Chapter 5 Answers. Copyright 2005 by Thomson Nelson

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1 Chapter 5 Answers Problem of the Week p Freya s new bike has a mass of 6 kg. The length of the bike is 1.9 m. The wheels are 520 mm in width. The seat is 82 cm from the ground in height. 2. For example, no. The perimeters are approximately 180 cm for A (3 60), 390 cm for B (3 130), and 540 cm for C (540). To put trim around the circumference of all of the table covers, she would need 1110 m, or 11.1 m. Since she has 10 m of trim, she could trim B and C, but not A. Chapter 5 Mental Math (Master) pp a) 3500 km b) 1500 ml c) 2000 kg d) 200 km 2. a) 10 cm b) 5 cm c) 7600 m d) 1 dm 3. a) 30 cm b) 4000 km c) 75 cm d) 250 cm e) 45 cm 4. a) 21 cm b) 75 cm c) 40 cm d) 50 cm 5. a) 100 cm b) 200 cm c) 240 cm d) 200 m e) 1500 km 6. a) 20 cm b) 1500 cm c) 800 m d) 800 m 7. a) 240 b) 200 c) 100 d) 45 e) a) 70 min b) 45 min c) 20 min d) 25 min e) 51 min 9. a) 2 h 10 min b) 1 h 45 min c) 35 min d) 3 h 25 min e) 1 h 50 min Scaffolding for Getting Started Activity (Master) pp B. For example, it is less than 1 m because it is 0.81 m long. C. For example, it is less than 1 m because it is 0.21 m wide. D. For example, I predict that the perimeter will be more than 1 m and will be about 2 m. The perimeter was 2.04 m so my prediction was good. E. For example, I measured in centimetres because I find it easier to measure in whole numbers. F. For example, Katie would need 2.04 m of tape. G. For example, I know that each skateboard is about 1 m long. I know that 1 km = 1000 m, so I will need 1000 skateboards to make 1000 m. It takes 2.04 m of tape to go around the perimeter of one board, so it will take = 2040 m for 1000 boards. It will take about 2040 m or 2.1 km of tape. Scaffolding for Do You Remember? (Master) p a) 1 km = 1000 m b) 1 m = 100 cm c) 1 m = 1000 mm d) 1 cm = 10 mm 2. a) 6 km b) 23 cm c) 31 m 3. C 4. a) It was 8:43 when he started. b) It was 11:17 when he finished. c) 2 hours 34 minutes had passed. Chapter 5 Test (Master) pp For example, Mark lives mm = 75 m from the park, 0.7 km or 700 m from the library, and 750 m from the school. Mark lives closest to the park. 2. For example, you can measure 300 mm with the 30 cm ruler twice to measure 600 mm and then measure 150 mm with the ruler. 3. a) For example, I estimated the circumference to be 10.5 cm (3 3.5 cm) and I measured it to be 11 cm. b) For example, I estimated the circumference to be 7.5 cm (3 2.5 cm) and I measured it to be 7.9 cm. 4. a) 20 units b) 17.4 units Copyright 2005 by Thomson Nelson Chapter 5 Answers 67

2 5. 6. a) For example, to calculate the perimeter of a rectangle, double the width and double the length, and add these together. b) For example, yes. If you double the perimeter, you double the length and the width. For a rectangle that has a length of 5 and a width of 7, the perimeter is 24. If the length is 7 2 = 14 and the width is 5 2 = 10, the perimeter is 48 cm, which is double the perimeter of the original rectangle. 7. a) 140 mm b) 32 m minutes 9. For example, no. She started at 03:58:10 and stopped at 04:02:58, which is 4 minutes 48 seconds. 10. For example, the first place runner won by 32 seconds. 11. a) :33 b) The baby was born 5 h 27 min before noon. Chapter 5 Task (Master) pp Understand the Problem I know Adrick wants to walk steps on the map, 1 cm = 0.25 km I need to know the length of my step the perimeter of each park how many times around each park steps is my walking speed how long it will take to walk steps Make a Plan I will measure my step from my back heel to the toe of my front heel. I will measure the length of the sides to find the perimeter of each park. I will use the scale to figure out the distance around the park in metres and in kilometres. I will change 0.25 km to 250 m because it is easier for me to work with. I will calculate how many metres I will travel in steps using a table and a calculator. I will figure out how many times around the park I need to go to walk steps using a table and a calculator. I will figure out about how many steps I take in 1 minute using a stopwatch. I will use a table to figure out how many minutes it will take to go steps. Carry out the Plan A. My step measures 50 cm. B. The perimeter of Wilmot Park is 4.6 cm The perimeter of O Dell Park is 21 cm on the map. on the map. cm m cm m Since 4.6 cm is between 1000 and Since 21 cm is 5250 m, the perimeter 1250 m, or about 1150 m, the perimeter of O Dell Park is 5250 m. of Wilmot Park is 1150 m. 68 Chapter 5: Measuring Length and Time Copyright 2005 by Thomson Nelson

3 C. The length of my step is 50 cm so 2 steps = 100 cm, which is 1 m. Number of steps Distance 2 1 m 10 5 m m m m The distance needed to travel steps is 5000 m. Since the perimeter of Wilmot Park is 1150 m, Adrick needs to walk around the park a little more than 4 times. Times around Wilmot Park Distance travelled m m m m m The perimeter of O Dell Park is 5250 m. To travel 5000 m, Adrick needs to walk a little less than once around the park. D. I can walk about 100 steps in 1 minute. E. I can use a table to figure out how long it will take to walk steps. Time Steps 1 min min min min It will take Adrick 100 minutes or 1 hour 40 minutes to walk steps around each park. Lesson 2 Answers (continued from p. 19) b) For example, measure 300 mm on the string with the ruler and make a mark. Then measure another 300 mm from the mark. Then measure another 42 mm to make = 642 mm. c) For example, since 0.1 m = 10 cm, I measured 10 cm with my ruler. 5. For example, since 0.45 m = 45 cm, measure 30 cm with a ruler, make a mark on the fabric, and then measure another 15 cm ( = 45 cm). 6. a) b) 7. For example, she can see how many steps it takes her to get across the room and then multiply that number by 60. She can convert to metres by using decimals (60 cm = 0.60 m). 8. a) For example, yes. Since I know that cm = 900 m and I know that 1000 m = 1 km, I know that they live less than 1 km apart. b) For example, kilometres is a better unit for describing a large distance since the numbers are smaller. 9. For example, since I know that 1.5 cm = 15 mm, I can divide 15 by 200 to find the thickness of one piece of paper in millimetres. Copyright 2005 by Thomson Nelson Chapter 5 Answers 69

4 Lesson 5 Answers (continued from p. 34) 5. The perimeter is 50 cm. 6. Aaron would need 88 cm of trim. 7. a) You would need 18 m of fencing. b) You would need 26 m of fencing. 8. The perimeter of the basketball court is 70.6 m. 9. For example, the perimeter of rectangle A is 23 cm. Rectangle B has a perimeter of 22 cm. So rectangle A has a greater perimeter by 1 cm. 10. a) For example, if you add 5 m to the length the perimeter goes up by 10 m. The perimeter of the original rectangle is 24 m. The length of the new rectangle is = 12 cm so the perimeter is 34 m. b) For example, if you triple the length and the width, you also triple the perimeter. The new length is 7 3 = 21 and the new width is 5 3 = 15 so the perimeter is 72 cm. 11. For example, make a chart of the different border sizes. The perimeter must be 1.8 m = 180 cm. The greatest size border is 10 cm. Border Length size Length Width + width Perimeter 1 cm 30 cm 24 cm 54 cm 108 cm 5 cm 38 cm 32 cm 70 cm 140 cm 10 cm 48 cm 42 cm 90 cm 180 cm 12. For example, yes his rule is correct. To calculate the perimeter of a rectangle, you have to add the 4 sides. Since there are 2 lengths and 2 widths, you could also double the length and the width and add them together. 13. a) For example, 4 cm 3 cm 2 cm 1 cm 5 cm b) For example, the perimeters are 14 cm, 6 cm, and 16 cm All the perimeters are even. This makes sense because you add the 2 sides and multiply by 2 to calculate the perimeter. Whenever you multiply a whole number by 2, you get an even number. Lesson 6 Answers (continued from p. 39) 5. For example, create a table. Distance (km) Time (minutes) cm Since 62 km is halfway between 60 and 64 km, it would take them halfway between 45 and 48 minutes or about 46.5 minutes to get to Cale s grandmother s house. 70 Chapter 5: Measuring Length and Time Copyright 2005 by Thomson Nelson

5 6. a) For example, create a table to solve the problem. Distance (km) Time (minutes) It would take him 115 minutes to run 40 km. b) For example, 2 hours 24 minutes = = 144 minutes to run the Boston Marathon. Since = 29 minutes, it took him 29 minutes longer to run the Boston Marathon. 7. For example, create a table. Airplane Kilometres travelled Kilometres travelled in one hour in 90 minutes De Havilland Dash Canadair Regional Jet Boeing The Boeing goes = 45 km farther than the Canadair Regional Jet and = 765 km farther than the De Havilland Dash For example, the tables are: Tamara Time (minutes) Distance (m) Bronwyn Time (minutes) Distance (m) Bronwyn walks = 800 m farther than Tamara in 1 hour. Problem Bank Answers (continued from p. 51) 8. For example, Width Length Perimeter 1 cm 7 cm 16 cm 2 cm 8 cm 20 cm 3 cm 9 cm 24 cm 4 cm 10 cm 28 cm 5 cm 11 cm 32 cm The length is 11 cm m Copyright 2005 by Thomson Nelson Chapter 5 Answers 71

6 10. For example, since the cyclist rides 225 m in 1 min, the cyclist can ride 2250 m in 10 min, which is 2.25 km. Time Distance 10 min 2.25 km 20 min 4.5 km 30 min 6.75 km 40 min 9 km 50 min km 60 min 13.5 km 70 min km It would take about 70 minutes, or 1 hour 10 minutes. 11. For example, Time Distance 60 min 90 km 120 min 180 km 180 min 270 km Since 230 km is about halfway between 180 and 270 km, the time it takes to drive 230 km is about halfway between 120 and 180 minutes or about 150 minutes min 33 s. The fifth-place runner crossed the finish line 9 minutes 33 seconds after the winner. 13. For example, I started brushing my teeth at 9:13:18. I finished at 9:14: 52. How long did I brush my teeth? 14. For example, the time the next to last flight left was 17:45. The time the last flight left was 19:45. The last flight left 2 hours after the next to last flight. Chapter Review Answers (continued from p. 52) 8. a) 18 m. For example, = 9, 9 2 = 18 b) 54 km. For example, = 27, 27 2 = For example, no. The perimeter for a 22 by 29 sheet of paper is 102 cm. For half a sheet, it is 73 cm, which is more than half of 102 cm. 10. The perimeter is 1400 cm. Time Distance 1 s 19 cm 10 s 190 cm 50 s 950 cm 100 s cm For example, since 1400 cm is about halfway between 950 cm and 1800 cm, the time it takes the spider is about halfway between 50 s and 100 s or about 75 s. 11. For example, yes. He started brushing at 08:36:52 and finished at 08:39: The gold medallist won by 5 seconds. 13. a) :03 b) For example, he was born 2 h 57 min before midnight. 72 Chapter 5: Measuring Length and Time Copyright 2005 by Thomson Nelson

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