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Name © Pearson Education, Inc. 4 2. The Perez family is driving to visit relatives. The trip is 184 miles, and they have driven 48 miles. How many more miles do they need to travel? A 142 miles B 136 miles C 128 miles D 112 miles 3. Los Angeles is one of the largest cities in the United States. The population of Houston is less than Los Angeles. Chicago has a population greater than Houston, but less than Los Angeles. Phoenix has fewer people than Houston. Which lists the population of the cities from greatest to least? A Chicago, Los Angeles, Houston, Phoenix B Los Angeles, Houston, Phoenix, Chicago C Los Angeles, Chicago, Houston, Phoenix D Los Angeles, Phoenix, Chicago, Houston 3-1 4. What is the value of the 4 in 541,000? 5. Order the numbers from least to greatest. 146,552 145,525 145,552 6. Compare. Use #, $, or %. 345,765 387,328 7. Una put the same amount of carnations into 4 vases. If you use a total of 32 carnations, how many are in each vase? 8. Look for a pattern and write the missing numbers. 2, 8, 14, 20, 26, , , Topic 3 28443_ANC-NATGR4_T3-1_working.in25 25 Daily Spiral Review 3-1 1. Celia used an addition expression to find 6 ! 5. Which expression did she use? A 5"5"5 B 5"5"5"5"6 C 5"5"5"5"5"5 D 5"5"5"5"5 Daily Spiral Review 25 2/21/08 11:41:01 AM Name © Pearson Education, Inc. 4 2. The Perez family is driving to visit relatives. The trip is 184 miles, and they have driven 48 miles. How many more miles do they need to travel? A 142 miles B 136 miles C 128 miles D 112 miles 3. Los Angeles is one of the largest cities in the United States. The population of Houston is less than Los Angeles. Chicago has a population greater than Houston, but less than Los Angeles. Phoenix has fewer people than Houston. Which lists the population of the cities from greatest to least? A Chicago, Los Angeles, Houston, Phoenix B Los Angeles, Houston, Phoenix, Chicago C Los Angeles, Chicago, Houston, Phoenix D Los Angeles, Phoenix, Chicago, Houston 3-1 4. What is the value of the 4 in 541,000? forty thousand 5. Order the numbers from least to greatest. 146,552 145,525 145,552 145,525; 145,552; 146,552 6. Compare. Use #, $, or %. 345,765 387,328 # 7. Una put the same amount of carnations into 4 vases. If you use a total of 32 carnations, how many are in each vase? There are 8 carnations in each vase. 8. Look for a pattern and write the missing numbers. 2, 8, 14, 20, 26, 32, 38, 44 Topic 3 28443_ANC-NATGR4_T3-1_working.in25 25 Daily Spiral Review 3-1 1. Celia used an addition expression to find 6 ! 5. Which expression did she use? A 5"5"5 B 5"5"5"5"6 C 5"5"5"5"5"5 D 5"5"5"5"5 Daily Spiral Review 25 2/21/08 11:40:04 AM 26 Nat_AncTopic_3.indb 26 Problem of the Day 3-1 Topic 3 Problem of the Day 3-1 Write a number sentence and solve. 3-1 1/31/08 11:09:21 AM © Pearson Education, Inc. 4 Problem of the Day Antonio had $134 in his savings account. He put in $67 more. How much was in Antonio’s account then? Name 1. Which of the following is the correct multiplication sentence for 4 ! 4 ! 4 ! 4 ! 4 ! 4? A 4 " 4 # 16 Quick Check 3-1 2. Which of the following shows the correct array for a multiplication sentence for 3 ! 3 ! 3 ! 3? A Quick Check Check 3-1 3-1 Quick B 4 " 5 # 20 C 6 " 4 # 24 D 8 " 3 # 24 B C D © Pearson Education, Inc. 4 3. Writing to Explain Draw an array using Xs to write a multiplication sentence and an addition sentence that you could use to show how 12 juice boxes could be arranged. Topic 3 Nat_AncTopic_3.indb 27 27 1/31/08 11:09:22 AM Name 1. Which of the following is the correct multiplication sentence for 4 ! 4 ! 4 ! 4 ! 4 ! 4? A 4 " 4 # 16 Quick Check 3-1 2. Which of the following shows the correct array for a multiplication sentence for 3 ! 3 ! 3 ! 3? A Quick Check Check 3-1 3-1 Quick B 4 " 5 # 20 C 6 " 4 # 24 D 8 " 3 # 24 B C D 3. Writing to Explain Draw an array using Xs to write a multiplication sentence and an addition sentence that you could use to show how 12 juice boxes could be arranged. © Pearson Education, Inc. 4 See student samples to the right. Topic 3 Nat_AncTopic_3.indb 27 27 1/31/08 2:33:00 PM Name Reteaching Meanings of Multiplication 3-1 Addition sentence: 5 ! 5 ! 5 ! 5 " 20 Multiplication sentence: Reteaching 3-1 4 # 5 " 20 There are 4 rows of 5. There are 3 boxes. There are 7 books in each box. Addition sentence: WWW WW WWWW WWW WWW WWW WWWW WW WWW WWW WW WW WWW WWW WW WWWW WWW WWW WWW WWWW WW WWW WWW WW WW WWW WWW WW WWWW WWW WWW WWW WWWW WW WWW WWW WW WW WWW 7 ! 7 ! 7 " 21 There are 3 groups of 7. Multiplication sentence: 3 # 7 " 21 Write an addition sentence and a multiplication sentence for each picture. 1. 2. Write a multiplication sentence for each addition sentence. 3. 10 ! 10 ! 10 ! 10 " 40 5. Number Sense Explain how multiplication can help you find 6 ! 6 ! 6. 28 Nat_AncTopic_3.indb 28 © Pearson Education, Inc. 4 4. 3 ! 3 ! 3 ! 3 ! 3 ! 3 " 18 Topic 3 1/31/08 11:09:24 AM Name Reteaching Meanings of Multiplication 3-1 Addition sentence: 5 ! 5 ! 5 ! 5 " 20 Multiplication sentence: Reteaching 3-1 4 # 5 " 20 There are 4 rows of 5. There are 3 boxes. There are 7 books in each box. Addition sentence: WWW WW WWWW WWW WWW WWW WWWW WW WWW WWW WW WW WWW WWW WW WWWW WWW WWW WWW WWWW WW WWW WWW WW WW WWW WWW WW WWWW WWW WWW WWW WWWW WW WWW WWW WW WW WWW 7 ! 7 ! 7 " 21 Multiplication sentence: There are 3 groups of 7. 3 # 7 " 21 Write an addition sentence and a multiplication sentence for each picture. 1. 6 ! 6 ! 6 " 18; 3 # 6 " 18 4 ! 4 ! 4 " 12; 3 # 4 " 12 or 3 ! 3 ! 3 ! 3 " 12; 4 # 3 " 12 2. Write a multiplication sentence for each addition sentence. 4. 3 ! 3 ! 3 ! 3 ! 3 ! 3 " 18 4 # 10 " 40 6 # 3 " 18 5. Number Sense Explain how multiplication can help you find 6 ! 6 ! 6. 3 # 6 " 18 28 Nat_AncTopic_3.indb 28 © Pearson Education, Inc. 4 3. 10 ! 10 ! 10 ! 10 " 40 Topic 3 1/31/08 2:33:02 PM Name Practice 3-1 Meanings of Multiplication Write an addition sentence and a multiplication sentence for the picture. 1. Practice 3-1 Write a multiplication sentence for each addition sentence. 2. 4 ! 4 ! 4 ! 4 " 16 3. 10 ! 10 ! 10 ! 10 ! 10 ! 10 " 60 4. Number Sense How could you use multiplication to find 7 ! 7 ! 7? 5. A classroom desk has 4 legs. How many legs do 5 desks have altogether? 6. Danielle planted 3 seeds in 6 different pots. How many seeds did she plant? 7. Which is the multiplication sentence for 2 ! 2 ! 2 ! 2? A 4 # 4 " 16 B 2#2"4 C 4#2"8 D 2 # 6 " 12 © Pearson Education, Inc. 4 8. Writing to Explain Explain how you can use multiplication to find 2 ! 2 ! 2 ! 2. Topic 3 Nat_AncTopic_3.indb 29 29 1/31/08 11:09:27 AM Name Practice 3-1 Meanings of Multiplication Write an addition sentence and a multiplication sentence for the picture. 1. Practice 3-1 10 # 10 # 10 " 30; 3 ! 10 " 30 Write a multiplication sentence for each addition sentence. 2. 4 ! 4 ! 4 ! 4 " 16 3. 10 ! 10 ! 10 ! 10 ! 10 ! 10 " 60 4 ! 4 " 16 6 ! 10 " 60 4. Number Sense How could you use multiplication to find 7 ! 7 ! 7? 3 ! 7 " 21 5. A classroom desk has 4 legs. How many legs do 5 desks have altogether? 20 legs 6. Danielle planted 3 seeds in 6 different pots. How many seeds did she plant? 18 seeds 7. Which is the multiplication sentence for 2 ! 2 ! 2 ! 2? A 4 # 4 " 16 B 2#2"4 C 4#2"8 D 2 # 6 " 12 © Pearson Education, Inc. 4 8. Writing to Explain Explain how you can use multiplication to find 2 ! 2 ! 2 ! 2. Sample answer: Multiplication can be used to find the total. I know there are 4 equal groups and there are 2 in each group. 4 ! 2 " 8 Topic 3 Nat_AncTopic_3.indb 29 29 1/31/08 2:33:04 PM Name Enrichment 3-1 Hurray Array! Visual Thinking You can demonstrate multiplication by showing objects in an array. There are two ways to set up an array with two factors. Enrichment 3-1 For each array given, create a different array that shows the same factors. Then write the multiplication sentence for each picture. 1. " 2. " There are at least two arrays for any product: the product ! 1 and 1 ! the product. Sometimes there are other possible arrays for a product. 3. Draw the other array for the product 25. Write the multiplication sentence. 4. Draw the other array for the product 9. Write the multiplication sentence. Sometimes there are several different arrays that can be drawn for a product. © Pearson Education, Inc. 4 5. Draw an array for the product 28 that is not 28 ! 1, 1 ! 28, 7 ! 4, or 4 ! 7. Write the multiplication sentence for your array. 30 Nat_AncTopic_3.indb 30 Topic 3 1/31/08 11:09:28 AM Name Enrichment 3-1 Hurray Array! Visual Thinking You can demonstrate multiplication by showing objects in an array. There are two ways to set up an array with two factors. Enrichment 3-1 For each array given, create a different array that shows the same factors. Then write the multiplication sentence for each picture. 1. " 2. " For 1–5, check students’ arrays. 4 ! 6 " 24 6 ! 4 " 24 3 ! 6 " 18 6 ! 3 " 18 There are at least two arrays for any product: the product ! 1 and 1 ! the product. Sometimes there are other possible arrays for a product. 3. Draw the other array for the product 25. Write the multiplication sentence. 5 ! 5 " 25 4. Draw the other array for the product 9. Write the multiplication sentence. 3!3"9 Sometimes there are several different arrays that can be drawn for a product. 5. Draw an array for the product 28 that is not 28 ! 1, 1 ! 28, 7 ! 4, or 4 ! 7. Write the multiplication sentence for your array. © Pearson Education, Inc. 4 14 ! 2 " 28 or 2 ! 14 " 28 30 Nat_AncTopic_3.indb 30 Topic 3 1/31/08 2:33:05 PM Name 1. Which number is fifty-three thousand, one hundred thirteen? A 530,113 B 53,130 C 53,113 D 5,313 © Pearson Education, Inc. 4 3. Georgia made $123 mowing lawns over the past four weeks. Sidney made $96 mowing lawns over the same amount of time. How much money did they make altogether? A $219 B $223 C $239 D $242 3-2 5. Ike wants to run 1,000 laps around a track in three months. Ike has already run 438 laps. How many more laps does he have left to meet his goal? 6. Look for a pattern. Write the next three numbers. 5, 9, 13, 17, , , 7. Carol, Ana, Gloria, and Luz are standing in a line. Gloria is first. Luz is not last and is ahead of Carol. Ana is behind Gloria and Carol. In what order are the girls in line? Daily Spiral Review 3-2 2. The Electronic Experts store sold 8,124 computers last year. The store also sold 2,336 printers. How many computers and printers did the store sell last year? A 10,460 B 10,640 C 10,840 D 10,940 Daily Spiral Review 8. James has 8 model cars. Rita and James have 17 model cars altogether. How many model cars does Rita have? 4. Which numbers are written in order from least to greatest? A 423, 415, 430, 402 B 430, 423, 415, 402 C 415, 402, 430, 423 D 402, 415, 423, 430 Topic 3 Nat_AncTopic_3.indb 31 31 1/31/08 11:09:29 AM Name 1. Which number is fifty-three thousand, one hundred thirteen? A 530,113 B 53,130 C 53,113 D 5,313 © Pearson Education, Inc. 4 3. Georgia made $123 mowing lawns over the past four weeks. Sidney made $96 mowing lawns over the same amount of time. How much money did they make altogether? A $219 B $223 C $239 D $242 3-2 5. Ike wants to run 1,000 laps around a track in three months. Ike has already run 438 laps. How many more laps does he have left to meet his goal? 562 laps 6. Look for a pattern. Write the next three numbers. 5, 9, 13, 17, 21, 25, 29 7. Carol, Ana, Gloria, and Luz are standing in a line. Gloria is first. Luz is not last and is ahead of Carol. Ana is behind Gloria and Carol. In what order are the girls in line? Daily Spiral Review 3-2 2. The Electronic Experts store sold 8,124 computers last year. The store also sold 2,336 printers. How many computers and printers did the store sell last year? A 10,460 B 10,640 C 10,840 D 10,940 Daily Spiral Review Gloria, Luz, Carol, Ana 8. James has 8 model cars. Rita and James have 17 model cars altogether. How many model cars does Rita have? 9 model cars 4. Which numbers are written in order from least to greatest? A 423, 415, 430, 402 B 430, 423, 415, 402 C 415, 402, 430, 423 D 402, 415, 423, 430 Topic 3 Nat_AncTopic_3.indb 31 31 1/31/08 2:33:06 PM 32 Topic 3 28443_ANC-NATGR4_T3-2_working.in32 32 Problem of the Day 3-2 Problem of the Day 3-2 3-2 2/21/08 12:04:48 PM © Pearson Education, Inc. 4 Problem of the Day The country of Indonesia is a group of islands between Asia and Australia. It has an area of 704,400 square miles and has a population of 241,973,880 people. Write the word form for each number. Name Quick Check 3-2 1. Which number comes next in the pattern? 57, 66, 75, 84, . A 88 B 93 C 97 D 104 Quick Check 3-2 2. Look at the display below. What is the product for this array? A 32 B 40 C 48 D 56 © Pearson Education, Inc. 4 3. Writing to Explain Seven people each brought two chairs to a family picnic. How many chairs will there be altogether if another person does the same? Topic 3 Nat_AncTopic_3.indb 33 33 1/31/08 11:09:31 AM Name Quick Check 3-2 1. Which number comes next in the pattern? 57, 66, 75, 84, . A 88 B 93 C 97 D 104 Quick Check 3-2 2. Look at the display below. What is the product for this array? A 32 B 40 C 48 D 56 3. Writing to Explain Seven people each brought two chairs to a family picnic. How many chairs will there be altogether if another person does the same? © Pearson Education, Inc. 4 See student samples to the right. Topic 3 Nat_AncTopic_3.indb 33 33 1/31/08 2:33:08 PM Name Reteaching 3-2 Reteaching 3-2 Patterns for Facts Pattern Example All multiples of two are even numbers. 2, 18, 44 All multiples of 5 end in 0 or 5. 25, 100, 220 For all multiples of nine, the sum of the digits is always a multiple of 9. 27 2 ! 7 " 9 63 6 ! 3 " 9 1. 9 # 5 2. 2 # 8 3. 5 # 8 4. 9 # 4 5. 9 # 3 6. 2 # 7 7. 5 # 3 8. 5 # 6 9. 9 # 2 10. 5 # 7 11. 6 # 3 12. 2 # 6 13. How many baseball cards are in 4 packages? 14. How many stickers do you get if you buy 9 packages? Item Number in Package Baseball cards 5 Stickers 2 Coupons 9 © Pearson Education, Inc. 4 15. How many coupons do you get if you buy 7 packages? 34 Nat_AncTopic_3.indb 34 Topic 3 1/31/08 11:09:32 AM Name Reteaching 3-2 Reteaching 3-2 Patterns for Facts Pattern Example All multiples of two are even numbers. 2, 18, 44 All multiples of 5 end in 0 or 5. 25, 100, 220 For all multiples of nine, the sum of the digits is always a multiple of 9. 27 2 ! 7 " 9 63 6 ! 3 " 9 1. 9 # 5 2. 9 # 3 6. 9 # 2 10. 45 5. 18 3. 2 # 7 7. 5 # 7 11. 16 27 9. 2 # 8 14. How many stickers do you get if you buy 9 packages? 5 # 3 8. 6 # 3 12. 18 Item 9 # 4 36 15 35 20 4. 40 14 13. How many baseball cards are in 4 packages? 5 # 8 5 # 6 30 2 # 6 12 Number in Package Baseball cards 5 Stickers 2 Coupons 9 18 15. How many coupons do you get if you buy 7 packages? © Pearson Education, Inc. 4 63 34 Nat_AncTopic_3.indb 34 Topic 3 1/31/08 2:33:09 PM Name Practice 3-2 Patterns for Facts 1. 5 ! 4 2. 2 ! 3 3. 9 ! 7 4. 5 ! 2 5. 8 ! 2 6. 5 ! 3 7. 9 ! 8 8. 9 ! 4 10. 2 ! 7 " Practice 3-2 9. 9 ! 6 " 11. 5 ! 5 " Algebra Find the missing number. 12. ! 9 " 45 13. 2 ! " 14 14. A package of baseball cards includes 5 cards. How many baseball cards are in 5 packages? 15. What is the value of the missing number? 9! " 36 A 6 B 4 C 3 D 2 © Pearson Education, Inc. 4 16. Writing to Explain Milton needs to find the product of two numbers. One of the numbers is 9. The answer also needs to be 9. How will he solve this problem? Explain. Topic 3 Nat_AncTopic_3.indb 35 35 1/31/08 11:09:33 AM Name Practice 3-2 Patterns for Facts 1. 2. 5 ! 4 2 ! 3 6 20 5. 3. 6. 8 ! 2 16 5 ! 3 63 7. 15 54 10. 2 ! 7 " 10 8. 9 ! 8 72 14 5 ! 2 11. 9 ! 4 36 5 ! 5 " 25 Practice 3-2 9. 9 ! 6 " 4. 9 ! 7 Algebra Find the missing number. 12. 5 13. 2 ! ! 9 " 45 7 " 14 14. A package of baseball cards includes 5 cards. How many baseball cards are in 5 packages? 25 baseball cards 15. What is the value of the missing number? 9! " 36 A 6 B 4 C 3 D 2 © Pearson Education, Inc. 4 16. Writing to Explain Milton needs to find the product of two numbers. One of the numbers is 9. The answer also needs to be 9. How will he solve this problem? Explain. Sample answer: Milton will multiply 9 ! 1 " 9. The product of any number and 1 equals that number. Topic 3 Nat_AncTopic_3.indb 35 35 1/31/08 2:33:10 PM Name Enrichment 3-2 Patterns, Patterns, Everywhere Patterns Complete each pattern and write the rule for the pattern you find. Hint: The pattern may involve more than one operation. For example, the numbers 2, 4, 16, 32, 128 form a pattern of multiplying by 2, then multiplying by 4. Pattern Rule Enrichment 3-2 1. 2 4 8 16 5 10 50 100 500 1 9 9 81 81 7 0 0 0 5 5 25 25 125 1 1 2 6 24 2. 3. 4. 5. 6. © Pearson Education, Inc. 4 7. Although a single starfish may have as many as 44 arms, we are most familiar with starfish that have 5 arms. Write a number pattern for 6 starfish if each had 5 arms. How many arms would those starfish have in all? 36 Nat_AncTopic_3.indb 36 Topic 3 1/31/08 11:09:34 AM Name Enrichment 3-2 Patterns, Patterns, Everywhere Patterns Complete each pattern and write the rule for the pattern you find. Hint: The pattern may involve more than one operation. For example, the numbers 2, 4, 16, 32, 128 form a pattern of multiplying by 2, then multiplying by 4. Pattern Rule Enrichment 3-2 1. 2 4 8 16 32 5 10 50 100 500 1 9 9 81 81 7 0 0 0 0 5 5 25 25 125 1 1 2 6 24 2. 3. 4. 5. 6. 64 ! 2 1,000 729 ! 2, ! 5 ! 9, ! 1 !0 0 125 120 ! 1, ! 5 ! 1, ! 2, ! 3, ! 4 . . . 5, 10, 15, 20, 25, 30; 30 arms 36 Nat_AncTopic_3.indb 36 © Pearson Education, Inc. 4 7. Although a single starfish may have as many as 44 arms, we are most familiar with starfish that have 5 arms. Write a number pattern for 6 starfish if each had 5 arms. How many arms would those starfish have in all? Topic 3 1/31/08 2:33:11 PM Name 1. Ronni estimated the sum of 5,823 and 863 by rounding each number to the nearest hundred and then adding. What was Ronni’s estimate for 5,823 ! 863? A 6,700 B 7,000 C 7,200 D 7,600 © Pearson Education, Inc. 4 3. A CD case holds 9 CDs. Randall has 9 CD cases. How many CDs are there in all? A 18 B 54 C 81 D 100 3-3 5. Write a number pattern for 8 starfish if each has 5 arms. 6. What number does the art below show? 7. Kyle counted 9 windows on the first floor of a building that has 6 floors. Each floor has about the same number of windows. Estimate the number of windows in the building. Daily Spiral Review 3-3 2. A grocery store had 176 cans of green beans on the shelf on Monday. By Friday, 37 cans had been sold. How many cans were left? Use mental math to subtract. A 127 B 139 C 143 D 151 Daily Spiral Review 8. The printer sent 4,200 newspapers for delivery one day. How many boxes of newspapers would there be if the newspapers were packed in groups of one hundred? 4. There are 12 rows of seats in a section of an auditorium, and 9 seats per row. How many seats are there in all? A 21 B 99 C 108 D 109 Topic 3 Nat_AncTopic_3.indb 37 37 1/31/08 11:09:36 AM Name 1. Ronni estimated the sum of 5,823 and 863 by rounding each number to the nearest hundred and then adding. What was Ronni’s estimate for 5,823 ! 863? A 6,700 B 7,000 C 7,200 D 7,600 © Pearson Education, Inc. 4 3. A CD case holds 9 CDs. Randall has 9 CD cases. How many CDs are there in all? A 18 B 54 C 81 D 100 3-3 5. Write a number pattern for 8 starfish if each has 5 arms. 5, 10, 15, 20, 25, 30, 35, 40 6. What number does the art below show? 238 7. Kyle counted 9 windows on the first floor of a building that has 6 floors. Each floor has about the same number of windows. Estimate the number of windows in the building. Daily Spiral Review 3-3 2. A grocery store had 176 cans of green beans on the shelf on Monday. By Friday, 37 cans had been sold. How many cans were left? Use mental math to subtract. A 127 B 139 C 143 D 151 Daily Spiral Review 60 windows 8. The printer sent 4,200 newspapers for delivery one day. How many boxes of newspapers would there be if the newspapers were packed in groups of one hundred? 42 boxes 4. There are 12 rows of seats in a section of an auditorium, and 9 seats per row. How many seats are there in all? A 21 B 99 C 108 D 109 Topic 3 Nat_AncTopic_3.indb 37 37 1/31/08 2:33:12 PM 38 Nat_AncTopic_3.indb 38 Problem Problem of of the the Day Day 3-3 3-3 Topic 3 Problem of the Day 3-3 1/31/08 11:09:37 AM © Pearson Education, Inc. 4 Problem of the Day In which step will the number 200,000 appear? (Hint: Look for a pattern.) Step 1: 194,000 Step 2: 195,000 Step 3: 196,000; and so on. 3-3 Name Quick Check 3-3 1. Which property is best represented by the display below? !!! 3 groups of 0 A Zero Property of Multiplication B Commutative Property of Addition 2. Which of the following is the missing number? !6"6 A 6 B 2 C 1 D 0 Quick Check 3-3 C Commutative Property of Multiplication D Identity Property of Multiplication © Pearson Education, Inc. 4 3. Writing to Explain Briefly explain the Commutative Property of Multiplication. Write a number sentence that shows this property. Topic 3 Nat_AncTopic_3.indb 39 39 1/31/08 11:09:39 AM Name Quick Check 3-3 1. Which property is best represented by the display below? !!! 3 groups of 0 A Zero Property of Multiplication B Commutative Property of Addition 2. Which of the following is the missing number? !6"6 A 6 B 2 C 1 D 0 Quick Check 3-3 C Commutative Property of Multiplication D Identity Property of Multiplication 3. Writing to Explain Briefly explain the Commutative Property of Multiplication. Write a number sentence that shows this property. © Pearson Education, Inc. 4 See student samples to the right. Topic 3 Nat_AncTopic_3.indb 39 39 1/31/08 2:33:15 PM Name Reteaching Multiplication Properties 3-3 You can use the Properties of Multiplication to help you find products. Commutative Property of Multiplication: You can multiply any two numbers in any order. 2!3"3!2 Identity Property of Multiplication When you multiply any number by 1, the product is that number. Reteaching 3-3 7!1"7 Zero Property of Multiplication When you multiply any number by 0, the product is also 0. 3!0"0 1. 7 ! 3 " 3 ! 2. 4 ! 0 " 3. 5 ! 4 " 4 ! 4. 2 ! 1 " 5. 0 ! 7 " 6. 8 ! 3 " 3 ! 7. 9 ! 1 " 1 ! 8. 1 ! 5 " 10. Writing to Explain Explain how you know that in ? ! 6,273 " 6,273, the ? will be 1. 40 Nat_AncTopic_3.indb 40 © Pearson Education, Inc. 4 9. Number Sense How do you know that 35 ! 5 " 5 ! 35 without finding products? Topic 3 1/31/08 11:09:39 AM Name Reteaching 3-3 Multiplication Properties You can use the Properties of Multiplication to help you find products. Commutative Property of Multiplication: You can multiply any two numbers in any order. 2!3"3!2 Identity Property of Multiplication When you multiply any number by 1, the product is that number. Reteaching 3-3 7!1"7 Zero Property of Multiplication When you multiply any number by 0, the product is also 0. 3!0"0 1. 7 ! 3 " 3 ! 3. 5 ! 4 " 4 ! 5. 0 ! 7 " 7. 9 ! 1 " 1 ! 7 5 0 9 2. 4 ! 0 " 4. 2 ! 1 " 6. 8 ! 3 " 3 ! 8. 1 ! 5 " 0 2 8 5 9. Number Sense How do you know that 35 ! 5 " 5 ! 35 without finding products? 10. Writing to Explain Explain how you know that in ? ! 6,273 " 6,273, the ? will be 1. Sample answer: Any number multiplied by 1 is that number. 40 Nat_AncTopic_3.indb 40 © Pearson Education, Inc. 4 The Commutative Property of Multiplication states the product is the same regardless of the order in which the two numbers are multiplied. Topic 3 1/31/08 2:33:16 PM Name Practice 3-3 Multiplication Properties 1. ! 0 4 ! 1 8 5. 2. ! 1 3 ! 3 0 6. 9. 1 ! 1 " 3. ! 7 1 ! 4 1 7. 4. ! 5 0 ! 6 0 8. 10. 9 ! 0 " 11. 0 ! 0 " Practice 3-3 Algebra Find the missing number. 12. !9"0 13. 1 ! "4 14. Ray has 4 boxes with 5 pens in each box. Kevin has 5 boxes with 4 pens in each. Who has more pens? 15. Which property can help you find the missing number? !9"0 © Pearson Education, Inc. 4 16. Writing to Explain Steve needs to find the product of two numbers. One of the numbers is 6. The answer also needs to be 6. How will you solve this problem? Explain. Topic 3 Nat_AncTopic_3.indb 41 41 1/31/08 11:09:41 AM Name Practice 3-3 Multiplication Properties 1. ! 5. ! 2. 0 4 ! 0 6. 1 8 ! 8 9. 1 ! 1 " 11. 0 ! 0 " 1 0 1 3 3 3 0 0 3. ! 7. ! 4. 7 1 ! 7 8. 4 1 4 10. 9 ! 0 " ! 0 5 0 0 6 0 0 Practice 3-3 Algebra Find the missing number. 12. 0 !9"0 13. 1 ! 4 "4 14. Ray has 4 boxes with 5 pens in each box. Kevin has 5 boxes with 4 pens in each. Who has more pens? They have the same number of pens, because 4 ! 5 " 5 ! 4. 15. Which property can help you find the missing number? Zero Property of Multiplication !9"0 16. Writing to Explain Steve needs to find the product of two numbers. One of the numbers is 6. The answer also needs to be 6. How will you solve this problem? Explain. © Pearson Education, Inc. 4 Sample answer: Steve will multiply 6 ! 1 " 6. The product of any number and 1 equals that number. Topic 3 Nat_AncTopic_3.indb 41 41 1/31/08 2:33:17 PM Name Enrichment How Does Your Garden Grow? Area is the name for the number of square units that are in a given space. You can figure out the area of a rectangle as you would an array. You can also break apart a rectangle to form different combinations and still have the same area. 3-3 Visual Thinking Enrichment Enrichment 3-3 3-3 Here is Mary’s garden: 4 ! 6 = 24 square units. Draw lines and write the first letter of the flower to show several possible planting plans. 1. 2. 2 6 tulips 2 4 roses 2 2 marigolds 4 4 tulips 2 2 roses 2 2 marigolds 4. 3. 4 5 tulips 3 1 roses 1 1 marigolds © Pearson Education, Inc. 4 3 4 tulips 1 6 roses 3 2 marigolds 42 Nat_AncTopic_3.indb 42 Topic 3 1/31/08 11:09:42 AM Name Enrichment 3-3 How Does Your Garden Grow? Area is the name for the number of square units that are in a given space. You can figure out the area of a rectangle as you would an array. You can also break apart a rectangle to form different combinations and still have the same area. Visual Thinking Enrichment Enrichment 3-3 3-3 Here is Mary’s garden: 4 ! 6 = 24 square units. Sample answers given. Draw lines and write the first letter of the flower to show several possible planting plans. 1. 2. T R R T M 2 6 tulips 2 4 roses 2 2 marigolds M 4 4 tulips 2 2 roses 2 2 marigolds 4. 3. T M R R M 4 5 tulips 3 1 roses 1 1 marigolds © Pearson Education, Inc. 4 3 4 tulips 1 6 roses 3 2 marigolds T 42 Nat_AncTopic_3.indb 42 Topic 3 1/31/08 2:33:18 PM Name Daily Spiral Review 3-4 5. Michael has a marble collection. On Monday, he gave 17 marbles to Lily. On Tuesday, he gave 10 marbles to Jose. On Wednesday, Michael had 34 marbles left in his collection. How many marbles did Michael have to start? 2. Mateo, Andrea, and Louis have 18 apples altogether. If they each have the same number of apples, how many apples do they each have? A 3 B 5 C 6 D 18 6. Karen organized her butterfly pins into 4 groups. Each group has 6 pins in it. How many pins does Karen have altogether? Write a number sentence to solve the problem. Daily Spiral Review 3-4 1. There are 402 students at Bakerville Elementary School. There are 366 students at Austintown Elementary School. How many more students are at Bakerville? A 26 B 36 C 42 D 46 7. Paul has the following coins. How much money does he have? © Pearson Education, Inc. 4 3. Which is the word form for the number 7,077? A Seven thousand, seven B Seven thousand, seventy C Seven thousand, seventy-seven D Seven thousand, seven hundred seven 4. Which digit is in the thousands place in the number 39,271? A 1 B 3 C 7 D 9 8. Look at the drawing below. What is a number sentence for the array? Topic 3 Nat_AncTopic_3.indb 43 43 1/31/08 11:09:44 AM Name Daily Spiral Review 3-4 1. There are 402 students at Bakerville Elementary School. There are 366 students at Austintown Elementary School. How many more students are at Bakerville? A 26 B 36 C 42 D 46 5. Michael has a marble collection. On Monday, he gave 17 marbles to Lily. On Tuesday, he gave 10 marbles to Jose. On Wednesday, Michael had 34 marbles left in his collection. How many marbles did Michael have to start? 2. Mateo, Andrea, and Louis have 18 apples altogether. If they each have the same number of apples, how many apples do they each have? A 3 B 5 C 6 D 18 6. Karen organized her butterfly pins into 4 groups. Each group has 6 pins in it. How many pins does Karen have altogether? Write a number sentence to solve the problem. 61 marbles 7. Paul has the following coins. How much money does he have? © Pearson Education, Inc. 4 3. Which is the word form for the number 7,077? A Seven thousand, seven B Seven thousand, seventy C Seven thousand, seventy-seven D Seven thousand, seven hundred seven 4. Which digit is in the thousands place in the number 39,271? A 1 B 3 C 7 D 9 $0.56 8. Look at the drawing below. What is a number sentence for the array? 3 ! 4 " 12 Topic 3 Nat_AncTopic_3.indb 43 Daily Spiral Review 3-4 24 pins; 4 ! 6 " 24 43 1/31/08 2:33:19 PM 44 Nat_AncTopic_3.indb 44 Problem of the Day 3-4 Topic 3 Problem of the Day 3-4 Write three number sentences that have a product of 12. 3-4 Problem of the Day 1/31/08 11:09:45 AM © Pearson Education, Inc. 4 Name Quick Check 3-4 1. 5 ! 4 " (5 ! 1) # (5 ! __ ) " 20 A 2 B 3 C 4 D 5 2. 4 ! 8 " (4 ! 2) # (4 ! __ ) " 32 A 2 B 4 C 6 Quick Check 3-4 D 8 © Pearson Education, Inc. 4 3. Writing to Explain Roberto has 30 pennies. He puts the pennies in 6 groups of 5 pennies. This can be written as 6 ! 5 " 30. Break this into 2 simpler multiplications. Explain how these simpler multiplications are another way that Roberto can group his pennies. Topic 3 Nat_AncTopic_3.indb 45 45 1/31/08 11:09:46 AM Name Quick Check 3-4 1. 5 ! 4 " (5 ! 1) # (5 ! __ ) " 20 A 2 B 3 C 4 D 5 2. 4 ! 8 " (4 ! 2) # (4 ! __ ) " 32 A 2 B 4 C 6 Quick Check 3-4 D 8 3. Writing to Explain Roberto has 30 pennies. He puts the pennies in 6 groups of 5 pennies. This can be written as 6 ! 5 " 30. Break this into 2 simpler multiplications. Explain how these simpler multiplications are another way that Roberto can group his pennies. © Pearson Education, Inc. 4 See student samples to the right. Topic 3 Nat_AncTopic_3.indb 45 45 1/31/08 2:33:22 PM Name Reteaching 3-4 3 and 4 as Factors You can use breaking apart to find a product. Find 4 ! 5. 4 groups of 5 are the same as 2 groups of 5 and 2 groups of 5. 2 5 10 Reteaching 3-4 2 5 10 4 ! 5 " (2 ! 5) # (2 ! 5) " 10 # 10 " 20 Use breaking apart to find each product. 1. 3 ! 5 2. 3 ! 8 3. 4 ! 9 4. 3 ! 7 5. 4 ! 8 6. 3 ! 6 7. 3 ! 4 8. 4 ! 4 10. 4 ! 9 " 11. 4 ! 8 " 12. 3 ! 9 " © Pearson Education, Inc. 4 9. 4 ! 6 " 46 Nat_AncTopic_3.indb 46 Topic 3 1/31/08 11:09:47 AM Name Reteaching 3-4 3 and 4 as Factors You can use breaking apart to find a product. Find 4 ! 5. 4 groups of 5 are the same as 2 groups of 5 and 2 groups of 5. 2 5 10 Reteaching 3-4 2 5 10 4 ! 5 " (2 ! 5) # (2 ! 5) " 10 # 10 " 20 Use breaking apart to find each product. 1. 2. 3 ! 5 15 5. 6. 32 3 ! 6 18 24 32 4. 4 ! 9 36 7. 21 3 ! 4 12 10. 4 ! 9 " 12. 3 ! 9 " 3 ! 7 8. 36 27 4 ! 4 16 © Pearson Education, Inc. 4 11. 4 ! 8 " 3. 24 4 ! 8 9. 4 ! 6 " 3 ! 8 46 Nat_AncTopic_3.indb 46 Topic 3 1/31/08 2:33:23 PM Name Practice 3-4 3 and 4 as Factors Use breaking apart to find each product. 1. 3 ! 7 2. 4 ! 9 3. 3 ! 4 4. 4 ! 6 5. 4 ! 5 " 6. 3 ! 9 " 7. 3 ! 5 " 8. 3 ! 6 " 9. 4 ! 7 " 10. 3 ! 8 " Practice 3-4 11. Number Sense Sara traced circle stencils for her project. She needs 4 rows of 6 circle stencils. She thought that 4 rows of 6 is the same as 3 rows of 8 and 2 rows of 8. Is this correct? Explain. 12. Which of the following is equal to the product of 3 ! 3? A 9!1 B 3!1 C 4!2 D 6!3 © Pearson Education, Inc. 4 13. Writing to Explain Explain how the three multiplication sentences are related. 2 ! 12 3!8 4!6 Topic 3 Nat_AncTopic_3.indb 47 47 1/31/08 11:09:49 AM Name Practice 3-4 3 and 4 as Factors Use breaking apart to find each product. 1. 3 ! 7 2. 21 5. 4 ! 5 " 8. 3 ! 6 " 4 ! 9 36 20 18 6. 3 ! 9 " 9. 4 ! 7 " 3. 3 ! 4 12 27 28 4. 7. 10. 4 ! 6 24 3!5" 15 3!8" 24 Practice 3-4 11. Number Sense Sara traced circle stencils for her project. She needs 4 rows of 6 circle stencils. She thought that 4 rows of 6 is the same as 3 rows of 8 and 2 rows of 8. Is this correct? Explain. Sample answer: No, 3 rows of 8 and 2 rows of 8 equal 5 rows of 8, not 4 rows of 6. 12. Which of the following is equal to the product of 3 ! 3? A 9!1 B 3!1 C 4!2 D 6!3 13. Writing to Explain Explain how the three multiplication sentences are related. 2 ! 12 3!8 4!6 © Pearson Education, Inc. 4 Sample answer: They all have the same product, 24. Topic 3 Nat_AncTopic_3.indb 47 47 1/31/08 2:33:24 PM Name Enrichment 3-4 Recycling Numbers Miles and Cynthia participated in a weeklong recycling project. Cynthia collected 4 cans every day, and Miles collected 3 cans every day. Patterns 1. Fill in the table to show how many cans each student has collected by the end of each day. Days 1 2 Miles 3 6 Cynthia 4 8 3 4 5 6 7 Enrichment 3-4 2. At the end of the week, how many cans did Cynthia collect? 3. At the end of the week, how many cans had Miles collected? 4. If the pattern had continued for another week, a total of 14 days, how many cans would Cynthia have collected? How many would Miles have collected? 5. The project was such a success, it was continued for 30 days. Complete the bar graph to compare the total cans collected by Miles and Cynthia. Cans Collected After 30 Days Cynthia 0 48 Nat_AncTopic_3.indb 48 20 40 60 80 100 120 140 © Pearson Education, Inc. 4 Miles Topic 3 1/31/08 11:09:50 AM Name Enrichment 3-4 Recycling Numbers Miles and Cynthia participated in a weeklong recycling project. Cynthia collected 4 cans every day, and Miles collected 3 cans every day. Patterns 1. Fill in the table to show how many cans each student has collected by the end of each day. Days 1 2 Miles 3 6 Cynthia 4 8 3 4 5 6 7 9 12 15 18 21 12 16 20 24 28 2. At the end of the week, how many cans did Cynthia collect? Enrichment 3-4 Cynthia collected 28 cans. 3. At the end of the week, how many cans had Miles collected? Miles collected 21 cans. 4. If the pattern had continued for another week, a total of 14 days, how many cans would Cynthia have collected? How many would Miles have collected? Cynthia: 56 cans; Miles: 42 cans 5. The project was such a success, it was continued for 30 days. Complete the bar graph to compare the total cans collected by Miles and Cynthia. Sample answer: Cans Collected After 30 Days Cynthia 0 48 Nat_AncTopic_3.indb 48 20 40 60 80 100 120 140 © Pearson Education, Inc. 4 Miles Topic 3 1/31/08 2:33:25 PM Name 1. Mark, Julia, and Noah each have 5 crackers. How many crackers do they have altogether? A 5 B 10 C 15 D 20 © Pearson Education, Inc. 4 3. Lynda wants to buy a new bicycle. The bicycle she wants costs $306. So far, she has saved $130. How much more money does Lynda need to buy the bicycle? A $176 B $184 C $234 D $246 3-5 5. Complete the number sentence and find the product. 5 ! 9 " (5 ! 1) + (5 ! )" 6. Look for a pattern. Write the next two numbers. 4, 8, 12, 16, , 7. Maggie, Louisa, Grace, and Donna are standing in a line. Grace is first. Donna is not last and is ahead of Maggie. Louisa is behind Grace and Maggie. In what order are the girls in line? 8. Write two number sentences using 3, 8, and 24 to show the Commutative Property of Multiplication. Daily Spiral Review 3-5 2. At the school bake sale, Ms. Dorrit’s class sold 57 brownies. Ms. Temple’s class sold 84 brownies. How many brownies did they sell altogether? A 111 B 141 C 147 D 1,311 Daily Spiral Review 4. Which numbers are written in order from least to greatest? A 1,287, 1,276, 1270 B 650, 715, 651 C 515, 502, 531 D 802, 815, 830 Topic 3 Nat_AncTopic_3.indb 49 49 1/31/08 11:09:51 AM Name 1. Mark, Julia, and Noah each have 5 crackers. How many crackers do they have altogether? A 5 B 10 C 15 D 20 © Pearson Education, Inc. 4 3. Lynda wants to buy a new bicycle. The bicycle she wants costs $306. So far, she has saved $130. How much more money does Lynda need to buy the bicycle? A $176 B $184 C $234 D $246 3-5 5. Complete the number sentence and find the product. 5 ! 9 " (5 ! 1) + (5 ! 45 8 )" 6. Look for a pattern. Write the next two numbers. 4, 8, 12, 16, , 20 24 7. Maggie, Louisa, Grace, and Donna are standing in a line. Grace is first. Donna is not last and is ahead of Maggie. Louisa is behind Grace and Maggie. In what order are the girls in line? Grace, Donna, Maggie, Louisa 8. Write two number sentences using 3, 8, and 24 to show the Commutative Property of Multiplication. Daily Spiral Review 3-5 2. At the school bake sale, Ms. Dorrit’s class sold 57 brownies. Ms. Temple’s class sold 84 brownies. How many brownies did they sell altogether? A 111 B 141 C 147 D 1,311 Daily Spiral Review 3 ! 8 " 24, 8 ! 3 " 24 4. Which numbers are written in order from least to greatest? A 1,287, 1,276, 1270 B 650, 715, 651 C 515, 502, 531 D 802, 815, 830 Topic 3 Nat_AncTopic_3.indb 49 49 1/31/08 2:33:26 PM 50 Nat_AncTopic_3.indb 50 Problem of the Day 3-5 Topic 3 Problem of the Day 3-5 How many items are in an array with 7 columns and 6 rows? Write a number sentence that uses breaking apart to find the product. 3-5 Problem of the Day 1/31/08 11:09:52 AM © Pearson Education, Inc. 4 Name Quick Check 3-5 Use breaking apart to solve the following. Circle the letter of the correct answer. 1. 4 ! 7 " (4 ! 2) # (4 ! ) " 28 A 2 B 3 C 4 D 5 2. 5 ! 8 " (5 ! 2) # (5 ! ) " 40 A 4 B 5 C 6 Quick Check 3-5 D 11 © Pearson Education, Inc. 4 3. Writing to Explain Miranda multiplied 7 ! 7, and it helped her find the product of 7 ! 8. Draw a picture and explain what she means. Topic 3 Nat_AncTopic_3.indb 51 51 1/31/08 11:09:53 AM Name Quick Check 3-5 Use breaking apart to solve the following. Circle the letter of the correct answer. 1. 4 ! 7 " (4 ! 2) # (4 ! ) " 28 A 2 B 3 C 4 D 5 2. 5 ! 8 " (5 ! 2) # (5 ! ) " 40 A 4 B 5 C 6 Quick Check 3-5 D 11 3. Writing to Explain Miranda multiplied 7 ! 7, and it helped her find the product of 7 ! 8. Draw a picture and explain what she means. © Pearson Education, Inc. 4 See student samples to the right. Topic 3 Nat_AncTopic_3.indb 51 51 1/31/08 2:33:28 PM Name Reteaching 3-5 6, 7, and 8 as Factors You can use breaking apart to find a product. Find 8 ! 5. 8 groups of 5 are the same as 2 groups of 5, 2 groups of 5, 2 groups of 5, and 2 groups of 5. 2 5 10 2 5 10 2 5 10 2 5 10 8 ! 5 " (2 ! 5) # (2 ! 5) # (2 ! 5) # (2 ! 5) Reteaching 3-5 " 10 # 10 # 10 # 10 " 40 Use breaking apart to find each product. 1. 7 ! 5 2. 8 ! 3 3. 7 ! 9 4. 7 ! 7 5. 8 ! 4 6. 8 ! 8 7. 6 ! 3 8. 7 ! 4 Compare. Use <, >, or " to fill in each 8!7 10. 7 ! 6 6!6 © Pearson Education, Inc. 4 9. 7 ! 6 . 52 Nat_AncTopic_3.indb 52 Topic 3 1/31/08 11:09:54 AM Name Reteaching 3-5 6, 7, and 8 as Factors You can use breaking apart to find a product. Find 8 ! 5. 8 groups of 5 are the same as 2 groups of 5, 2 groups of 5, 2 groups of 5, and 2 groups of 5. 2 5 10 2 5 10 2 5 10 2 5 10 8 ! 5 " (2 ! 5) # (2 ! 5) # (2 ! 5) # (2 ! 5) Reteaching 3-5 " 10 # 10 # 10 # 10 " 40 Use breaking apart to find each product. 1. 2. 7 ! 5 35 5. 8 ! 3 24 8 ! 4 6. 32 8 ! 8 7. 8!7 7 ! 7 49 6 ! 3 8. 18 7 ! 4 28 . 10. 7 ! 6 > 6!6 © Pearson Education, Inc. 4 < 4. 7 ! 9 63 64 Compare. Use <, >, or " to fill in each 9. 7 ! 6 3. 52 Nat_AncTopic_3.indb 52 Topic 3 1/31/08 2:33:28 PM Name Practice 3-5 6, 7, and 8 as Factors Use breaking apart to find each product. 1. 7 ! 3 2. 8 ! 5 3. 4. 8 ! 2 6 ! 4 5. 6 ! 3 " 6. 8 ! 3 " 7. 7 ! 5 " 8. 6 ! 6 " 9. 6 ! 7 " 10. 7 ! 9 " 11. Number Sense Meghan planted seeds for her project. She needs 7 rows of 9 seeds. She thought that 7 rows of 9 is the same as 3 rows of 9 and 2 rows of 9. Is this correct? Practice 3-5 12. Which of the following is equal to the product of 8 ! 3? A 7!4 B 6!4 C 6!2 D 8!2 © Pearson Education, Inc. 4 13. Writing to Explain Explain how the three multiplication sentences are related. 6!2 4!3 12 ! 1 Topic 3 Nat_AncTopic_3.indb 53 53 1/31/08 11:09:55 AM Name Practice 3-5 6, 7, and 8 as Factors Use breaking apart to find each product. 1. 7 ! 3 21 18 6 ! 6 " 36 2. 3. 8 ! 5 40 4. 8 ! 2 16 24 6 ! 7 " 42 5. 6 ! 3 " 6. 8 ! 3 " 8. 9. 7. 10. 6 ! 4 24 7 ! 5 " 35 7 ! 9 " 63 11. Number Sense Meghan planted seeds for her project. She needs 7 rows of 9 seeds. She thought that 7 rows of 9 is the same as 3 rows of 9 and 2 rows of 9. Is this correct? Practice 3-5 Sample answer: No, 3 rows of 9 and 2 rows of 9 equal 5 rows of 9, not 7 rows of 9. 12. Which of the following is equal to the product of 8 ! 3? A 7!4 B 6!4 C 6!2 D 8!2 13. Writing to Explain Explain how the three multiplication sentences are related. 6!2 4!3 12 ! 1 © Pearson Education, Inc. 4 They all have the same product, 12. Topic 3 Nat_AncTopic_3.indb 53 53 1/31/08 2:33:30 PM Name Enrichment 3-5 Cube Turning A lettered cube has 6 sides with a different letter on each side. Each letter can be shown in 4 different positions. Visual Thinking 1. How many different ways can the cube be displayed? B C E E CD D E C D E A D F F B © Pearson Education, Inc. 4 F E B B F F A E Enrichment 3-5 DA E C F F E E C E A D D DA A 6. F F C 5. CD C 4. B 3. BC A 2. AB E D F Example: AB Fill in the missing letters in the position they would be seen on the cube. The first one has been done for you as an example. 54 Nat_AncTopic_3.indb 54 Topic 3 1/31/08 11:09:56 AM Name Enrichment 3-5 Cube Turning A lettered cube has 6 sides with a different letter on each side. Each letter can be shown in 4 different positions. Visual Thinking 1. How many different ways can the cube be displayed? 24 different ways BC E CD CED DA E E D D C F F C B © Pearson Education, Inc. 4 F E B B A C F B B F F A E A C D A DA E Enrichment 3-5 E A F F F E B C E E D D A 6. DA F C 5. F BC 4. CD B 3. BC A 2. AB E D F Example: AB Fill in the missing letters in the position they would be seen on the cube. The first one has been done for you as an example. 54 Nat_AncTopic_3.indb 54 Topic 3 1/31/08 2:33:31 PM Name 1. Tyler and his father are raising funds for a new animal shelter. So far, Tyler has raised $2,789. His father has raised $1,286. How much have they raised altogether? A $3,005 B $3,065 C $4,065 D $4,075 © Pearson Education, Inc. 4 3. Randy bought a pair of jeans for $15.98. How could he pay using the fewest coins and bills? A 15 one-dollar bills, 1 quarter, 14 nickels, 3 pennies B 3 five-dollar bills, 2 quarters, 8 nickels, 3 pennies C 1 ten-dollar bill, 1 five-dollar bill, 3 quarters, 2 dimes, 3 pennies D 2 five-dollar bills, 5 one-dollar bills, 1 quarter, 7 dimes, 3 pennies 3-6 Class Number of Cans Collected Ms. Hammond Mr. Black Ms. Swift 534 502 492 4. The three fourth-grade classes are collecting cans for a recycling drive. To the nearest hundred, how many cans have the students in Mr. Black’s class collected? 5. About how many more cans has Ms. Hammond’s class collected than Ms. Swift’s class? 6. Richard knows that 4 ! 3 is 12. Write a number sentence to show how he can use this product to find 4 ! 4. 7. At a golf tournament, Owen scored a 75 on his first round, 79 on his second round, and 82 on his third round. What was Owen’s total score? Topic 3 Nat_AncTopic_3.indb 55 Daily Spiral Review 3-6 2. Tina is reading a book that has 18 chapters. If she reads 2 chapters each night, how many nights will it take her to finish the book? A 9 nights B 18 nights C 20 nights D 36 nights Daily Spiral Review 55 1/31/08 11:09:58 AM Name 1. Tyler and his father are raising funds for a new animal shelter. So far, Tyler has raised $2,789. His father has raised $1,286. How much have they raised altogether? A $3,005 B $3,065 C $4,065 D $4,075 © Pearson Education, Inc. 4 3. Randy bought a pair of jeans for $15.98. How could he pay using the fewest coins and bills? A 15 one-dollar bills, 1 quarter, 14 nickels, 3 pennies B 3 five-dollar bills, 2 quarters, 8 nickels, 3 pennies C 1 ten-dollar bill, 1 five-dollar bill, 3 quarters, 2 dimes, 3 pennies D 2 five-dollar bills, 5 one-dollar bills, 1 quarter, 7 dimes, 3 pennies 3-6 Class Number of Cans Collected Ms. Hammond Mr. Black Ms. Swift 534 502 492 4. The three fourth-grade classes are collecting cans for a recycling drive. To the nearest hundred, how many cans have the students in Mr. Black’s class collected? 500 5. About how many more cans has Ms. Hammond’s class collected than Ms. Swift’s class? 40 6. Richard knows that 4 ! 3 is 12. Write a number sentence to show how he can use this product to find 4 ! 4. (4 ! 3) " (4 ! 1) # 12 " 4 # 16 7. At a golf tournament, Owen scored a 75 on his first round, 79 on his second round, and 82 on his third round. What was Owen’s total score? 236 Topic 3 Nat_AncTopic_3.indb 55 Daily Spiral Review 3-6 2. Tina is reading a book that has 18 chapters. If she reads 2 chapters each night, how many nights will it take her to finish the book? A 9 nights B 18 nights C 20 nights D 36 nights Daily Spiral Review 55 1/31/08 2:33:33 PM 56 Nat_AncTopic_3.indb 56 Problem of the Day 3-6 Topic 3 Problem of the Day 3-6 What is the rule for the pattern? 66, 77, 88, 99,.... 3-6 Problem of the Day 1/31/08 11:09:59 AM © Pearson Education, Inc. 4 Name Quick Check 3-6 Use breaking apart and patterns to solve the following. Circle the correct answer. 1. 6 ! 11 " (6 ! 8) # (6 ! ) A 2 B 3 C 4 D 5 2. 10 ! 11 " (10 ! 10) # ( ! 1) Quick Check 3-6 A 1 B 5 C 10 D 12 © Pearson Education, Inc. 4 3. Writing to Explain Tanya feeds her cat 11 treats each week. Every 8 weeks, she runs out of treats and has to buy a new box. How many treats come in each box? Explain how to use multiplication to find the answer. Topic 3 Nat_AncTopic_3.indb 57 57 1/31/08 11:10:01 AM Name Quick Check 3-6 Use breaking apart and patterns to solve the following. Circle the correct answer. 1. 6 ! 11 " (6 ! 8) # (6 ! ) A 2 B 3 C 4 D 5 2. 10 ! 11 " (10 ! 10) # ( ! 1) Quick Check 3-6 A 1 B 5 C 10 D 12 3. Writing to Explain Tanya feeds her cat 11 treats each week. Every 8 weeks, she runs out of treats and has to buy a new box. How many treats come in each box? Explain how to use multiplication to find the answer. © Pearson Education, Inc. 4 See student samples to the right. Topic 3 Nat_AncTopic_3.indb 57 57 1/31/08 2:33:36 PM Name Reteaching 3-6 10, 11, and 12 as Factors Here are some easy ways to multiply numbers by 10, 11, and 12. Multiples of 10 Any whole number multiplied by 10 will always equal that number with an additional zero in the ones place. For example, 2 ! 10 " 20, 22 ! 10 " 220, and 220 ! 10 " 2,200. You can also break apart equations to help find products. Reteaching 3-6 Multiples of 11 To find 12 ! 11, think of 11 as 10 # 1. 12 ! 10 " 120, 12 ! 1 " 12, 120 # 12 " 132, so 12 ! 11 " 132. Multiples of 12 To find 6 ! 12, think of 12 as 10 # 2. 6 ! 10 " 60, 6 ! 2 " 12, 60 # 12 " 72, so 6 ! 12 " 72. 1. 5 ! 11 " 2. 12 ! 4 " 3. 10 ! 9 " 4. 7 ! 12 " 5. 12 ! 11 " 6. 8 ! 10 " 7. Number Sense Explain how 9 ! 10 can help you find 9 ! 11. There are 11 players on the field for each football team during a game. How many players would there be on 8. 4 teams? 10. 10 teams? 11. 11 teams? 58 Nat_AncTopic_3.indb 58 © Pearson Education, Inc. 4 9. 8 teams? Topic 3 1/31/08 11:10:01 AM Name Reteaching 3-6 10, 11, and 12 as Factors Here are some easy ways to multiply numbers by 10, 11, and 12. Multiples of 10 Any whole number multiplied by 10 will always equal that number with an additional zero in the ones place. For example, 2 ! 10 " 20, 22 ! 10 " 220, and 220 ! 10 " 2,200. You can also break apart equations to help find products. Reteaching 3-6 Multiples of 11 To find 12 ! 11, think of 11 as 10 # 1. 12 ! 10 " 120, 12 ! 1 " 12, 120 # 12 " 132, so 12 ! 11 " 132. Multiples of 12 To find 6 ! 12, think of 12 as 10 # 2. 6 ! 10 " 60, 6 ! 2 " 12, 60 # 12 " 72, so 6 ! 12 " 72. 1. 5 ! 11 " 4. 7 ! 12 " 55 84 2. 12 ! 4 " 5. 12 ! 11 " 48 132 3. 10 ! 9 " 6. 8 ! 10 " 90 80 7. Number Sense Explain how 9 ! 10 can help you find 9 ! 11. 9 ! 10 " 90, 1 ! 9 " 9, 90 # 9 " 99 8. 4 teams? 9. 8 teams? 10. 10 teams? 11. 11 teams? 58 Nat_AncTopic_3.indb 58 44 players 88 players 110 players 121 players © Pearson Education, Inc. 4 There are 11 players on the field for each football team during a game. How many players would there be on Topic 3 1/31/08 2:33:37 PM Name Practice 3-6 10, 11, and 12 as Factors 1. 4 ! 10 " 2. 12 ! 2 " 3. 10 ! 6 " 4. 11 ! 1 " 5. 4 ! 12 " 6. 8 ! 11 " 7. 9 ! 10 " 8. 12 ! 3 " 9. 10 ! 7 " 10. 11 ! 5 " 11. 10 ! 5 " 12. 6 ! 12 " 13. Number Sense Beatrice multiplied 10 ! 9. She quickly found the answer by placing a 0 behind the 9 to get an answer of 90. Is this reasonable? Practice 3-6 There are 12 months in 1 year. How many months are in 14. 2 years? 15. 3 years? 16. 5 years? 17. In the classroom there are 5 round tables. There are 4 students sitting at each table. How many students are sitting at the tables altogether? 18. How much money is 12 dimes? A $0.60 B $1.00 C $1.20 D $2.00 © Pearson Education, Inc. 4 19. Writing to Explain Explain how to find 7 ! 11. Topic 3 Nat_AncTopic_3.indb 59 59 1/31/08 11:10:03 AM Name Practice 10, 11, and 12 as Factors 1. 4 ! 10 " 40 2. 12 ! 2 " 24 4. 11 ! 1 " 11 5. 4 ! 12 " 48 7. 9 ! 10 " 90 8. 12 ! 3 " 36 10. 11 ! 5 " 55 11. 10 ! 5 " 50 3-6 3. 10 ! 6 " 6. 8 ! 11 " 9. 10 ! 7 " 12. 6 ! 12 " 60 88 70 72 13. Number Sense Beatrice multiplied 10 ! 9. She quickly found the answer by placing a 0 behind the 9 to get an answer of 90. Is this reasonable? Practice 3-6 Sample answer: Yes, that rule tells how to find each multiple of 10. There are 12 months in 1 year. How many months are in 14. 2 years? 15. 3 years? 16. 5 years? 24 months 36 months 60 months 17. In the classroom there are 5 round tables. There are 4 students sitting at each table. How many students are sitting at the tables altogether? 20 students 18. How much money is 12 dimes? A $0.60 B $1.00 C $1.20 D $2.00 19. Writing to Explain Explain how to find 7 ! 11. © Pearson Education, Inc. 4 Sample answer: Use breaking apart: (7 ! 10) " (7 ! 1) # 70 " 7 # 77 Topic 3 Nat_AncTopic_3.indb 59 59 1/31/08 2:33:38 PM Name Enrichment 3-6 Break the Codes Visual Thinking The symbols in each set of problems represent whole numbers. Break the codes. Hint: Here’s how you might break one code. @ M 27 Think: @ @ 24 is a double. @ @ 24 The two addends are the same, so @ 12. 1. 3. 11 1 , 8 48 , 5. Nat_AncTopic_3.indb 60 4. 12 , 6. 18 90 60 7. 2. , 8. 33 9 , 28 16 , 11 , 16 40 64 , , © Pearson Education, Inc. 4 Enrichment 3-6 Since 27 12 15, M 15. Topic 3 1/31/08 11:10:04 AM Name Enrichment 3-6 Break the Codes Visual Thinking The symbols in each set of problems represent whole numbers. Break the codes. Hint: Here’s how you might break one code. @ M 27 Think: @ @ 24 is a double. @ @ 24 The two addends are the same, so @ 12. 1. 11 1 3. 11, 8 48 5. 12 , 12 9 , 1 18 90 9 , 4 33 9 3 10 28 16 Nat_AncTopic_3.indb 60 , 11 12, 16 40 64 60 7 8. 11 , 6. 4. 7. 2. 5 , 3 4 1 2, 8 © Pearson Education, Inc. 4 Enrichment 3-6 Since 27 12 15, M 15. Topic 3 1/31/08 2:33:39 PM Name Daily Spiral Review 3-7 1. Peter has $8.08 in his pocket. He finds a quarter on the sidewalk and puts it in his pocket. How much money does he have in his pocket now? A $8.10 B $8.25 C $8.33 D $8.38 4. What kind of figure has 3 sides? 2. Yvette’s computer has a folder with files shown in rows and columns. There are 4 rows and 12 columns. Which number sentence shows how many files the folder has? A 4 ! 12 " 48 B 12 # 4 " 8 C 4 $ 12 " 16 D 12 % 4 " 3 6. The table shows how much money four friends have. Place the amounts in order from greatest to least. Amount $15.80 $15.72 $16.10 $16.02 © Pearson Education, Inc. 4 Person Sven Rita Wendy Carlos Daily Spiral Review 3-7 3. Nick has 1,263 baseball cards. He gives 374 to his younger sister. How many baseball cards does Nick have now? A 889 B 899 C 989 D 999 5. Nina has 763 pennies in a jar. Daryl has 839 pennies in a jar. Round each amount to the nearest hundred. Topic 3 Nat_AncTopic_3.indb 61 61 1/31/08 11:10:06 AM Name Daily Spiral Review 3-7 1. Peter has $8.08 in his pocket. He finds a quarter on the sidewalk and puts it in his pocket. How much money does he have in his pocket now? A $8.10 B $8.25 C $8.33 D $8.38 4. What kind of figure has 3 sides? 2. Yvette’s computer has a folder with files shown in rows and columns. There are 4 rows and 12 columns. Which number sentence shows how many files the folder has? A 4 ! 12 " 48 B 12 # 4 " 8 C 4 $ 12 " 16 D 12 % 4 " 3 6. The table shows how much money four friends have. Place the amounts in order from greatest to least. 5. Nina has 763 pennies in a jar. Daryl has 839 pennies in a jar. Round each amount to the nearest hundred. Nina: 800, Daryl: 800 $16.10, $16.02, $15.80, $15.72 Amount $15.80 $15.72 $16.10 $16.02 © Pearson Education, Inc. 4 Person Sven Rita Wendy Carlos Daily Spiral Review 3-7 3. Nick has 1,263 baseball cards. He gives 374 to his younger sister. How many baseball cards does Nick have now? A 889 B 899 C 989 D 999 Triangle Topic 3 Nat_AncTopic_3.indb 61 61 1/31/08 2:33:41 PM 62 Nat_AncTopic_3.indb 62 Problem of the Day 3-7 Topic 3 Problem of the Day 3-7 When will be the next year of the Tiger? Year of the Horse? Chinese Zodiac Pig Dog er 1982 1983 st 1995 4 9 o 9 1 1 o R 198 93 19 3-7 p Monke Shee 1992 y 1991 se 003 2004 or 0 H 99 2 2 1 00 2 1/31/08 11:10:08 AM © Pearson Education, Inc. 4 Problem of the Day on Snake Drag 1989 1988 2 2000 001 Tige Ox r 1986 H 1985 t a 1 Ra 84 1997 998 1 198 re 99 7 19 996 9 1 Name Quick Check 3-7 1. The United States flag had 25 stars in 1837. The flag has twice as many stars today. Which bar diagram shows how many stars the flag has today? ? A 25 25 25 ? B 2. Nina is 48 inches tall. Rafael is 53 inches tall. Which number sentence tells you how many inches taller Rafael is than Nina? A 48 ! 53 " 101 B 101 # 53 " 48 C 53 ! 5 " 58 D 53 # 48 " 5 25 ? C 25 25 25 25 ? D 25 25 25 4. Ian is 6 years old. His brother Curtis is 3 times as old. Which number sentence tells you how old Curtis is? Quick Check 3-7 3. Kerry is watering her plants. The plant at her desk needs 5 times as much water as the plant by her window does. The plant by her window needs 2 pints of water. How much water does the plant at her desk need? A 3 $ 6 " 18 B 3 $ 3 $ 3 " 27 A 3 pints C 10 pints C 3!3!3"9 B 7 pints D 14 pints D 9 $ 2 " 18 © Pearson Education, Inc. 4 5. Writing to Explain Adam’s pet frog can jump 4 times as far as Sonya’s. Sonya’s frog can jump 8 inches. Use a picture and a number sentence to tell how many inches Adam’s frog can jump. Topic 3 Nat_AncTopic_3.indb 63 63 1/31/08 11:10:09 AM Name Quick Check 3-7 1. The United States flag had 25 stars in 1837. The flag has twice as many stars today. Which bar diagram shows how many stars the flag has today? ? A 25 25 25 ? B 2. Nina is 48 inches tall. Rafael is 53 inches tall. Which number sentence tells you how many inches taller Rafael is than Nina? A 48 ! 53 " 101 B 101 # 53 " 48 C 53 ! 5 " 58 D 53 # 48 " 5 25 ? C 25 25 25 25 ? D 25 25 25 4. Ian is 6 years old. His brother Curtis is 3 times as old. Which number sentence tells you how old Curtis is? Quick Check 3-7 3. Kerry is watering her plants. The plant at her desk needs 5 times as much water as the plant by her window does. The plant by her window needs 2 pints of water. How much water does the plant at her desk need? A 3 $ 6 " 18 B 3 $ 3 $ 3 " 27 A 3 pints C 10 pints C 3!3!3"9 B 7 pints D 14 pints D 9 $ 2 " 18 © Pearson Education, Inc. 4 5. Writing to Explain Adam’s pet frog can jump 4 times as far as Sonya’s. Sonya’s frog can jump 8 inches. Use a picture and a number sentence to tell how many inches Adam’s frog can jump. See student samples to the right. Topic 3 Nat_AncTopic_3.indb 63 63 1/31/08 2:33:44 PM Name Reteaching Problem Solving: Draw a Picture and Write an Equation 3-7 Draw a Picture and Write an Equation Step 1: Read and Understand Step 2: Plan and Solve Step 3: Look Back and Check Janie is in the fourth row of the marching band. There are 7 rows of musicians with 8 in each row. How many musicians are ahead of Janie? How many musicians are behind Janie? You can draw a picture of the musicians: Write an A for each musician ahead of Janie, a B for each musician behind Janie, and a J for each musician in Janie’s row. How many musicians are there in all? You can multiply 7 ! 8 " 56 musicians, or add 24 # 8 # 24 " 56 musicians. Solve AAAAAAAA AAAAAAAA AAAAAAAA JJJJJJJJ BBBBBBBB BBBBBBBB BBBBBBBB James has 12 seashells mounted in a row. The 6 shells in the center of the row are nautilus shells. Is there the same number of shells on either side of the nautilus shells? Draw a picture to help you solve the problem. © Pearson Education, Inc. 4 Reteaching 3-7 You need to find how many are ahead of Janie and behind Janie. 64 Nat_AncTopic_3.indb 64 Topic 3 1/31/08 11:10:10 AM Name Reteaching Problem Solving: Draw a Picture and Write an Equation 3-7 Draw a Picture and Write an Equation Step 1: Read and Understand Step 2: Plan and Solve Step 3: Look Back and Check Janie is in the fourth row of the marching band. There are 7 rows of musicians with 8 in each row. How many musicians are ahead of Janie? How many musicians are behind Janie? You can draw a picture of the musicians: Write an A for each musician ahead of Janie, a B for each musician behind Janie, and a J for each musician in Janie’s row. How many musicians are there in all? You can multiply 7 ! 8 " 56 musicians, or add 24 # 8 # 24 " 56 musicians. Reteaching 3-7 You need to find how many are ahead of Janie and behind Janie. Solve AAAAAAAA AAAAAAAA AAAAAAAA JJJJJJJJ BBBBBBBB BBBBBBBB BBBBBBBB James has 12 seashells mounted in a row. The 6 shells in the center of the row are nautilus shells. Is there the same number of shells on either side of the nautilus shells? Draw a picture to help you solve the problem. Yes, there are 3 shells to the left and 3 shells to the right. © Pearson Education, Inc. 4 Check students’ drawings. 64 Nat_AncTopic_3.indb 64 Topic 3 1/31/08 2:33:45 PM Name Practice 3-7 Problem Solving: Draw a Picture and Write an Equation For 1 through 4, write an equation and solve. Use the picture to help. 1. John is running in a marathon. The marathon is 25 miles long. After two hours, John has run 7 miles. How many miles does John have left to run? 2. A summer camp has divided its campers into 4 groups of 25 campers. How many campers are at the summer camp? ? campers 25 miles 7 25 25 25 25 ? miles 3. Karen is 5 feet tall. In Karen’s backyard there is an oak tree 4 times as tall as she is. How tall is the oak tree? 4. Micah’s room has four sides and a perimeter of 48 feet. If 3 of the sides are 12 feet long, how long is the fourth side? ? feet Oak tree 5 ft Karen 5 ft 5 ft 5 ft 48 feet 5 ft 12ft 12ft 12ft ? Practice 3-7 5. On Monday, Chris had $250 in his savings account. On Friday, he spent $16 at the movies. On Saturday, he deposited a $120 check. Which number sentence below shows how much money Chris has? © Pearson Education, Inc. 4 A 250 ! 16 ! 120 B 250 ! 16 " 120 C 250 " 16 " 120 D 250 " 16 ! 120 6. Writing to Explain Melissa is making bookmarks from a piece of ribbon that is 12 inches long. Each bookmark is 4 inches long. She drew this picture to see how many bookmarks she could make from the ribbon. What did she do wrong? 12 in. in all 4 inches 4 inches 4 inches 4 inches Topic 3 Nat_AncTopic_3.indb 65 65 1/31/08 11:10:11 AM Name Practice 3-7 Problem Solving: Draw a Picture and Write an Equation For 1 through 4, write an equation and solve. Use the picture to help. 1. John is running in a marathon. The marathon is 25 miles long. After two hours, John has run 7 miles. How many miles does John have left to run? 2. A summer camp has divided its campers into 4 groups of 25 campers. How many campers are at the summer camp? 25 # 4 " 100 campers 25 ! 7 " 18 mi ? campers 25 miles 7 25 25 25 25 ? miles 3. Karen is 5 feet tall. In Karen’s backyard there is an oak tree 4 times as tall as she is. How tall is the oak tree? 5 # 4 " 20 feet 4. Micah’s room has four sides and a perimeter of 48 feet. If 3 of the sides are 12 feet long, how long is the fourth side? 48 ! 12 ! 12 ! 12 " 12 feet ? feet Oak tree 5ft Karen 5ft 5ft 5 ft 48 feet 5 ft 12ft 12ft 12ft ? Practice 3-7 5. On Monday, Chris had $250 in his savings account. On Friday, he spent $16 at the movies. On Saturday, he deposited a $120 check. Which number sentence below shows how much money Chris has? © Pearson Education, Inc. 4 A 250 ! 16 ! 120 B 250 ! 16 " 120 C 250 " 16 " 120 D 250 " 16 ! 120 6. Writing to Explain Melissa is making bookmarks from a piece of ribbon that is 12 inches long. Each bookmark is 4 inches long. She drew this picture to see how many bookmarks she could make from the ribbon. What did she do wrong? 12 in. in all Nat_AncTopic_3.indb 65 4 inches 4 inches 4 inches 4 inches She should have divided it into 3 pieces that were 4 in. long. Topic 3 65 1/31/08 2:33:46 PM Name Picture It! Draw pictures or bar diagrams to help you solve the problems below. Enrichment 3-7 Visual Thinking 1. Mr. Byfield and Ms. Fuentes both have 24 students in their classes. Half of the students in Mr. Byfield’s class are girls. There are 2 more girls in Ms. Fuentes’ class than in Mr. Byfield’s. How many girls are in Ms. Fuentes’ class? 2. There are 12 small containers of milk in a case. Travis has 5 cases of milk in his store. He sold 2 small containers. How many containers does Travis now have? 4. At the fourth-grade craft sale, Karen sold 6 pot holders for $4 each. Larry made $5 more than Karen selling bookmarks. How much did Larry make? © Pearson Education, Inc. 4 Enrichment 3-7 3. A hotel is 7 stories high. Skyscraper A has 28 more stories than the hotel. Skyscraper B has 3 more stories than Skyscraper A. How many stories does Skyscraper B have? 66 Nat_AncTopic_3.indb 66 Topic 3 1/31/08 11:10:14 AM Name Enrichment 3-7 Picture It! Draw pictures or bar diagrams to help you solve the problems below. Visual Thinking 1. Mr. Byfield and Ms. Fuentes both have 24 students in their classes. Half of the students in Mr. Byfield’s class are girls. There are 2 more girls in Ms. Fuentes’ class than in Mr. Byfield’s. How many girls are in Ms. Fuentes’ class? 14 2. There are 12 small containers of milk in a case. Travis has 5 cases of milk in his store. He sold 2 small containers. How many containers does Travis now have? 58 3. A hotel is 7 stories high. Skyscraper A has 28 more stories than the hotel. Skyscraper B has 3 more stories than Skyscraper A. How many stories does Skyscraper B have? Enrichment 3-7 38 4. At the fourth-grade craft sale, Karen sold 6 pot holders for $4 each. Larry made $5 more than Karen selling bookmarks. How much did Larry make? $29 © Pearson Education, Inc. 4 Check students’ drawings. 66 Nat_AncTopic_3.indb 66 Topic 3 1/31/08 2:33:48 PM Name Topic 3 Multiple-Choice Test Mark the best answer. 1. Which has the same value as 4 ! 6? (3-1) 4. Each clover has 3 leaves. A 4"4"4"4 B 6"4"6"4 C 6"6"6"6 D 4"6 2. Juan bought 3 bags of oranges. Each bag had 2 oranges in it. How many oranges did he have? (3-3) A 9 B 7 C 6 D 5 3. Which is a way to find 6 ! 9? (3-5) A (6 ! 2) " (6 ! 16) B (6 ! 4) " (6 ! 5) C (6 ! 5) " (6 ! 6) D (6 ! 6) " (5 ! 3) If Ricardo counted the leaves in groups of 3, which list includes numbers he could have named? (3-2) A 3, 6, 10, 13 B 9, 12, 16, 18 C 13, 16, 19, 22 D 6, 9, 12, 15 5. Patrick bought 8 cartons of eggs. Each carton had 6 eggs. Which number sentence can be used to find the total number of eggs Patrick bought? (3-6) A 8!6# B "6=8 C 8"6# Topic 3 Nat_AncTopic_3.indb 67 67 Topic 3 Multiple-Choice Test © Pearson Education, Inc. 4 D 8$6# 1/31/08 11:10:15 AM Name Topic 3 Multiple-Choice Test Mark the best answer. 1. Which has the same value as 4 ! 6? (3-1) 4. Each clover has 3 leaves. A 4"4"4"4 B 6"4"6"4 C 6"6"6"6 D 4"6 2. Juan bought 3 bags of oranges. Each bag had 2 oranges in it. How many oranges did he have? (3-3) A 9 B 7 C 6 D 5 3. Which is a way to find 6 ! 9? (3-5) A (6 ! 2) " (6 ! 16) B (6 ! 4) " (6 ! 5) C (6 ! 5) " (6 ! 6) D (6 ! 6) " (5 ! 3) If Ricardo counted the leaves in groups of 3, which list includes numbers he could have named? (3-2) A 3, 6, 10, 13 B 9, 12, 16, 18 C 13, 16, 19, 22 D 6, 9, 12, 15 5. Patrick bought 8 cartons of eggs. Each carton had 6 eggs. Which number sentence can be used to find the total number of eggs Patrick bought? (3-6) A 8!6# B "6=8 C 8"6# Topic 3 Nat_AncTopic_3.indb 67 67 Topic 3 Multiple-Choice Test © Pearson Education, Inc. 4 D 8$6# 1/31/08 2:33:49 PM Name Topic 3 Free-Response Test Give each answer. Write an addition sentence and a multiplication sentence for each picture. Write the missing number. 6. 7 ! 1 " 1 ! 7. 6 ! 8 " 1. !6 Use breaking apart to find each product. 8. 7 ! 5 (7 ! 2) # (7 ! 2. # ) " 9. 3 ! 4 (1 ! 4) # ( # ! 4) " 10. 6 ! 12 Skip count to find the number that comes next. (3 ! 12) # ( # ! 12) " 3. 10, 12, 14, 16, ? 4. 25, 30, 35, 40, ? © Pearson Education, Inc. 4 Topic 3 Free-Response Test 5. 18, 27, 36, 45, ? 70 Nat_AncTopic_3.indb 70 Topic 3 1/31/08 11:10:19 AM Name Topic 3 Free-Response Test Give each answer. Write an addition sentence and a multiplication sentence for each picture. Write the missing number. 7. 6 ! 8 " 1. 5!5!5" 15; 3 # 5 " 15 8 !6 Use breaking apart to find each product. 8. 7 ! 5 3 ) 21 " 35 (7 ! 2) # (7 ! 14 # 2. 7 6. 7 ! 1 " 1 ! 9. 3 ! 4 (1 ! 4) # ( 6 ! 6 ! 6 ! 6 " 24; 4 # 6 " 24 Skip count to find the number that comes next. 4 # 8 2 " ! 4) 12 10. 6 ! 12 (3 ! 12) # ( 3 ! 12) 36 # 36 " 72 3. 10, 12, 14, 16, ? 18 4. 25, 30, 35, 40, ? 45 Topic 3 Free-Response Test 54 70 Nat_AncTopic_3.indb 70 © Pearson Education, Inc. 4 5. 18, 27, 36, 45, ? Topic 3 1/31/08 2:33:53 PM Name Topic 3 Performance Assessment Mr. Harrison’s class has been learning about earth science. Mr. Harrison and several students brought their rock collections to school. Mr. Harrison brought in a catalog that sells the two different rock display containers shown below. Display Box Display Box Holds 4 rocks Holds 6 rocks $3 $5 1. Maggie wants to buy 4 of the containers that hold 6 rocks. How much money will she spend? 2. Travis has filled 3 of the containers that hold 4 rocks. How many rocks does Travis have? 3. Linette has twice the number of rocks that Travis has. How many rocks does Linette have? 4. Write and answer the hidden question or questions. Then, solve the problem. Angela has 18 rocks. She bought 2 containers that hold 6 rocks each. How many more 6-rock containers does she need to buy? How much money will she spend on containers in all? 72 Nat_AncTopic_3.indb 72 Days 7 Rocks 3 14 © Pearson Education, Inc. 4 Topic 3 Performance Assessment 5. Ramirez went rock hunting every week, or every 7 days. He collected 3 rocks each time he went. Complete the table to find out how many days it took for Ramirez to collect 24 rocks. Topic 3 1/31/08 11:10:21 AM Name Topic 3 Performance Assessment Mr. Harrison’s class has been learning about earth science. Mr. Harrison and several students brought their rock collections to school. Mr. Harrison brought in a catalog that sells the two different rock display containers shown below. Display Box Display Box Holds 4 rocks Holds 6 rocks $3 $5 1. Maggie wants to buy 4 of the containers that hold 6 rocks. How much money will she spend? 4 ! 5 " $20 2. Travis has filled 3 of the containers that hold 4 rocks. How many rocks does Travis have? 3 ! 4 " 12 3. Linette has twice the number of rocks that Travis has. How many rocks does Linette have? 12 ! 2 " 24 4. Write and answer the hidden question or questions. Then, solve the problem. Angela has 18 rocks. She bought 2 containers that hold 6 rocks each. How many more 6-rock containers does she need to buy? How much money will she spend on containers in all? 2 ! 6 " 12; 18 # 12 " 6; She needs 1 more container, 3 ! $5 " $15. 72 Nat_AncTopic_3.indb 72 Days 7 14 Rocks 3 6 21 28 35 42 49 56 9 12 15 18 21 24 © Pearson Education, Inc. 4 Topic 3 Performance Assessment 5. Ramirez went rock hunting every week, or every 7 days. He collected 3 rocks each time he went. Complete the table to find out how many days it took for Ramirez to collect 24 rocks. Topic 3 1/31/08 2:33:54 PM