Problem of the Week p. 2 cm cm I can cut the cake to make 5 cuts across and 5 cuts down. So there are 25 pieces. I could make 25 15 = $.75 = (5 6 cm) + 2 = (5 4 cm) + Chapter 6 Mental Math (Master) pp. 5 54 1. a) 171 b) 1510 c) 1998 d) 1 e) 60 f) 801 e) For example: I could double the answer because 4 is half of 8. f) For example: I could add 1 to the answer because 199 is 1 less than 200. 2. a) 280 b) 90 c) 00 d) 0 e) 600 f) 80. a) 1000 b) 600 c) 900 d) 000 e) 1600 f) 7200 4. a) 400, 418 b) 2000, 1945 c) 16 000, 14 805 d) 500, 540 e) 1000, 1045 5. a) 65 b) 9 c) 40 d) 480 e) 1500 6. a) 96 b) 140 c) 558 d) 4064 e) 5994 f) 950 7. a) 99 b) 96 c) 60 d) 88 e) 144 f) 12 g) 84 h) 60 8. a) 10 b) 20 c) 80 d) 8 e) 200 f) 50 g) 200 h) 20 9. a) 10 6 = 60 c) 80 = 240 e) 200 = 600 g) 200 5 = 1000 b) 20 6 = 120 d) 8 10 = 80 f) 50 8 = 400 h) 20 8 = 160 10. a) 200 b) 200 c) 00 d) 180 e) 400 f) 900 g) 800 h) 800 11. a) 200 8 = 1600 c) 00 8 = 2400 e) 400 9 = 600 g) 800 5 = 4000 b) 200 6 = 1200 d) 180 10 = 1800 f) 900 8 = 7200 h) 800 7 = 5600 12. a) 1200 b) 4500 c) 400 d) 600 e) 900 f) 500 g) 900 h) 400 1. a) 400 b) 2000 kg c) 900 cm Scaffolding for Getting Started Activity (Master) pp. 69 70 A. You need 520 cm of willow for 8 dreamcatchers. For example, 65 8 520 You will need 1000 cm of string to make 8 dreamcatchers. For example, 125 8 1000 B. 1 m = 100 cm 5 m = 500 cm 6 m = 600 cm 10 m = 1000 cm I know they need between 5 m and 6 m of willow because 520 is between 500 cm and 600 cm. I know they need exactly 10 m of string because 1000 cm is exactly 10 metres. C. For example: I used mental math to answer Part B because I can multiply by 100 in my head. D. 520 cm 1000 cm For example: to find out how much will be needed for 4 dreamcatchers, I will divide the numbers by 2 because 4 is half of 8. (260 cm, 500 cm) To find out how much will be needed for 16 dreamcatchers, I will multiply the numbers by 2 because 16 is double 8. (1040 cm, 2000 cm). 81
E. For example: there are 4 people in our class. I know that 16 + 16 + 2 = 4 To find the amount of willow, I will add 1040 + 1040 + 65 To find the amount of string, I will add 2000 + 2000 + 250 We will need 2145 cm of willow and 4250 cm of string. Scaffolding for Do You Remember? (Master) p. 71 1. a) 5 400 = 2000; 5 500 = 2500; therefore 5 548 is about 2250. b) 6 5 = 0, so 6 50 = 00; 6 2 8 8 is about 50. 2. a) 6000 b) 80. a) 92 b) 4. a) 195 b) 2610 5. a) 144 = 48 b) 48 $5 = $240 c) $240 = $720 or 144 $5 = $720 Scaffolding for Lesson 2 (Master) p. 72 1. a) 45 6 is close to 00 6 = 1800. Answer is reasonable. b) 124 5 is close to 1000 5 = 5000. Answer is reasonable. c) 12 18 is close to 10 20 = 200. Answer is not reasonable. d) 15 19 is close to 15 20 = 00. Answer is reasonable. e) 24 29 is close to 20 0 = 600. Answer is not reasonable. f) 9 9 is close to 40 40 = 1600. Answer is reasonable. Scaffolding for Lesson 5 (Master) p. 7 6. a) 100 + 40 + 4 = 144 b) 200 + 40 + 2 = 242 82 Chapter 6: Multiplication and Division
7. a) 2 2 b) 18 25 25 19 15 (5 ) 72 (9 8) 115 100 (5 20) 90 (9 10) 60 (20 ) 80 (10 8) 460 400 (20 20) 100 (10 10) 575 575 42 18 19 162 180 42 Estimate: Estimate: 2 25 is close to 20 25 = 500. Reasonable 18 19 is close to 18 20 = 60. Reasonable. c) 75 75 d) 45 74 74 69 20 (4 5) 405 00 280 (4 70) 2700 50 (70 5) 105 4900 (70 70) 5250 5550 5550 Estimate: Estimate: 75 74 is close to 80 70 = 5600. Reasonable 45 69 is between 40 70 = 2800 and 50 70 = 500. Reasonable. Scaffolding for Lesson 8 (Master) pp. 74 75 5. a) 66 b) 6 6 0 000 1000 66 600 200 6 0 10 6 6 2 0 1212 I know the answer is reasonable because 1000 = 000 c) 2001 d) 1800 600 201 180 60 21 21 7 0 667 4 2 8 5 5 0 2800 55 40 15 12 700 I know the answer is I know the answer is reasonable because reasonable because 600 = 1800 500 = 1500 10 71 I know the answer is reasonable because 4 700 = 2800 1458 1200 258 240 18 18 0 400 80 6 486 8
e) 764. The answer is reasonable because 9 800 = 7200 f) 786 R 6. The answer is reasonable because 7 800 is 5600 g) 812 R 4. The answer is reasonable because 8 800 = 6400 h) 842 R 4. The answer is reasonable because 6 800 = 4800. Chapter 6 Test (Master) pp. 77 78 1. a) 7 4 = 28, so 7 40 = 280 b) 6 8 = 48, so 600 8 = 4800 c) 4 4 = 16, so 40 40 = 1600 d) 8 = 24, so 80 0 = 2400 2. 12 4 = 48. 44 58 = 2552 cm 4. a) 15 cm 2. It is reasonable because I know that 2 15 = 0, so 20 15 = 00. b) 2 2 = 1024 cm 2. It is reasonable because I know that 0 0 = 900 and 1024 is a bit bigger. 5. a) 500 b) 400 c) 200 d) 400 6. a) Not reasonable. 2628 6 = 48 b) Reasonable. c) Reasonable d) Not reasonable. 228 4 = 807 7. a) 68 seconds. I multiplied 4 by 2 mentally. b) About 7 seconds. I divided 500 by 100 to get 5 and then divided 4 by 5 in my head by rounding to 5 5 = 7. c) About 15 m. I used a calculator to find 500 4 = 14.7. This is about 15. 8. The speed is reported as an estimate because they use the word about. If the data is an estimate, then the answers will also be estimates. Chapter 6 Task (Master) pp. 78 79 Sample Answers Part 1 A. 25 256 $1645 $7 $8 + $2048 $1645 $2048 $69 The Boy Scouts raised $69. The first answer is reasonable because 7 $200 is $1400 and my answer of $1645 is close to that. The second answer is reasonable because 4 $250 = $1000 so 8 $250 is $2000 and my answer of $2056 is close to that. The answer to my addition question is reasonable because $1645 + $2000 = $645 which is close to my answer of $69. 84 Chapter 6: Multiplication and Division
B. 95 1140 12 $4 180 $4560 10 900 50 1140 The Girl Guides raised $4560 I know my first answer is reasonable because 12 100 is 1200, which is close to my answer of 1140. I know my second answer is reasonable because 1100 $4 = 4400, which is close to my answer of $4560. C. $4560 69 $867 The Girl Guides raised $867 more than the Boy Scouts. Part 2 D. A possible answer using division. Boy Scouts a) $10 000 $ 69 $6 07 The Boy Scouts need to raise $607 more. b) 7 6 0 7 1 600 900 7 7 1 0 901 The Boy Scouts need to sell 901 boxes of hot chocolate to reach their goal. c) 8 6 0 7 1 5600 700 707 640 80 67 64 8 788 The Boy Scouts need to sell 789 tins of popcorn to reach their goal. The Boy Scouts could sell about 400 of each item to reach their goal. $400 $7 = $2800 $400 $8 = $200 $2800 + $200 = $6000 plus the money already raised is $969, which is close to $10 000. Estimation a) I know my answer is reasonable because 10 000 4 000 = 6 000, which is close to my answer of 607. b) I know my answer is reasonable because 600 7 is 900, which is close to my answer of 901. c) I know my answer is reasonable because 6400 8 is 800, which is close to my answer of 788. 85
Girl Guides a) $10 000 $4 560 $ 5 440 The Girl Guides need to raise $5440 more. b) 4 5 4 4 0 1 4400 1100 1040 1000 250 40 40 10 0 160 The Girl Guides need to sell 160 more boxes of cookies. Estimation a) I know my answer is reasonable because 10 000 5000 = 5000, which is close to my answer of $5440. b) I know my answer is reasonable because 4 1200 = 4800 and 4 1500 = 6000. I overestimated and underestimated so I know my answer must be in between 1200 and 1500, which it is. A possible solution that does not use division: Boy Scouts Boxes sold Money raised 25 $1645 470 $290 705 $495 The Boy Scouts would need to sell 705 25 = 470 more boxes of hot chocolate to raise about half of their $100 000. Tins sold Money raised 256 $2048 512 $4096 612 $4896 The Boy Scouts would need to sell 612 256 = 56 more tins of popcorn to raise about half of their $10 000. Estimation Boy Scouts 470 rounds to 500 7 = $500 56 rounds to 400 8 = $200 $6700 + 69, rounded to 700 = 10 400. My answer is reasonable because 10 400 is a little over 10 000. I rounded up both times so I would expect this. Girl Guides $4560 (amount of money raised from first sale) + $4560 = $910. They can also sell 200 more boxes to get even closer to their goal. 4 200 = 800. $910 + 800 = $990. The Girl Guides need to sell 1140 + 200 = 140 more boxes to get to their goal of $10 000. Estimation Girl Guides 140 rounds off to 100 4 = 1000 4 + 00 4 = 4000 + 1200 = 5200 4560 rounds to 4500 + 4500 9700 My answer is reasonable because 9700 is a little less than 10 000. I rounded down both times so I would expect this. 86 Chapter 6: Multiplication and Division
Lesson 1 Answers (continued from p. 15) 5. 900 0 6. a) 0 cm 40 cm = 1200 cm 2 b) 50 cm 80 cm = 4000 cm 2 c) 60 cm 60 cm = 600 cm 2 7. a) 10 10 = 100; 1 1 = 1 and multiply by 100 b) 20 10 = 200; 2 1 = 2 and multiply by 100 c) 0 50 = 1500; 5 = 15 and multiply by 100 d) 20 50 = 1000; 2 5 = 10 and multiply by 100 e) 50 80 = 4000; 5 8 = 40 and multiply by 100 f) 90 90 = 8100; 9 9 = 81 and multiply by 100 Lesson 2 Answers (continued from p. 19) 6. a) For example: divide 6 by 4 to get 9 groups; multiply 9 by 5 to get the maximum number of straws (15). 6 50 = 00 straws, which is not enough; 7 50 = 50 so they need at least 7 bags of 50 straws. b) For example: 10 5 = 50 and 15 is close to 50. Lesson 5 Answers (continued from p. 1) 2. For example: because 9 = 27 and 27 can be written as 2 tens 7 ones. The 2 represents the 2 tens (the 7 is in the ones place in 57).. a) b) 22 15 10 100 20 200 0 22 15 110 220 0 c) Mental math: 15 22 = fifteen 22s = ten 22s + five 22s = 220 + 110 = 0 Number line: 10 15 = 150 10 15 = 150 15 15 0 150 00 15 0 87
4. a) 12 16 = 192 b) 22 18 = 96 5. a) 11 21 = 21 b) 200 + 0 + 1 = 21 6. a) 144 cm 2 b) 242 cm 2 7. a) 2 25 = 575; the answer is reasonable because 20 25 = 500 and the answer is close to 500 b) 18 19 = 42; the answer is reasonable because 20 20 = 400 and the answer is close to 400 c) 75 74 = 5550; the answer is reasonable because 80 70 = 5600 and the answer is close to 5600 d) 45 69 = 105; the answer is reasonable because 50 70 = 500 and the answer is close to 500 8. 45 1 = 195 min 9. 2 45 = 105 10. 5 24 = 840 cm 11. a) For example: how many apples are there in 6 crates if each crate contains 28 apples? b) 6 28 = 1008 c) For example: 6 28 is less than 40 0 = 1200, so 1008 is reasonable. Lesson 7 Answers (continued from p. 4) 6. c) For example: $516 is between $4800 and $5400, so the cost of a television is between $800 ($4800 6) and $900 ($5400 6). $195 is between $000 and $500, so the cost of a computer monitor is between $600 ($000 5) and $700 ($500 5). The television costs more. 7. a) For example: 1512 is between 1400 and 1600, so the quotient is between 1400 2 = 700 and 1600 2 = 800. I estimate the quotient is about 750. b) For example: 6655 is between 600 and 7200, so the quotient is between 600 9 = 700 and 7200 9 = 800. I estimate the quotient is about 750. c) For example: 4218 is between 4200 and 4500, so the quotient is between 4200 = 1400 and 4500 = 1500. 4218 is much closer to 4200, so I ll estimate 1400. d) For example: 5846 is between 5600 and 6400, so the quotient is between 5600 8 = 700 and 6400 8 = 800. 5846 is closer to 5600, so I ll estimate 725. e) For example: 55 is between 000 and 600, so the quotient is between 000 6 = 500 and 600 6 = 600. I estimate the quotient is about 550. f) For example: 528 is between 4900 and 5600, so the quotient is between 4900 7 = 700 and 5600 7 = 800. I estimate the quotient is about 750. 88 Chapter 6: Multiplication and Division
Lesson 8 Answers (continued from p. 47). a) 675 R1 b) 4 2 7 0 1 4 2 7 0 1 2400 600 2400 01 280 21 20 1 01 280 70 21 20 5 1 675 R1 c) 4 675 + 1 = 2700 + 1 = 2701 4. For example: both numbers are close to 6540 and are easily divided by 7. 600 is an underestimate of 6540 and 7000 is an overestimate of 6540. 5. a) 1212. 66 is close to 600 = 1200, so 1212 is reasonable. b) 71 R. 2855 4 is close to 2800 4 = 700, so 71 is reasonable. c) 667. 2001 is close to 2100 = 700, so 667 is reasonable. d) 486. 1458 is close to 1500 = 500, so 486 is reasonable. e) 764. 6876 9 is between 600 9 = 700 and 7200 9 = 800, so 764 is reasonable. f) 786 R6. 5508 7 is close to 5600 7 = 800, so 786 R6 is reasonable. g) 812 R4. 6500 8 is close to 6400 8 = 800, so 812 R4 is reasonable. h) 842 R4. 5056 6 is between 4800 6 = 800 and 5400 6 = 900, so 842 R4 is reasonable. 6. For example: to check Question 5 b), 71 4 + = 2852 + = 2855; 71 R is correct. 7. For example: half of 67 is less than 400 2 = 1700, and 1869 is much greater than 1700. 8. For example: the total mass of the 8 snowmobiles is 4060 2100 = 1960 kg. Each snowmobile has a mass of 1960 8 = 245 kg. 9. For example: $080 is to be shared equally by 6 people. How much money does each person get? 51 R2 6 0 8 0 000 80 78 2 Each person gets $51 with $2 left over. They can divide that $2 to get another cents each and 2 cents left over. 6 51 + 2 = 078 + 2 = 080. So 51 R2 is correct. 89