. 3 pt ϭ 12.1. Tons Pounds 1 6. 2 c ϭ pt 21. ϭ 7. oz 3. 12 ft ϭ 15. 60 in. ϭ 11. (277) AF 1. 3 T ϭ 19. MR 1. 3 gal ϭ 22. 2 lb ϭ 17. 7 ft ϭ 4. 36 ft ϭ 13. 13 qt ϭ Algebra & Functions Complete the table. 2 mi ϭ 9. Gallons Quarts Pints Cups 1 12 16 64 Pounds 1 2 3 4 29. pages 370–373. How many feet long is the piece of ribbon? drink a total of 3 gallons of milk each week. 10 c ϭ oz 23. 13 yd ϭ 8.000 lb ϭ 20. 27. 4 ft ϭ 14. 2 qt ϭ yd ft ft in. 5 ft 8 in. 33. Lesson 3. The 6 members of the Brown family long. 2. Chapter 9. 21 ft ϭ 5. 10.3. 144 in. ft gal yd qt lb qt 2.000 16 © McGraw-Hill School Division 32 48 Problem Solving 32.Print This Page Name Convert Customary Units Complete. 28. 4 T 800 lb ϭ Print This 9–3 Page P PRACTICE in. ϭ pt 24. 2 mi ϭ 6. 2. 12 pt ϭ 9. MR 1. 24 in.280 Yards 4 6 8 2 3 4 5 6 7 8 Cups 1 2 3 4 5 6 1 2 1 10 12 14 3 2 16 Ounces 8 4 Pounds 1 3 Miles 1 2 3 16 24 32 40 48 1 2 3 Complete. Think: 8 quarts Ϭ 4 ϭ 2 gallons Inches 12 24 36 48 60 72 84 96 108 Feet 5.760 3.3 Use with Grade 4.840 © McGraw-Hill School Division Gallons Feet 1 2 3 4 5 6 7 8 9 Yards 1. Think: 2 gallons ϫ 4 ϭ 8 quarts Cups Pints Quarts To convert a smaller unit to a larger unit. multiply. To convert a larger unit to a smaller unit. (278) .280 10.520 5. ft gal c 2. 1.3. 2 qt ϭ 12. ϭ 5. 5 yd ϭ 7.Print This Page Name Convert Customary Units Print This 9–3 Page R RETEACH You can use tables to help you convert customary units of measure. 2 1 divide. 3 pt ϭ in. 6 ft ϭ 6. Lesson 3. 12 qt ϭ 10. pages 370–373.560 15.1. 2 lb ϭ ft pt yd oz 3. 48 oz ϭ yd qt pt lb AF 1. 3 mi ϭ 11. 8 c ϭ 8. 3 ft ϭ 4. Chapter 9. 3. move ahead 1 space.Print This Page Name Convert Customary Units Can You Convert? Play with a partner. Print This 9–3 Page E ENRICH Start qt oz in.1. Convert that number to a larger or smaller unit of measure. You can convert 17 or 71 quarts to cups. pages 370–373. 2. Move that many spaces. Lesson 3. (279) AF 1. you land on a qt square. Chapter 9. lb ft gal yd c pt qt © McGraw-Hill School Division oz in. • The player who reaches FINISH first wins. You roll a 1 and a 7. or a combination of units. • Then roll two number cubes. move back 1 space. roll one number cube. lb c ft gal yd pt Finish Use with Grade 4. For example. • If your answer is correct. or gallons. If it is incorrect. • For each turn. Take turns. pints. MR 1.3 . ” Explain your thinking: 3. “The track is less than 2 miles long. Print This 9–4 Page P PRACTICE Reading Skill Robert says.1. 3. A running track is 3.600 yards.000 feet.2.” Explain your thinking: 2.560 feet. “The cooler holds 32 quarts. 2.” Explain your thinking: © McGraw-Hill School Division 4.” Anthony says. Lesson 4. “The track is more than 2 miles long. Pablo says.500 yards from the school.Print This Page Name Problem Solving: Reading for Math Check for Reasonableness Circle the statement that is reasonable.1. The distance from April’s home to the school is 10. 1. Brian says. “We ran about 30. Robert and Anthony ran 3 miles. 2.” Explain your thinking: Use with Grade 4. MR 1.2 . pages 374–375.” Rachel says.000 feet. “We ran about 15. 3. Chapter 9. “The cooler holds 2 quarts.” April’s sister says.” John says. (280) NS 1.5. “Our home is about 30. A cooler holds 8 gallons of sports drink. April says “Our home is about 3.000 yards from the school.3. Is this statement reasonable? 3.2.2 . B The cabinet is 8 feet high. reasonable because F You divide quarts by 2 to find gallons. H 78 inches is greater than 7 feet. B The stage is 12 yards long. Lesson 4. Is this statement reasonable? 1.5. Chapter 9. 3. The stage is 31 feet long. B There are 4 gallons in a quart. MR 1. Mary’s statement is not reasonable A The cabinet is 7 feet high. The television cabinet is 78 inches high.Print This Page Name Problem Solving: Reading for Math Check for Reasonableness Choose the correct answer. G 78 inches is equal to 7 feet. H You multiply quarts by 2 to find gallons. Spencer’s statement is to solving this problem? A There are 2 gallons in a quart. Ms. J You multiply quarts by 4 to find gallons. Is this statement reasonable? 5. 2.1. reasonable because F 30 feet is less than 10 yards. D There are 4 quarts in a gallon. Spencer says the stand sells 9 gallons of punch. J 31 feet equals 11 yards. Ms. The director says the stage is more than 10 yards long. Which of these statements is true? Print This 9–4 Page P PRACTICE Math Skills Test Prep 2. D None of the above because F 78 inches is less than 7 feet. C The cabinet is more than 8 feet high. pages 374–375.3. Which of these statements is true? 4. (281) NS 1. G You divide quarts by 4 to find gallons. C There are 2 quarts in a gallon. Use with Grade 4. C The stage is 31 feet long. The director’s statement is A The stage is 11 yards long. 2. Mary says this is more than 7 feet high. The refreshment stand sells 36 quarts of punch. Which of the following is important © McGraw-Hill School Division 6. G 30 feet equals 10 yards. J 78 inches is greater than 8 feet. 3. H 31 feet equals 10 yards. D The stage is 36 inches long.1. H You need to divide 225 by 3 to find the width in yards.200 yards from the says the sled is more than 5 feet long. Is her statement reasonable? © McGraw-Hill School Division bus stop. MR 1. The popcorn stand sells 100 ounces 14.600 feet. The manager says that this is more than 10 pounds of peanuts. Is his statement reasonable? ounces of peanuts. J You need to multiply 150 by 3 to find the width in feet.2 .2. Tyler walks 4 miles from his home to the movie theater. Lesson 4. The theater is 150 feet long. Meg says Solve. 2. Explain your answer.1. Which of these statements is false? Print This 9–4 Page P PRACTICE Math Skills Test Prep 8. pages 374–375. Chapter 9. because F You need to divide 75 by 3 to find the width in yards. Is his statement reasonable? that the movie star is more than 80 inches tall. 2. Ned says the theater is 225 yards wide.5.Print This Page Name Problem Solving: Reading for Math Check for Reasonableness Choose the correct answer.3. 3. The theater is 75 feet long. Earl’s house is 1.000 feet. (282) NS 3. Is his statement reasonable? Use with Grade 4. 10. Ben says this is 1. He says he walks more than 20. G You need to multiply 75 by 3 to find the width in feet. The refreshment stand sells 144 of popcorn. Tammy’s sled is 65 inches long. Earl says that is 3. Ned’s statement is not reasonable A B C D The theater is 75 feet wide. Is this statement reasonable? 7. Is his statement reasonable? 13.1.600 pounds of popcorn. The theater is twice as long as it is wide. The theater is 75 feet wide. Is her statement reasonable? 11. She 12. 3. The theater is twice as long as it is wide. A movie star is 6 feet tall. 9. the distance from Chicago to New York 12. 3 cm B. One brick measures 92 mm. the distance from Sue’s house to school 7. 3 m B. the height of a fourth-grader 9. (283) MR 1. 30 dm B.3 . 140 mm A. Lesson 5. 6. the height of a door 10. pages 378–379. 1 cm B. the length of a piece of chalk 8. 140 cm C. 7 km C.200 km B. 20 dm 13. 300 mm C. the largest step you can take 3. the distance from the tip of your hand Print This 9–5 Page P PRACTICE to the elbow 5.1. 200 cm A. 20 cm B. 7 cm B. thickness of a nickel Circle the letter of the correct estimate. 1. 2. 6 dm B. Norma bicycles 1 km in 4 minutes.000 m A. 7 m C. Chapter 9. 20 m A. 6 cm A. 1 dm A. 1.000 mm B. 6 km C. the length of Ben’s foot Problem Solving 15. 2.000 dm C. 5. 3 dm A. the width of a pencil point 14. 2.Print This Page Name Explore Metric Length Estimate and then measure. the width of your classroom 2. the thickness of a book © McGraw-Hill School Division A. 2 km C. 30 cm A. the length of a classroom 11. What is About how many kilometers will she bicycle in 60 minutes? its measurement to the nearest cm? Use with Grade 4. the width of a window in your classroom 4. 1 mm C. 3 mm C. Tell what unit and tool you use. 16. Print This Page Name 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 Print This 9–5 Page R RETEACH Metric Units of Length 10 millimeters (mm) ϭ 1 centimeter (cm) 10 centimeters (cm) ϭ 1 decimeter (dm) 100 centimeters (cm) ϭ 1 meter (m) 1,000 meters (m) ϭ 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. 3. © McGraw-Hill School Division 4. Circle the letter of the correct estimate. 5. the width of a button 6. the length of a dollar bill Use with Grade 4, Chapter 9, Lesson 5, pages 378–379. (284) A. 18 cm A. 15 dm B. 18 mm B. 15 mm C. 2 mm C. 15 cm MR 1.1, 2.3 Print This Page Name Explore Metric Length Connect the Dots Use a centimeter ruler to connect only those dots that are the given distance apart. 1. 4 cm 2. 2 cm Print This 9–5 Page E ENRICH 3. 5 cm 4. 3 cm © McGraw-Hill School Division Use with Grade 4, Chapter 9, Lesson 5, pages 378–379. (285) MR 1.1, 2.3 Print This Page Name Metric Capacity and Mass Estimate and then measure the capacity of each object. 1. a water glass 3. a cereal bowl 2. a large pot 4. a milk carton Print This 9–6 Page P PRACTICE 5. Order the objects above from least to greatest capacity. Estimate and then measure the mass of each object. 6. a box of crayons 8. a paper clip 7. a book 9. a pencil 10. Order the objects above from least to greatest mass. 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 © McGraw-Hill School Division Algebra & Functions Complete the table. 15. Liters Milliliters 1 1,000 2 3 4,000 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) 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 Metric Capacity and Mass Milliliters and liters measure capacity in the metric system. Print This 9–6 Page R RETEACH Metric Units of Capacity 1,000 milliliters (mL) ϭ 1 liter (L) 1cm 1cm 1cm 1 Liter A cube 1 centimeter (cm) long, 1 centimeter wide, and 1 centimeter high will hold 1 milliliter (mL) of water. Mass is the amount of matter that makes up an object. This bottle holds 1 liter (L) or 1,000 milliliters (mL) of water. Metric Units of Mass 1,000 grams (g) ϭ 1 kilogram (kg) The mass of a paper clip is about 1 gram (g). The mass of the book is about 1 kilogram (kg) or 1,000 grams (g). Circle the letter of the correct estimate. © McGraw-Hill School Division 1. mass of a bar of soap 2. mass of an iron 3. amount of water in a bathtub 4. mass of a horse 5. a bottle cap A. 120 g A. 1 g A. 100 mL A. 500 g A. 3 mL B. 120 kg B. 100 g B. 100 L B. 500 kg B. 300 mL C. 12 kg C. 1 kg C. 1,000 mL C. 1,000 g C. 3 L Use with Grade 4, Chapter 9, Lesson 6, pages 380–383. (287) MR 1.1, 2.3 Print This Page Name Metric Capacity and Mass Who Invented It? Compare. Choose >, <, or ϭ. 1. 50 mL Print This 9–6 Page E ENRICH 5L Ͻ W 70 mL Ͻ B ϭ T ϭ B 2. 4,000 mL 3L Ͻ B ϭ C 3. 3 L 400 mL Ͻ M ϭ N 11 L ϭ D Ͼ G 4. 1 L Ͼ A 5. 8 L Ͼ L 7,500 mL Ͻ M ϭ C 80 L ϭ U 8L Ͻ H ϭ M 6. 10,000 mL Ͼ L 7. 12 L Ͼ A Ͼ B 9. 5 kg Ͻ C 12,000 mL Ͻ H 4 kg Ͻ R 70 g Ͻ I ϭ J 12 kg Ͻ S ϭ T ϭ I ϭ E 8. 75,000 mL 5,000 g Ͻ M ϭ A 6 kg Ͻ S ϭ T Ͼ T 10. 400 g Ͼ I 11. 8,400 mL Ͻ C Ͼ R 12. 6,000 g Ͼ U 13. 1 kg Ͼ O 14. 7 kg Ͼ R 15. 5 kg 6,900 g Ͻ F ϭ G 69,000 g Ͻ R ϭ S Ͼ H 16. 10,000 g © McGraw-Hill School Division Ͼ E Ͼ P Ͼ R 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 9 10 11 12 13 14 15 16 Use with Grade 4, Chapter 9, Lesson 6, pages 380–383. (288) MR 1.1, 2.3 Print This Page Name Convert Metric Units Complete. 1. 5 m ϭ 4. 10 mm ϭ 7. 3,000 mL ϭ 10. 6,000 mL ϭ 13. 700 cm ϭ 16. 10,000 g ϭ 19. 20 cm ϭ 22. 10 m ϭ 24. 600 mm ϭ 26. 4,000 m ϭ 28. 20,000 mL ϭ Print This 9–7 Page P PRACTICE cm cm L 2. 2 L ϭ 5. 5 kg ϭ 8. 300 cm ϭ mL g m g mL m mm 23. 5 cm ϭ 3. 7 kg ϭ 6. 2 m ϭ 9. 4,000 g ϭ 12. 40 cm ϭ 15. 2 km ϭ 18. 4 m ϭ 21. 5 L ϭ g dm kg dm m mm mL L 11. 40 kg ϭ m 14. 10 L ϭ kg 17. 6,000 cm ϭ mm cm cm km L 20. 3 dm ϭ mm cm L kg 25. 8,000 mm ϭ 27. 7,000 mL ϭ 29. 70,000 g ϭ Compare. Write >, <, or ϭ. 30. 5,000 g 33. 60 cm 36. 3 km 39. 500 dm 5 kg 6m 300 m 5 dm 31. 20 L 34. 300 cm 37. 900 mm 40. 7 dm 200 mL 3m 9 cm 7,000 mm 32. 50 cm 35. 2,500 mL 38. 13 L 6 dm 2L 1,300 mL 18 L © McGraw-Hill School Division 41. 18,000 mL Problem Solving 42. Dottie has 1 kg 200 g of food for her 43. A 1 L bottle of water is half full. How cat. How many grams of cat food does she have? many milliliters of water are in the bottle? Use with Grade 4, Chapter 9, Lesson 7, pages 384–385. (289) AF 1.3; MR 1.1, 2.3 Print This Page Name Convert Metric Units You can convert metric units to compare. Metric Units Length 1 centimeter (cm) ϭ 10 milliliters (mm) 10 centimeters (cm) ϭ 1 decimeter (dm) 10 decimeters (dm) ϭ 1 meter (m) 1,000 meters (m) ϭ 1 kilometer (km) Mass 1 kilogram (kg) ϭ 1,000 grams (g) 1 gram (g) ϭ 1,000 milligrams (mg) Capacity 1 liter (L) ϭ 1,000 milliliters (mL) Print This 9–7 Page R RETEACH Convert 9 dm to centimeters (cm). To convert a larger unit to a smaller unit, multiply. Think: 1 dm ϭ 10 cm 9 dm ϭ ? cm 9 dm ϭ 9 ϫ 10 cm 9 dm ϭ 90 cm Complete. 1. 5 m ϭ © McGraw-Hill School Division Convert 6,000 mg to grams (g). To convert a smaller unit to a larger unit, divide. Think: 1 g ϭ 1,000 mg 6,000 g ϭ ? mg 6,000 g ϭ 6,000 Ϭ 1,000 mg 6,000 g ϭ 6 mg cm g cm L mm kg 2. 8 L ϭ 4. 70 mm ϭ 6. 2 m ϭ 8. 300 cm ϭ 10. 70 dm ϭ 12. 40 cm ϭ mL cm dm m m dm 3. 6 kg ϭ 5. 8 dm ϭ 7. 2,000 mL ϭ 9. 9 cm ϭ 11. 5,000 g ϭ Use with Grade 4, Chapter 9, Lesson 7, pages 384–385. (290) AF 1.3; MR 1.1, 2.3 Print This Page Name Convert Metric Units Metric Match Game Use index cards to make the cards shown below. Print This 9–7 Page E ENRICH 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 • Mix up the cards and place them facedown. Players take turns turning over two cards. © McGraw-Hill School Division • 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 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? Print This 9–8 Page P PRACTICE 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? 3. The parrot house has 2 times as 4. The parrots get food 20 minutes before 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? 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? 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? © McGraw-Hill School Division 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 He has a 7-cup container and a 5-cup container. • Dan has containers that hold What do you need to find? • You need to find how to use the containers to measure cups.Print This Page Name Problem Solving: Strategy Logical Reasoning Page 387.1. How can he use the containers to measure 6 cups? Step 1 Read Be sure you understand the problem. You can use the difference in the amount each container can hold to measure exactly 6 cups. Read carefully. Choose a strategy. Lesson 8. Step 2 Plan I Make a plan. (293) MR 1. Use with Grade 4. What do you know? • Dan needs to put cups of sea salt in a saltwater tank.2 . 2. I I I © McGraw-Hill School Division I I I I I I 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 Use logical reasoning to solve the problem. cups and cups. 3. pages 386–387.3. Chapter 9. 3. Problem 1 Print This 9–8 Page R RETEACH Dan needs to put 6 cups of sea salt into the saltwater tank.1. 4.1. Fill the 5-cup container Sea Salt in Sea Salt in 7-cup Container 5-cup Container 0 5 cups 0 0 0 5 cups 5 cups 5 cups Sea Salt in Tank 0 0 from the 7-cup container. Print This 9–8 Page R RETEACH Solve Complete the table. Marcia arrives at the theater 10 minutes before Sam. How can you check your answers? © McGraw-Hill School Division Practice 1. How much sea salt is in the tank now? 5. 3. 3.M. Fill the 7-cup container. Paul arrives 10 minutes before Lynn. When do the others arrive at the theater? Use with Grade 4.2 . Repeat steps 1–3. pages 386–387. A worker has a 4-gallon pail and a 9-gallon pail.Print This Page Name Problem Solving: Strategy Logical Reasoning Step 3 Carry out your plan. Steps 1. How can he use pails to fill a 10-gallon tank with water? 2. Pour what is left in the 7-cup container into the tank.1. 2. How much sea salt is in the tank now? Step 4 Look Back Is the solution reasonable? Reread the problem. Lynn gets to the theater at 6:30 P. Sam arrives 25 minutes after Lynn. (294) MR 1. Lesson 8.3. It will show how to use the 7-cup container and the 5-cup container to measure exactly 6 cups. Repeat steps 1–3. 2. 3. Chapter 9. 20°F B. MR 1. 20°F B. to swim in the swimming pool 9. temperature in cafeteria 6. The temperature of a can of soup on 18. 1. 65°C B. Then use Fahrenheit and Celsius thermometers to measure each temperature. temperature in classroom Print This 9–9 Page P PRACTICE Circle the letter of the correct estimate.3 . What is the soup’s temperature now? water in a swimming pool was 25°C. 20°C A. At 9:00 P. to go sledding in the snow © McGraw-Hill School Division A.8. to go to the beach 10. 10°C A. to walk your dog Problem Solving 17. temperature outside 2. 25°C A. 30°F B. warm water 3. to picnic in the park 14. cool water 5. (295) NS 1. pages 388–389. 30°F B. temperature in freezer 4. Lesson 9. to rake leaves 15. 20°C A. to go skiing 8.1. 70°C A. 70°F B.M. 30°C A.Print This Page Name Temperature: Fahrenheit and Celsius Give a reasonable temperature for each. 7. At noon the temperature of the the shelf is 45°F. 2. By how much did the water temperature drop? Use with Grade 4. 65°F 16. 80°F B. to work in the garden 12. 30°C A. Joy heats the soup to 25°F above its shelf temperature. Chapter 9. 80°C A. 25°F B. 20°F B. to sleep comfortably 11. 20°C A. 10°F B. the temperature was 17°C. to shiver without a coat 13. 39°F B.Print This Page Name Temperature: Fahrenheit and Celsius Temperature is measured in degrees Celsius (°C) or in degrees Fahrenheit (°F). pages 388–389. Compare the two scales shown at the right. Lesson 9. the temperature of a fever 8. –10 –20 – 20 10 – 10 20 0 4. 10°F B. Chapter 9. 100°C A. 30°C A.1. 20°C A. temperature at an outdoor ice rink 10. 120 130 140 150 160 170 © McGraw-Hill School Division Circle the letter of the correct estimate. 10 – 10 20 30 40 0 – 20 0 10 3. 30°F B. 2.3 . the temperature of warm water 7. (296) – 20 A. the temperature of cold water 6. temperature on a hot beach 11. 10°C 50 60 70 B. 100°F B. 5. 20 – 10 30 0 40 50 10 60 230 220 210 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 –10 –20 Fahrenheit Celsius –30 – 20 – 10 0 10 20 30 40 50 60 70 80 90 100 110 2.8. Print This 9–9 Page R RETEACH Write the temperature in degrees Celsius (°C) and degrees Fahrenheit (°F). room temperature 9. 10°C A. 1. MR 1. 39°C A. comfortable outdoor temperature Use with Grade 4. 20°F B. 70°C A. 10°F NS 1. 70°F B. Use the thermometers above to help you. MR 1. Lesson 9. how much does the Fahrenheit temperature change? 3. When the Celsius temperature changes 10 degrees.8.1. 2. Chapter 9. 1.Print This Page Name Temperature: Fahrenheit and Celsius 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 60 50 40 30 20 10 0°C 0 – 10 – 20 – 20 70 60 50 40 30 20 10 0 – 10 – 20 – 20 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 –10 –20 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 –10 –20 Print This 9–9 Page E ENRICH 100°F 32°F Celsius Fahrenheit The thermometers are drawn so that equivalent measures are the same height on both scales. pages 388–389. (297) NS 1. What pattern do you see that will help you predict Fahrenheit temperatures based on Celsius temperatures? Use with Grade 4.3 . Write the equivalent temperatures in degrees Fahrenheit. © McGraw-Hill School Division 10°C 30°C ϭ 20°C 40°C ϭ 2. Print This Page Name Problem Solving: Application Applying Measurement Record your data. Use with Grade 4.1. Martin make for the birthday party? Explain. Chapter 9. (298) MR 1. Lesson 10. 2.3 . pages 390–391. Items Ingredients Amount of Each Cost of Each Ingredient Ingredient 9–10 Part A WORKSHEET Decision Making Print This Page Total Cost for Item Sandwiches Fruit Salad Punch © McGraw-Hill School Division Your Decision How much of each item should Mr. Chapter 9. MR 1. Show your work.6.3. pages 392–393.3 . Lesson 10. 2.2. Start Temperature Finish Temperature Black Paper 9–10 Part B WORKSHEET Math & Science Print This Page Difference White Paper Aluminum Foil 1. Work Space © McGraw-Hill School Division 2. Find the difference between each start and finish temperature.Print This Page Name Problem Solving: Application Which color heats up the most? Record the temperature of each thermometer. 3. (299) NS 1. Which color heated up the most? The least? Use with Grade 4. 2.2. 2. Chapter 9. pages 392–393. Show your work.6.3. 2. Why did you have to put the thermometers under the sun or a lamp? 5.2. Use with Grade 4. MR 1. (300) NS 1. If you were playing outside on a sunny day. 2. which color clothing would you like to wear? Why? © McGraw-Hill School Division 6.Print This Page Name Problem Solving: Application Which color heats up the most? 3. 3. Use subtraction to find how many more degrees the hottest 9–10 Part B WORKSHEET Math & Science Print This Page thermometer changed than the coolest. Is this a big difference? Work Space 4. Lesson 10. Explain the results of the activity in terms of reflection or absorption of light.3 . Lesson 1. 2. pages 408–411. 10. and vertices it has. 8. 6. Identify the 3-dimensional shape. (301) MG 3. Algebra & Functions 11. 3.6 . edges. 5. What could the next shape be? Use with Grade 4. 1. Chapter 10. © McGraw-Hill School Division 9. Tell how many faces. Copy and fold.Print This Page Name 3-Dimensional Figures Identify the 3-dimensional figure the object looks like. 7. Print This 10–1 Page P PRACTICE 4. 4. Count the number of faces. Look at the cube below.Print This Page Name 3-Dimensional Figures Print This 10–1 Page R RETEACH A 3-dimensional figure usually rests on one of its faces. cylinder 7. vertices. Shape of Base Number of Flat Faces and Bases Number of Straight Edges Number of Vertices 1. vertices A cube has 8 vertices. © McGraw-Hill School Division 6. Chapter 10. 5. Complete the chart. face A cube has 6 faces. Lesson 1. which is called a base. (302) MG 3.6 . pages 408–411. 3. triangular prism rectangular prism triangular pyramid square pyramid cone 2. sphere Use with Grade 4. and edges it has. Name 3Dimensional Figure edge A cube has 12 edges. A dodecahedron has triangular faces. Each triangular face has edges. Use the information about polyhedrons to complete the sentences. a cube has (6 ϫ 4) Ϭ 2 ϭ 12 edges. 1. edges. A tetrahedron has 4 triangular faces. • Each face of a polyhedron is the same size and shape. Print This 10–1 Page E ENRICH Cube Tetrahedron Octahedron Dodecahedron Icosahedron Look at the cube. An octahedron has Each triangular face has An octahedron has 3. • Each edge of a polyhedron is the same length. © McGraw-Hill School Division )Ϭ2ϭ 2. pentagonal faces. • It has 6 square faces. pages 408–411. An icosahedron has 20 triangular faces. (303) . MG 3. • Each square face has 4 edges. • Each angle of each face is equal. (4 ϫ A tetrahedron has edges. edges. edges. Use with Grade 4. edges. Chapter 10. • Since 2 sides meet at each edge. Lesson 1. edges.Print This Page Name 3-Dimensional Figures Polyhedrons The 3-dimensional figures shown below are called polyhedrons.6 Each pentagonal face has A dodecahedron has Each triangular face has An icosahedron has 4. edges. Identify the figure. 3). 5) © McGraw-Hill School Division 12. 7. (2. 2). (5. a 6-sided figure 10. Print This 10–2 Page P PRACTICE Tell whether each figure is open or closed. (4. (3. Lesson 2. a 5-sided figure 9. Is it a polygon? If so. Draw the figure and identify it. 6. pages 412–415. an 8-sided figure Algebra & Functions Locate each set of points. 3) 5 4 3 2 1 O 1 2 3 4 5 5 4 3 2 1 O 1 2 3 4 5 Use with Grade 4. a 4-sided figure that is not a square 8. Then connect the points to make a geometric figure. 2). 5. classify the figure. (5. (304) MG 3. 2). 2. Chapter 10. 4. 3.Print This Page Name 2-Dimensional Figures and Polygons 1. 11. (2. 3). Use a separate sheet of paper.8 . (2. 5. © McGraw-Hill School Division 4. Use with Grade 4. These figures are not polygons. pages 412–415. 2.Print This Page Name 2-Dimensional Figures and Polygons A polygon is a closed 2-dimensional figure that has straight sides. 1. Open Figures Closed Figures Print This 10–2 Page R RETEACH These figures are polygons. square 4 straight sides rectangle 4 straight sides triangle 3 straight sides pentagon 5 straight sides Identify each polygon. Chapter 10.8 . hexagon 6 straight sides octagon 8 straight sides 3. Lesson 2. 6. (305) MG 3. Use all five figures to form each of the large polygons shown below. (306) MG 3. tangram 4 © McGraw-Hill School Division Tangrams: G C Use with Grade 4. Lesson 2. tangram 2 3. pages 412–415. The figures can be put together to form different shapes— sometimes even animal shapes! Cut out the five figures at the bottom of the page. tangram 3 4.Print This Page Name 2-Dimensional Figures and Polygons Tangrams A tangram is a Chinese puzzle that is made of 2-dimensional figures. Print This 10–2 Page E ENRICH 1. Chapter 10.8 . tangram 1 2. 2) Use with Grade 4. Line segment OP: 6 5 4 3 2 1 1 2 3 4 5 6 MG 3. pages 416–419. Line Segments. Then connect the points to draw line segments. Chapter 10. G O H K 8. S T V © McGraw-Hill School Division Algebra & Functions Locate the set of points.2 (1. 4) (2.Print This Page Name Lines. l 6. 2) (3. C D 3. 4) (4. 2) (2. and Rays Identify each figure. S Q R T 4.1. A B Print This 10–3 Page P PRACTICE 2. 7. 10. I K L J 5. 4) Line segment QR: (1. 3. 1. 2) (4. (307) . 9. Lesson 3. 4) (3. M N O P Identify the parts of a circle. Classify the lines as perpendicular or parallel. A radius is the distance from the center of a circle to every point on a circle. 4. A chord is a line that connects two points on a circle. Parallel lines never meet. 2. 7.2 . Identify the parts of a circle. Intersecting lines meet. A diameter is a chord that goes through the center of the circle. Chapter 10. 9. It has two endpoints. (308) MG 3.Print This Page Name Lines. Use with Grade 4. and Rays A line goes on forever in both directions A line segment is part of a line. 3. Lesson 3. Perpendicular lines form square corners. 1. Print This 10–3 Page R RETEACH A ray has one endpoint. pages 416–419. © McGraw-Hill School Division 5. 6.1. 3. Identify each figure. Line Segments. 8. Lesson 3. pages 416–419.2 . Write E for an even vertex and O for an odd vertex. Vertex 3 has an odd number of lines meeting at that point. Can you trace the figures below without lifting your pencil or retracing any line? Label each vertex even or odd.1. This vertex can be called an even vertex. Look at Figure A and Figure B below. Chapter 10. Line Segments. and Rays 1. Can you trace Figure A without lifting your pencil if you start at any vertex? 4. 3. Can you trace Figure B without lifting your pencil if you start at any vertex? 3. Use with Grade 4.Print This Page Name Lines. Vertex 4 has an even number of lines that meet at that point. 5. Can you trace each figure Print This 10–3 Page E ENRICH Can You Trace a Figure Without Lifting Your Pencil? 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. Label each vertex in the figures. O E © McGraw-Hill School Division E O O E E O O O E O O Figure C Figure D Figure E 6. (309) MG 3. Vertex 3 can be called an odd vertex. 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. In Figure A. 3. 5. 9. pages 420–421. 10. Write the degree measure and fraction of a turn for each angle. 7. 6. 8. a 3-sided figure with 3 acute angles © McGraw-Hill School Division Use with Grade 4.5 .Print This Page Name Angles Write acute. obtuse. 2. (310) MG 3. or right for each angle. Chapter 10. Print This 10–4 Page P PRACTICE 4. Lesson 4. Draw each figure. 1. a 4-sided figure with 1 right angle 11. This triangle has 3 angles. 4. Write acute. Lesson 4. An obtuse angle is greater than a right angle. 2. This pentagon has 2 2 1 angles. 8. 5. 1. 6. (311) . An acute angle is less than a right angle. This kite has 2 angles and 2 angles. Complete. Use the corner of a sheet of paper to help you. 7. 11. Chapter 10. MG 3.Print This Page Name Angles Angles are formed by two rays that have the same endpoint. 10. Print This 10–4 Page R RETEACH A right angle forms a square corner. 3. Identify each angle. angles. obtuse. pages 420–421. and angle. or right.5 Use with Grade 4. © McGraw-Hill School Division 9. 1. pages 420-421. Draw lines to show the 4 angles. Shade and number the 3 angles. 1 3 2 3 1 1 2 2 Print This 10–4 Page E ENRICH 3 Step 1: Step 2: Step 3 Draw a triangle. Cut along the lines. 2 1 3 2 1 3 2. and put them together to see if you are correct. What do you think the sum of the angles of a quadrilateral is? © McGraw-Hill School Division 5. Lesson 4.5 . Follow the steps below. Use with Grade 4. 1 3 2 Triangle 1 Triangle 2 Triangle 3 4. (312) MG 3. Chapter 10. Follow Steps 1–3 for each triangle below. cut them out.Print This Page Name Angles Angle Sums What is the sum of the angles of a triangle? The sum will always be 180º or a straight line. Then shade the corners. Then draw lines to show each angle. Draw a quadrilateral. 3. Place the corners of the pieces together to form a straight line. 3. Lesson 5. All rectangles are parallelograms.7. Both say their desks are rectangles. 8. and 4 right angles. Sue’s desk has equal sides of 20 11. (313) MG 3. Problem Solving © McGraw-Hill School Division 10. Explain why. isosceles. 7. All squares are rhombuses. pages 422–425. Print This 10–5 Page P PRACTICE Identify each quadrilateral.Print This Page Name Triangles and Quadrilaterals Classify each triangle as equilateral. or obtuse. 6. Tell if each statement is true or false. Who is correct? sticks. He pushes one corner of the square and makes a rhombus. 4. How are the square and rhombus alike? How are they different? Use with Grade 4.8 . or scalene. Some right triangles are also equilateral triangles. 2. 5. 3. Mike makes a square out of wooden inches and 4 right angles. Nancy’s desk has two sides of 20 inches. 9. two sides of 30 inches. 1. Then classify each triangle as right. acute. Chapter 10. 3. An acute triangle has three acute angles (less than 90º). A rectangle has 4 right angles. An isosceles triangle has at least two sides of equal length. 5. Classify each triangle by its sides and angles. © McGraw-Hill School Division Identify each quadrilateral in as many ways as you can.8 . Its opposite sides are equal and parallel. 3. Its opposite sides are parallel. Lesson 5. A square has 4 equal sides and 4 right angles. 6. (314) MG 3. pages 422–425. A parallelogram has opposite sides that are equal and parallel. 2. An equilateral triangle has three sides of equal length. A right triangle has one right angle (exactly 90º). All quadrilaterals have 4 sides and 4 angles. 4. An obtuse triangle has one obtuse angle (greater than 90º and less than 180º). 1. A rhombus has 4 equal sides. Use with Grade 4. Print This 10–5 Page R RETEACH A scalene triangle has no sides of equal length.7.Print This Page Name Triangles and Quadrilaterals You can classify a triangle by the lengths of its sides or the measures of its angles. Chapter 10. A trapezoid has 1 pair of parallel sides. Print This Page Name Triangles and Quadrilaterals Geometry Bingo Play this bingo game with 2–3 players. Lesson 5. Be sure to mix up the names. Chapter 10. Print This 10–5 Page E ENRICH • The first player to have markers that fill any row. • Work together to make the bingo game. • Players take turns drawing index cards. Each player places a game marker on the matching figure drawn on the bingo card. column.7. On an index card. 3. pages 422–425. or diagonal wins. write each of the names for geometric figures shown in the box below. (315) MG 3. parallel lines parallelogram radius rhombus hexagon isosceles triangle intersecting lines ray right angle octagon acute triangle obtuse triangle perpendicular lines chord acute angle cube equilateral triangle right triangle line segment diameter obtuse angle pentagon trapezoid scalene triangle B I N G O © McGraw-Hill School Division FREE Use with Grade 4. • Shuffle the index cards and place them face down. • Then draw each figure in one of the squares on the bingo card below.8 . What is the length of the missing side of the doorway? Use with Grade 4. MR 1.2 . Phyllis designed this doorway.1. What two shapes make up this doorway? 4. 2. Lesson 6.1. pages 426–427. Print This 10–6 Page P PRACTICE Reading Skill 1. Howie used the above figure in a painting. 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. 3. 3. 3.7. Describe the figure in more than one way. (316) MG 3.8.4. Chapter 10. 4 ft 4 ft 6 ft 4 ft © McGraw-Hill School Division 4 ft 3.3. Use the illustration below to solve problems 3–4.Print This Page Name Problem Solving: Reading for Math Use a Diagram Use the illustration to solve problems 1–2. 2. 2. What is the length of Side C? 5.2 . What is the length of Side C? F 3 centimeters G 6 centimeters H 10 centimeters MG 3. Chapter 10.3. (317) 6 cm 6. A 2. What is the length of Side A of the triangle? 1. You can find the length of Side C 8 inches long? F Yes G No H The answer cannot be found using the information in the diagram. B 4 in. 3. B the length of Side C is greater than the lengths of the other two sides of the triangle. C The length of side B must be equal to 8 inches. B The length of side B must be less than 8 inches. C The length of Side A must be greater than 6 inches. 3. Lesson 6. Which statement is true? 4.1. Can the length of side B be A The length of side B must be greater than 8 inches. This figure is composed of a parallelogram and an equilateral triangle. Can the length of side B be 8 inches long? 3.7. Which statement is true? Print This 10–6 Page P PRACTICE Math Skills Test Prep 6 in. B Side A has the same length as one side of parallelogram.1. F 4 inches G 6 inches H 12 inches 4 in. This figure is composed of an isosceles triangle and a rectangle. 3.Print This Page Name Problem Solving: Reading for Math Use a Diagram Choose the correct answer. C no two sides of the triangle have equal lengths. Use with Grade 4.4. 2. 2. This figure is composed of a rhombus and a triangle. What is the length of Side A? A All sides of the figure are the same length. 4 in. © McGraw-Hill School Division C 3 cm 10 cm because A two sides of an isosceles triangle are equal. pages 426–427. MR 1.8. Suppose Robert added 2 feet to the height of the frame. 2. Max draws a rectangle with sides of the shape into two parts by drawing a line from one corner of the square.1. 3. What shapes make up the frame? What shape is made by the outer edge of the frame? 3 ft 3 ft 10. to the opposite corner. C Each side of the parallelogram has the length of 2 centimeters. (318) MG 3.2 .3. pages 426–427. Use with Grade 4. 2. What kind of triangle did she draw? 12. This figure is a parallelogram. How would you describe the two A You cannot tell the lengths of the unlabeled sides of the parallelogram. MR 1. Then he divided 13. 3.7. 3. Chapter 10. H They are equilateral triangles.1. Can the lengths of the other two sides of the triangle be 6 inches? Explain. G They are isosceles triangles. 6 inches and 9 inches. but kept the width the same. Robert drew a square.Print This Page Name Problem Solving: Reading for Math Use a Diagram Choose the correct answer. Orson designed this picture frame.4. Use data from the illustration to answer problems 9–10. B Only two sides of the parallelogram have a length of 2 centimeters. He uses one of the short sides of the rectangle as a side of a scalene triangle. through the center. Name two ways to describe the two smaller shapes he created.8. Suppose you draw a line segment from point A to point C. What shape would be made by the outer edge of the frame? © McGraw-Hill School Division 11. The length of this segment is 5 cm. Lesson 6. Solve. How would you describe the two new figures you made? 7. Which of these statements is true? Print This 10–6 Page P PRACTICE Math Skills Test Prep A 2 cm D 6 cm C B 8. Wendy drew a triangle in which three angles were less than 90°. 9. new figures you made? F They are scalene triangles. 4. Then write whether the figures are congruent.4 . Copy the figure on a separate piece of dot paper. © McGraw-Hill School Division Algebra & Functions Use separate grid paper. Draw a figure on a coordinate grid. Use with Grade 4. 10. 11. 2. 6. pages 430–433. 7. 12. Draw a figure on a coordinate grid. 9. Then draw a similar figure that is one half the size of the original. Chapter 10. Then draw a similar figure that is two times the size of the original. Then draw one congruent figure and one similar figure. (319) MG 3. Print This 10–7 Page P PRACTICE 3. Write the ordered pairs for all vertices. 8. Write the ordered pairs for all vertices. Lesson 7.3. 3.Print This Page Name Congruent and Similar Write whether the figures are similar. 1. 5. If you can make it fit exactly on top of the other figure.3. 6.Print This Page Name Congruent and Similar Similar Figures Congruent Figures Print This 10–7 Page R RETEACH 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. You may trace the figures. Then write whether the figures are congruent. the figures are congruent. Lesson 7. Chapter 10. © McGraw-Hill School Division 5. Write whether the figures are similar. pages 430–433. (320) MG 3. 3. 1. 4. 3. trace one figure. 2.4 . Use with Grade 4. Figure C is congruent to Figure 3.4 . Figure B is similar to Figure ABCD. Figure BC is congruent to Figure 4. Lesson 7. . pages 430–433.Print This Page Name Congruent and Similar 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.3. Look at the first drawing. How many sets of congruent and similar figures can you find in the drawing at the right? Name each pair or set of figures. 3. B C D F G 5. Figure A is the rectangle in the upper left corner. Chapter 10. to Figure EF. 2. The first one is done for you. Figure F is congruent to Figure E I and Figure 6. (321) MG 3. Figure EF is similar to Figure Print This 10–7 Page E ENRICH A . Figure I is . 1. © McGraw-Hill School Division J O Q P M L N K Use with Grade 4. . Complete the sentences. H 7. Figure AB is the top rectangle. translation 8. 6. and Rotations Write translation. 2. 7. (322) MG 3. 4. pages 434–435. Chapter 10. Print This 10–8 Page P PRACTICE 3.Print This Page Name Explore Translations. reflection © McGraw-Hill School Division 9. then rotation 10. reflection. 1. translation. Reflections. then reflection Use with Grade 4. or rotation to describe how the figure was moved. 5. Draw the movement of each figure on the dot paper. rotation.4 . Lesson 8. © McGraw-Hill School Division 7. You can turn a figure around a point to show a rotation. or rotation to tell how each figure was moved. reflection. pages 434-435 (323) MG 3.Print This Page Name Explore Translations. 4.4 . 2. 3. 5. Write translation. Chapter 10. You can flip a figure over a line to show a reflection. Reflections. 8. 9. Use with Grade 4. Print This 10–8 Page R RETEACH You can slide a figure across a line to show a translation. 6. 1. Lesson 8. and Rotations You can move figures in different ways. and choose another movement card. Repeat until you have chosen 4 movement cards. (324) MG 3. Trace it again. Rotation Print This 10–8 Page E ENRICH Turn your shape around a point. Choose one shape card. Follow the instructions on that card. trace that shape. Reflections. Trade your artwork with a partner. On another sheet of paper.4 . Use with Grade 4. Trace it again. Chapter 10.Print This Page Name Explore Translations. Sample Artwork Which cards were chosen to draw this artwork? © McGraw-Hill School Division Create another shape and another rule for a movement cards. Try to guess which movement cards your partner chose to create the drawing. Then choose a movement card. Then cut out the movement cards. Lesson 8. and Rotations Shape Art Cut out the shape cards and turn them face down. Movement Cards Translation Slide your shape 1 inch to the right. Shape Cards Reflection Flip over your shape to the right. Trace it again. Return the movement card to the bottom of the pile. pages 434–435. Place those cards face down in another pile. pages 436–439. Complete the drawing to make it symmetrical. draw its lines of symmetry. draw a figure with bilateral symmetry. 13. 12. Chapter 10. 14. Lesson 9. 5. draw a figure with rotational symmetry. Print This 10–9 Page P PRACTICE 4. 8. Use with Grade 4. 7. (325) MG 3.Print This Page Name Symmetry Is the dotted line a line of symmetry? 1. On a separate sheet of paper. 2.4 . Is the figure symmetrical? If yes. On a separate sheet of paper. 10. 6. 3. 9. © McGraw-Hill School Division 11. The top figure matches the original figure. Is the dashed line a line of symmetry? Then trace each figure. Figure B has rotational symmetry. Figure B 1. Step 2: Fold it along one of the dashed lines.Print This Page Name Symmetry Follow these steps to find out if a figure has bilateral symmetry. Step 4: Turn the top figure 180º. Chapter 10. The halves match. 4. so all the lines are lines of symmetry. Figure A Follow these steps to find out if Figure B has rotational symmetry. Put your pencil point on the dot in the center. Step 3: Unfold the figure. 5. Turn the top of figure 180º. Step 3: Turn the top figure 90º. How many lines of symmetry does Figure B have? Look at each figure. The figure has bilateral symmetry. pages 436–439 (326) MG 3. Step 2: Place it on top of the original Figure B. Use with Grade 4. Does the top figure match the original? Does Figure A have rotational symmetry? 2. Turn it to see if it has rotational symmetry. Step 1: Trace Figure B and cut it out. 3. The figures match.4 . Step 4: Fold the figure along the other dashed lines. Lesson 9. Print This 10–9 Page R RETEACH The two halves match. Place Figure A you traced on top of original Figure A. Step 1: Trace Figure A and cut it out. The dashed line is a line of symmetry. Fold Figure B you traced to find its lines of symmetry. © McGraw-Hill School Division Put your pencil point in the center. Draw the line or lines of symmetry. (327) MG 3. Print This 10–9 Page E ENRICH © McGraw-Hill School Division G4_C10_L09_E01_MA01 Use with Grade 4.Print This Page Name Symmetry Circle each letter that has one or more lines of symmetry. Lesson 9. pages 436–439.4 . Chapter 10. 4.Print This Page Name Problem Solving: Strategy Find a Pattern Use data from this tessellation to solve problems 1–4. Art On May 15. 5. Which box should Mr. 2. Suppose you extend this design. a painting by Van Gogh sold for $75. Two days later. a painting by Renoir sold for $4. 3. How many large T-shirts does he buy? How many small T-shirts does he buy? 6. Complete the missing pieces of the pattern. (328) MG 3. Lesson 10. Ervin use if he wants to put an equal number of jars in each box? How many boxes will he need? finding a pattern in a tessellation. 1. A large T-shirt costs $15 and a small T-shirt costs $12. Chapter 10.2 . What shapes do you see in a repeated pattern? Print This 10–10Page P PRACTICE 2. Aaron spends $69. Aaron buys 5 Picasso T-shirts for his family. How are the shapes moved? 3.1.000. Share it with others. Mr. pages 440–441. Ervin has 32 jars of paint. Use any strategy.000 less than that amount. How much did Renoir’s painting sell for? © McGraw-Hill School Division Strategy: 7.000. 2.000.3. 1990. How many rhombuses will there be in all? Mixed Strategy Review Solve. Create a problem which involves small boxes that will hold 4 jars and a large box that will hold 6 jars. Strategy: Use with Grade 4. MR 1. He has Strategy: 8. You have a total of 20 small right triangles. 4.8. 2.2 .3. Find shapes that look familiar. pages 440–441.4.1. Look for a pattern to see how these shapes have been moved. (329) MG 3. What do you know? • The illustration shown is a tessellation. © McGraw-Hill School Division I I I I I I I I I 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 Looking for a pattern will help you solve the problem. Chapter 10. MR 1. Use with Grade 4. Step 2 Plan I Make a plan. Problem 1 Print This 10–10Page R RETEACH What shapes do you see in a repeated pattern? How are the figures moved? Step 1 Read Be sure you understand the problem. Choose a strategy. Read carefully. Lesson 10.Print This Page Name Problem Solving: Strategy Find a Pattern Page 441.8. 2. What do you need to find? • You need to identify . 3. Chapter 10. What shapes do you see in a repeated 2. What shapes do you see? To find how these shapes have been moved. Did you answer the question? Yes No What other strategies could you use to solve the problem? © McGraw-Hill School Division Practice Use data from this tessellation to solve. pages 440–441. What is one way to describe how the figures moved? Step 4 Look Back Is the solution reasonable? Reread the problem.3. (330) MG 3. 2. 1.4. Use with Grade 4.2 . look for examples of rotations. Print This 10–10Page R RETEACH Solve Look for shapes you know. MR 1. 2. 3.Print This Page Name Problem Solving: Strategy Find a Pattern Step 3 Carry out your plan. Lesson 10.8. Complete the missing pieces of the pattern? How are they moved? tessellation.1. and reflections. translations. 1. 8 mm 11 mm 8 mm 8 mm 11 mm 6 mm 4. perimeter ϭ 24 ft perimeter ϭ 55 yd Problem Solving © McGraw-Hill School Division 10. 8. 4 ft 8 ft 9. 5.1. 7. 9 mm 10 mm 11 mm 3. 8 in.Print This Page Name Perimeter Find the perimeter of each figure. Chapter 10. pages 442–445. Gerry plans a rectangular garden 11. (331) NS 3.8 . Algebra & Functions Find the length of each missing side. What is the perimeter of the fence? Use with Grade 4. 6. 5 cm 4 cm 10 cm 7 cm Print This 10–11 Page P PRACTICE 2. A fence around a rectangular corral plot that is 30 ft long and 15 ft wide. 11 yd 11 yd 11 yd 11 yd perimeter ϭ 24 in. MG 3. 8 in. Lesson 11. What is the perimeter of the garden plot? has a length of 180 ft and a width of 90 ft. 4 in. 1. add the lengths of the sides. 5 in.1. To find the perimeter of the rectangle. 4 in. Find the perimeter of each figure. 2. Chapter 10. add the lengths of all the sides. 5 in.Print This Page Name Perimeter Perimeter is the distance around a closed figure. 4 ft 4 ft ϩ ϭ 4. (332) NS 3. 10ft 15ft 10ft ϩ 15ft 50ft 15 ft 10 ft 15 ft 10 ft Print This 10–11 Page R RETEACH The perimeter of the rectangle is 50 ft. 3 in. MG 3. 6 in. 5m 7m 7m ϩ ϩ 5. ϩ 3. Lesson 11. 6 dm 6 dm 6 dm 6 dm 6 dm 6 dm 7. 5 in. ϩ 8 ft 8 ft 8 ft ϭ 5m 8 ft 3 ft © McGraw-Hill School Division 6. To find the perimeter. 5 in. pages 442–445.8 . 8. 5 in. 4 in. 4 in. 5 cm 6 cm 7 cm 5 cm 6 cm Use with Grade 4. Try to do this in two different ways. MG 3. pages 442–445. Number of regions: 6 Perimeter of each region: 12 units Use with Grade 4.1. Number of regions: 4 Perimeter of each region: 10 units 2. Number of regions: 5 Perimeter of each region: 12 units © McGraw-Hill School Division 3. Divide each square below into the number of regions and the perimeter given. Print This 10–11Page E ENRICH The square at the right is divided into two regions. Each region has a perimeter of 8 units. Each region has a perimeter of 10 units.Print This Page Name Perimeter Create a Perimeter Each square at the right is divided into three regions.8 . Lesson 11. 1. Chapter 10. (333) NS 3. 1. AF 1. (334) MG 1. Print This 10–12Page P PRACTICE 4. 4 ft 4 ft 5. 6. 10 cm 12 cm 11. 2 yd 5 yd 2 in. length: 7 cm width: 8 cm width: 7 cm width: 4 cm Find the area and perimeter of each figure. 1. 2 in.4 . Chapter 10.Print This Page Name Area Find the area of each figure. length:7 cm 9. 6 mm 25 mm Use with Grade 4. 2. 1 m 4m 12. Lesson 12.2. pages 446–449. Tell what the figure is and find the area. Use graph paper to draw each figure. © McGraw-Hill School Division 10.3. 3. length: 5 cm 8. 7. 4 in. 2. 7 in.4 . 3 yd 5 yd 8. • Multiply the length times the width. 1. 6. 1.2. (335) MG 1. 6 ft 9 ft 7.Print This Page Name Area Area is the number of square units needed to cover a region or figure. pages 446–449. 5 ϫ 5 ϭ 25 The area is 25 square units. 4m 6m Use with Grade 4. 3. Complete. Lesson 12. 2 in. There are 25 square units. The area is 25 square units.3. • Count the number of square units. Chapter 10. 3 ft 8 ft © McGraw-Hill School Division 4. AF 1. 4 in. Print This 10–12Page R RETEACH length: width: area ϭ units units square units length: width: area ϭ units units square units Find the area of each figure. 5. You can use these two ways to find the area of a rectangle or square. (336) MG 1. pages 446–449. 2.3.2. Chapter 10.4 . 1. Lesson 12. AF 1. © McGraw-Hill School Division 5. 3. Use with Grade 4. 6. 4.Print This Page Name Area 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: Print This 10–12Page E ENRICH Aϭ 1 2 ϫ (number of dots on the polygon) Ϫ 1 ϩ (number of dots inside the polygon) Here’s how to use the formula to find the area of this polygon below. A ϭ (1 2 ϫ 12) Ϫ 1 ϩ 3 A ϭ (6 Ϫ 1) ϩ 3 Aϭ5ϩ3 Aϭ8 Find the area of each polygon. 1. 10. (337) NS 3. 14. MG 1. 2. height: 4 in. 3.1. 7. length: 10 ft width: 5 in. width: 8 m height: 6 m width: 2 cm height: 8 cm width: 12 ft height: 5 ft Use with Grade 4. length: 5 m 15. 6. 5. Chapter 10. 12. 11. pages 450–451. 1.Print This Page Name Explore Volume Find the volume of each rectangular prism. Lesson 13. © McGraw-Hill School Division 13. Print This 10–13Page P PRACTICE 4. length: 9 in. 8.4 . 9. length: 7 cm 16. 1. There are 3 layers. • Count the number of cubes in one layer. Volume is measured in cubic units. 3 cm 2 cm 5. (338) NS 3. Print This 10–13Page R RETEACH 3 4 3 length: width: height: © McGraw-Hill School Division length: width: height: cm3 volume ϭ cm3 length: width: height: volume ϭ cm3 volume ϭ 4. Lesson 13. 5 cm 2 cm 2 cm 4 cm 6 cm Use with Grade 4.1. • Multiply: length ϫ width ϫ height V ϭ length ϫ width ϫ height V ϭ 4 ϫ 3 ϫ 3 ϭ 36 The volume is 36 cubic units. Chapter 10. 2.Print This Page Name Explore Volume Volume is the amount of space a 3-dimensional figure encloses. 12 ϩ 12 ϩ 12 ϭ 36 The volume of the cube is 36 cubic units. The bottom layer has 12 cubes. pages 450–451. You can use these two ways to find the volume of a rectangular or square prism.4 . MG 1. Find the volume of each rectangular prism. 2 cm 4 cm 6. 3. Print This Page Name Explore Volume Volume Patterns 1. What pattern do you see? Use with Grade 4.1. width. Compare the volumes of the original and doubled prisms. (339) NS 3. Chapter 10. Complete the table. What do you think will happen to the volume if you double the length. pages 450–451. MG 1. and height of Prism A? 6 cm 4 cm 8 cm Prism A Doubled 3. Was your answer to exercise 2 correct? 4. What is the volume of Prism A? 3 cm 2 cm 4 cm Print This 10–13Page E ENRICH Prism A 2. Lesson 13.4 . Original Rectangular Prism © McGraw-Hill School Division 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 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 5. Find the volume of Prism A doubled. 1.3 .1.1. 2. MR 1.2.3. pages 452–453. Harris’s garden? Explain.Print This Page Name Problem Solving: Application Analyze Data and Make Decisions Record your data in the chart. 1. 1.4. Size of Garden Perimeter of Garden Cost of Fencing Material 10–14 Part A WORKSHEET Decision Making Print This Page Cost of Fencing and Installation © McGraw-Hill School Division Your Decision What is your recommendation for Mr. Lesson 10. Chapter 10. (340) MG 1. Use with Grade 4. pages 454–455. Lesson 14. Drawing of Structure 10–14 Part B WORKSHEET Math & Science Print This Page Rating: 1 (best)–5 (worst) 1. (341) MG 3. 3. Chapter 10.8. 3.7.4.1.2 .3.3.Print This Page Name Problem Solving: Application How well do you make patterns? Record your ratings. 2. 3. How well did you follow directions? Do you have enough data to decide? © McGraw-Hill School Division Use with Grade 4. MR 1. 3. Chapter 10. Make a list of words that helped you give directions. 3.1. 3.2 . Lesson 14. What was easy or hard when following directions? 4. 2. What was easy or hard when giving directions? 10–14 Part B WORKSHEET Math & Science Print This Page 3.Print This Page Name Problem Solving: Application How well do you make patterns? 2.3. MR 1. pages 454–455. 3.4. Use with Grade 4. Describe how a camouflage pattern gives some animals a survival advantage.7.3. (342) MG 3. © McGraw-Hill School Division 5. 3.8. 5 7 © McGraw-Hill School Division 12. Draw a rectangle with the fraction shaded. 5. Lesson 1. 1 3 10. 4 8 13. 1. 1. 2. 9. 4 5 11. 7.7 . pages 470-471. 4 9 14. Print This 11–1 Page P PRACTICE 4. (343) NS 1. 8.5. 5 6 Use with Grade 4. Chapter 11. 6. 3.Print This Page Name Parts of a Whole Write a fraction for the part that is shaded. Lesson 1. Chapter 11. 3. 2. 1. parts shaded parts in all fraction © McGraw-Hill School Division part shaded parts in all fraction parts shaded parts in all fraction parts shaded parts in all fraction Use with Grade 4. 5. Print This 11–1 Page R RETEACH 4 parts shaded 7 parts in all 4 7 shaded parts shaded → 4 → numerator parts in all → 7→ denominator 2 parts shaded 5 parts in all 2 5 shaded parts shaded → 2 → numerator parts in all → 5 → denominator Complete to write a fraction for the part that is shaded. 1. (344) NS 1.7 .5. pages 470–471. part shaded parts in all fraction 4. parts shaded parts in all fraction 6.Print This Page Name Parts of a Whole A fraction can name parts of a whole. (345) NS 1.Print This Page Name Parts of a Whole Fraction Design Print This 11–1 Page E ENRICH Design a quilt. white. Lesson 1. blue.7 . What part of your quilt is red? white? . and blue crayons. and purple crayons to color the squares below. Use red. blue? purple? Design a flag. What part of your flag is red? yellow? green? blue? Use with Grade 4. Use red.5. © McGraw-Hill School Division 2. pages 470–471. green. 1. yellow. Chapter 11. 1. What part of the students are in the chorus? president. Draw a picture. One of four animals is a chimpanzee. What part of the class did not vote for president? Use with Grade 4. 3. Chapter 11. Lesson 2.7 . Five of 12 students are in the school 12. 1. pages 472–473. All of five kittens are smiling. 2.5. and then write a fraction. Six of eleven balloons are blue.Print This Page Name Parts of a Group Write a fraction that names what part is shaded. 5. 6. 9. 1. (346) NS 1. © McGraw-Hill School Division Problem Solving 11. Print This 11–2 Page P PRACTICE 4. 7. 8. 10. Twenty of 25 students voted for class chorus. Four out of seven hats have stars. pages 472–473. Chapter 11. 3. 5 8 are shaded. Lesson 2.Print This Page Name Parts of a Group A fraction can name part of a group.5. Complete. 4 7 are not shaded. Use with Grade 4. 1. 3 7 Print This 11–2 Page R RETEACH are shaded. 1. 2. shapes shaded shapes in all fraction that is shaded © McGraw-Hill School Division shapes shaded shapes in all fraction that is shaded fraction that is not shaded fraction that is not shaded Write a fraction that names what part is shaded. There are 7 squares in all. 3 8 are not shaded. There are 8 circles in all. 5.7 . 4. (347) NS 1. 5. pages 472–473. 2 5 4 2. 1 3 4. (348) NS 1.Print This Page Name Parts of a Group Draw the Group Each fraction tells what part of a group the shaded figure or figures represent. 2 8 9 9. 1.7 . 5 6 5. 1. Lesson 2. How did you decide how many triangles to draw in exercise 1? Use with Grade 4. 3 8 6. 4 7 8. 1 2 7. Complete the group for each fractional part. 16 Print This 11–2 Page E ENRICH 3. 10 © McGraw-Hill School Division 10. Chapter 11. 4. 24 ϭ 32 Complete the pattern of equivalent fractions.Print This Page Name Find Equivalent Fractions and Fractions in Simplest Form Draw an equivalent fraction for each. 4 ϭ 5 14. 1 4 1 4 1 4 3. 1 ϭ 6 2 10. 4 ϭ 1 4 11. 4 ϭ 5 10 9. 9 12 ϭ 4 Name an equivalent fraction for each. 12. 4Ϭ2 10 Ϭ ϭ 2 5. Paul caught 9 bass and 3 trout. 8 ϭ 20 24. 6 ϭ 12 18. 2Ϭ2 8Ϭ ϭ 1 7. 6 ϭ 15 15. 4 ϭ 10 17. 3 ϭ 21 22. 4 ϭ 12 Write each fraction in simplest form.2 . pages 474–477. 6 ϭ 18 20. A box contains 6 red pencils and 8 31. 9 ϭ 24 26. 1 ϭ ϭ ϭ ϭ ϭ 3 6 9 12 15 18 Problem Solving 30. 12 ϭ 24 27. 8 ϭ 12 21. Lesson 3. 1ϫ 5ϫ4 ϭ 20 8. 1 6 1 2 1 6 1 6 Print This 11–3 Page P PRACTICE 2. 5 ϭ 15 © McGraw-Hill School Division 25. 1 5 1 5 1 5 1 5 1 1 1 1 1 1 8 8 8 8 8 8 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 Complete to find equivalent fractions. 16. What fraction of the pencils are red? fraction of the fish were trout? Use with Grade 4. 1. 10 ϭ 30 23. What black pencils. 1 ϭ ϭ ϭ ϭ ϭ 4 8 12 16 20 24 29. 1ϫ 2ϫ8 ϭ 16 6.5. 28. 3 ϭ 18 19. (349) NS 1. AF 2. Chapter 11. 3 ϭ 7 13. 3 ϭ 3 ϫ 5ϫ 5 ϭ 6. ϭ 2 6 1ϫ3 3ϫ3 4 12 ϭ 3 9 1ϫ4 3ϫ4 ϭ 4 12 1. (350) NS 1. 3. 3 ϭ 3 ϫ 4ϫ 4 ϭ 5. 7. 6 factors of 8: 1. the simplest 6 ϭ 6Ϭ2 ϭ 3 8 4 8Ϭ2 form of 6 is 3 . So. 2. Show 6 8 in simplest form. 9. Find the greatest common factor So. AF 2. 3 4 ϭ 8 3 5 ϭ 10 3 6 ϭ 12 © McGraw-Hill School Division 4. 9. 8. of the numerator and denominator. its numerator and denominator have only 1 as a common factor.2 . pages 474–477. 3. Divide the numerator and denominator by the greatest common factor. To find an equivalent fraction. multiply the numerator and denominator by the same number. 2. 4 The greatest common factor is 2.5. and are equivalent fractions. 1ϫ2 3ϫ2 Print This 11–3 Page R RETEACH Simplest Form When a fraction is in simplest form. 4 8 ϭ 2 10 ϭ 4 12 ϭ Use with Grade 4. 2. 3 ϭ 3 ϫ 6ϫ 6 ϭ Write each fraction in simplest form. Chapter 11.Print This Page Name Find Equivalent Fractions and Fractions in Simplest Form Equivalent Fractions Equivalent fractions name the same part. Lesson 3. 2 3 6. 8 4 Complete to find equivalent fractions. factors of 6: 1. 2. 1. 1 3. 1 3 3 7 © McGraw-Hill School Division 5 12 5 6 8 8 1 1 4 6 5 8 Cross out each fraction in simplest form and the letter below it. 1 2 5 9 6 7 7 8 5 6 11 2 4 8 3 6 4. 5 9 3 5 8. 2 3 6 9 6. (351) NS 1. 6 8 8 12 4 16 5 25 4 7 8 12 10 16 3 4 7. AF 2. Cross out the fraction that does not belong. 2 8 3 12 5. Use with Grade 4. Lesson 3. 1. pages 474–477. 1 3 2 7 3.Print This Page Name Find Equivalent Fractions and Fractions in Simplest Form Which Does Not Belong? Look at the fractions in each exercise.5. Chapter 11.2 . Then write a fraction that does belong. 2 3 5 5 9. 3 8 5 8 Print This 11–3 Page E ENRICH 2. 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. Lesson 4. 7 . 3 3 20. . . . 7 8 18. 1 1 19. 10 17.Print This Page Name Compare and Order Fractions Complete. 1 2 4. Ͻ. 4 . 4. 3. 5 7 . 8 9 15. 1 4 . 4 9. Pat eats 3 2 28. Order the amounts from greatest to least. 2 3 23. . Write Ͼ. . Order from greatest to least. 4 9 6. 16 © McGraw-Hill School Division . . pages 478–481. 3 5 2 3 2 3 2 15 7 8 3 4 7 10 8. 1 4. . 2 5 7 5. Who eats more cake? Explain. 10 1 3 3 4 12 15 1 4 5 6 4 5 Print This 11–4 Page P PRACTICE 2. Chris eats 3 4 of a pizza. 4 3 3 25. or ϭ. 10 2 7 4 5 4 20 13 16 4 9 5 16 3. Chapter 11. 9 7 3 26. 3. Problem Solving 1 27. 8 1 2 22. 12 .5. 2. . Karl eats 1 2 of a pizza. 3 4 9. 1. . pizza. 5 6 . 1.9 . Tim eats 3 of a of the cake. 2 5 7. 12 9 16. 1 5 12. Sandra eats 1 6 of the cake. . . 12 7 13. 1 5 11. 3 . 1 2. 4 5 5 10. 2 5 24. (352) NS 1. 3 4 3 14. 4 . 9. 4 9. 5 1 3 21. 20 . 7 8. 1 4 Order from least to greatest. 5. 8 1 1 9. 6. 6. . 8.9 . 3. . Lesson 4. Put the fractions in order from least to greatest. 2 5 7. 6 6. 2. 1. Chapter 11. 3. 2 3 Order the fractions from least to greatest: 1 6. or ϭ. 3 4 2 4 3 10 5 10 2 3 1 3 4. 4 . 1 6 3 6 4 6 ϭ ϭ ϭ 1 6 4 6 3 6 ϭ ϭ ϭ 1 6 3 6 2 3 3 2 From least to greatest. 4 8 © McGraw-Hill School Division 1 2 5 6 2 3 1 4 3 8 Write the fractions in order from least to greatest. Print This 11–4 Page R RETEACH Step 1 Write each fraction as an equivalent fraction with the same denominator. 3.5. Use with Grade 4. 6 5 3 8. . the fractions are 1 6.Print This Page Name Compare and Order Fractions You can use equivalent fractions to compare and order fractions. Ͻ. 2 3 . 6. Complete. 3 4. 12 . . Write Ͼ. 1 6 2 3 3 6 Step 2 Compare the numerators. 6. 1. pages 478 – 481. (353) NS 1. . The player who draws the greater fraction takes both cards. • Each player draws a card at the same time from his or her pile. 1. 1 2 1 3 1 4 Print This 11–4 Page E ENRICH 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 © McGraw-Hill School Division 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 4.5. Chapter 11. (354) NS 1. each player draws another card.Print This Page Name Compare and Order Fractions Fraction War Play this game with a partner. Shuffle them and then place them facedown in a pile in front of you.9 . Your partner will do the same thing. the player with the greater number of cards wins. • Cut out the cards below. • When the piles of cards are gone. The player with the greater fraction also takes the fraction cards that were equal. Lesson 4. pages 478–481. If both fractions are equal. Then solve the problem. 1 1. Jack spends 1 hour in an amusement park. those students went on the roller coaster.1. . How many minutes does Jack wait in lines? There are 24 hours in 1 day. Vivian buys a bag of popcorn. Two dozen students went to the amusement park. 3. 2. pages 482–483. How many feet wide is the flag? © McGraw-Hill School Division One yard is the same as 3 feet. Two thousand pounds equal 1 ton. He spends 4 of his time Print This 11–5 Page P PRACTICE Reading Skill waiting in lines. 5. Solution: One pound equals 16 ounces. The bag holds 1 4 pound of popcorn. How many ounces did each friend drink? One quart equals 32 ounces. Lesson 5. Solution: 1 2.3. Solution: A yard is a measure of length. Leora buys a quart container of iced tea to share with her friends. 4.1. Chapter 11. The width of the flag 2 is 3 of its length. How many students went on the roller coaster? A dozen is the same as 12. At the amusement park. (355) MR 1.Print This Page Name Problem Solving: Reading for Math Check for Reasonableness Circle the statement that helps you solve the problem. 3. How many ounces is that? 1 1 3 is greater than 4 . 1 Each friend drinks 4 of the iced tea. A group of 3 of There are 60 minutes in 1 hour.2 One cup equals 8 ounces. Solution: Use with Grade 4. A flag at the amusement park is 4 yards long. Solution: 3. G less than 3. J less than 20 minutes. What prior knowledge do you need Print This 11–5 Page P PRACTICE Math Skills Test Prep 2. B Of Fun Time’s amusement parks. 1 C 5 6 is greater than 6 .S. How many minutes does Nick spend on rides? 5. A reasonable answer for this in order to solve this problem? A 5 6 means 5 of 6 equal parts. How many Fun Time Amusement Parks are in the United States? 3. Of these students. C There are 60 minutes in an hour. There is a Fun Time Amusement Park in France. pages 482–483. 3. B 5 6 is less than 1. H greater than 3 but less than 9. He spends 2 3 of his time on rides. Chapter 11. D All of the above problem would be that Fun Time has F 16 amusement parks in the United States.3.Print This Page Name Problem Solving: Reading for Math Check for Reasonableness Choose the correct answer. problem would be F greater than 18. H greater than 20 minutes but less than 1 hour. A reasonable answer for this order to solve the problem? A Fun Time has 16 amusement parks. Which information is not needed in 4. © McGraw-Hill School Division Nick spends 2 hours in the amusement park. Which of the following information 6. 3 4 are in the United States. D 18 is divisible by 9. 3. A group of 18 students goes to the amusement park. G 12 amusement parks in the United States. Fun Time International has 16 amusement parks.1.2 . How many students go on the bumper cars? 1. 3 4 are in the United States. H 4 amusement parks in the U. C Fun Time has an amusement park in France. J greater than 9 but less than 18. Lesson 5. Use with Grade 4. 2. (356) problem would be F 2 hours. G more than 60 minutes but less than 120 minutes. Of these amusement parks. MR 1. A reasonable answer for this is important to solve the problem? A There are 24 hours in 1 day. D There are 36 rides in the amusement park.S J no amusement parks in the U. B Nick goes on 4 rides.1. 5 6 go on the bumper cars. A dozen students go to the 1 amusement park. She went on the roller coaster 2 3 of the time. how many students go on the Space Shot? 7. H 20 students. J 16 students. pages 482–483. If 4 of the students go on the Water Slide and 2 of the students go on the 5 Space Shot. A group of 40 students goes to the amusement park. How people are in the car? many rides does he go on? Use with Grade 4. (357) MR 1. 9.3. Each car of the Sling Shot can hold 15 people.2 . There are 32 rides at an amusement park. How many students were there for the first time? 13. A group of 3 of 12.Print This Page Name Problem Solving: Reading for Math Check for Reasonableness Choose the correct answer.1. What prior knowledge do you need 3 Print This 11–5 Page P PRACTICE Math Skills Test Prep 8. How many rides does he go on? How many roller-coaster rides did Donna take? 11. 10. An amusement park has 36 rides.1. 3. A car is 2 5 full. G 24 students. How many students go on the Super Cycle? amusement park. 2 5 were there for the first time. Bobby goes on 1 2 of them. Norman goes on 3 8 of the rides. There were 25 students at the © McGraw-Hill School Division these students goes on the Super Cycle. 3 2 3 problem would be F 40 students. Of these students. How many 14. Lesson 5. A reasonable answer for this in order to solve this problem? A 20 Ͼ 25 B 4 means 3 ϫ 4 C 5 means 2 of 5 equal groups D 4 Ͻ1 Solve. 2. 3. Chapter 11. Donna took 18 rides. 3. 3 of 21 ϭ 20. On Monday he practices 1 5 of that time. participate in sports. Of the 24 fourth graders in Mrs. 7 of 14 ϭ 14. 3 4 of 20 ϭ 2 3 of 24 ϭ 4 5 of 15 ϭ Find the fraction of each number. 6 of 12 ϭ 13. 7 of 21 ϭ 18. 3 of 15 ϭ 11. 8 of 40 ϭ 19. 7. 3 4 of 16 ϭ 6. pages 484–485. 9 of 18 ϭ 16. 6 of 36 ϭ 23. 4 of 20 ϭ 21. Chapter 11. 5 of 30 ϭ 12. 7 of 28 ϭ © McGraw-Hill School Division 1 5 2 5 2 3 8. How many hours does Steven practice cello on Monday? Use with Grade 4. 26. 1. 2. 2 of 18 ϭ 10. 10 of 60 ϭ 7 3 1 4 1 3 Problem Solving 25. 5 of 30 ϭ 22. Lesson 6.5 . Print This 11–6 Page P PRACTICE 1 3 of 6 ϭ 5. 8 of 16 ϭ 24. (358) NS 1.Print This Page Name Explore Parts of a Group Use the squares to help you find the fraction of each group. 7 of 49 ϭ 6 1 1 1 3 2 9. 2 3 of 18 ϭ 4. How many fourth-grade students participate in sports? 1 4 week. 8 of 32 ϭ 15. 10 of 40 ϭ 17. Steven practices cello 15 hours a Williams’ class. You want to find 2 5 of 20 counters. 4 of 20 ϭ 1 © McGraw-Hill School Division 7. 1. 2 5 of 20 is 8. Circle the part of each group. 3 of 15 ϭ 2 5. Print This 11–6 Page R RETEACH There are 8 counters in 2 groups. 4 of 12 ϭ 3 6. 6 of 30 ϭ 1 8. Divide the 20 counters into 5 equal groups. Suppose you have 20 counters. 5 of 10 ϭ 2 3.5 . 3 of 6 ϭ 1 4. Lesson 6.Print This Page Name Explore Parts of a Group You can use counters to find a part of a group. Chapter 11. The denominator tells you how many equal groups to make. So. pages 484–485. 6 of 18 ϭ 5 9. (359) NS 1. 2 of 8 ϭ 1 2. Complete. 5 of 10 ϭ 4 Use with Grade 4. Sam slices 4 of the bread. How many pounds does he use? 3. How much is that? 6. 1 1 How much chicken is left? Use with Grade 4. George boils 6 of the eggs. Jon barbecues 4 of the sausage and uses the rest for appetizers. pages 484–485. How many pounds does she use? 4. Chapter 11. Melanie uses 5 of the potatoes for 3 18 pounds of chicken 20 pounds of sausage potato salad. How much is that? © McGraw-Hill School Division 5 3 1 7. 3 How many pounds does he barbecue? How many pounds does he use for appetizers? 8. How much ground beef is that? Grocery List 12 pounds of ground beef 2. Bob cooks 6 of the chicken for chicken salad. How many eggs does he boil? 5. 1. Barb adds salt and pepper to 4 of the 3 Print This 11–6 Page E ENRICH ground beef. (360) NS 1.5 . Lesson 6. Jan grills 2 of the chicken. Mark uses 3 of the ground turkey to 2 9 pounds of ground turkey 15 pounds of potatoes 36 eggs 16 loaves of bread make meatballs.Print This Page Name Explore Parts of a Group Cooking with Fractions Use the grocery list to answer each question. Sarah uses 8 of the bread for stuffing. Aida drank 9 6 4 30. 6 ϭ 14. 1. 10 ϭ 13. 84 ϭ 20. 1. 1 25. 0 1 8 1 6 1 4 3 4 1 2 5 8 3 4 7 8 1 18 1 16 1 14 1 14 3 12 18 14 18 1 5 3 7 2 21. What is this as a mixed © McGraw-Hill School Division Tuesday she ran 41 2 miles. 38 ϭ 10. 28 ϭ 18. 4 ϭ 30 2 21 6 9 3. 6 ϭ 64 2 13 1 7 4. Claudia ran 43 miles on Monday. Lesson 7. pages 486–487. Ben measures ten one-fourths of a 28. Who drank more juice? Explain. Jared drank 7 cups of juice. 56 ϭ 17. 2 ϭ 7. On which day did Claudia run a longer distance? Explain. 4 ϭ 16. Ͻ. Mary worked 81 hours on Monday 2 cups. 2 ϭ 15. or ϭ. 45 ϭ 11. On which and 83 5 day did she work longer? Explain. Use with Grade 4. On 1 cup of water. 1 1 8 8 8 23. 1 3 4 Problem Solving 27. (361) NS 1. 36 ϭ 19. 5 ϭ 48 3 19 5 10 Algebra & Functions Use the number line to compare. 2 ϭ 6. 3 ϭ 8. Chapter 11. 2 17 8 17 8 11 2 26. 1 1 6 24. hours on Tuesday. Write Ͼ. 6 ϭ 40 2 22 2 8 Print This 11–7 Page P PRACTICE 2. 17 ϭ 12.9 .Print This Page Name Mixed Numbers Rename as a mixed number or fraction in simplest form. number? 29. 1 1 4 11 8 15 8 22.5. 66 ϭ 9. 7 ϭ 5. 8 ϭ 8 Write the mixed number as a fraction. 1 1 4 ϭ 11. 1. 31 8 4. Add the numerator to the product. 4 1 3 ϭ 8. 7 3 3.6 3 5 ϭ 12. 8 2 3 ϭ 13. 1. 7 4 2. Step 2. Multiply the whole number by the denominator. 13 5 = (5 ϫ 1) ϩ 3 5 = 5ϩ3 5 = 8 5 Write the fraction as a mixed number or whole number. Lesson 7. 7. Step 1. Chapter 11.9 . 3 5 6 ϭ Use with Grade 4. 13 4 13 4 13 4 ϭ ϭ ϭ 4 4 ϩ ϩ 4 4 ϩ ϩ 4 4 ϩ ϩ 1 31 4 1 1 1 4 1 4 You can also use multiplication and addition to write a mixed number as a fraction. 4 ϭ © McGraw-Hill School Division 9 5.Print This Page Name Mixed Numbers You can use models to help you write 13 4 Print This 11–7 Page R RETEACH as a mixed number.5 2 7 ϭ 10.5. (362) NS 1. 3 ϭ 11 6. pages 486–487. Write both the fraction and the mixed number. Lesson 7.Print This Page Name Mixed Numbers Fractions Between Print This 11–7 Page E ENRICH Shade the fraction bars to show a fraction between the two whole numbers given. Shade the fraction bars to show a fraction between 2 and 3.9 . Shade the fraction bars to show a fraction between 2 and 3. Chapter 11. Fraction: Mixed number: 2. Fraction: Mixed number: 3. pages 486–487. 1. (363) NS 1. Fraction: Mixed number: © McGraw-Hill School Division 4.5. 1. Shade the fraction bars to show a fraction between 1 and 2. Fraction: Mixed number: Use with Grade 4. Shade the fraction bars to show a fraction between 2 and 3. 1. 12. certain. SDP 2.2 . It will be sunny or rainy tomorrow. 13. or equally likely you will pick a red ball? 6 black pencils. Chapter 11. or impossible. Is it unlikely. .Print This Page Name Likely and Unlikely Describe the probability of picking a certain shape from the bag. or 4. 3. Use the words likely. MR 1. Is it unlikely. The month after September will be November. It will snow in Alaska this year. or equally likely you will pick a red pencil? Use with Grade 4. pages 490–491. 5. more likely. Print This 11–8 Page P PRACTICE 3. 2. spinning 6 8. 2. A bag contains 3 red and 7 white 15. unlikely. spinning 1. spinning 3 or 4 10.1.5. or 4 2 4 2 2 2 2 3 2 1 2 4 3 Describe the probability. equally likely. Lesson 8. spinning 1 9. spinning 2 6.or Describe the probability of spinning the number. less likely. 11. © McGraw-Hill School Division Problem Solving 14. spinning 3 7. A box contains 6 red pencils and balls. . (364) NS 1. or likelihood. that you will land on an odd or even number.5. 2. to land on a 8 7 6 5 1 2 3 4 3. that you will land on a number less than 9. Use with Grade 4. • It is certain that you will spin a number greater than 0. It is © McGraw-Hill School Division 4. It is number greater than 8. Chapter 11. 3. 7 8 8 8 Look at the spinner at the right. that something will happen is called probability. Use the words likely. • The probability of spinning a 7 is unlikely. It is 5. SDP 2. You could spin 1. equally likely. The probability of spinning 12 2. unlikely. Lesson 8.Print This Page Name Likely and Unlikely The chance. • The probability of spinning an 8 is likely. It is that you will land on a number greater than 2.1. • It is impossible to spin an 8. MR 1. or impossible to describe the probability. 1. There are 6 possible outcomes. (365) NS 1. 5. Print This 11–8 Page R RETEACH 6 5 4 1 2 3 Look at the spinner at the right. certain. that you will land on a number less than 2. • The probability of spinning each number is equally likely. pages 490–491. or 6. Look at the spinner at the right. It is 6.2 . 4. Guess Number of Correct Numbers Print This 11–8 Page E ENRICH Number of Digits in the Correct Position 1. (366) NS 1. 4. Chapter 11. 6. Partner A chooses a secret 4-digit number and writes it on a sheet of paper. • Continue playing until the secret 4-digit number is guessed. Example: The secret number is 1. He or she writes the number of digits that are correct. 2. • Players then switch roles. • Based on that information. pages 490–491.5. 8. 5. 3.093. 9. 7. © McGraw-Hill School Division 1. 10. The number of digits in the correct position is 1.1. Lesson 8. 8. 6. 2. SDP 2. 4. 9. • Player B guesses a 4-digit number and writes in the first row of the guess chart. Player B makes a second guess. Player A also writes the number of digits that are in the correct position. MR 1. • Player A looks at the 4-digit number and then fills in the second chart. The number of correct digits is 2.Print This Page Name Likely and Unlikely Guess the Number • Play this game with a partner. 3.198. 10.2 . 5. 7. or until 10 guesses have been used. What strategy did you use in guessing the numbers? Use with Grade 4. The first guess is 6. Karen turns over 5 paper cups. 2. red blue blue blue green 13.2 . hexagon 12. red or blue 18. purple © McGraw-Hill School Division 17. 7. pages 492–493. 3 or 4 6. Greg has a coin in one of his closed 20. SDP 1. triangle or square Find the probability of picking the color. circle 8. blue or green Problem Solving 19. What is the probability that Greg’s friend will pick the hand the coin is in? hides a coin under one of them. Lesson 9. 1 Print This 11–9 Page P 3 PRACTICE 4 4 4 3 4 4 3.1. triangle 9. What is the probability that Steven will guess which cup the coin is under? Use with Grade 4. 4 4. pentagon 11. Chapter 11. She hands. 3 2. blue 14.5. 2 2 4 2 2 5. (367) NS 1. red red red red 15.Print This Page Name Explore Probability Find the probability of spinning the number. 1 1. green 16. 5 Find the probability of picking the shape. square 10. Lesson 9. 3. B 8. a pad of paper 14. a pair of scissors 13. SDP 1. Probability ϭ number of favorable outcomes number of possible outcomes You can use probability to predict an outcome.2 . pages 492–493.Print This Page Name Explore Probability You can use a fraction to show a probability. an eraser 12. A 7. The probability of picking a The probability of picking a The probability of picking a is 2 5.1. is 1 5. If you pick one of these counters without looking. (368) NS 1. D A B C C D B C C C B Find the probability of picking each item. 1. 2. 2. Print This 11–9 Page R RETEACH Find the probability of picking each shape.5. Find the probability of picking each letter. a pencil 10. a pen 11. a crayon Use with Grade 4. 4. there are 5 possible outcomes. Chapter 11. © McGraw-Hill School Division 9. is 2 5. C 6. 5. Toss two number cubes numbered 1–6 120 times. You get the sums 2–12 when you toss two number cubes and add the numbers. Use tally marks to record your results in the table below. Number Cube (120 tosses) 1 2 3 4 5 6 3.1. 2. Chapter 11.2 . Use with Grade 4. What if you toss 3 numbers cubes? What sums would be least likely to come up? Explain.Print This Page Name Explore Probability Experimental Probability 1. What if you toss a number cube numbered 1– 6 120 times? Print This 11–9 Page E ENRICH About how many times do you think you will toss the number 1? Explain. Lesson 9. pages 492– 493. SDP 1. What if you toss two number cubes 72 times? Record your sums in the table below.5. (369) NS 1. Sum of Numbers on Two Number Cubes (72 tosses) 2 3 4 5 6 7 8 9 10 11 12 © McGraw-Hill School Division 4. 2. Print This Page Name Problem Solving: Strategy Draw a Tree Diagram Use a tree diagram to solve. 1. You spin a spinner with 4 equal Print This 11–10 Page P PRACTICE 2. Karen throws a dart at a target with 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? 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? 3. The Boardwalk Shop sells souvenir 4. Boardwalk Burgers sells burgers made 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? from beef, turkey, chicken, or soy. Burgers can have no cheese, Swiss cheese, or American cheese. How many different choices are there? © McGraw-Hill School Division 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? 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: 7. Marnie brought $75 to the Strategy: 8. Create a problem which can be amusement park. She has $39 left. How much money did Marnie spend? 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 Problem Solving: Strategy Draw a Tree Diagram Page 495, Problem 1 Print This 11–10 Page R RETEACH 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 What do you need to find? • You need to find or , . Step 2 Plan I I Make a plan. Choose a strategy. I © McGraw-Hill School Division I I I I I I I 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 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 Problem Solving: Strategy Draw a Tree Diagram Step 3 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 heads tails 2 heads tails 4 heads tails 6 Print This 11–10 Page R RETEACH Solve Outcome 1-heads 1-tails Step 4 Look Back © McGraw-Hill School Division Is the solution reasonable? Reread the problem. 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? 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? Use with Grade 4, Chapter 11, Lesson 10, pages 494–495. (372) SDP 2.1, 2.2; MR 1.1, 2.3, 2.4, 3.1, 3.2 Print This Page Name Explore Making Predictions Use the spinner for exercises 1–6. 1. If you spin the spinner 100 times, what Print This 11–11 Page P PRACTICE is the probability you will land on A? 2. If you spin the spinner 50 times, what is the probability you will land on B? C A A B A B 3. If you spin the spinner 100 times, what is the probability you will land on C? C C A A 4. If you spin the spinner 100 times, what is the probability you will land on a shaded section? 5. If you spin the spinner 50 times, what 6. If you spin the spinner 50 times, what is the probability you will land on an unshaded section? is the probability you will land on an A or a B? Use a number cube with the sides labeled 1–6 for problems 7–10. 7. Predict the number of times 3 will © McGraw-Hill School Division 8. If you toss the number cube 60 times, come up if you toss the number cube 30 times. how often might 4 come up? 9. Is it reasonable to predict that you will 10. Can you predict exactly how many toss a 4 on the number cube 2 out 12 tosses? times 5 will come up when you toss a number cube labeled 1–6? Use with Grade 4, Chapter 11, Lesson 11, pages 496–497. (373) NS 1.5; SDP 1.1, 2.1 Print This Page Name Explore Making Predictions 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 4 3 2 5 1 Print This 11–11 Page R RETEACH 3 1 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? 3. The probability of landing on a striped © McGraw-Hill School Division section is 2 out of 5. 4. The probability of landing on a red 5. Is it reasonable to predict that the section is 1 out of 5. spinner will land on a section that is not shaded 6 out of 30 times? Use with Grade 4, Chapter 11, Lesson 11, pages 496–497 (374) NS 1.5; SDP 1.1, 2.1 Print This Page Name Explore Making Predictions Could It Happen? Print This 11–11 Page E ENRICH 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? My school is having a raffle for a computer. Each ticket costs $3.00. My friend says that if each student in our class buys a ticket our class has a great chance of winning the computer for our classroom. What do you think? Sincerely, Mouse Potato Could It Happen? Could It Happen? Dear Could It Happen? There are 30 people trying out for 15 parts in the school play. I don’t want to try out unless I have a pretty good chance of getting a part. What do you think the chances are that I will get the part? Regards, Broadway Bound © McGraw-Hill School Division 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 Applying Probability Record your data. Game Fair or unfair? Why? 11–12 Part A WORKSHEET Decision Making Print This Page 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 Checkerboard B © McGraw-Hill School Division 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 Problem Solving: Application How does size affect how fast a solid dissolves? Make your own chart to record the dissolving time for each seltzer tablet. 11–12 Part B WORKSHEET Math & Science Print This Page © McGraw-Hill School Division 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 Problem Solving: Application How does size affect how fast a solid dissolves? 2. What would happen if you broke the seltzer tablet into 11–12 Part B WORKSHEET Math & Science Print This Page 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 conclusions? Explain your answer. © McGraw-Hill School Division 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 how much salt will you need? Use with Grade 4. 3 ϩ 3 ϭ 9 9 18. 1 6 ϩ 6 8 5 30. ϩ 3 9 2 9 8. Lesson 1. 6 7 ϩ 7 2 7 29. 1 4 ϩ 4 6 28. Write each sum in simplest form. ϩ ϩ 1 6 2 6 3. ϩ 6 10 8 10 7. Do you have enough paper now? How long is your piece of paper? dough. ϩ 2 12 4 12 5. 3 ϩ 3 ϭ 4 4 20. 1 ϩ 7 ϭ 8 8 17. 1 3 1 3 Print This 12–1 Page P PRACTICE 2. pages 516–517. ϩ 2 4 2 4 9. 12 ϩ 12 1 1 © McGraw-Hill School Division Problem Solving 31. 5 ϩ 5 ϭ 8 8 21. 7 ϩ 8 ϭ 12 12 23. ϩ 2 8 4 8 10. ϩ 3 5 3 5 11. (379) NS 1. If you want to double the recipe. Chapter 12. Ͻ. 5 ϩ 4 ϭ 8 8 19. 9 ϩ 3 ϭ 15 15 Algebra & Functions Compare. ϩ 3 15 3 15 6. You want to make some salt ceramic for a mural. The recipe calls for 2 3 cup of salt. 2 ϩ 2 ϭ 16 16 14. You need at least 1 4 yards of paper 1 32. 3 25. ϩ 3 12 5 12 13. 3. 1. You tape together 2 pieces of paper that are 3 4 yard each. or ϭ.1 . ϩ 2 7 2 7 4.5. 3 ϩ 3 ϭ 18 18 16.Print This Page Name Add Fractions with Like Denominators Add. 13 ϩ 12 ϭ 16 16 22. 10 ϩ 10 1 1 3 27. 5 ϩ 7 ϭ 11 11 24. 2 9 ϩ 9 1 1 2 26. 3 ϩ 2 ϭ 10 10 15. Write Ͼ. ϩ 7 9 6 9 12. pages 516–517. (380) NS 1. 1 8 1 8 1 1 1 8 8 8 3 8 2.5. 1 4 1 4 1 1 4 4 2 4 3. Lesson 1. 1 ϩ 4 ϭ 8 8 12. 1 1 10 10 2 10 1 1 1 10 10 10 ϭ ϩ 1 6 ϭ ϩ ϭ ϩ 3 10 7. 2 ϩ 4 ϭ 14. 1 1 1 1 1 10 10 10 10 10 5 10 1 1 1 1 10 10 10 10 © McGraw-Hill School Division ϩ 3 6 ϩ 8 8 4 10 ϭ 11. 1 1 6 6 1 1 6 6 1 1 1 1 6 6 6 6 1 3 2 6 Print This 12–1 Page R RETEACH 1 3 ϩ 2 6 ϭ 4 6 ϭ 2 3 Add. 1 1 1 1 6 6 6 6 4 6 1 6 5. 1 4 1 4 1 4 1 4 6. Chapter 12.1 . 1 1 6 6 2 6 1 1 1 6 6 6 ϭ 8. 2 ϩ 6 ϭ Use with Grade 4. 1 ϩ 2 ϭ 5 5 10.Print This Page Name Add Fractions with Like Denominators You can use fraction strips to add fractions with like denominators. 1. Write each sum in simplest form. 3. 1 1 3 3 2 3 1 3 ϭ ϩ ϭ ϩ ϭ ϩ 1 3 4. 3 ϩ 4 ϭ 12 10 12 10 9. 2 ϩ 5 ϭ 12 12 13. Which fractions would you like to roll each time? Explain. That player should also write a number sentence that shows the addition. 1 6 and each hexagon • The first player rolls the two number cubes and shows the fractions with the triangle pattern blocks.Print This Page Name Add Fractions with Like Denominators Hexagon Roll Game Play with a partner to form hexagons. call out “Hexagon!” to score 1 point. pages 516–517 (381) NS 1. Chapter 12.1 . You will need two number cubes and triangle and hexagon pattern blocks. Use with Grade 4. 1 . 5. 3. 3.5. Print This 12–1 Page E ENRICH 2 6 2 6 5 6 5 6 • Write the following fractions on each side of two number cubes: 0. Lesson 1. © McGraw-Hill School Division • If the triangle pattern blocks form a whole hexagon. Then he or she finds the sum of the fractions by combining the pattern blocks. 2. • Take turns and continue playing for 5 rounds. 4. 6 6 6 6 6 • Each triangle pattern block stands for stands for 1. The player with more points wins the game. or ϭ. pages 518–519. Ͻ. 4 Ϫ 3 ϭ 5 5 19. At lunch you cut a sandwich into 4 parts and eat 3 of the parts. 9 Ϫ 5 ϭ 10 10 24. What fraction of the sandwich is left? 35. 7 Ϫ 6 11 11 33. 7 Ϫ 3 10 5 12 5 11 10 8 10 14 15 9 13 Ϫ Ϫ Ϫ 2 10 13 15 2 13 © McGraw-Hill School Division 30. Write Ͼ. 1. Ϫ 7 10 2 10 8.5. 5 Ϫ 4 ϭ 7 7 17. Ϫ 7 12 1 12 10. 11 Ϫ 10 15 15 32. 5 Ϫ 1 ϭ 16 16 15. 5 Ϫ 2 9 9 6 9 Ϫ 7 12 7 11 3 9 29. 2 Ϫ 2 ϭ 3 3 26. 4 5 2 5 Print This 12–2 Page P 4 9 1 9 PRACTICE 2. Ϫ 11 12 8 12 13. Ϫ 7. 10 Ϫ 5 ϭ 11 11 22. 12 Ϫ 5 13 13 Problem Solving 34. Ϫ Ϫ 5 7 3 7 3.Print This Page Name Subtract Fractions with Like Denominators Subtract. 7 Ϫ 4 ϭ 12 12 21. 5 Ϫ 1 12 12 Ϫ Ϫ 31. 8 Ϫ 2 ϭ 9 9 27. 7 Ϫ 2 ϭ 9 9 14. Chapter 12. Lesson 2. 7 Ϫ 3 ϭ 8 8 25. 28. (382) NS 1. 9 Ϫ 8 ϭ 11 11 Algebra & Functions Compare. Ϫ 8 9 2 9 5. For breakfast and lunch you drink 2 3 of a quart of milk. 11 Ϫ 8 ϭ 12 12 23. Ϫ 4 15 1 15 11. Ϫ 5 6 1 6 6. 7 Ϫ 3 ϭ 8 8 16. Ϫ 6 10 4 10 9. How much of the quart is left? Use with Grade 4. Ϫ 8 11 4 11 12. 7 Ϫ 5 ϭ 12 12 20. 8 Ϫ 1 ϭ 9 9 18. 3. Write each difference in simplest form.1 . Ϫ 5 8 1 8 4. 5 5 Ϫ 5 ϭ 8 5 14. Lesson 2.Print This Page Name Subtract Fractions with Like Denominators You can use fraction strips to subtract fractions with like denominators. 1 9. Write each difference in simplest form. 1 1 1 1 1 6 6 6 6 6 5 6 Ϫ 1 4 ϭ Ϫ ϭ Ϫ 4 6 ϭ 4. 1 1 1 1 1 1 1 8 8 8 8 8 8 8 7 8 6. pages 518–519. 3. 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 9 12 © McGraw-Hill School Division Ϫ 3 8 ϭ Ϫ 1 12 ϭ Subtract. 1. 1 3 2 3 1 3 1 3 3. 3 4 Ϫ 4 ϭ 7 1 12. 1 1 1 1 1 1 1 8 8 8 8 8 8 8 7 8 8. 10 Ϫ 10 ϭ Use with Grade 4. 1 5 4 5 Print This 12–2 Page R RETEACH 1 5 1 5 1 5 1 5 Ϫ ϭ 3 5 Subtract. 3 3 Ϫ 3 ϭ 7 3 13. Write each difference in simplest form.5. 12 Ϫ 12 ϭ 2 10. Chapter 12. 16 Ϫ 16 ϭ 3 11.1 . 1 1 1 1 1 8 8 8 8 8 5 8 5. 1 1 1 1 1 10 10 10 10 10 5 10 Ϫ 2 8 ϭ Ϫ 1 8 ϭ Ϫ 1 10 ϭ 7. 1 1 1 4 4 4 3 4 2. (383) NS 1. Print This Page Name Subtract Fractions with Like Denominators Fraction Subtraction Riddle When is it bad luck to have a black cat follow you? Subtract. Write each difference in simplest form. Print This 12–2 Page E ENRICH A 5 8 E R 5 16 O 9 10 Ϫ 2 8 Ϫ 4 16 Ϫ 5 10 23 24 Ϫ 2 24 Y 7 10 U E 15 16 W 7 16 Ϫ 4 10 Ϫ 3 16 Ϫ 5 16 6 10 Ϫ 5 10 E 11 16 H S 7 8 M 13 24 Ϫ 7 16 Ϫ 2 8 Ϫ 1 24 18 20 Ϫ 2 20 N 7 12 © McGraw-Hill School Division O A 13 16 U 13 15 Ϫ 3 12 Ϫ 4 16 Ϫ 4 15 11 12 Ϫ 6 12 1 10 5 8 1 4 1 3 3 10 7 8 5 12 3 5 2 5 1 16 3 8 4 5 9 16 3 4 1 2 1 8 Use with Grade 4. Chapter 12. find the letter that goes with each difference.5. (384) NS 1. To solve the riddle. pages 518–519. Write the letters on the lines below.1 . Lesson 2. 3. Her friends eat 7 pieces. She sells 9 of them. Michael fills 10 bowls with fruit salad. 3.1.4. What is the total amount of nuts in the recipe? 4. Nicole drinks 1 quart of orange juice 8 and 3 quart of water. Kerstin cuts a pie into a dozen Print This 12–3 Page P PRACTICE Reading Skill pieces. Lesson 3. How much butter does he use altogether? 5. Chapter 12. Mary makes a batch of 16 muffins. (385) MR 1. What part of the bowls is left? Use with Grade 4.1. 2.3. How much did 8 8. What part of the batch is left? 6. How many more cups 4 of raisins than nuts are needed? 3. How many pounds of meat does Nick buy? © McGraw-Hill School Division 7. Kevin uses 1 stick of butter for 8 one recipe and 5 stick of butter for 8 another recipe.2 . 3. Tell how you chose the operation. 2.Print This Page Name Problem Solving: Reading for Math Choose an Operation Solve. What part of the pie is left? 2. A recipe calls for 3 cup of raisins and 4 1 cup of nuts. A recipe calls for 3 cup of 8 macadamia nuts and 5 cup of 8 cashew nuts. 1. she drink in all? He serves 8 bowls to his guests. pages 520–521. Nick buys 3 pound of roast beef and 4 1 4 pound of ham. Lesson 3. Which statement is true? 6. pages 520–521. What do you have to do to solve 4. Her family eats 10 squares.1. B Find the total of two equal amounts. B The recipe uses 8 cup of beef broth. B There is a total of 16 squares of cake. 2. Which of the following can you use A The recipe uses more water than beef broth. C Ashley’s family eats 16 squares of cake.Print This Page Name Problem Solving: Reading for Math Choose an Operation Choose the correct answer.2 . (386) to solve the problem? F 16 ϩ 16 G 16 Ϫ 16 H 16 Ϫ 16 10 6 16 16 10 10 MR 1.4. A recipe calls for 8 cup of beef broth and 8 cup of water. Chapter 12. How much more provolone cheese than Swiss cheese does Ted buy? 3. What part of the cake is left? 5. How much more provolone cheese 3 this problem? A Find the difference between two amounts. Which of these statements is true? 3 1 Print This 12–3 Page P PRACTICE Math Skills Test Prep 2. C The recipe uses 8 cup of water 1 1 to solve the problem? F 8ϩ8 G 8Ϫ8 H 8ϫ8 1 3 1 3 1 3 1 Tim buys 4 pound of provolone cheese and 4 pound of Swiss cheese. C Find the total of two unequal amounts. 3. Which of the following can you use A There is a total of 10 squares of cake.1. Use with Grade 4. than Swiss cheese does Ted buy? F 1 pound G 4 pound H 2 pound 1 3 © McGraw-Hill School Division Ashley cuts a cake into 16 squares. How much liquid does it call for in all? 1.3. 2. 3. What part of the pie is left? 15. Amy buys 1 pound of turkey and 4 1 pound of honey-roasted ham. Patrick bought 4 pound of cookies. What is the total amount of nuts solve this problem? A addition B subtraction C multiplication Solve.4. He ate 1 pound of the cookies.1. Adela makes 20 cookies. (387) MR 1. How 4 much of the cookies is left? Use with Grade 4.2 . What part of the 20 cookies is left? 5 11. What operation would you use to 5 7 Print This 12–3 Page P PRACTICE Math Skills Test Prep 8. much meat did she buy altogether? She eats one slice. Chen buys 8 pound of American cheese and 7 pound of Swiss cheese. 3. What is the total amount of nuts she uses? 7. 7 9. pages 520–521. A recipe for custard uses 3 cup of milk. She gives amount of fruit he buys? 15 cookies to her friends.1.3. Chapter 12. Max buys 8 pound of apples and 3 pound of grapes. 3. What is the total 8 she uses? F 1 2 cups G 2 cup H 4 cup 1 1 1 10. How 4 many tablespoons of nutmeg and cocoa does she use altogether? © McGraw-Hill School Division 13. How much more milk 8 does the pudding use than the custard recipe? 3 16. Marge cuts a cherry pie into 8 slices. Kathryn uses 3 tablespoon of nutmeg 4 and 3 tablespoon of cocoa. Janell uses 8 cup of pine nuts and 8 cup of peanuts. 2. 8 How much more Swiss cheese than American cheese does he buy? 12. 2. How 4 14. Lesson 3. A recipe for pudding uses 7 cup 8 of milk.Print This Page Name Problem Solving: Reading for Math Choose an Operation Choose the correct answer. Lesson 4. Write each sum in simplest form.Print This Page Name Explore Adding Fractions with Unlike Denominators Add.5. 3 ϩ 3 ϩ 2 ϭ 5 10 23. 1 6 1 6 1 6 1 3 1 1 6 6 3. Chapter 12. 1 ϩ 1 ϭ 2 8 16. 1 ϩ 3 ϭ 10 5 21. 1 6 ϭ 1 4 111 888 111 888 4. 3 ϩ 1 ϭ 8 4 19. 1. (388) . 2 ϩ 1 ϭ 3 6 20. 1 1 1 10 10 10 111 10 10 10 3 10 1 4 1111 8888 1 2 4 8 1111 10 10 10 10 2 5 4 10 111111 888888 3 4 ϩ ϩ 3 8 3 8 ϩ ϩ ϩ ϩ 3 8 3 8 ϭ 3 10 ϭ 6 8 ϭ 7. 1 ϩ 5 ϭ 4 8 12. 1 ϩ 3 ϭ 5 10 14. 2 ϩ 7 ϭ 3 12 18. 5 ϩ 1 ϭ 12 4 © McGraw-Hill School Division 11. 7 ϩ 1 ϭ 9 3 9. 5. 2 ϩ 5 ϭ 3 6 17. 1 6 1 6 1 6 1 2 1 1 1 6 6 6 1 2 3 6 ϩ ϩ 1 2 1 4 1 4 ϩ ϩ 1 3 2 6 ϩ ϩ 1 4 ϭ 111 888 111 888 1 6 ϭ 1 5 1 5 6. 1 ϩ 2 ϭ 6 3 15. 1 2 1 1 4 4 1 2 2 4 Print This 12–4 Page P PRACTICE 1 4 1 4 2. pages 524–525. 3 ϩ 7 ϭ 4 8 1 22. 1 ϩ 1 ϩ 1 ϭ 3 2 4 NS 1. 3. 3 ϩ 5 ϭ 12 6 8. 1 ϩ 1 ϭ 3 12 13.1 Use with Grade 4. 2 ϩ 2 ϭ 3 9 10. 1 ϩ 1 ϩ 1 ϭ 8 4 2 24. 1 ϩ 1 ϭ 6 3 14. 3. 2 ϩ 2 ϭ 9 3 11. 1 ϩ 3 ϭ 10 5 13. 1 ϩ 1 ϭ 6 2 4. Add. 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 12 1 6 1 6 1 6 1 6 10 12 1 6 5 6 Add the twelfths. 5 ϩ 1 ϭ 8 4 15. (389) NS 1. Write each answer in simplest form. 3 4 9 12 ϩ 1 12 ϭ ϭ ϩ 1 12 is 5 6. 2 ϩ 1 ϭ 12 2 6. Lesson 4.1 . 3 ϩ 1 ϭ 8 2 12. pages 524–525. 1 ϩ 2 ϭ 6 3 3. 3 ϩ 2 ϭ 12 6 5. 1 ϩ 5 ϭ 2 12 10. Add 3 4 Print This 12–4 Page R RETEACH ϩ 1 12 .5. You may use fraction strips to help you. 2 ϩ 1 ϭ 3 9 Use with Grade 4.Print This Page Name Explore Adding Fractions with Unlike Denominators You can use fraction strips to find equivalent fractions before you add. 1 1 4 1 4 1 4 1 12 Compare fourths to twelfths: 9 12 is equivalent to 3 4. So. 3 ϩ 1 ϭ 4 8 8. Chapter 12. 1. 4 ϩ 1 ϭ 10 2 9. 3 ϩ 2 ϭ 5 10 2. 1 ϩ 1 ϭ 4 2 © McGraw-Hill School Division 7. 3. Lesson 4. 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 3. (390) NS 1. Each sum is in simplest form. 1 3 3 10 1 10 2 5 © McGraw-Hill School Division 3 8 1 12 1 8 1 3 1 6 1 3 3 4 1 4 11 8 3 4 1 2 1 2 2 3 1 2 1 4 3 4 3 8 3 4 11 2 1 1 4 3 4 1 5 8 Use with Grade 4. pages 524–525. Circle each addition sentence you find.Print This Page Name Explore Adding Fractions with Unlike Denominators Hidden Sentences The squares contain hidden addition sentences. 3 4 5 12 2 3 1 4 4. 1.5.1 . Chapter 12. Look from left to right and top to bottom to find the hidden addition sentences. 1 3 2 8 5 8 7 8 Print This 12–4 Page E ENRICH 2. . 1 ϩ 5 ϩ 1 ϭ 2 6 3 24. boarded the plane. 7 ϩ 1 ϭ 9 3 21.M. ϩ ϩ 2 3 1 2 3. 1 ϩ 5 ϭ 4 12 22. At 6:00 P. ϩ 1 2 3 5 10. ϩ 1 3 2 5 9. 1 ϩ 3 ϭ 4 8 17. 1 4 ϩ 12 2 27. ϩ 1 2 5 6 11. 3 ϩ 1 ϭ 10 2 15. Write Ͼ. 6 of the passengers 1 one day and 3 4 the next. 12 ϩ1 4 1 4 ϩ 2 3 1 6 1 26. 1 ϩ 2 ϭ 4 3 18. Your family ate 2 of a box of cereal 1 30. 1 ϩ 5 ϭ 6 12 16. 1. 1 ϩ 1 ϩ 3 ϭ 8 2 4 Algebra & Functions Compare. ϩ 3 5 7 10 13. ϩ 2 3 3 4 4.. Chapter 12. 3 5 ϩ 10 1 2 ϩ 1 2 1 4 1 3 © McGraw-Hill School Division 3 12 ϩ ϩ Problem Solving 29. ϩ 1 6 2 3 8.1 . Ͻ. Did you eat more or less than 1 box of cereal? Explain.5. 2 6 ϩ 6 4 28. pages 526–529. ϩ 1 5 2 15 6. (391) NS 1.M. What fraction of the passengers are on the plane? Use with Grade 4. 9 25. 1 4 1 8 Print This 12–5 Page P 1 6 1 4 PRACTICE 2. 3 ϩ 3 ϭ 4 8 20. At 6:10 P. Write each sum in simplest form. ϩ 1 2 7 8 12. or ϭ. Lesson 5. ϩ 7. 2 3 of the passengers boarded. 1 ϩ 1 ϭ 2 4 14. ϩ 5 6 1 3 5. 10 ϩ 3 ϭ 12 4 23. 2 ϩ 1 ϭ 5 3 19. 3.Print This Page Name Add Fractions with Unlike Denominators Add. 7 12 ϩ2 6 10. ϭ 5 6 Find each equivalent fraction. ϩ 1 3 1 6 11. (392) NS 1. 1 2 ϭ 6 ϩ3 4ϭ 8 7 ϩ 12 ϭ 12 2 ϩ 10 ϭ 10 ϩ1 3ϭ 6 5.Print This Page Name Add Fractions with Unlike Denominators You can use fraction strips to help you record the steps when you add unlike fractions. 7 8 ϭ 8. 6 10 ϭ 10 6. pages 526–529. ϩ 1 4 1 2 12. 5 12 ϩ1 4 Use with Grade 4. Use the common denominator.1 . ϩ 4 6 1 6 5 6 1 1 1 1 6 6 6 6 ϭ 4 6 2 3 4 6 ϩ ϩ 1 6 1 6 Write the answer in simplest form if necessary. 1. Then add.5. You may use fraction strips to help you add. Lesson 5. 3 4 ϭ 9 7. Using Pencil and Paper Find equivalent fractions. Add 2 3 Print This 12–5 Page R RETEACH ϩ1 6. 4 5 ϭ 10 4. 1 8 ϭ 8 2. 1 3 ϭ 12 3. 2 3 Using Fraction Strips 1 3 1 3 1 6 1 6 Add the numerators. Write the sum in simplest form. 9 10 ϭ ϩ1 5 ϭ 10 © McGraw-Hill School Division 2 ϩ1 6ϭ ϭ ϩ3 4 ϭ ϩ3 5 9. Chapter 12. 3. 1 4 9 11 1 16 7 11 6 11 7 16 1 8 3.Print This Page Name Add Fractions with Unlike Denominators Fraction Magic Squares In a magic square. What is the magic sum? 4. (393) NS 1. the sum of each row. The magic sum is 1 11 . 3. 4 1. Chapter 12. and diagonal is the same. Lesson 5. column. The magic sum is 15 16 . Complete each magic square. 8 11 Print This 12–5 Page E ENRICH 2.5. What is the magic sum? 1 6 1 2 3 5 1 3 7 18 1 9 2 5 1 5 © McGraw-Hill School Division 5. pages 526–529.1 . How did you find the magic sum in exercise 3? Use with Grade 4. How much does it cost to buy 2 sandwiches and 3 drinks? 1 3.95 for 5 pounds $0. What is the price for 1 pound of apples? water. 3. Drinks cost Print This 12–6 Page P PRACTICE 2. There are twice as many red pepper plants as green pepper plants.99. 5.1. 2. MS 1. Yogurt comes in a cup or a cone. or rainbow sprinkles.4. Health An ounce of cheddar cheese Strategy: 8. 1. (394) NS 1. and strawberry. There are 24 plants in a garden. 4 1 pound of turkey. Recipe A uses 2 cup of chicken broth 1 cup of water. Lesson 6. vanilla.2. Share it with others. Tracy buys 3 pound of roast beef. 1 pound of turkey. Sandwiches cost $4.2 . pages 530–531. Strategy: Use with Grade 4. Ken buys 4 pound of roast beef. Create a problem for which you has 114 calories. Use any strategy. and 3 pound of 2 8 ham. chocolate sprinkles. Who buys more meat? How much more does that person buy? Mixed Strategy Review Solve. Which recipe uses more liquid? 4. How many different choices are there? © McGraw-Hill School Division Strategy: 7.Print This Page Name Problem Solving: Strategy Solve a Simpler Problem Solve using a simpler problem. Recipe B uses and 4 1 1 3 cup of chicken broth and 3 cup of of apples. How many more calories does an ounce of cheddar cheese have than an ounce of brie cheese? could use a simpler problem to help you find the answer. 6.5. 1.95. and 3 pound of 2 8 1 ham. Chapter 12. An ounce of brie cheese has 95 calories. You can have no sprinkles. The Yogurt Cart has the following 3 There are 4 more tomato plants than red pepper plants. How many of each kind of plant is in the garden? flavors: chocolate. A customer pays $3. Chapter 12. 1. MS 1.2.2 . Lesson 6. (395) NS 1. per pound. Who spends more money? How much more? Step 1 Read Be sure you understand the problem. per pound.99 per pound. per pound.29 per pound.4. Read carefully. Problem 1 Print This 12–6 Page R RETEACH Josh buys a 5-pound watermelon at $0. Plan I I I © McGraw-Hill School Division I I I I I I I I I I 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 Use simpler numbers to make up a problem similar to the one you need to solve. pounds of watermelon at pounds of grapes at pounds of watermelon at pounds of grapes at per pound.5. Choose a strategy. Then solve the real problem the same way. pages 530–531. Use with Grade 4. What do you know? • Josh buys He also buys • Sabrina buys She also buys What do you need to find? • You need to find Step 2 Make a plan. 3.29 per pound and 3 pounds of grapes at $0.1.49 per pound and 2 pounds of grapes at $1. 2. Sabrina buys an 8-pound watermelon at $0.Print This Page Name Problem Solving: Strategy Solve a Simpler Problem Page 531. pages 530–531.10 Sabrina: watermelon: $0.29 ϭ $2. Does your answer make sense? Explain.97 $2.30 per lb 8 ϫ $0.09 per pounds.03 ϭ $0.30 per lb 2 ϫ $1.58 $2. (396) NS 1.5. © McGraw-Hill School Division Practice 1.1.00 ϭ $3. Josh: 5 lb ϫ $0. Chapter 12.29 Ϫ $5.40 $2.26 Step 4 Sabrina spends $0.58 ϭ $5.50 ϭ $2. Josh: watermelon: $0.50 per lb grapes: $1. Jane buys 3 pound of 8 1 cashew nuts.32 3 lb ϫ $0.49 ϭ $2. Who buys more nuts? How much more? Use with Grade 4.00 per lb 3 ϫ $1. MS 1. Kostas buys 8 pound of cashew nuts. 3.32 ϩ $2.99 ϭ $2.29 ϭ $2.4.60 ϭ $5. Lesson 6. 2 pound of walnuts. Which fruit does he spend more on? How much more? 7 2.45 2 lb ϫ $1. Robert buys 4 pounds of apples for $0.00 5 ϫ $0.Print This Page Name Problem Solving: Strategy Solve a Simpler Problem Step 3 Print This 12–6 Page R RETEACH Solve Carry out your plan.60 grapes: $1. 5 1 pound 8 pound of walnuts.50 ϩ $2.40 ϩ $3. 3 and 8 pound of peanuts. 2.97 ϭ $5.40 Now solve the real problem the same way.30 ϭ $2.29 $5.2 .89 per pounds and 3 pounds of grapes for $1.26 more. 1.50 $2.03 Sabrina: 8 lb ϫ $0.30 ϭ $2.45 ϩ $2.00 ϭ $5.2. Look Back Is the solution reasonable? Reread the problem. and 2 of peanuts. 4 5 Ϫ 10 ϭ 1 21. pages 532–533. Lesson 7. 3 4 Ϫ 3 ϭ 1 15. 1 2 Ϫ 10 ϭ 1 17. 1 4 11 88 2. 1 4 Ϫ 6 ϭ © McGraw-Hill School Division 1 8. Chapter 12.Print This Page Name Explore Subtracting Fractions with Unlike Denominators Subtract. 7 9 Ϫ 3 ϭ 5 12. 1 3 1 3 3. 1 4 Ϫ 12 ϭ 10. 1 2 Ϫ 8 ϭ 1 19. 1. 2 3 Ϫ 6 ϭ 1 20. 4 6 ϭ 6. 3. 1 2 111111 12 12 12 12 12 12 1 3 1 2 11 10 10 11 12 12 Ϫ 2 12 2 12 1 5 Ϫ 1 10 1 10 1 6 Ϫ 1 12 6 12 Ϫ ϭ 2 10 Ϫ ϭ 2 1 12 Ϫ 12 ϭ 1 7.5. 1 2 Ϫ 12 ϭ 3 16. 3 4 Ϫ 8 ϭ NS 1. 5 6 Ϫ 3 ϭ 1 14. (397) . 7 Ϫ 1 ϭ 12 3 2 11.1 Use with Grade 4. 1 2 1 1 1 6 6 6 Print This 12–7 Page P PRACTICE 1 1 1 1 6 6 6 6 1 2 1 4 2 8 Ϫ Ϫ 1 8 1 8 2 3 Ϫ Ϫ 1 5 1 6 1 6 1 2 Ϫ Ϫ 1 6 1 3 2 6 ϭ 5. Write each difference in simplest form. 12 Ϫ1 4 ϭ 1 13. 3 6 ϭ 4. 1 2 Ϫ 5 ϭ 1 9. 5 6 Ϫ 12 ϭ 3 18. 1 2 Ϫ 8 ϭ 1 10. 2 3 Ϫ 6 ϭ 5 18. 2 1. 1 2 Ϫ 10 ϭ © McGraw-Hill School Division 5 8. 4 5 Ϫ 10 ϭ 1 12. 5 6 Ϫ 12 ϭ 3 9. 10 Ϫ1 2 ϭ 1 6. 4 5 Ϫ 10 ϭ 5 15. Subtract 1 4 Print This 12–7 Page R RETEACH Ϫ1 8. 11 12 Ϫ 6 ϭ 7 16. 5 6 Ϫ 3 ϭ 3 7. Subtract the eighths. Write each difference in simplest form. 3 4 Ϫ 8 ϭ 3 14. 3 4 Ϫ 2 ϭ 4. 2 3 Ϫ 6 ϭ 1 11. Chapter 12. 7 Ϫ 1 ϭ 12 3 5 5. 1 4 ϭ1 8. 5 6 Ϫ 12 ϭ Use with Grade 4.1 . (398) NS 1. 2 8 Ϫ Ϫ 1 8 1 8 ϭ 1 8 So. 1 4 1 1 8 8 1 1 8 8 Compare fourths to eighths: 2 8 is equivalent to 1 4.5. Subtract. You may use fraction strips to help you. Lesson 7.Print This Page Name Explore Subtracting Fractions with Unlike Denominators You can use fraction strips to find equivalent fractions before you subtract fractions with unlike denominators. 10 Ϫ3 5 ϭ 1 17. pages 532–533. 1 5 Ϫ 10 ϭ 1 3. 3. 7 9 Ϫ 3 ϭ 5 13. 1 2 Ϫ 12 ϭ 1 2. pages 532–533.1 . 1 4 1 2 3 8 1 4 7 8 7 12 5 8 1 2 3 5 1 8 1 3 © McGraw-Hill School Division 5. 3. 5 12 1 2 1 4 1 12 5 6 2 3 3 4 Print This 12–7 Page E ENRICH 1 18 1 6 1 6 7 12 3. 1. Write the difference in simplest form in the outer circle. 1 12 7 12 5 9 5 6 2 3 1 3 1 2 2. 1 4 3 4 5 6 1 2 5 8 11 12 1 8 5 12 1 3 1 3 5 12 Use with Grade 4. Chapter 12. 1 2 2 3 7 12 1 6 1 3 1 2 1 6 6. 7 10 9 10 7 10 1 5 3 10 4 5 1 10 4. Lesson 7. (399) NS 1.5.Print This Page Name Explore Subtracting Fractions with Unlike Denominators Fraction Wheels Subtract the fraction in the center from each fraction in the inner circle. 5 ϭ2 9 Ϫ 9 Problem Solving 34. Ϫ 3 4 1 2 9. 5 ϭ2 6 Ϫ 3 2 30. He uses 6 2 3 yard.Print This Page Name Print This Subtract Fractions with Unlike Denominators P 12–8 Page PRACTICE Subtract.1 . 12 Ϫ1 6 ϭ 7 25. How much ribbon does Pam yard to make a kite. 1 2 Ϫ 6 ϭ 7 22. Joe has 5 yard of fabric. 1 2 Ϫ 5 ϭ Algebra & Functions Find each missing number. 1 2 Ϫ 4 ϭ 7 26. 7 10 Ϫ1 5 5. 5 8 Ϫ 4 ϭ 7 16. 4 5 Ϫ 10 ϭ 1 19. (400) NS 1. 1. Write each difference in simplest form. 12 Ϫ1 2 ϭ 1 14. Ϫ 1 5 2 15 4. 1 28. 1 4 Ϫ 12 ϭ 3 18. She uses 8 1 2 35. 1 ϭ1 2 Ϫ 3 1 32. Ϫ 3 4 1 8 1 13. 7 8 Ϫ 2 ϭ © McGraw-Hill School Division 8 1 29. Lesson 8. Pam has 7 yard of ribbon. 7 9 Ϫ 3 ϭ 5 24. 9 10 Ϫ3 5 8. Ϫ 3 5 3 10 10. 4 9 Ϫ 3 ϭ 1 20. Chapter 12. Ϫ 5 6 2 3 7. Ϫ Ϫ 3 4 5 12 3. 11 12 Ϫ5 6 6. 2 3 Ϫ 6 ϭ 2 1 33. 3. 2 3 Ϫ 12 ϭ 1 27. 1 3 1 12 2. 2 3 Ϫ 6 ϭ 1 17. 10 Ϫ2 5 ϭ 1 15. 3 8 Ϫ 4 ϭ 1 23. 3 4 Ϫ 12 ϭ 3 1 31. Ϫ 5 9 1 3 11. 4 5 Ϫ 10 ϭ 1 21.5. pages 534–537. Ϫ 2 3 2 9 12. How much have left? fabric does Joe have left? Use with Grade 4. 7 10 2 5 Using Fraction Strips 1111111 10 10 10 10 10 10 10 1 1 5 5 1111 10 10 10 10 1111111 10 10 10 10 10 10 10 7 10 7 10 ϭ 7 10 Subtract the numerators. 7 9 ϭ 8. Ϫ 4 5 1 2 Use with Grade 4. 7 12 ϭ 12 3. 1. 1 2 ϭ 8 4. 4 5 ϭ 10 ϭ 10 6. 2 3 ϭ Ϫ 3 10 2 Ϫ1 6ϭ ϭ Ϫ1 3 4 ϭ Ϫ 12 9. Lesson 8. Write the difference in simplest form. 3 4 ϭ 9 7. 4 Ϫ 10 3 10 ϭ 4 10 Ϫ Ϫ 2 5 4 10 Write the answer in simplest form if necessary.1 . You may use fraction strips to help you subtract. Chapter 12.5. Ϫ 1 2 1 5 10. ϭ 3 10 Find each equivalent fraction. (401) NS 1.Print This Page Name Print This Subtract Fractions with Unlike Denominators R 12–8 Page RETEACH You can use fraction strips to help you record the steps when you subtract unlike fractions. 7 8 ϭ 8 2. Then subtract. 3. 6 10 Ϫ1 5 12. pages 534–537. 2 3 ϭ 6 Ϫ3 4ϭ 8 Ϫ2 6 ϭ 12 Ϫ1 8ϭ 8 Ϫ1 6ϭ 6 © McGraw-Hill School Division 5. Ϫ 1 2 1 3 11. Subtract 7 10 Ϫ2 5. Use the common 7 10 denominator. Using Pencil and Paper Find equivalent fractions. The other player takes a turn. in simplest form. Mix them up. If there is no match. Then arrange the cards in 4 rows of 6 cards each. 3 4 Ϫ 1 8 5 8 • Place the 24 cards facedown. You should have 24 cards. Also write each difference. • Continue taking turns until all the cards have been matched. pages 534–537. Chapter 12. © McGraw-Hill School Division Use with Grade 4.5. Write each subtraction sentence on a separate index card. If a player turns over a subtraction sentence and its matching difference. the player turns over both cards. Lesson 8. then he or she keeps the cards and takes another turn. • Take turns turning over two cards. 3. on a separate index card. (402) NS 1. The player with more pairs of cards wins.Print This Page Name Print This Subtract Fractions with Unlike Denominators E 12–8 Page ENRICH Fraction Memory Game How good is your memory? Play this memory game with a partner.1 . • Make up 12 subtraction sentences with unlike denominators on cards like the sample below. 3. Then use the property to write a different number sentence. 2 ϩ 3 ϭ 5 10 14.2. 10 ϩ 17 ϭ 17 ϩ 5 3 4 ϩ (4 7 ϩ 9) ϭ (4 ϩ 7) ϩ 5 9 4. AF 1. ϩ0ϭ ϭ 2 3 1 2 5.1. 3 ϩ 1 ϭ 8 2 Associative Commutative Use with Grade 4. 1 ϩ ( 1 3 ϩ 4) ϭ 2 Commutative Associative 13.Print This Page Name Properties of Fractions Use properties to find each missing number. MR 1. 7 1. 8 9 ϩ ϩ 8 9 ϭ 3 5 ϩ 1 3 1 2 4 8. 1 ϩ ( 1 ϩ 1 ) ϭ 12 6 2 16.1. 1. 9. (403) NS 1. 7. ( 1 2 ϩ 3) ϩ 4 ϭ 2 ϩ ( ϩ1 4) 3 4 4 3. 1 ϩ 3 ϭ 4 8 1 10.5. ( 4 5 ϩ 2) ϩ 3 ϭ 5 ϩ ( ϩ2 3) Add.3 . 2 ϩ 1 ϭ 9 3 1 12. pages 538–539. Lesson 9. 10 ϩ Print This 12–9 Page P PRACTICE ϭ 7 10 1 1 1 2. 1 ϩ ( 1 3 ϩ 2) ϭ 3 Commutative Associative 11. Chapter 12. 1 ϩ 2 ϭ 4 3 Identity © McGraw-Hill School Division Identity 15. 1 3 ϩ 6. Ϫ0ϭ 9 10 ϭ ϩ 1 1 2 10.2.Print This Page Name Properties of Fractions You can use the Commutative.3 . 12 ϩ ϭ ϭ 4 7 3 4 1 1 1 6. Commutative Property The order of the addends does not change the sum. Chapter 12. AF 1. 3 ϩ 1 ϭ 8 2 Associative Commutative 3. 3. 1. ( 2 5 ϩ 2) ϩ 3 ϭ 5 ϩ ( ϩ1 3) Use with Grade 4. 5. and Associative properties to help you add fractions. pages 538–539. 1 8 ϩ 3 9. Identity. 1 4 1 4 1 4 1 8 1 8 1 8 1 8 1 8 Print This 12–9 Page R RETEACH 1 4 1 4 1 4 11 11 11 88 88 88 3 4 11 11 11 88 88 88 ϩ 1 8 = 7 8 ϩ 3 4 = 7 8 Identity Property The sum of 0 and any fraction is that fraction. 1 ϩ ( 1 4 ϩ 2) ϭ 8 2.5. 4 7 ϩ 7. ( 1 3 ϩ 6 ) ϩ 12 ϭ Identity © McGraw-Hill School Division Associative Use the properties to find each missing number. (3 ϩ 1) ϩ 8 8 4 8 ϩ0ϭ 4 5 ϭ 3 8 ϩ (1 ϩ 4) ϭ 1 8 8 Add.1. MR 1.1. 4 5 Associative Property The way you group the fraction addends does not change the sum. 1 1. Lesson 9. Then use the property to write a different number sentence. ( 1 3 ϩ 6) ϩ 2 ϭ 3 ϩ ( ϩ1 2) ϩ 1 2 1 8 3 12 8. 3 ϩ 3 ϭ 5 10 1 3 4. (404) NS 1. 3 g g x x Use with Grade 4. ( b ϩ d ) ϩ f ϭ b ϩ ( d ϩ f ) 3.5. MR 1. Then write a fraction as an example for each property in each clue. pages 538–539. (405) . 2 A 3 A 4 C S S O I D V E N T I T Y 6 S O C S M I 1 C O M M U T A T C I A T I V E Across © McGraw-Hill School Division 5 I U T A T I V E T I V E D E N T I T Y 1. AF 1. s ϩ ( u ϩ w ) ϭ ( s ϩ u ) ϩ w 4. Write it in proper place in the crossword puzzle. h ϩ 0 ϭ h a c t e a c e r v r t v m o o m 6.1. b ϩ d ϭ d ϩ b a c c a Down 2. 3.Print This Page Name Properties of Fractions Crossword Property Puzzle Print This 12–9 Page E ENRICH Identify the property in each clue.2. 1. y ϩ 0 ϭ y NS 1.1. Lesson 9. n ϩ p ϭ p ϩ n 5. Chapter 12. pages 540–541.1. Lesson 10. NS 1. Add Other Juices to This Juice Orange Juice Pineapple Juice Grapefruit Juice Cranberry Juice Grape Juice Apple Juice Mixed Berry Juice Mixed Citrus Juice 12–10 Part A WORKSHEET Decision Making Print This Page Possible Combinations and Total Amounts of Juice Your Decision © McGraw-Hill School Division What combinations of juices can Joseph and his sisters use to make exactly one quart of fruit punch? Use with Grade 4. 3.1 . Chapter 12. 3. 2.1. (406) MR 1.Print This Page Name Problem Solving: Application Analyze and Make Decisions Record your data.3.5. 2 .3. Material Balloon Observations 12–10 Part B WORKSHEET Math & Science Print This Page Cubes Crayons Sock Hand 1. Chapter 12. Wear goggles in case the balloon bursts.1.Print This Page Name Problem Solving: Application Which objects can hold a static charge? Safety Be careful when working with scissors. Record your observations. What happened to the string when a charged object came near it? © McGraw-Hill School Division 2. 2. pages 542–543. 3. Which objects held a static charge? How do you know? Use with Grade 4.1. Lesson 10. 3. (407) MR 1. 2.3.1. What fraction of the objects held a static charge? Construct a circle graph to 4. Explain the results of the activity in terms of static electricity.1. Use with Grade 4.2 . What fraction of all the objects in the world do you think hold a static charge? Think about how the objects you used represent all things in the world. Chapter 12. 3. 3. pages 542–543. Lesson 10.Print This Page Name Problem Solving: Application Which objects can hold a static charge? display your results. © McGraw-Hill School Division 5. 12–10 Part B WORKSHEET Math & Science Print This Page 3. (408) MR 1. 100 18. Chapter 13. 20 32. 100 19.6 27 4 21. 9. 10 70 14. (409) . 3. 1. Write each as a decimal. 10 27. 6. 11. 2 30. 5 NS 1. © McGraw-Hill School Division 13. 100 26. 50 10 1 66 5 78 15. 2. 12. 7. 10 29. 100 28.Print This Page Name Explore Fractions and Decimals Write a fraction and a decimal for each shaded part. 10 25. Then write the fraction in simplest form. 10 22. Print This 13–1 Page P PRACTICE 5. 100 23. 100 8 17. Lesson 1. 100 24. 4 3 10 7 1 13 16. pages 558–559. 25 31. 100 20. 10. 4. 5 4 4 3 90 5 2 Use with Grade 4. 8. You can shade the model to 1 1 show 100 . You can write 10 as a decimal: 0.04 7 10 7 100 0.4 0. Chapter 13.Print This Page Name Explore Fractions and Decimals You can use models to show decimals.08 Look at each model. Look at each model. 1. 4. pages 558–559. You can write 100 as a decimal: 0. 0.52 8 10 8 100 0. Lesson 1.7 0. 7. Use with Grade 4. Print This 13–1 Page R RETEACH This model shows 1. 4 10 4 100 2. 8. © McGraw-Hill School Division 6. Circle the fraction and the decimal for the shaded part.01.1. 5. This model shows 1 divided into 100 equal parts. You can shade the model to 1 1 show 10 .8 0. This model shows 1 divided into 10 equal parts.07 52 100 5 10 0. Write a decimal for each shaded part. 3. (410) NS 1.5 0.6 . Write the fractions in the left-hand column above as decimals. 0.17 12. Write the number of the exercise on the blank.8 To solve the riddle below. write the letters above the numbers. 0. 0.22 10. 10 6. Write the decimals in the left-hand column above as fractions. (411) NS 1.6 . Lesson 1.5 3. 0. Chapter 13. pages 558–559. 100 4. What kind of coat can be put on only when wet? © McGraw-Hill School Division A 7 8 1 9 6 10 5 3 11 2 4 12 13. 0. 100 8. 10 2. The first one is done for you. Use with Grade 4.Print This Page Name Explore Fractions and Decimals Riddle Fun Match each of the ten fractions and decimals below with its word name at the right.89 11 7.03 9. 0. 1. 0. 14. 90 100 2 63 7 Print This 13–1 Page E ENRICH C three hundredths A eleven hundredths O ninety-nine hundredths I five tenths A twenty-two hundredths T eight tenths P sixty-three hundredths T eighty-nine hundredths N ninety hundredths O seven tenths F two tenths A seventeen hundredths 5.99 11. Write the number in words. 5. ninety-nine hundredths 1 2 6. 4. (412) NS 1.6. 1 2. 5 9. 10 1 7 7. six hundredths 17.7 . seventeen hundredths 20. 2. three tenths 18. or 1. A 23. C Problem Solving 25. Chapter 13. 100 12. B 24. Write the number as a decimal. 100 2 1 8.Print This Page Name Tenths and Hundredths Write a fraction and a decimal for each part that is shaded. Use with Grade 4. Print This 13–2 Page P PRACTICE Write each as a decimal. fifteen hundredths 16. Lesson 2. D C D 1 21. 1. 100 96 7 14. Lora walks for five tenths of an hour. 1. 10 10. 4 11. A 0 © McGraw-Hill School Division B 1 2 22. 26. two tenths 15. Peter’s house is 0. two tenths Write a fraction and a decimal for each point.78 mile from school. 2 13. Then write the fraction in simple form. pages 560–561. five tenths 19. 3. Tell if it is close to 0. pages 560–561. Then write the fraction in simplest form. 8. Use with Grade 4. 7.6. 1. A model and a place-value chart can also help you write a fraction for a decimal. Lesson 2. Using Models Using Paper and Pencil Ones 0 Think: 5 10 • Print This 13–2 Page R RETEACH Tenths 5 5 10 Hundredths ϭ1 2 Think: 0.7 . © McGraw-Hill School Division 5. 4.Print This Page Name Tenths and Hundredths You can use a model and a place-value chart to read and write decimals. Chapter 13. 3.5 ϭ Ones 0 • ϭ1 2 Hundredths 0 ϭ 6 10 Tenths 6 6 100 Think: 0. 6. (413) NS 1. 1. 2.60 ϭ Think: 60 100 ϭ3 5 ϭ 6 10 ϭ3 5 Write a fraction and a decimal for each shaded part. 3. 0.45.6.5 D. 1.45 (1) (2) C. pages 560–561.4’ .5" B.9 (1) 0.95 (1) 0. © McGraw-Hill School Division 7.4 (1) 0. 6. Here are some examples of different ways to show 0.7 .78 (1) 0.6 (1) 0. 9. D 0. (414) NS 1.61 (1) 0. A. Write the decimals using each of the notations shown above.5 (1) (2) (2) (2) (2) 0. 0. 8.4 . Use with Grade 4. A B C (1) 1. 5. Which notation is most like the one we use today? Which notation did you find the most difficult to use? Explain. Chapter 13. Lesson 2.Print This Page Name Tenths and Hundredths Decimal History Other symbols for decimals were used in England and Europe before the eighteenth century. Print This 13–2 Page E ENRICH 0|45 0. 4.67 2. seventy-two thousandths 18. Joe weighs 0. Chapter 13. 1. 1. (415) NS 1.6 millimeters 6 0.000 24 11.000 225 7.000 999 15. 1.Print This Page Name Thousandths Write each as a decimal. four thousandths 28. Write this as a decimal. © McGraw-Hill School Division meters decimeters 0.000 370 3. 1.6 .000 60 17. pages 562–563. 1.000 36 8.009 14 Problem Solving 30. 1. nine thousandths 21.000 4 5. Jaime bats three hundred one this in words. 1. six hundred ninety thousandths 24.06 centimeters 0. 1. 1. 1. 1. five hundred thousandths 23. twenty-five thousandths 20. thousandths for the season.000 3 12. 1. two thousandths 26.000 123 Print This 13–3 Page P PRACTICE 2.000 17 6. 6 1. 1.000 25 4.000 9 16. ninety-five thousandths 25. 1. Lesson 3. three hundred twenty-nine thousandths 22.000 120 14. Use with Grade 4. 1. Write 31. 29.625 g of rice.000 10. one hundred ninety-nine thousandths Algebra & Functions Complete. sixteen thousandths 19.000 12 13.000 1 9. eleven thousandths 27. 1. 513 Using Paper and Pencil Ones • Tenths Hundredths Thousandths Ones • Tenths Hundredths Thousandths 0 Think: 7 1. Think: 7 1. 4. © McGraw-Hill School Division 3. (416) NS 1. Lesson 3.000 ϭ 0.007 0 7 0 Think: 513 1.000 The first decimal square is divided into hundredths. 2. The second decimal square shows thousandths. The second decimal square shows thousandths. 1. pages 562–563. Think of dividing each hundredth into 10 equal parts.000 0 ϭ 0.Print This Page Name Thousandths You can use models and a place-value chart to read and write decimals. Chapter 13. Using Models Print This 13–3 Page R RETEACH The first decimal square is divided into hundredths.007 = 0.000 5 ϭ 0. Think of dividing each hundredth into 10 equal parts.513 1 3 Write each as a decimal and a fraction. Use with Grade 4. Think: 513 1.6 . 000 600 1.5 0.01 0. Lesson 3.850 Use with Grade 4. pages 562–563. Print This 13–3 Page E ENRICH 0.000 255 1. • The first player turns over two cards.005 0. If the cards show an equivalent fraction and decimal.000 0. Chapter 13.8 0.000 10 1. • Players take turns until all the cards have been matched. • The player with more cards wins.7 0.35 0.255 0. he or she keeps the cards.85 0. • Try to remember which fractions and decimals have been turned over.3 0.345 0.2 0.25 0. • Cut out the cards below.40 0. Mix them up and place them facedown in six rows of six. the cards are turned over again and left in the same position.000 345 1.75 0. (417) NS 1.50 © McGraw-Hill School Division 35 100 85 100 1 4 3 4 2 5 1 2 5 1.9 1 2 3 10 1 5 7 10 4 5 9 10 0.Print This Page Name Thousandths Decimal Memory Game Play this memory game with a partner.6 .000 850 1. If the cards do not match.600 0. 75 Answer: 4 3.4. MR 1. Lesson 4.1. A survey question asked bus riders how often they took the bus. A survey question asked people how they got to work most often. 4 said fewer than 5 times per week. Which answer got the greater number of responses? fraction 1 4 decimal ϭ ϭ 0.7 of the time.3 said bus and 10 said subway. Write both numbers in that form. Of 1 said 5 or more times per week and 0.Print This Page Name Problem Solving: Reading for Math Choose a Representation Circle the word fraction or decimal to tell how you will represent the numbers in the problem.2 . 2. Lauren takes the © McGraw-Hill School Division subway to work 0. (418) NS 1.3 ϭ Answer: 2.75 those who answered. Who takes the subway to work the greater part of the time? fraction 4 5 decimal ϭ ϭ 0.7 Answer: Use with Grade 4. Ashley takes the subway to work 5 of the time. Do more Print This 13–4 Page P PRACTICE Reading Skill riders take the bus or the subway? fraction ϭ 4 10 decimal 0. 4 Of those who answered. pages 564–565. Chapter 13. 3. 1. Then compare the data to solve the problem. 0.2. C Subtract 10 Ϫ 7.5 of the people surveyed ride the subway? 1.4.8 Ͼ 0. Max says he takes the subway a greater part of the time than Tonya does.7. © McGraw-Hill School Division because F 10 ϭ 0. and compare it to 0.4. Which statement is true? 6.75. and 4 ϭ 0.7 ϭ 10 . 10 1 1 1 1 1 Tonya takes the subway 8 out of 10 days. Chapter 13. Is it reasonable to say that 0. and 10 ϭ 0. and 2 ϭ 0.4. G 10 ϭ 0.1. G 1 Ϫ 2 ϭ 2 . The statement is not reasonable A Ten out of 40 people say they never walk to work. (419) because F 40 ϭ 4 . F 10 Ͻ 20.2 . Which of the following plans can 4. G 1 Ϫ 4 ϭ 4 . 10 out of 40 people say they never walk to work.5. Which statement is true? Print This 13–4 Page P PRACTICE Math Skills Test Prep 2. B Write a fraction for 0. Use with Grade 4.7 and 2 compare it to 10 .5. Is it reasonable to say that 0.7. H 0. 10 4 4 1 3 3 10 1 1 NS 1. H 20 ϭ 2 .4 of the people never walk to work? 5. and 0. and 10 Ͼ 10 . H 40 ϭ 10 . C Thirty out of 40 people say they never walk to work. MR 1.2. 2. 3. Is his statement reasonable? 3. B Ten out of 20 people say they ride the subway at least once a week. not 0. The statement is reasonable because A Twenty people say they ride the subway at least once a week. Max’s statement is not reasonable help you solve this problem? A Write a decimal for 10 . Max takes the subway 0. B Four out of 10 people never walk to work. and 2 ϭ 0.7.25.4. Lesson 4. In a survey. and 4 ϭ 0. 7 7 8 8 8 8 In a survey.7 of the time. C Ten percent of the people ride the subway at least once a week.8. not 0. pages 564–565.Print This Page Name Problem Solving: Reading for Math Choose a Representation Choose the correct answer. 10 out of 20 people say they ride the subway at least once a week. 1 said the train was faster.5 of the people who © McGraw-Hill School Division answer say that they are very satisfied with subway service.4 of the 1 time. 0. 0. G Write a fraction for 0.1 said the bus. 1 1 days.1 said the bus was faster. Who takes the bus more days? [HINT: June has 30 days. Which statement is true? Print This 13–4 Page P PRACTICE Math Skills Test Prep 8. Who walks to work a greater part of the time? 10. A reporter says that the express 2 bus is late 10 of the time. Train Y is on time or early 2 of the time. Solve. the train or the bus.] 13. 2. Of the people surveyed.2 of the days. 3.9 of those days. George walks to work 6 out of 10 help you solve this problem? F Write a decimal for 4 . Is his statement reasonable? time. Janice walks to work 0. the train or the bus? 7. MR 1. Which answer got more responses. pages 564–565.Print This Page Name Problem Solving: Reading for Math Choose a Representation Choose the correct answer. Train Q is on time or early 0. and compare it to 0. A survey question asks people which is faster. In a survey. and write it as a decimal. H Subtract 4 from 1. Rita takes the bus 10 of the days in June. Which of the following plans can A Of the people surveyed. Are more people very satisfied or somewhat satisfied? 12. 0. The rest of the people said that neither was faster. Alfredo walks to work 15 out of 20 14. C Of the people surveyed. 1 4 said neither was faster. Four tenths of the people say that they are somewhat satisfied. Chapter 13. Which train is on time or early a lesser part of time? 11. Is the reporter’s statement reasonable? Use with Grade 4. The express bus is late 0.1. 9.4. 3 4 said the train and 0. Colleen takes the bus 18 of the days 7 in June. He says he walks to work 0.2.2 . B Of the people surveyed. (420) NS 1.1.7 of 10 days. Lesson 4.1 and 3 compare it to 4 . Lesson 5. 6 100 6 21.000 60 24. 11 100 1 26. 27 100 21 15. Write as a decimal. 9 100 19 27.000 5 11.000 5 18. seven and seventy hundredths Problem Solving 30. 11 100 3 20. 76 1. What decimal shows the number of red backpacks? Use with Grade 4. 3. Out of 100 pairs of shoes in a sporting 31.000 375 22.000 16 16. 2. 19 1. Out of 1. 18 100 98 17. 9 100 5 7.000 125 8. 4. 25 1. 9 10 1 13. (421) NS 1. pages 568–569. 8 1. 24 100 © McGraw-Hill School Division 4 25. eight and three tenths 29.Print This Page Name Decimals Greater Than 1 1. 2 10 9 14. 10 1. 23 10 8 23. What decimal shows the number of running shoes? and the rest are green. 53 are running shoes. 1 100 25 6. 6 100 2 9.000 12 19.000 backpacks. 13 1.000 37 12.6 . 3 1. Print This 13–5 Page P PRACTICE Write as a mixed number in simplest form and a decimal to tell how much is shaded. 8 1. Chapter 13. 7 10 3 5. 17 10 7 10. 6 100 26 28. 25 are red goods store. Mixed Number: 1 10 Decimal: 1. Chapter 13. 1 9 10 6. 1. 5. 4. © McGraw-Hill School Division Write a decimal and the word name. 3. Write a mixed number and a decimal to tell how much is shaded. 3 5 100 Use with Grade 4. 2.6 .36 Read: two and thirty-six hundredths Look at each model. (422) NS 1.7 Read: one and seven tenths 7 Print This 13–5 Page R RETEACH 36 Mixed Number: 2 100 Decimal: 2. You can use models to help you write mixed numbers as decimals. pages 568–569.Print This Page Name Decimals Greater Than 1 A mixed number is made up of a whole and a part of a whole. Lesson 5. 3 7 13. 36 10 8 28 tenths 15. 1. fifteen and eight 9 6. 5 11. 2. 5 9. 12 10 six tenths 20. . eleven and 3. 7. 1 2 14. 7 8 . 6 3 Down 20. . 5. Chapter 13. 3 4 7 . two and thirty. Each decimal point has a space of its own. 7 . 1 9 6 9 . 2 . 43 6 100 51 37 48 12.five 8 3. 4 3 4 . 8 0 . 4. ninety-nine and sixty- hundredths three hundredths NS 1. 15. 27 9. 21. 6 100 37 15. 53 100 2. . 12. 3 100 7 11. 8 3 5 16. 9 8. 2 1 1 . 57 100 10. thirty-five hundredths 13. 3 3 19. 7 9 Across 1. 5 3 10 5 8. 0 5 7 3 6 . 2 7 . pages 568–569. 4 8 . 3 100 1. 10. 1 5 .6 Use with Grade 4. thirty-three and 7. 3 3 . 6 . 44 10 and twenty-one hundredths 19. seventy-eight and seven tenths 16. 3. 5 3 . 7 17. Write the decimal for the fraction or word name given in the ACROSS and DOWN clues below. 38 100 75 seventy-nine hundredths 21. 6 5 10 28 17.Print This Page Name Decimals Greater Than 1 Decimal Crossword Print This 13–5 Page E ENRICH Complete the decimal crossword puzzle. seven and nineteen 14. 18. 37 10 © McGraw-Hill School Division 18. Lesson 5. 2 8 6 . 80 100 5. 34 100 4. 6. . (423) . . 8 2 . 1 0. 2. 1. On Tuesday he ran 100 meters in 10.12 29. 2. 9. 7.10 22.02. 1.78. 0.87 26. 2.6 km long.99 © McGraw-Hill School Division 35. 11.2 4.78 1.01 0.9 seconds. 10. 7.06 km long. Lesson 6.99 23. 1. 16.001 32.02. 16. 1. Chapter 13. 5.6 19. 12.2.75 17.16.17 34.87 12. 31.22.44 22.2 seconds. 1.88.1 Problem Solving 37. 6. 16. 11.06.16 12.106 9. 0.54 15. 25. 1.9 24.1 12. 11. 1.22 28. pages 570–573.11 20. On Monday Ken ran 100 meters in 38.99. 16.07 30.117 9. 1. 1. 0. Jadwin Bridge is 1.70 5.160 10. 2. 9.99 11.99 36.06 9.09 10. 11. 1. 0. 0.111 Write in order from least to greatest.7 0.2 0. 8. 18.17. 9. 1. 10.1 8.01 16.99.13 18. (424) NS 1.7. On which day did Ken run faster? Seely Bridge is 1.011. 0.12 33.03 14.107 5.99 5.7.1 18.07. Ͻ. 1. 9. 0. 10. 1. 0. 0.3 16.0 18. or ϭ. 6. 10.11.9 .08. 6.11 16.9.6. 14.6.8. 1. 9. 19. 16. Write Ͼ. 2.001.160 6.02 2. Which bridge is longer? Use with Grade 4.1 1.16 10. 21. Print This 13–6 Page P PRACTICE 0.9 3.12 21.1 10. 14.22 Write in order from greatest to least.06 13.99 13. 1. 1.57 14.98 27. 9. 0. 5.11 2.Print This Page Name Compare and Order Decimals Compare.1.5 7.01.21.300 9.08.61. 68. or ϭ. 0. 1. 1. Chapter 13.75 0.7.75 Ͻ 3.68.9 Use with Grade 4.77 0.7 0. 0.03 0. 7. 5.75 Ͻ 3.68 2. 0.29 0.66 0.33 0.68.7 9. Print This 13–6 Page R RETEACH 3.29.66.24 0.60 4. 0.68. Order the numbers from least to greatest. Lesson 6.77. 0. 0. The order from least to greatest is 2.2.63 Ͻ 3.03.30 NS 1.24 8. 0. 2. 1. 0.30 Write the decimals in order from least to greatest.63 and 3. © McGraw-Hill School Division 0. 0.06 0. 1. 0. 3.33. Write Ͼ.60 10.75.75 Order the decimals. Since 2 Ͻ 3. 0.75 Ͻ 3. (425) . Ͻ. pages 570–573. Since 63 100 68 Ͻ 100 .Print This Page Name Compare and Order Decimals You can use models to compare and order decimals. 0. 2. Compare.63 Ͻ 3. 3. 3.06.25 0. Think: 2. 6.25.63 Compare the decimals.6. 0.63 Ͻ 3. 35.7. It is greater than 10.79 8.84 8.6. pages 570–573. It is less than 8. It is greater than 10. Explain how you found the answer to Puzzle 3. Arrange the decimals in the box in order from least to greatest.1. Puzzle 8 The decimal is less than 10. It is less than 0.5. It is greater than 10. Use with Grade 4. Puzzle 6 The decimal is greater than 10. © McGraw-Hill School Division 1.02.89 10.30. 2. Print This 13–6 Page E ENRICH 10. It is less than 8. 1.9. (426) NS 1.85.08 0. 1.33 10.25 8.8.85.43 10. Puzzle 9 The decimal is greater than 8.2. It is less than 10.85 Puzzle 2 The decimal is less than 10. 1.4.8 Puzzle 1 The decimal is greater than 0.9 .75. It is less than 0.01 0. Lesson 6.Print This Page Name Compare and Order Decimals Puzzles Choose the decimal from the box that solves each puzzle. Puzzle 3 The decimal is greater than 8. Use a decimal only once. Puzzle 5 The decimal is greater than 0. It is less than 8.07. Puzzle 4 The decimal is less than 10. Puzzle 7 The decimal is greater than 8.25. Chapter 13. He the storeroom.Print This Page Name Problem Solving: Strategy Draw a Diagram Draw a diagram to solve. What was the population of Amarillo? Strategy: Strategy: © McGraw-Hill School Division 7.8 miles north of Hightown.4 miles west of the school. East Ridge is 1. tickets. (427) NS 1. MR 1.9 miles north of Bay school. How many floors away is the cafeteria from Ed’s office? goes north 9 blocks. which tables should be used? How many of these tables will be needed? solve by drawing a diagram. Abilene. East Ridge is 2. Create a problem which you could City Hall. William lives 1.8 miles east of the Print This 13–7 Page P PRACTICE 2. or upper deck. A cab driver leaves his garage. 2. He walks down 6 floors to the cafeteria. Strategy: Use with Grade 4. Lesson 7. Social Studies In 1996. Amarillo. You can buy an individual seat or a pair of seats. or single game tickets. and north 8 blocks.3. There are 48 people at a dinner at 8. Texas has a population that was 83.9 miles east of William. How many choices do you have? Texas. Use any strategy. Is William closer to CD World or to Sound City? Edge. middle deck.4. 2. 1. 20-game tickets.3 miles south of Silver Hills. 3. Chapter 13.2 .2. Sound City is 2. The City Sports Center offers season 6.1. How far is Bay Edge from Hightown? 3. Ed walks up 2 floors from his office to 4.130. To have full tables. Silver Hills is 3. had a population of 122. CD World is 1. pages 574–575.885 greater than the population of Abilene. How many blocks is he from his garage? Mixed Strategy Review Solve. 5. You want to use small tables that seat 5 people and large tables that seat 8 people. Share it with others. Seats are available for the lower deck. south 6 blocks. show the distance between Bergen Mall and Loews Mall.Print This Page Name Problem Solving: Strategy Draw a Diagram Page 575. Plan I I I I I I I I I I I I 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. What do you know? • Loews Mall is • Bergen Mall is • King’s Mall is What do you need to find? • You need to find . Use your drawing to solve the problem. 2. Along that line.2 . 2. Which mall is the closest to Kendra’s town? the farthest from her town? Step 1 Be sure you understand the problem.1. 3. Choose a strategy. Read miles east of Kendra’s town. Then show the distance between Bergen Mall and King’s Mall.3. pages 574–575.4.9 miles east of her town. The Loews Mall is 3. Extend the line in either direction if you need to.9 miles east of Bergen Mall. King’s Mall is 2. (428) NS 1. Draw a line segment to show the distance between Kendra’s town and Loews Mall. Step 2 Make a plan. Lesson 7. Read carefully.2. © McGraw-Hill School Division Use with Grade 4.8 miles west of the Loews Mall. Problem 1 Print This 13–7 Page R RETEACH Kendra wants to go to a mall. MR 1. The Bergen Mall is 1. miles west of the Loews Mall. miles east of Bergen Mall. Chapter 12. 9 cm 1. How many floors away is Randi’s office from Norma’s? Use with Grade 4. (429) NS 1.3.7 miles west of Jerry. Does your answer make sense? Did you check your answer? © McGraw-Hill School Division Practice 1.4.2 miles east of Allison. Who is farthest from the beach? 2. pages 574–575. Chapter 13.8 cm 2. Phil lives 1. Draw a diagram. Loews Mall Bergen Mall King’s Mall 3. 2. Lesson 7.9 miles ϭ 3. She then goes down 7 floors to the copy room. 3. Randi is in the copy room.9 cm E Mall is closest to Kendra’s town.2 . Step 4 Look Back Is the solution reasonable? Reread the problem. Mall is farthest from her town.2.8 miles ϭ 1. 2. Jerry lives 1.Print This Page Name Problem Solving: Strategy Draw a Diagram Step 3 Print This 13–7 Page R RETEACH Solve Carry out your plan. Allison lives 2.9 cm 1.9 miles ϭ 2.8 cm 2. Norma goes up 4 floors from her office to her manager’s office. Use 1 cm to show 1 mile.9 cm N Kendra‘s Town Bergen Mall Loew‘s Mall King‘s Mall W S 3.1. Randi goes up 1 floor to her office.6 miles west of the beach. MR 1. 006 51.333 55. 90.102 53.98 27. 78. Lesson 8.61 13. 9. 3. 71.462 Problem Solving 57.96 33. 6. 7.409 40.07 20. 29.84 18.24 28. 36.346 g. 53.51 10.27 26.266 47. Jason weighs 152. 6.54 34. 63. 9. 25. What is 58. 45. 66.236 41.25 25. pages 576–577. 64.01 7.3 . 19.115 52.277 39. 19.555 49.2. 1. 8. 17.85 Round to the nearest hundredth.666 54. 13.47 5.Print This Page Name Round Decimals Round to the nearest whole number. 8.4 16. 7. 9. 88.5 12. 51. What is his its weight to the nearest hundredth of a gram? weight to the nearest pound? Use with Grade 4.186 42.55 31.8 15.56 2. 7.93 32. 6. 12.8 6. 2. 87. 37.26 29.123 44. 4.999 56. 26.71 Print This 13–8 Page P PRACTICE 4. 17.44 Round to the nearest tenth.46 19. 13.6 lb.48 3. 4. 52.89 24.64 30. 2.1 9. A vitamin pill weighs 2. 53.246 © McGraw-Hill School Division 38.62 11.199 48.055 46. 1. 45. 1.69 35.09 8.275 43. 93. 61. 1.97 36. 37.24 21. 47.008 45. 3. 9. Chapter 13. (430) NS 1. 32.981 50.09 14. 1. 3. 1. 78.43 22. 3. 91.58 23. 31. 6.8 to the nearest whole number.2. So.56 1.3 is closer to 8 than 9.52 13. To round a decimal to the nearest whole number. 1.9 9. Chapter 13.3 rounds down to 8.0 8.7 © McGraw-Hill School Division Round to the nearest tenth. Use the number line above to help you. 1. round up to the nearest one. 8.55 1.3 8. 9.53 1.8 is closer to 10 than 9.7.9 10. 8.54 1.67 1.50 1.6 than 1. 8.58 1.59 15. 1. If the ones digit is less than 5.69 1. pages 576–577.8 2. So. 1.1 6.3 8.6.64 14.6 5.8 rounds up to 10. If the hundredths digit is less than 5.68 11. round up to the nearest tenth.1 8. look at the digit in the tenths place.56 rounds up to 1.57 1.62 1. 8. 9. So.61 rounds down to 1.2 9.2 8.52 1.70 Think: 1.3 9. Think: 9.63 1. To round to the nearest tenth. 1. 9.2 7.6 than 1. 9.65 1.64 1.Print This Page Name Round Decimals You can use a number line to help you round decimals.56 is closer to 1. 9.7 8.55 10. 9.66 1.66 Use with Grade 4.5 4.601.5 8. Use the number line above to help you.1 9. Think: 1. If the ones digit is 5 or greater.59 1.4 8.63 16.61 is closer to 1. Think: 8.0 Round 8.7 9. 1.0 9. 1. 1.6 8.8 9.4 9. 1. 1. If the hundredths digit is 5 or greater. Print This 13–8 Page R RETEACH 8.5 9.61 1. So. round down to the nearest one.3 to the nearest whole number.5. 8.4 3.51 1. Round each decimal to the nearest whole number.51 12.3 . round down to the nearest tenth. 1.68 1.8 8. 1. Round 9. look at the digit in the hundredths place. (431) NS 1.6 9. 1. Lesson 8. 566 7. You get 28. Chapter 13.334 2. You get 12. pages 576–577.45.446 6. You get 28.444 124. What number am I? 203. (432) NS 1.959 28. 1. Round me to the nearest hundredth. What number am I? 12.002 28.3 . You get 124. Print This 13–8 Page E ENRICH Round me to the nearest tenth. What number am I? 27. Round me to the nearest whole number. Round me to the nearest whole number. You get 16.456 124. You get 124. Use with Grade 4. You get 17. Round me to the nearest tenth. Round me to the nearest tenth. You get 12.486 3. Round me to the nearest hundredth.48. You get 203.5.458 203.94. You get 5. You get 5.00. 1. Round me to the nearest tenth.5. Circle the mystery number.4.3.456 203. You get 28.316 5. Lesson 8.937 16. Round me to the nearest hundredth. Round me to the nearest whole number. What number am I? 16. Round me to the nearest hundredth.2. Create you own mystery number puzzle.Print This Page Name Round Decimals Decimal Detective Use the clues to solve each riddle.934 4. You get 124.479 12. Round me to the nearest hundredth. Round me to the nearest whole number.0.008 5. Exchange your puzzle with a friend to solve. What number am I? 5. Round me to the nearest tenth. Round me to the nearest tenth. You get 5. You get 16.32. © McGraw-Hill School Division What number am I? 124. The sum of my digits is 20.9.295 5. Round me to the nearest whole number. You get 203.557 12.899 16. You get 12. Round me to the nearest whole number. (433) NS 1. pages 578–579. © McGraw-Hill School Division Use with Grade 4. MR 1.2. Chapter 13. 2.1. Name of Item Items for Business District Number Bought 13–9 Part A WORKSHEET Decision Making Print This Page Total Cost Items for Area Where People Live Your Decision What models should Kit and Rammel buy for the area where people live? What models should they buy for the business district? Explain. Lesson 9.Print This Page Name Problem Solving: Application Applying Decimals Record your data.3 . 2 . MR 1. Chapter 13. At which distance was it easiest to make strikes? Explain your answer. © McGraw-Hill School Division In ten tries.6.3.1. Distance Attempts Strikes 13–9 Part B WORKSHEET Math & Science Print This Page Strikes Thrown (as a decimal) 1. Lesson 9. 2.5 m 10 3m 10 4.5 m 10 6m 10 1.5 meters away? Use with Grade 4. 1.2. pages 580–581.Print This Page Name Problem Solving: Application How does distance affect how many strikes you throw? Record your data. 3. (434) NS 1. how many strikes do you think you will be able to throw from 1. If you made a lot of strikes. What fraction of all throws are strikes? Write the fraction as a decimal. Lesson 9. How did the results compare to what you thought the 13–9 Part B WORKSHEET Math & Science Print This Page results would be? 3. (435) NS 1. MR 1. 1.Print This Page Name Problem Solving: Application How does distance affect how many strikes you throw? 2. Use with Grade 4. © McGraw-Hill School Division 5.6. 3. Chapter 13. Order the decimals in the table from least to greatest.1. Use your answer in number 3 to compare your ability to throw strikes with Major League Baseball pitchers.2 . pages 580–581. 2. was the decimal bigger or smaller than the other numbers? 4.3.2. 13. 0.7 ϩ 2. Another 2.49 ϭ Problem Solving 28. 4.7 ϩ 1.79 1.6 ϩ 1. 11.5 ϩ 0.4 ϩ 0. 2.67 ϩ 2.45 ϭ 0.3 ϩ 1.76 ϩ 0.9 6. 0. Chapter 14.85 ϩ 2.4 ϩ 0. One apple weighs 0.88 2.8 ϩ 0. (436) NS 2.4 0. 14. pages 596–597.9 ϭ 21. 19.32 ϭ 23.56 ϩ 0. 18. 1.23 ϭ © McGraw-Hill School Division 20. Print This 14–1 Page P PRACTICE 1.4 0.99 ϩ 0.9 9. Lesson 1. 2.78 ϭ 24.6 cm long and 29.8 5.8 cm long.7 ϩ 3. 3.14 ϩ 1.62 ϩ 0. How long is the entire strip of paper? apple weighs 0. 1.92 ϭ 25. 0. are taped together.Print This Page Name Explore Adding Decimals Use the models to find each sum.1 .87 kg.2 ϭ 27. 16. 0.5 ϩ 1.8 7. 3.43 ϭ Find each sum.71 ϩ 0. 15. How much do the two apples weigh together? Use with Grade 4. 3.3 ϩ 0.53 0.7 0.44 ϩ 0.46 ϩ 1.17 ϭ 22.13 0. 17. 0. 1.9 0.8 8.86 ϩ 0. 10.98 ϭ 26.12 ϩ 2. Two strips of paper.96 ϩ 2.26 kg. 2. 2.76 ϩ 1. 0.5 ϩ 2. 0.59 2.6 ϩ 0. 2.2 ϭ 0. 12.6 0. 31 ϭ 5. 4.45 ϭ Use with Grade 4. 0. Draw 10 by 10 grids to help you.4 ϩ 1.5 ϩ 0. (437) NS 2.24 ϭ 6. Lesson 1. pages 596–597.7 dark gray.1 .39 ϭ © McGraw-Hill School Division 7.5 ϭ 3. 2. 1.85 ϭ 2.55.8 ϩ 0. 2.52 ϩ 0. Chapter 14.62 ϭ 9. 1. 2.85.5 ϭ 8.84 ϩ 0. 1. 0.85 with stripes. 2.65 ϩ 0.77 ϩ 0. 0.34 ϭ 2.7 ϩ 0.36 ϭ Color 0. 1. Print This 14–1 Page R RETEACH Write a decimal to show the total number of shaded squares. 1. So. Add.3 ϩ 1.Print This Page Name Explore Adding Decimals You can use models to help you add decimals. Add 1.55 Color 1.7 ϩ 0.75 ϩ 0. 8 0.8 0.4 0.3 1.1 2.2 0.4 0.7 3.2 8.2 Use with Grade 4. You may move across.4 7.6 1. 2. Lesson 1.6 1.9 0. © McGraw-Hill School Division Start ↓ 3.1 4.6 0.8 1.2 ↑ Finish 0. or diagonally. Start ↓ 5.Print This Page Name Explore Adding Decimals Magic Boxes and Mazes Fill in the boxes so that each row. and diagonal adds up to the same sum. column. (438) .9 2.1 1.1 3.5 0.3 0. pages 596–597. 4. 1.7 0.3 0.1 1. Chapter 14. Print This 14–1 Page E ENRICH 0.3 0. 1.7 0.9 1.6 Move through the maze from start to finish by adding numbers that will give you the finish number. 6.1 1. up.7 2.5 1.2 2. down.0 0.7 0.0 0.9 ↑ Finish NS 2.3 0.6 1. 73 ϭ 28.621 9. Lora spends $2.6 26. 21. ϩ 9.288 ϩ 21. 3.44 1.0 13. Lesson 2.774 0.74 36. 0.0 ϩ 4. ϩ 5.984 ϩ12. ϩ 26.759 8. 9.75 ϩ 12.7 ϩ 2. ϩ 8. 2.975 6.167 ϩ 2.567 25.12.3 ϩ 7.869 ϩ 9.151 15.687 ϩ 19. 4.4 2.1 . .30 ϩ 9.343 ϩ 10.12 2. Chapter 14. Add Add Problem Solving 35.259 11.60 ϩ 0.129 11. 8.29 ϩ 0.76 ϭ 31.125. 1.314 ϭ 32.7 ϩ 21.602 3. 3. 1.3 22. 4. 12.39 on envelopes.36 ϩ 0.2 ϩ 8. 0.2 ϩ 17.262 4.9.25 23. 8.604 10. 4.32 13.5. 7.38 32. pages 598–601.Print This Page Name Add Decimals Add. 4. How much does he spend? Use with Grade 4.35 ϩ 8.6 12. 6.25 4.031 ϭ 30.187 ϩ 6. . 25.2 ϩ 6.99. 1.215 18.3 3. 1. 12.70 0.5 ϩ 11.94 16. Print This 14–2 Page P PRACTICE 0. 2. 8. 7.97 and $1.408 21.267 4. .36 ϩ 5. 4. ϩ 7. ϩ 12. 2.30 6.64 on stamps and 36.20 13.67 ϩ 1.407 14.45 5. ϩ 4. How much does she spend? boxes for $6. (439) NS 2. Ben buys packing tape for $2. 7.67 ϩ 1.948 19. 23.135.3.35 ϭ 29. 34. ϩ 0.42 ϩ 7. ϩ 1.97 12.874 17.373 ϩ 5. .142 24.708 12.3 ϭ 27.254 20. © McGraw-Hill School Division 33.697 ϩ 9.5 ϭ Find the number you need to add to complete the pattern. Using Models Regroup Color 1.25 ϩ 1. 1 1.52 ϩ 0. 0. Regroup if needed.28.9 ϩ 0. 1. 0.8 ϭ 3.34 dark gray. Print This 14–2 Page R RETEACH Using Paper and Pencil Add each place.15 ϭ 6.34 ϩ 1. 0.62 Find each sum. 1.35 ϭ 8. 1. pages 598–601. Chapter 14.85 ϩ 0.4 ϭ 2. 1.85 ϭ Use with Grade 4.35 ϭ 9. 2.24 ϩ 0. Add 1. (440) NS 2.5 ϩ 1.1 . 1.5 ϩ 0.6 ϩ 1. Count the number of squares you shaded. Color 1.7 ϩ 1.34 ϩ 1.28 with stripes. 0.28 2.03 ϭ 4. Draw 10 by 10 grids to help you. Lesson 2.38 ϭ © McGraw-Hill School Division 7.Print This Page Name Add Decimals You can use models to help you add decimals.8 ϭ 5. 2 . 4 0 . 3. 5 9 .3 3 6 . 1 8 6 . 4 12. 1 8 2 . 9 ϩ 8 . 9 9 1 . 8 . 3 . 1 . 1 3 2 . 6 .9 ϩ ϩ $ ϩ1 . $ 8 ϩ1 3 .5 1 . 9. 9. 1. 7 . 8 6 3. 18. $7 6 . $ 4. 3 . 6 5 4. Chapter 14. ϩ ϩ1 $ 8. 2 4 ϩ . 9 21. 1 4 6 2 3 . 9 ϩ 7 22. (441) NS 2. 13. 2 ϩ ϩ 17. 5 1 4 . 3 4 . pages 598–601. 4 8 9 3 2 2 . . 4 7 . 1 11. 5 . 3 . 1 1 0 .6 .1 . 2 9. 9 14. 2 $10 . 7 . $ 6 2 . 6 2 5 3.Print This Page Name Add Decimals Digit Detective Find the missing digits. 4 ϩ 1 . 3 ϩ 2 24. 2 ϩ 3 1 . 6 .7 3 . 2 6 0 . 2 7 . 5. Lesson 2. 1 8 . 3 7 $ 6 2. 4 . 6 . 2 7. 4 8 6 . 0 3 . 2 1 Use with Grade 4. 1 6 15. 4 . 8 7 16. 20. 4 7 . 4 ϩ 3 $ 23. 3 7 7. 8 . . 1 ϩ © McGraw-Hill School Division . 6 9 . . 10.6 4 6. Print This 14–2 Page E ENRICH . 7 8. $2 . 0 ϩ2 . 8 3 5 7. 6 1 ϩ 4 ϩ 3 ϩ 1 . 8 5 ϩ . 6 3 . 8 . 4 19. 6 7 6 9 . 1 3 . 7 6 . 1 3 9 . 4 5 ϩ 1. . 2 5. 1 . 1 5 . 7 7 . 6 9 2. 7 ϩ 1 0 ϩ . 7 8. 5.46 11. 7. pages 602–603.2 ϩ 3. Estimate to check for reasonableness. 2.7 ϩ 8. 6.1 .7 miles. 22.90 ϩ 9.76 ϩ 9.6 31.015 ϭ Algebra & Functions Compare.6 3.6 ϩ 1.8 6.59 Print This 14–3 Page P PRACTICE 9. 1.9 miles. 3.12 ϩ 4. 45.67 ϩ 9. 7.90.32 ϩ 7.5 ϩ 6.9 ϭ 19.8 ϩ 6. 5. (442) NS 2.6 ϩ 2.2 ϩ 4. 9.1 29.1.1 ϩ 9.2 5.9 ϩ 1.06 ϩ 9. 6.95 7.50 3.2.3 3.1.1 27. 4.1 ϩ 3.Print This Page Name Estimate Sums Estimate.19 ϩ $9.15 ϩ 8.7 ϩ 7.1 9.178 ϩ 6.10 ϭ 24.7 ϩ 2.1 33.63 ϩ 3.6 Problem Solving 34.94 ϭ 17. 7.95 ϭ 22. Sean drives the car 12.98 12. $6.9 ϩ 6.92 ϩ 4.1 32.15 ϭ 23. 4. 8. Lenny buys one CD for $12. 2.3 ϩ 2. About what does the odometer show now? another CD for $18.1 ϩ 9.18 2.45 ϩ 8.9 ϩ 4.75 and 17.75 ϩ 8.2 26.55 ϭ 15.67 ϩ 21. 4. 9.2 ϩ 5.1 8. 13.9 ϩ 7. Chapter 14.4 5.9 ϩ 3.76 ϩ 9. 8.7 ϩ 7.75 ϩ $9.7 ϩ 5.5 28. 25. 2.6 10.7 ϩ 9.1 ϩ 1. 31. $33.1 ϩ 9.6 2. 9. $6. 1.4 4.25 ϭ 16. MR 2.35 ϩ $5. Round to the nearest whole number.30 ϩ $7.4 ϩ 2. $3. 6.90 ϩ $8.6 ϩ 9.3 ϭ 20. Write Ͼ or Ͻ.9 © McGraw-Hill School Division 1.75 ϭ 21. 19. 3.56 8. 3.15 Add.2 30.90 ϭ 14. 19.95 ϩ $8. $10.25 ϩ $3.3 6. 4.79 ϩ 7. About how much does Lenny pay for the two CDs? Use with Grade 4.472 ϩ 8. Lesson 3.8 ϩ 8. The odometer on a new car shows 35. 1.6 ϭ 18.1 ϩ 8. 0 7 4. Add. 2 5 . Estimate each sum.25 is about $17. 9 7.1 . round each decimal to the nearest whole number. 1. ↓ ↓ Round each number 23 ϩ4 to the nearest whole number.4 7 10.00 to the nearest dollar. 4 8 ϩ 3 . 7 5 11. Chapter 14. Lesson 3.00 So. 9. $ 6 . 6. 7 ϩ 3. 3 ϩ 5 . 3 8 Use with Grade 4.2 5. 23 ϩ 4 ϭ 27 Print This 14–3 Page R RETEACH Estimate $7. 8 . Show how you rounded. (443) NS 2.49. So. 22.Print This Page Name Estimate Sums To estimate the sums of decimals. 7 5 ϩ 1 2 . 8 9 ϩ $ 4 . $8. 5 2 ϩ $ 1 . 6 7 3. 3 4 © McGraw-Hill School Division 8.4 9. Circle the digits in the place to which you will round each number. MR 2. Add. 1 5 . Then add the rounded numbers.25 ↓ ↓ Round each number $8. 5.2. 4. $ 8 .95 ϩ $9. $ 1 5 .00 ϩ $9. Estimate 22.00 ϩ $9.52 ϩ 4. 3.00 = $17.7 4 12. $7. 2 9 2.95 ϩ $9.00.52 ϩ 4.1.9 7 ϩ 8. 9 5 ϩ $ 2 . 7 ϩ 8 .4 7 ϩ 6.49 is about 27.1. $ 5 . pages 602–603. 5 9 6.6 3 ϩ 1 8. 5 0 ϩ $2 4 . 1 7 . 2. 38 2.98 Use with Grade 4. • Player 1 chooses a number from below and writes it in the first box for that round.48 5.1.76 0.74 4. You may check your results with a calculator.96 5. • Players take turns until each player has four numbers.1 . pages 602–603.61 2.59 5.27 7. (444) NS 2.2.08 8.16 4.55 3. Chapter 14. 2.47 1.19 3.5 3.58 7.91 4.1. Lesson 3.63 6.89 6. Then find the difference between each sum and 16. • Player 2 chooses any number that is not crossed out and follows the same steps.49 4.63 3.23 2.03 5.75 4.24 7.64 2. MR 2.77 3. • Add the numbers.Print This Page Name Estimate Sums Four for 16 Use estimation to try to choose four numbers that will have a sum close to 16.89 1.56 4.69 3. • The player with the sum closer to 16 wins that round.35 2.81 2.13 8. 3.31 1.99 3.19 2.30 3. He or she crosses out the number below. Round 1 Players Player 1 Player 2 2 Player 1 Player 2 3 Player 1 Player 2 4 Player 1 Player 2 © McGraw-Hill School Division Print This 14–3 Page E ENRICH Numbers Sum How Close to 16? 5 Player 1 Player 2 3.72 4.18 4.57 3. 5 ϭ 13.35 ϭ 12. pages 604–605.7 ϭ 0.35 miles more than last week. Rachel bikes 3. How many miles does Mark have left to finish the loop? 9.3 Ϫ 4. How much farther does Print This 14–4 Page P PRACTICE Reading Skill Chico bike than Tom? 4.5 miles so far.4 ϩ 4. Mark is biking around a 9. Chico bikes 4.6 Ϫ 3.9 Explain: 2.Print This Page Name Problem Solving: Reading for Math Choose the Operation Circle the number sentence you would use to solve the problem. Keiko rode her bike 8. How far did Keiko ride this week? 8.6 ϩ 3. Tom bikes 3.1.1.05 Explain: 3. He has biked 4.7 miles to the park.7 ϭ 0.2 ϩ 2. (445) NS 2.4 Ϫ 4. 2. Then tell how you decided whether to use addition or subtraction. she rode 4.3 4.35 ϭ 4.4 miles last week.2-mile loop.4. 3.3 ϩ 4. Lesson 4.7 ϭ 5.8 9. MR 1. Chapter 14.7 miles.7 ϭ 8.8 Explain: Use with Grade 4. Then she bikes 2.5 ϭ 4.2 miles to the mall. 1. This week.6 miles.2 .75 8.5 Explain: © McGraw-Hill School Division 4.9 3.2 Ϫ 2. How many miles does she bike? 3. 9 ϭ 7.4. C The ride from school to the park is 2. Then he walks 0.4 ϩ 0.35 It is 5.4 Ϫ 0.9 ϭ 1. 3.6 ϭ 11.6 C 8. Which number sentence can you use is true? A Hiroshi walks to school. Then he rides 2.6 miles.75 ϭ 7. Lesson 4. Which of the following statements Print This 14–4 Page P PRACTICE Math Skills Test Prep 2. © McGraw-Hill School Division to solve this problem? F 5. She has completed 1.8 miles G 9 miles H 8.9 ϩ 2. Which could you use to solve 6.25 miles in all.75 miles of the trip so far.85 Michael takes the train for 8. How many miles does Michael travel? 5. How many miles does Michael the problem? A 8.6 miles from Sarah’s house to the museum.25 Ϫ 2.4 travel? F 16.75 ϭ 3.8 H 4. 2.25 miles from home to school.6 ϩ 5. C Add to find the total number of miles in the round trip.Print This Page Name Problem Solving: Reading for Math Choose the Operation Choose the correct answer. Which number sentence can you use this problem? A Add to find the total amount of miles that Sarah travels to the museum.1.9 miles.15 G 2.4 ϩ 8.9 miles to the park.25 ϩ 2. B Subtract to find the number of miles Sarah has left.2 . B Hiroshi rides 4. (446) NS 2.6 Ϫ 1. pages 604–605. What do you have to do to solve 4. How many miles does Sarah have left? 3.6 B 8. How far does Mikio ride? 1.4 miles.35 H 5.6 ϩ 1.2 G 5. to solve this problem? F 4.9 ϭ 5.4 miles Use with Grade 4. Chapter 14.1. MR 1. Mikio rides his bike 4. 31 miles. Roland bikes 8. B Roland bikes 4.62 ϭ 12.24 Ϫ 4. How much farther does Roland bike than Paul? 7.1 miles to the movie theater. Nicole than he did yesterday.1.4.62 ϭ 3. Paul bikes 4. How much longer is the train trip than the road? 11.62 ϭ 9.75 miles yesterday.65 miles less than last week.2 miles from Morris Hills. The train trip from Springfield to 10. How far did he bike this week? © McGraw-Hill School Division to the record store. 12. Shore Road is 6. How many miles does she have left? Use with Grade 4.24 ϩ 4.3 miles long. How many miles does she bike altogether? 13.Print This Page Name Problem Solving: Reading for Math Choose the Operation Choose the correct answer.25 miles from home This week he biked 1.62 ϩ 4. 2.2 .6 miles.62 miles.24 miles last week. How far did Eddie ride today? has biked 2. 3. The next stop. to solve this problem? F 8. is 3. How long is the train trip from Springfield to Peapack? Snug Harbor is 8. Chapter 14. C Paul bikes 4. He rode 5. Then she bikes 1. Which of the following statements Print This 14–4 Page P PRACTICE Math Skills Test Prep 8.86 Solve.The train trip from Point Dume to Morris Hill is 6.2 miles along Shore Road so far. Eddie rode 1. The road from Point Dume to Snug Harbor is 9.62 G 4.1.24 miles. MR 1.2 miles. pages 604–605. 9. (447) NS 2. Myra bikes 3. Which number sentence can you use is true? A Paul bikes farther than Roland. Peapack.62 miles.9 miles more today 14.24 H 8. Lesson 4.62 miles. Daniel biked 6. 5 ϭ 28.35 ϭ Find each difference.55 m long is cut from it.8 Ϫ 0.6 3.7 Ϫ 0.7 Ϫ 2. 12.6 1. A piece 34.48 3. How much of the wire is left? Use with Grade 4.67 Ϫ 0.95 Ϫ 0.66 Ϫ 2.59 2. 2. 1. pages 608–609. Chapter 14. 2. 0.1 . 18.16 ϭ Problem Solving 33.06 9.5 Ϫ 1. 4.12 m long.91 0. 2.6 cm long. 2.3 1.74 Ϫ 0. 23. 0.9 3.57 ϭ 31. 14. 11.12 0. 17.9 cm long is cut from it.03 Ϫ 0.02 Ϫ 1.7 Ϫ 0.35 5.70 Ϫ 0.7 Ϫ 0.6 Ϫ 1. 16. 1.7 ϭ 1. 22.14 ϭ 26.54 8.69 6.80 Ϫ 0.67 1.07 ϭ 25. 21. Print This 14–5 Page P PRACTICE 0.34 ϭ 29. 20.47 1. 13. 10.13 0.73 Ϫ 0.6 7.12 Ϫ 0.4 Ϫ 0. 0. How much of the board is left? piece 1.34 ϭ 32. 15. A 1.6 Ϫ 1.25 0.68 Ϫ 0. 7.48 2.1 ϭ 0. Lesson 5. © McGraw-Hill School Division 24.8 Ϫ 1. 1. 3. 1.0 Ϫ 1.2 Ϫ 0.79 2.6 ϭ 27.57 ϭ 30.9 Ϫ 0.11 Ϫ 1.1 Ϫ 1.52 Ϫ 0.8 Ϫ 0.Print This Page Name Explore Subtracting Decimals Use the models to find each difference.2 Ϫ 1. (448) NS 2.04 Ϫ 1. 0. A piece of wire is 2. 3. A board is 2. 19. 2.7 Ϫ 1.7 1.8 Ϫ 0. 0. 1. pages 608–609.Print This Page Name Explore Subtracting Decimals You can use models to help you subtract decimals.8 Ϫ 0.85.9. 1. 1. Subtract 1.3 ϭ 3.07 ϭ © McGraw-Hill School Division 7. 0.7 Ϫ 0. So.9.85 Ϫ 1. 0.8 Ϫ 0. 4. 1. 1.56 ϭ 5. 1.45 ϭ Use with Grade 4.57 ϭ 6. Draw 10 by 10 grids to help you.55 ϭ Cross out 0.3 ϭ 2. Chapter 14.95.9 Ϫ 0.35 Ϫ 1. 1.9 ϭ 0.49 ϭ 9. 0. Lesson 5.85 Ϫ 0. Print This 14–5 Page R RETEACH Write a decimal to show how many squares are not crossed out.85 Ϫ 0.1 .95 Shade 1. (449) NS 2. Subtract.6 Ϫ 1.80 Ϫ 0.22 Ϫ 0. 0. 1.09 ϭ 8. 6 4 5.5 Use with Grade 4.4.1 .85 1.88 5.88 2.67 5 4.5.Print This Page Name Explore Subtracting Decimals Magic Triangles In a magic triangle.8 0.92 2.35 0. each side of the triangle has the same sum.73 © McGraw-Hill School Division 4.85 5.48 5 1. (450) NS 2.9 7.05 2 4 5. Lesson 5.3 5.08 Choose numbers from the box so each side of the triangle has a sum of 24.9 4. Chapter 14.35 8.22 4.19 5. Choose numbers from the box so each side of the triangle has a sum of 22. 5.22 2. 3.19 7.84 4 3.6 6.73 2.3 6.8 Print This 14–5 Page E ENRICH 4 4.6 6. pages 608–609.48 4. 31 38. Ϫ 2. 3.7 5. pages 610–613.154 20.5 Ϫ 3.627 Ϫ 2.20 16. Chapter 14. 1. 8.43 Ϫ 0.83 Ϫ 3.3 4. 5.46 36.775 ϭ 30.35.03 10.25 ϩ b ϭ 10.52 37. Ϫ 4.027 Ϫ 3. 7. Lesson 6. Check each answer.66 3.50 13.04 Ϫ 7. Ϫ 3.04 Ϫ 3. MR 2. Christine buys a pair of socks for 40.44 Ϫ 3. 15. © McGraw-Hill School Division 35.60 7.50 2.6 Ϫ 2.67 19.000 23.22 9.64 ϭ 2.00 12.3 Ϫ 0.2 . 8.248 ϭ 34.07 ϭ 28. (451) NS 3.70 Ϫ 4.6 Ϫ 2. 9.4 ϭ 27. 6. 8. 4. 5.1.129 Ϫ 2.36 Ϫ 3.27 9.79 ϭ 33.88 ϭ 32.00 15.974 Ϫ 0. 8.Print This Page Name Subtract Decimals Subtract.12 Ϫ 1. a ϩ 7.076 21. 6. 9. 14.5 Ϫ 2. h Ϫ 4.36.7 Ϫ 2. 4. 6. 34. What is his change from a $20 bill? Use with Grade 4.867 ϭ 31. 7. 4.96 Ϫ 4.26 7. 7.097 ϭ Algebra & Functions Find each missing number.0 Ϫ 2.70 19.67 18. Matt buys a pencil for $0.024 Ϫ 0.08 ϭ 29.5 Problem Solving 39.7 6. Ϫ 0.7 7.896 Ϫ 2. 1.402 25. 8. Ϫ 0. 9.4 0.03 Ϫ 3.556 Ϫ 0.7 Ϫ 0. 0.2 Ϫ 0.075 17.08 ϭ 18.34 17. 8.09 1. 1. 6.97 Ϫ n ϭ 0.35. What is her change from a $10 bill? for $2.12 11.1 Ϫ 2.75.44 Ϫ 0.755 24.258 22. 4. and a ruler for $4. 5. Print This 14–6 Page P PRACTICE 0.17 Ϫ 2. a pen $8.93 ϭ 26. 59 0. 1.88 ϭ Use with Grade 4.5 ϭ 3. Count the number of squares not crossed out. Subtract 1.35 Ϫ 1.7.7 Ϫ 0.59.08 ϭ 6. Print This 14–6 Page R RETEACH Using Paper and Pencil Subtract each place. 1. 1. 0.65 Ϫ 1. Cross out 1.7 Ϫ 1.8 Ϫ 0. Draw 10 by 10 grids to help you.25 ϭ 5. Ϫ 1. Regroup if necessary.11 6 10 Find each difference.5 Ϫ 0.2 ϭ 2.48 ϭ © McGraw-Hill School Division 7. 0.59.18 ϭ 4. 1. (452) NS 3.8 Ϫ 1. pages 610–613.3 ϭ 9. MR 2. Chapter 14. Using Models Color 1.9 Ϫ 0. Lesson 6.06 Ϫ 0. Write zero as a 1. 1. 1.25 Ϫ 0.1.05 ϭ 8.2 . 0.Print This Page Name Subtract Decimals You can use models to help you subtract decimals.70 ← placeholder. 1. Print This Page Name Subtract Decimals Problem Generator • • • • a. Print This 14–6 Page E ENRICH 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. b. • • Ϫ • ϩ • 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? 3. What method did you use to find the answer in exercise 2? © McGraw-Hill School Division Use with Grade 4, Chapter 14, Lesson 6, pages 610–613. (453) ✄ 0 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 MR 2.2; NS 3.1 ✄ 0 1 Print This Page Name Estimate Differences Estimate. Round to the nearest whole number. 1. 6.3 Ϫ 2.6 4. 9.0 Ϫ 3.9 7. 8.57 Ϫ 3.52 10. $34.95 Ϫ $12.20 2. 7.1 Ϫ 4.8 5. 4.6 Ϫ 1.5 8. 17.26 Ϫ 13.78 11. 25.60 Ϫ 11.55 3. 8.7 Ϫ 5.2 Print This 14–7 Page P PRACTICE 6. 7.34 Ϫ 5.78 9. 26.14 Ϫ 12.95 12. 47.15 Ϫ 17.11 Subtract. Estimate to check for reasonableness. 13. 7.1 Ϫ 2.70 ϭ 16. 5.6 Ϫ 1.75 ϭ 19. 77.36 Ϫ 15.93 ϭ 21. 94.32 Ϫ 22.80 ϭ 23. 13.4 Ϫ 6.79 ϭ 25. $14.75 Ϫ $6.90 ϭ 14. 9.8 Ϫ 4.6 ϭ 17. 36.62 Ϫ 23.13 ϭ 15. 8.5 Ϫ 6.3 ϭ 18. 24.35 Ϫ 10.4 ϭ 20. $16.12 Ϫ $12.80 ϭ 22. $54.10 Ϫ $34.89 ϭ 24. 47.65 Ϫ 17.93 ϭ 26. 63.5 Ϫ 18.27 ϭ Algebra & Functions Compare. Write Ͼ or Ͻ. 27. 7.2 Ϫ 3.5 30. 8.3 Ϫ 6.6 33. 5.2 Ϫ 2.3 © McGraw-Hill School Division 8.8 Ϫ 5.4 28. 9.9 Ϫ 4.8 4.2 Ϫ 2.3 31. 9.1 Ϫ 8.7 9.7 Ϫ 7.9 34. 9.3 Ϫ 3.8 6.4 Ϫ 1.7 29. 7.6 Ϫ 2.2 2.1 Ϫ 1.1 32. 7.2 Ϫ 4.5 9.9 Ϫ 3.1 35. 8.1 Ϫ 4.6 5.6 Ϫ 1.3 6.8 Ϫ 5.8 7.2 Ϫ 5.1 Problem Solving 36. Jake has $25.75. He spends $13.15 37. Nancy ran a total of 5.7 miles today. on magazines. About how much money does Jake have left? She ran 3.2 miles this morning. About how many miles did Nancy run this afternoon? Use with Grade 4, Chapter 14, Lesson 7, pages 614–615. (454) NS 2.1, 2.2, 3.1; MR 2.1 Print This Page Name Estimate Differences To estimate differences of decimals, round each decimal to the nearest whole number. Then subtract the rounded numbers. Estimate 12.25 Ϫ 5.79. ↓ ↓ Round each number 12 – 6 to the nearest whole number. Subtract. 12 – 6 = 6 Print This 14–7 Page R RETEACH Estimate $6.25 Ϫ $4.79. ↓ ↓ Round each number $6.00 Ϫ $5.00 to the nearest dollar. Subtract. $6.00 Ϫ $5.00 ϭ $1.00 So, 12.25 Ϫ 5.79 is about 6. So, $6.25 Ϫ $4.79 is about $1.00. Circle the digits in the place to which you will round each number. Estimate each difference. Show how you rounded. 1. $ 7 . 2 4 Ϫ $ 3 . 6 9 2. 2 7 . 3 Ϫ 1 5 . 7 6 3. 1 2 . 4 Ϫ 3 . 7 4. 1 2 . 7 Ϫ 4 . 8 5. $ 2 5 . 7 5 Ϫ $ 7 . 8 0 6. 2 5 . 8 7 Ϫ 7 . 2 © McGraw-Hill School Division 7. 1 4 . 2 5 Ϫ 7 . 8 4 8. 1 0 . 9 7 Ϫ 7 . 4 9. 3 . 6 2 Ϫ 1 . 8 7 10. $1 0 . 2 5 Ϫ $ 3 . 4 5 11. $1 0 . 5 4 Ϫ $ 7 . 8 1 12. 4 3 . 7 Ϫ 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 Estimate Differences Dollars and Sense scissors markers notebook jeans paper Print This 14–7 Page E ENRICH $7.49 $2.89 $3.29 $14.95 $0.89 T-Shirt sweatshirt backpack sneakers radio $8.98 $12.98 $11.99 $29.99 $14.98 ruler glue pencils clock pen $0.99 $1.59 $1.29 $5.98 $1.19 About how much more would Group A cost than Group B? Group A 1. paper, glue Group B notebook, ruler Difference 2. sweatshirt, jeans T-Shirt, jeans 3. backpack, pencils clock, pen 4. markers, sneakers radio, scissors 5. clothing and shoes © McGraw-Hill School Division everything but clothing and shoes Estimate to solve. 6. Andy buys a box of markers. He gives 7. Heidi buys a clock. She gives the clerk the clerk $20. He receives $18.11 in change. Is the amount of change reasonable? Explain. $10. She receives $4.02 in change. Is the amount of change reasonable? Explain. Use with Grade 4, Chapter 14, Lesson 7, pages 614–615. (456) NS 2.1, 2.2, 3.1; MR 2.1 Print This Page Name Problem Solving: Strategy Solve Simpler Problems Solve using a simpler problem. 1. The tennis team travels to a statewide Print This 14–8 Page P PRACTICE 2. A bus ticket costs $8.75. A train 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? 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, 6. Science The first steam-powered $5.90 on a cab, and $11.20 on dinner. He has $30 left. How much money did Sam have when he started? railroad engine was built in England 1804. Thomas Edison tested an electricpowered railroad engine 76 years later. When did Edison test his engine? © McGraw-Hill School Division Strategy: 7. Teri has 17 model trains. She has a Strategy: 8. Create a problem for which you 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? 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 Problem Solving: Strategy Solve Simpler Problems Page 616, Problem 2 Print This 14–8 Page R RETEACH 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. What do you need to find? • You need to find how much hours for hours for Step 2 Make a plan. Choose a strategy. Plan I I I I I I I I I I 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 © McGraw-Hill School Division 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 Problem Solving: Strategy Solve Simpler Problems Step 3 Print This 14–8 Page R RETEACH Solve Solve this simpler problem. • A conductor works 8 hours for $18 an hour. The conductor earns 8 ϫ or . • A ticket checker works 8 hours at $13 an hour. The ticket checker earns 8 ϫ The total amount is ϩ or ϭ . . Now solve the real problem the same way. • A conductor works 8 hours at The conductor earns 8 ϫ • A ticket checker works 8 hours at The ticket checker earns 8 ϫ The total amount is ϩ or ϭ or an hour. . an hour. . Step 4 Look Back 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 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? 2. Gina buys 3 model planes for $14.95 each and 4 model trains for $7.29 each. How much money does Gina spend? Use with Grade 4, Chapter 14, Lesson 8, pages 616–617. (459) MR 1.1, 1.2, 2.2, 2.4, 3.2 Print This Page Name Use Properties to Add and Subtract Add or subtract mentally. 1. 3.56 ϩ 0.04 ϭ 4. 1.7 ϩ 1.3 ϭ 7. 6.04 Ϫ 6 ϭ 10. 12.13 Ϫ 0.14 ϭ 13. 17.01 ϩ 9.99 ϭ 16. 3.6 ϩ 4.7 ϩ 0.4 ϭ 18. 7.9 ϩ 2.8 Ϫ 0.9 ϭ 20. 9.3 Ϫ 2.6 ϩ 4.4 ϭ 22. 8.7 Ϫ 2.9 Ϫ 5.7 ϭ 2. 4.12 ϩ 1.7 ϭ 5. 8.87 ϩ 0.03 ϭ 8. 7.86 Ϫ 1.06 ϭ 11. 11.22 Ϫ 10.02 ϭ 14. 10.17 Ϫ 8.18 ϭ Print This 14–9 Page P PRACTICE 3. 4.5 Ϫ 4.5 ϭ 6. 5.08 ϩ 0.9 ϭ 9. 17.23 ϩ 0 ϭ 12. 15.66 Ϫ 10.44 ϭ 15. 15.44 Ϫ 3.22 ϭ 17. 13.1 ϩ 5.6 ϩ 3.9 ϭ 19. 7.5 ϩ 6.3 Ϫ 4.5 ϭ 21. 6.3 Ϫ 5.5 ϩ 1.7 ϭ 23. 9.1 ϩ 4.7 Ϫ 9.1 ϭ Algebra & Functions Find each missing number. 24. 4.9 ϩ b ϭ 6.0 26. 2.7 ϩ c ϭ 2.7 28. 14.12 Ϫ m ϭ 0 30. 6.3 Ϫ w ϭ 6.3 32. 2.7 ϩ 9.3 ϭ 9.3 ϩ n 25. (f ϩ 1.5) ϩ 3.5 ϭ 5 27. 10.6 Ϫ d ϭ 5 29. 3.7 ϩ h ϭ 6.3 ϩ 3.7 31. 4.2 ϩ t ϭ 10 33. a Ϫ 7.9 ϭ 0 © McGraw-Hill School Division 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 Use Properties to Add and Subtract You can use the Commutative, Associative, and Identity properties to add and subtract mentally. Look for compatible numbers. (1.3 ϩ 4.2) ϩ 1.7 (4.2 ϩ 1.3) ϩ 1.7 4.2 ϩ (1.3 ϩ 1.7) 4.2 ϩ 3.0 7.2 Look for zeros. Print This 14–9 Page R RETEACH Think: 1.3 and 1.7 are compatible. 5.35 ϩ 0 ϭ 5.35 Use the Commutative Property. 3.29 Ϫ 0 ϭ 3.29 Use the Associative Property. Add the compatible numbers. Look for the same number. Find the sum. 0.85 Ϫ 0.85 ϭ 0 16.5 ϩ 0 ϭ 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. Use mental math to add or subtract. 1. 2.6 ϩ 0.4 = 3. 1.5 ϩ 3.2 ϩ 1.5 = © McGraw-Hill School Division 2. 4.75 ϩ 0 = 4. 2.7 Ϫ 2.7 = 6. 4.7 Ϫ 0 ϩ 5.3 = 8. 10.10 Ϫ 5.01 = 10. 3.3 ϩ 3.3 = 12. 8.9 ϩ 2.9 Ϫ 8 = 14. 4.44 ϩ 4.44 = NS 3.1; AF 1.2, 1.3; MR 2.2 5. 6.78 Ϫ 6 = 7. 12.24 Ϫ 6.12 = 9. 1.8 ϩ 2.2 ϩ 1.3 = 11. 2.3 ϩ 3.5 = 13. 14.6 Ϫ 0 ϩ 5.4 = Use with Grade 4, Chapter 14, Lesson 9, pages 618–619. (461) © McGraw-Hill School Division 8. Chapter 14. AF 1. 4. 9.0 2. Use the code and properties to add or subtract the bottom number using mental math.5 2. (462) NS 3. MR 2.2 . 5. 5 6 7 8 9 1. 6. pages 618–619. Print This 14–9 Page E ENRICH 0 Example: 1 2 Ϫ 3 2. 1. Write the answers using numbers and the code symbols.3. 7. Lesson 9. 3.1.Print This Page Name Use Properties to Add and Subtract Crack the Code Use the symbols below to write the top numbers in exercises 1–6.2.5 4 ←Think: 0. Use the code to write all the numbers in exercises 7–9 before you check by adding. Which problem can you solve without using numbers? Use with Grade 4. 10. Check your symbol answers with a friend. NS 3. pages 620–621.) 14–10 Part A WORKSHEET Decision Making Print This Page Miles Traveled Costs Other Notes Your Decision © McGraw-Hill School Division What is your recommendation for the Lopez family? Explain. Use with Grade 4. 2.1.1 .2. Lesson 10. (463) MR 1. Chapter 14. Route (List all stops and highways used.Print This Page Name Problem Solving: Application Applying Adding and Subtracting Decimals Record your data and notes. Print This Page Name Problem Solving: Application How would you conserve electricity? Record data for your conservation plans in this chart. Lesson 10. MR 1.1. pages 622–623. Chapter 14. Plan Plan 1 Activity Time Saved 14–10 Part B WORKSHEET Math & Science Print This Page Money Saved Plan 2 Plan 3 © McGraw-Hill School Division Use with Grade 4.1. 2.3 . (464) NS 2. 3.3. 1. (465) NS 2. Which of your three plans might you actually use? Explain your answer.3 . How much money would you save in a month? in a year? 4. and stress to the environment. Compare the advantages and disadvantages of the different ways to produce electricity. 3. energy efficiency. pages 622–623. Which of your three plans would you prefer to use? Explain your answer.3.1. Think about costs.Print This Page Name Problem Solving: Application How would you conserve electricity? 14–10 Part B WORKSHEET Math & Science Print This Page 1. Lesson 10. © McGraw-Hill School Division Use with Grade 4. 2. 3. Chapter 14. Look at the plan you liked best. MR 1. 2.