page 1 Measurement – AP Book 6.2 AP Book ME6-8 page 266 1. 2. 3. 4. a) 5 fingers: 50 mm b) 7 fingers: 70 mm a) 38 mm b) 47 mm a) Teacher to check. b) Teacher to check. a) i) Same length ii) Same length b) 5. 12. a) b) 910 mm c) 45 cm d) 2 cm e) 6 200 mm Diagonal: 5.2 cm, 52 mm Sides: 5 cm, 1.5 cm 7. 10 8. 10 9. mm cm 130 13 320 32 mm cm 80 8 180 18 mm cm 2 130 213 1 700 170 mm cm 90 9 5 670 567 420 42 d) 70 mm cm dm 80 8 6 200 18. No, Rebecca is incorrect. When 3 cm is converted in millimetres it becomes 30 mm. 30 mm is greater than 7 mm. 19. a) 4 cm + 4 cm m mm 5 5 000 17 000 620 cm mm 300 30 4 40 cm dm 121 1 210 530 53 dm cm 10 1 32 320 95 5 50 5. Teacher to check. a) 4 m 23 cm 5 m 14 cm c) 6 m 27 cm 10. 10 d) 6 m 73 cm d) 7 cm + 7 cm + 4 cm + 4 cm + 4 cm 11. 100 e) 3 m 81 cm f) 2 m 3 cm e) 7 cm + 7 cm + 7 cm + 4 cm AP Book ME6-10 page 270 6. a) 283 cm b) 365 cm 1. Answers will vary. a) 7 cm – 4 cm c) 485 cm 2. About 28 m b) 4 cm + 4 cm – 7 cm (8 – 7) d) 947 cm 3. Teacher to check. e) 704 cm 4. Teacher to check. f) 640 cm 5. Answers will vary. a) 546 cm = 5 m 46 cm = 5.46 m b) 2 m 17 cm = 2.17 m c) 7 m 83 cm = 7.83 m d) 6 m 8 cm = 6.08 m e) 72 cm = 0.72 m f) 7 cm = 0.07 m c) 7 cm + 7 cm – 4 cm + 4 cm + 4 cm (14 – 12) d) 7 cm + 7 cm + 7 cm – 4 cm + 4 cm + 4 cm + 4 cm (21 – 16) e) 7 cm + 7 cm + 7 cm – 4 cm (21 – 4) d) 43 e) 46 cm f) 6 cm 13 cm 7 000 Teacher to check. 7 cm + 7cm + 4 cm + 4 cm f) c) 70 c) 8 180 mm 800 Teacher to check. 320 b) cm 8 9. c) 40 mm m 8. b) 11. a) 1 000 b) 7 cm + 4 cm BONUS: 58 cm 3. b) 20. Possible solutions: Yes. Teacher to check. AP Book ME6-9 page 269 Leg – More Eraser – Less Pencil – Answers will vary. Door - More 7. 6. 0 1 B E A C D 7. A kilometre is about 10 football fields long. 8. Answers will vary. AP Book ME6-11 page 271 1. 1. 100 17 950 7. 2. 4. c) 8 cm 5 g) 6. 17. Teacher to check. 10. Divide by 10. a) 10 31 16. Teacher to check. 60 mm 5. 310 Estimates will vary – teacher to check. c) 10 12 15. Teacher to check. 15 mm 4. 6 m, 60 dm, 600 dm, 6 000 mm. 120 72 cm 14. Teacher to check. b) 3. 1 10 13. Teacher to check lines: b) 30 mm i) 30mm 38 mm 10 cm dm ii) 20mm a) 2. cm f) Actual Lengths: 6. 70 mm Answers listed as columns: 8. 3 m, 30 dm, 300 cm, 3 000 mm 100 cents = 1 dollar and 100 cm = 1 m 9. Yes, Michelle is correct. She multiplies 6 m by 100 in order to convert the measure to cm (since there are 100 cm in a metre). 4 m, 40 dm, 400 cm, 4 000 mm 5 m, 50 dm, 500 cm, 5 000 mm Answer Key for AP Book 6.2 page 2 Measurement – AP Book 6.2 (continued) AP Book ME6-12 page 272 1. a) iii) 100 mm = 10 cm = 1 dm f) i) 1 000 times smaller ii) 1 000 times more iii) Multiply by 1 000 Largest = dm Smallest = mm 2. 3. b) smaller c) more a) 10 mm b) 10 cm c) 100 mm d) 10 dm e) 100 cm f) 1 000 mm a) i) 10 times smaller ii) 10 times more iii) Multiply by 10 i) 10 times smaller ii) 10 times more iii) Multiply by 10 g) i) ii) iii) 10 times smaller 10 times more h) d) i) 10 times smaller ii) 10 times more iii) Multiply by 10 7.53 cm = 75.3 mm e) i) ii) 10 times larger 10 times fewer i) 1 000 times smaller ii) 1 000 times more iii) Multiply by 1 000 i) ii) iii) a) m = metre → width of a swimming pool km = kilometre → distance of a marathon b) 4. mm = millimetre → thickness of a nail 2. 40 dm b) 130 mm c) 200 mm 5. 45¢ 6. Since the total weight of emily’s book is 3.703 kg and is less than her maximum weight of 4 kg, she can carry all her books in her backpack. 7. 8. 9. 3. 4. The perimeter is 244 cm (2.44 m), and is greater than 2.4 m. Both relations are 1 000 times larger units (1 kg = 1000 g; 1 km = 1000 m). Both realtions are 1 000 times smller in units ( 1 mg = 0.001 g; 1 mm = 0.001 m). 5. a) m b) dm c) m a) cm b) m c) cm d) cm e) m a) km b) m c) m d) cm e) km f) m g) cm 1. Western Red Cedar – 5 900 cm 1. Snowy Owl – 66 cm 2. Great Horned Owl – 63.5 cm 3. Great Gray Owl – 55 cm 4. Atlantic Puffin – 34.5 cm 7. Teacher to check. 8. a) 83 km, 2 260 m, 3.3 km b) 877 km, 47 m, 7.5 km 9. Answers will vary. AP Book ME6-14 page 276 1. m = metre → length of a soccer field 1 000 times fewer a) km = kilometre → diameter of the moon cm = centimetre → length of a ruler 1 000 times larger Divide by 1000 6. mm = millimetre → length of bee’s antenna cm = centimetre → diameter of a drum 2.14 g = 0.00214 kg Multiply by 10 2.6 dm = 26 cm 1. 5.2 g = 5 200 mg 7.2 = 72 mm c) AP Book ME6-13 page 274 8.53 kg = 8 530 g 3.5 = 35 mm b) Divide by 10 3.4 mm = 0.34 cm 2. a) 100 km/h b) 80 km/h c) 25 km/h d) 160 km/h a) 25 km b) 360 km c) 210 km d) 210 km 3. A sneeze is 49.5 km/h faster than a hurricane. 4. In 3 hours, Clare can cycle 18 km further than Erin. 5. a) 80 km/h b) 120 km/h 6. 7. Jinny, 1.05 km/h a) 20 km b) 10 km/h AP Book ME6-15 page 277 1. Teacher to check the comparisons. Measurements for each building are as follows: 2. Lodgepole Pine – 3 050 cm a) 47 mm, 329 m b) 33 mm, 231 m 3. Red Oak – 2 400 cm c) 28 mm, 196 m 4. White Birch – 2 000 cm d) 19 mm, 133 m e) 16 mm, 112 m f) 11.5 mm, 80.5 m g) 8 mm, 56 m h) 7 mm, 49 m Answer Key for AP Book 6.2 page 3 Measurement – AP Book 6.2 (continued) 2. 6.5 mm, 45.5 m Lock 7 and Lock 8 b) 4 073 m j) 8 mm, 56 m 5 010 m A – 24 m About 500 m Distance on map = 128 mm c) a) d) 6 002 m D – 30 cm Actual distance = 128 × 200 = 25 600 m = 25.6 km e) 13 241 m f) 20 002 m b) About 10 3. 42 mm 4. a) b) Since 2 buildings of the Wall Centre has 96 floors and is still shorter than the First Canadian Place, the 76 floors in the First Canadian Place are greater in height than two times the floors in the Wall Centre. 2. 3. FCP: 47 mm × 7 m/mm = 329 m 329 m ÷ 72 floors = 4.57 m / floor. 4. 5. 5. 1. Lock 2 and Lock 3 2. Actual distance = 20 × 200 = 4 000 m = 4 km 3. 183 min a) P = 18 cm b) P = 16 cm c) 191 min d) 250 m 232 m c) Yes; 1 × 7 a) $7.03 d) 12 × 1; 26 units b) $16.04 5. Answers will vary. c) $27.03 6. 14 cm d) 8.06 m 7. 1:6 e) 9.25 m f) 3.1 cm i) 9.025 kg 1. a) AP Book ME6-18 page 280 1. 2. a) 2+4+2+1+1+ 2 + 1 + 1 = 14 cm b) 3+6+3+2+1+ 2 + 1 + 2 = 20 cm 2. 4. Answers will vary. 5. Answers will vary. a) 528 cents 714 cents 1. c) 1 003 cents 10 3 12 4 14 5 16 6 18 c) 26 a) New P = 12 units b) or Original P = 12 units New P = 12 units c) Original P = 14 units a) 10 cm b) 8 cm c) 14 cm W L a) 24 m 1 2 2 1 d) 408 cents a) 602 cm b) 409 cm b) 28 cm c) 613 cm c) 6 km d) 1 153 cm d) 30 cm e) 1 420 cm 2. 2 Original P = 10 units C: 28 units Answers will vary. O Input × 2 + 6 B: 20 units 3. I b) A: 14 units b) 301 cm AP Book ME6-20 page 282 16.8 m AP Book ME6-19 page 281 9 002 m 10 × 1; 2 × 5 12 × 1; 2 × 6; 3×4 326 min Line should be placed 9 mm south of Lock 2 a) a) b) e) Teacher to check line. f) 4. f) 9.4 dm AP Book ME6-17 page 279 Estimations will vary. 124 min 8.007 L Twice the length of the Welland Canal = 2 × 44 km = 88 km B – 28 cm 3. a) h) 6. e) b) g) Rounding both lengths (the Welland Canal to 90 km and the Grand Canal to 1 800 km), we see that you would have to travel up and down the Welland Canal 20 times (1 800 ÷ 90) to travel the distance of the Grand Canal. Lock 1 and Lock 2 Distance on map = 20 mm Time spent stopped = 8 locks × 0.5 h/lock = 4 hours = 8 hours and 24 minutes NOTE: Answers may vary, depending on how students place their rulers. The following distances assume that students measure from (and to) the middle of each lock. Actual distance = 13 × 200 = 2 600 m = 2.6 km 4. Total time spent = 4 + 4.4 hrs = 8.4 hours AP Book ME6-16 page 278 Distance on map = 13 mm At 10 km/h, the boat would travel 20 km in two hours and would not reach Lock 8. Time spent travelling = 44 km ÷ 10 km/h = 4.4 hours Wall Centre: 19 mm × 7 m/mm = 133 m 133 m ÷ 48 floors = 2.77 m / floor 1. C – 6 km i) New P = 12 units 3. P = 6 units Answer Key for AP Book 6.2 page 4 Measurement – AP Book 6.2 (continued) W L 1 5 2 4 3 3 AP Book ME6-21 page 283 AP Book ME5-23 page 285 C: 11 m × 6 m 2 = 66 m 1. 1. D: 15 km × 10 km 2 = 150 km P = 12 units A: 10.8 cm a) 4 × 3 = 12 B: 8.8 cm b) 2×3=6 C: 15.6 cm c) 3×2=6 D: 15.6 cm W L E: 15.2 cm 1 7 F: 19.2 cm 2 6 3 4 2. a) W C 5 2 cm 6 cm 4 3 cm 9 cm 4 cm 12 cm P = 16 units W L 1 8 2 7 3 6 4 b) a) 5 1. Yes 8 cm b) 8 cm 3 × 7 = 21 A – 21 m b) 3 × 4 = 12 B – 20 cm c) 3×2=6 d) 4 × 6 = 24 a) b) 1 8 a) 8 cm 2 10 b) 3 cm 3 12 c) 4 cm 4 14 5 16 6 18 I O 1 8 2 12 3 16 4 20 5 24 28 c) 2. 3. 9 cm 2 4. 5. 6. 5. 3 cm Length = 3 units 6. 5 cm Width = 2 units 7. a) 2 cm , 2 cm , 4 cm , 2 2 2 3 cm , 6 cm , 5 cm To find the area, extend the lines through the shape. 2 Area of C = 8 cm 2 Answers will vary – teacher to check. Answers will vary – teacher to check. 5. 3 cm × 4 cm rectangle: 2. OPTION 2 b) 1 cm × 3 cm 2 = 3 cm c) 2 cm × 4 cm 2 = 8 cm Box 1: 2 × 5 = 10 Box 2: 3 × 4 = 12 Total Area: 10 + 12 = 22 d) 4 cm × 3 cm 2 = 12 cm e) 2 cm × 5 cm 2 = 10 cm Area = Length × Width 8. 3. Three possible rectangles: 1 × 12, 2 × 6, and 4 × 3. AP Book ME6-25 page 287 1. Shape P A A 12 cm 8 cm B 22 cm 30 cm 2 C 22 cm 18 cm 2 2 a) 2 cm × 5 cm 2 = 10 cm D 20 cm 21 cm 2 1 cm × 3 cm 2 = 3 cm E 26 cm 30 cm 2 b) F 14 cm 10 cm 2 c) 3 cm × 5 cm 2 = 15 cm G 22 cm 10 cm 2 a) 6m×7m 2 = 42 m OR 4 cm × 3 cm rectangle: 2 2 cm × 3 cm 2 = 6 cm Length = 4 units AP Book ME6-24 page 286 1. 2 4 × 3 = 12 2 Area of B = 4 cm 2 a) 2 Area of A = 6 cm 6 × 2 = 12 Length = 6 units b) –c) OPTION 1 Box 1: 2×2=4 Box 2: 3 × 6 = 18 Total Area: 4 + 18 = 22 2 2 2 Width = 3 cm (since you can find the width by dividing the area by the length, and 2 18 cm ÷ 6 cm is 3 cm) 3×2=6 4. 2 4. Width = 3 units 2 O Multiply INPUT by 4 and add 4; Base 10: 44 toothpicks 5. a) 2 a) I 6 C – 66 m Width = 2 units The circumference is about 3 times greater than the width. 2 5 × 3 = 15 c) Multiply INPUT by 2 and add 6; Base 10: 26 toothpicks b) 3. D – 150 km d) AP Book ME6-22 page 284 P = 18 units 4. 2. 2 b) 2. No 3. D&G 4. E – 26 cm b) 3m×7m 2 = 21 m B, C & G – 22 cm c) 4 cm × 8 cm 2 = 32 cm F – 14 cm a) A: 3 m × 7 m 2 = 21 m D – 20 cm A – 12 cm B: 4 cm × 5 cm 2 = 20 cm Answer Key for AP Book 6.2 page 5 Measurement – AP Book 6.2 (continued) 5. 2 b) 2 whole squares D – 21 cm 2 c) 3 whole squares C – 18 cm 2 d) 3 whole squares e) 8 whole squares f) 8 whole squares E & B – 30 cm F& G – 10 cm A – 8 cm 2 2 6. No g) 4 whole squares 7. Perimeter is the measure of the length along the outside edge of a shape. Area is the measure of the space contained within the edges of a shape. h) 5 whole squares i) 11 whole squares j) 13 whole squares k) 10 whole squares a) 7.5 square units b) 6 square units c) 7.5 square units a) More: shaded = 7 unshaded = 5 and 7 > 5 AP Book ME6-26 page 288 1. P A A 14 cm 10 cm 2 12 cm 2 16 cm 15 cm 2 D 10 cm 6 cm 2 E 18 cm 14 cm 16 cm b) 9 half squares = 4.5 total squares c) 14 half squares = 7 total squares b) 11. a) 4 half squares 10 000 times more; Multiply by 10 000; = 10 total squares 1.34 m 2 = 13 400 cm 6 full squares c) 146 500 cm = 7 total squares d) 1 000 cm e) 3 760 cm f) 72 000 cm i) a) Area ≈ 5 units 2 Perimeter ≈ 14 units b) Area ≈ 12 units 2 c) Area ≈ 6 units 2 b) 30 cm 2 c) 3 square units c) 32 berries d) 5 square units d) a) Triangle: 3 square units $10.00 – $5.98 = $4.02 2 6. 2 a) 6 cm b) 20 cm Rectangle: 2 square units 2 a) 3 × 3. Area = 9 b) 5 × 5. Area = 25 b) Teacher to check drawings. a) 5 × 2 rectangle b) 4 × 2 rectangle c) NOTE: For estimation questions, consider the diagonal of the square unit equals 1.5 cm. 3 whole squares d) 7. AP Book ME6-28 page 292 1. 2. 20 square units b) 48 – 20 Shaded = 28 Unshaded a) 3. 8 cm 18 cm 4. a) 6 wholes squares 5. b) 8.5 whole squares 600 cm 2 4:1 b) 60 : 15 c) 92 : 23 ii) One side is a fourth or quarter of the total perimeter. a) 30 : 5 b) 60 : 10 c) 36 : 6 d) 48 : 8 Patti is incorrect because 100 cm = 1 m, then 100 cm × 100 cm 2 = 10 000 cm and 2 1m×1m=1m . 4 2 AP Book ME6-30 page 294 8 1 1. Length Width 7 2 14 1 Length Width 6 3 9 2 18 1 Answers will vary. BONUS: a) 2 Width 2 5 5; 9 2. 2 2 Length 2 Triangle: 6 square units 4. 2 2 14 cm Rectangle: 3 square units 3. a) Triangle: 4 square units Rectangle: 4 square units AP Book ME6-27 page 289 Perimeter ≈ 11 units Triangle: 1 square unit Triangle:1 square unit 2. Perimeter ≈ 16 units 3 square units P = 10 cm; 2 2 half squares b) 5. b) 8 full squares P = 8 cm; 2 10 000 cm 10 000 times smaller; 1 square units P = 14 cm; 2 a) Area = 3 + 3 = 6 a) 2 1. Area = 3 + 4 = 7 2 square units 4. AP Book ME6-29 page 293 a) 10. a) Equal: shaded = 4 unshaded = 4 1 b) c) 12 cm a) 2; 4 4 square units 14 cm A = 6 cm 1. c) b) 2 2 G A = 3 cm 5. 7 half squares = 3.5 total squares 1 2 8 cm c) a) 1; 4 a) 12 cm b) b) Less: shaded = 3 unshaded = 4 and 3 < 4 F a) 9. 8.5 whole squares c) A = 10 cm 4. b) R C 3. 3. This table gives the shapes’ actual measurements only: B 2. 2. 8. 1 c) a) Yes. The part of the shape that was taken away from the first parallelogram, is the exact same that was added to the second parallelogram. b) Both have a base of 4 c) Both have a height of 5 d) Area = B × H a) 4 × 3 = 12 cm 2 Answer Key for AP Book 6.2 page 6 Measurement – AP Book 6.2 (continued) 3. 2 b) 7 × 2 = 14 cm a) 2 35 cm b) 12 cm D: st Area of 1 triangle = (2 × 4) ÷ 2 2 = 4 cm 2 2 c) 48 cm d) 22.2 cm a) A Area of 2 triangle = (1 × 4) ÷ 2 2 = 2 cm 2 Teacher to check that lines are drawn correctly. Base Height 4 4 B 2 5 C 4 5 D 3 4 b) a) nd AP Book ME6-31 page 295 1. 7. A: st Area of 1 triangle = (2 × 4) ÷ 2 2 = 4 cm 2. Area of Triangle A = Area of Parallelogram B ÷ 2 3. Teacher to check drawing. 4. A = (Base × Height) ÷ 2 5. Area of Triangle A = (4 × 4) ÷ 2 = 16 ÷ 2 2 = 8 cm nd Area of 2 triangle = (1 × 5) ÷ 2 2 = 2.5 cm Total Area of B 2 2 = 2.5 cm + 2.5 cm 2 = 5 cm C: st Area of 1 triangle = (3 × 5) ÷ 2 2 = 7.5 cm AP Book ME6-32 page 296 1. 2. 3. 4. nd Area of 2 triangle = (1 × 5) ÷ 2 2 = 2.5 cm Total Area of C 2 2 = 7.5 cm + 2.5 cm 2 = 10 cm 8. Each shape should have a height of two square units (double the height). 1. 2 a) 6 cm b) 6 cm 1 4 B 2 8 C .5 2 D 1 4 12 cm d) 12.8 cm 2 cm; 16 cm 6 cm 2 times 12. Teacher to check. 13. A - 150 cm 2 B - 200 cm a) 35 cm b) 170 cm d) 22 cm 16. 1 2 The triangle has the same base and height as the parallelogram. Therefore the area is half because when calculating the area of a triangle you divide by 2 (A = B × H ÷ 2) 2 6 cm b) 4 cm 17. 2 18. 2 c) 6 cm A 9 units 2 B 18 units 2 C 24 units 2 20 units 2 5. Area = 44 units 6. a) 2 P = 24 units A = 28 units b) 6.5 km; 5.5 km 2 a) D 15. 2 31.5 cm 2 Less (P = 10 cm) 2 c) 2 14. 2 2 19. P = 34 units A = 57 units 2 20. 12 b) 12 cm c) 1 × 3 × 4 = 12 cm d) 2 × 3 × 4 = 24 cm e) 3 × 3 × 4 = 36 cm 3 3 3 3 3 f) 36 cm g) 36 mL a) i) b) c) 3. 11. 2 a) 5 cm; 20 cm 10. 2 2. The area is quadrupled (mutliplied by 4). 9. 2 c) Area New Shape Area A C - 225 cm B: st Area of 1 triangle = (1 × 5) ÷ 2 2 = 2.5 cm nd c) Area of parallelogram 2 = 4 × 4 = 16 units The area of the triangle is 2 8 cm (half of 16, or 8 2) units . AP Book ME6-33 page 299 Shape Total Area of D 2 2 = 4 cm + 2 cm 2 = 6 cm Area of 2 triangle = (2 × 4) ÷ 2 2 = 4 cm Total Area of A 2 2 = 4 cm + 4 cm 2 = 8 cm b) Teacher to check drawings. 1×3×2 ii) 1×3×3 iii) 1×2×5 i) 5×3×2 ii) 5×3×3 iii) 5×2×5 V=L×W×H Answers will vary. Teacher to check. AP Book ME6-34 page 300 1. 2. a) 2 700 b) 48 000 c) 6 000 d) 3 400 e) 8 100 f) 1 200 g) 9 800 h) 4 050 i) 2 300 a) 5 000 kg b) 18 000 kg c) 6 000 kg explanation d) 50 000 kg 16 m. The shaded triangle is half of the square, therefore the area of the square is 16 2. m Becuase the shape is a square, we know all sides must be even (16 = 4 × 4). When all 4 sides are added, the result is 16cm. e) 1 500 kg f) 310 kg g) 45 500 kg 1 2 , see Q.16 for 4 cm. You can check you answer by inserting the numbers into the formula ( A = B × H ÷ 2). 3. h) 26 000 kg a) 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000 b) 25 Teacher to check. Answer Key for AP Book 6.2 Measurement – AP Book 6.2 (continued) c) page 7 Answers will vary – roughly 20 (1 000 kg = 50 kg × 20) 4. No, the total mass is about 1 250 kg or 1.25 tonnes and exceeds the 1 tonne limit. 5. 5 000 kg = 5 tonnes More. An elephant would eat about 1 050 kg in one week. 6. Yes, Merlinda family’s furniture weighs 1 000 kg, and is less than the maximum weight of the truck. Answer Key for AP Book 6.2
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