I can cut the cake to make 5 cuts across and 5 cuts down. So there are 25 pieces. I could make = $3.75

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Barnaby Baldwin
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1 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 = $.75 = (5 6 cm) + 2 = (5 4 cm) + Chapter 6 Mental Math (Master) pp 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 a) 280 b) 90 c) 00 d) 0 e) 600 f) 80. a) 1000 b) 600 c) 900 d) 000 e) 1600 f) a) 400, 418 b) 2000, 1945 c) , d) 500, 540 e) 1000, a) 65 b) 9 c) 40 d) 480 e) a) 96 b) 140 c) 558 d) 4064 e) 5994 f) a) 99 b) 96 c) 60 d) 88 e) 144 f) 12 g) 84 h) a) 10 b) 20 c) 80 d) 8 e) 200 f) 50 g) 200 h) a) 10 6 = 60 c) 80 = 240 e) 200 = 600 g) = 1000 b) 20 6 = 120 d) 8 10 = 80 f) 50 8 = 400 h) 20 8 = a) 200 b) 200 c) 00 d) 180 e) 400 f) 900 g) 800 h) a) = 1600 c) 00 8 = 2400 e) = 600 g) = 4000 b) = 1200 d) = 1800 f) = 7200 h) = a) 1200 b) 4500 c) 400 d) 600 e) 900 f) 500 g) 900 h) a) 400 b) 2000 kg c) 900 cm Scaffolding for Getting Started Activity (Master) pp A. You need 520 cm of willow for 8 dreamcatchers. For example, You will need 1000 cm of string to make 8 dreamcatchers. For example, 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

2 E. For example: there are 4 people in our class. I know that = 4 To find the amount of willow, I will add To find the amount of string, I will add We will need 2145 cm of willow and 4250 cm of string. Scaffolding for Do You Remember? (Master) p a) = 2000; = 2500; therefore is about b) 6 5 = 0, so 6 50 = 00; is about a) 6000 b) 80. a) 92 b) 4. a) 195 b) a) 144 = 48 b) 48 $5 = $240 c) $240 = $720 or 144 $5 = $720 Scaffolding for Lesson 2 (Master) p a) 45 6 is close to 00 6 = Answer is reasonable. b) is close to = Answer is reasonable. c) is close to = 200. Answer is not reasonable. d) is close to = 00. Answer is reasonable. e) is close to 20 0 = 600. Answer is not reasonable. f) 9 9 is close to = Answer is reasonable. Scaffolding for Lesson 5 (Master) p a) = 144 b) = Chapter 6: Multiplication and Division

3 7. a) 2 2 b) (5 ) 72 (9 8) (5 20) 90 (9 10) 60 (20 ) 80 (10 8) (20 20) 100 (10 10) Estimate: Estimate: 2 25 is close to = 500. Reasonable is close to = 60. Reasonable. c) d) (4 5) (4 70) (70 5) (70 70) Estimate: Estimate: is close to = Reasonable is between = 2800 and = 500. Reasonable. Scaffolding for Lesson 8 (Master) pp a) 66 b) I know the answer is reasonable because 1000 = 000 c) 2001 d) I know the answer is I know the answer is reasonable because reasonable because 600 = = I know the answer is reasonable because =

4 e) 764. The answer is reasonable because = 7200 f) 786 R 6. The answer is reasonable because is 5600 g) 812 R 4. The answer is reasonable because = 6400 h) 842 R 4. The answer is reasonable because = Chapter 6 Test (Master) pp a) 7 4 = 28, so 7 40 = 280 b) 6 8 = 48, so = 4800 c) 4 4 = 16, so = 1600 d) 8 = 24, so 80 0 = = = 2552 cm 4. a) 15 cm 2. It is reasonable because I know that 2 15 = 0, so = 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) a) Not reasonable = 48 b) Reasonable. c) Reasonable d) Not reasonable = 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 = This is about 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 Sample Answers Part 1 A $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 $ $2000 = $645 which is close to my answer of $ Chapter 6: Multiplication and Division

5 B $4 180 $ The Girl Guides raised $4560 I know my first answer is reasonable because is 1200, which is close to my answer of I know my second answer is reasonable because 1100 $4 = 4400, which is close to my answer of $4560. C. $ $867 The Girl Guides raised $867 more than the Boy Scouts. Part 2 D. A possible answer using division. Boy Scouts a) $ $ 69 $6 07 The Boy Scouts need to raise $607 more. b) The Boy Scouts need to sell 901 boxes of hot chocolate to reach their goal. c) 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 $ $200 = $6000 plus the money already raised is $969, which is close to $ Estimation a) I know my answer is reasonable because = 6 000, which is close to my answer of 607. b) I know my answer is reasonable because is 900, which is close to my answer of 901. c) I know my answer is reasonable because is 800, which is close to my answer of

6 Girl Guides a) $ $4 560 $ The Girl Guides need to raise $5440 more. b) The Girl Guides need to sell 160 more boxes of cookies. Estimation a) I know my answer is reasonable because = 5000, which is close to my answer of $5440. b) I know my answer is reasonable because = 4800 and = 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 $ $ $495 The Boy Scouts would need to sell = 470 more boxes of hot chocolate to raise about half of their $ Tins sold Money raised 256 $ $ $4896 The Boy Scouts would need to sell = 56 more tins of popcorn to raise about half of their $ Estimation Boy Scouts 470 rounds to = $ rounds to = $200 $ , rounded to 700 = My answer is reasonable because is a little over 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 = 800. $ = $990. The Girl Guides need to sell = 140 more boxes to get to their goal of $ Estimation Girl Guides 140 rounds off to = = = rounds to My answer is reasonable because 9700 is a little less than I rounded down both times so I would expect this. 86 Chapter 6: Multiplication and Division

7 Lesson 1 Answers (continued from p. 15) 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) = 100; 1 1 = 1 and multiply by 100 b) = 200; 2 1 = 2 and multiply by 100 c) 0 50 = 1500; 5 = 15 and multiply by 100 d) = 1000; 2 5 = 10 and multiply by 100 e) = 4000; 5 8 = 40 and multiply by 100 f) = 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) = 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) c) Mental math: = fifteen 22s = ten 22s + five 22s = = 0 Number line: = =

8 4. a) = 192 b) = a) = 21 b) = a) 144 cm 2 b) 242 cm 2 7. a) 2 25 = 575; the answer is reasonable because = 500 and the answer is close to 500 b) = 42; the answer is reasonable because = 400 and the answer is close to 400 c) = 5550; the answer is reasonable because = 5600 and the answer is close to 5600 d) = 105; the answer is reasonable because = 500 and the answer is close to = 195 min = = 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 = 700 and = 800. I estimate the quotient is about 750. b) For example: 6655 is between 600 and 7200, so the quotient is between = 700 and = 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 = is much closer to 4200, so I ll estimate d) For example: 5846 is between 5600 and 6400, so the quotient is between = 700 and = is closer to 5600, so I ll estimate 725. e) For example: 55 is between 000 and 600, so the quotient is between = 500 and = 600. I estimate the quotient is about 550. f) For example: 528 is between 4900 and 5600, so the quotient is between = 700 and = 800. I estimate the quotient is about Chapter 6: Multiplication and Division

9 Lesson 8 Answers (continued from p. 47). a) 675 R1 b) R1 c) = = For example: both numbers are close to 6540 and are easily divided by is an underestimate of 6540 and 7000 is an overestimate of a) is close to 600 = 1200, so 1212 is reasonable. b) 71 R is close to = 700, so 71 is reasonable. c) is close to 2100 = 700, so 667 is reasonable. d) is close to 1500 = 500, so 486 is reasonable. e) is between = 700 and = 800, so 764 is reasonable. f) 786 R is close to = 800, so 786 R6 is reasonable. g) 812 R is close to = 800, so 812 R4 is reasonable. h) 842 R is between = 800 and = 900, so 842 R4 is reasonable. 6. For example: to check Question 5 b), = = 2855; 71 R is correct. 7. For example: half of 67 is less than = 1700, and 1869 is much greater than For example: the total mass of the 8 snowmobiles is = 1960 kg. Each snowmobile has a mass of = 245 kg. 9. For example: $080 is to be shared equally by 6 people. How much money does each person get? 51 R Each person gets $51 with $2 left over. They can divide that $2 to get another cents each and 2 cents left over = = 080. So 51 R2 is correct. 89

Chapter 4 Answers. Chapter 4 Problems of the Week, p For example, I added each player s total points as follows:

Chapter 4 Answers. Chapter 4 Problems of the Week, p For example, I added each player s total points as follows: Chapter 4 Problems of the Week, p. 3 1. For example, I added each player s total points as follows: Chamberlain Jordan Abdul-Jabbar 4029 3041 2822 3596 2868 2596 3033 2752 2275 + 2948 + 2633 + 2152 13