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3B · Chapter 11 · Solutions

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Meters and Centimeters

Prerequisite

  1. 5 — Five hundred is five complete groups of one hundred: 100 + 100 + 100 + 100 + 100 = 500. Changing the unit does not change the quantity.
  2. 900 — Twelve hundreds minus three hundreds is nine hundreds.
  3. 1,035 — One thousand plus three tens and five ones gives 1,035. The zero in the hundreds place means there are no additional hundreds.

Understanding checks

  1. 325 cm — 3 m = 300 cm; add 25 to make 325 cm.
  2. 5 m 50 cm — Partition 550 into 5 full groups of 100 plus 50.
  3. 5 m 80 cm — Partition 580 into 5 full groups of 100 plus 80.

Guided

  1. 740 cm — 7 m = 700 cm; add 40 to make 740 cm.
  2. 6 m 40 cm — Partition 640 into 6 full groups of 100 plus 40.
  3. 775 cm — 7 m = 700 cm; add 75 to make 775 cm.
  4. 3 m 40 cm — Partition 340 into 3 full groups of 100 plus 40.
  5. 550 cm — 5 m = 500 cm; add 50 to make 550 cm.

Independent

  1. 675 cm — 6 m = 600 cm; add 75 to make 675 cm.
  2. 4 m 55 cm — Partition 455 into 4 full groups of 100 plus 55.
  3. 350 cm — 3 m = 300 cm; add 50 to make 350 cm.
  4. 6 m 20 cm — Partition 620 into 6 full groups of 100 plus 20.
  5. 5 m 75 cm — Partition 575 into 5 full groups of 100 plus 75.
  6. 620 cm — 6 m = 600 cm; add 20 to make 620 cm.
  7. 2 m 65 cm — Partition 265 into 2 full groups of 100 plus 65.
  8. 475 cm — 4 m = 400 cm; add 75 to make 475 cm.

Challenge

  1. 640 cm — There are 100 centimeters in one meter, so 6 m 40 cm equals 640 cm, not meters.
  2. 5 m 50 cm — Exchange 1 m for 100 cm: 5 m 120 cm − 70 cm = 5 m 50 cm.

Exit

  1. 680 cm — 6 m = 600 cm; add 80 to make 680 cm.
  2. 425 cm — 4 m = 400 cm; add 25 to make 425 cm.
  3. 820 cm — 8 m = 800 cm; add 20 to make 820 cm.

Subtracting from Meters

Prerequisite

  1. 355 cm — 3 m = 300 cm; add 55 to make 355 cm.
  2. 4 m 65 cm — Partition 465 into 4 full groups of 100 plus 65.
  3. 775 cm — 7 m = 700 cm; add 75 to make 775 cm.

Understanding checks

  1. 1 m 68 cm — Exchange one m for 100 cm, then subtract: 250 − 82 = 168 cm. Regroup the result into m and cm.
  2. 2 m 73 cm — Exchange one m for 100 cm, then subtract: 365 − 92 = 273 cm. Regroup the result into m and cm.
  3. 6 m 97 cm — Exchange one m for 100 cm, then subtract: 750 − 53 = 697 cm. Regroup the result into m and cm.

Guided

  1. 2 m 41 cm — Exchange one m for 100 cm, then subtract: 320 − 79 = 241 cm. Regroup the result into m and cm.
  2. 4 m 60 cm — Exchange one m for 100 cm, then subtract: 540 − 80 = 460 cm. Regroup the result into m and cm.
  3. 5 m 47 cm — Exchange one m for 100 cm, then subtract: 620 − 73 = 547 cm. Regroup the result into m and cm.
  4. 6 m 70 cm — Exchange one m for 100 cm, then subtract: 755 − 85 = 670 cm. Regroup the result into m and cm.
  5. 6 m 84 cm — Exchange one m for 100 cm, then subtract: 780 − 96 = 684 cm. Regroup the result into m and cm.

Independent

  1. 5 m 89 cm — Exchange one m for 100 cm, then subtract: 680 − 91 = 589 cm. Regroup the result into m and cm.
  2. 4 m 86 cm — Exchange one m for 100 cm, then subtract: 520 − 34 = 486 cm. Regroup the result into m and cm.
  3. 1 m 29 cm — Exchange one m for 100 cm, then subtract: 225 − 96 = 129 cm. Regroup the result into m and cm.
  4. 7 m 95 cm — Exchange one m for 100 cm, then subtract: 850 − 55 = 795 cm. Regroup the result into m and cm.
  5. 2 m 88 cm — Exchange one m for 100 cm, then subtract: 350 − 62 = 288 cm. Regroup the result into m and cm.
  6. 3 m 56 cm — Exchange one m for 100 cm, then subtract: 440 − 84 = 356 cm. Regroup the result into m and cm.
  7. 1 m 58 cm — Exchange one m for 100 cm, then subtract: 225 − 67 = 158 cm. Regroup the result into m and cm.
  8. 5 m 83 cm — Exchange one m for 100 cm, then subtract: 620 − 37 = 583 cm. Regroup the result into m and cm.

Challenge

  1. 740 cm — There are 100 centimeters in one meter, so 7 m 40 cm equals 740 cm, not meters.
  2. 6 m 50 cm — Exchange 1 m for 100 cm: 6 m 120 cm − 70 cm = 6 m 50 cm.

Exit

  1. 5 m 87 cm — Exchange one m for 100 cm, then subtract: 680 − 93 = 587 cm. Regroup the result into m and cm.
  2. 7 m 66 cm — Exchange one m for 100 cm, then subtract: 850 − 84 = 766 cm. Regroup the result into m and cm.
  3. 4 m 82 cm — Exchange one m for 100 cm, then subtract: 580 − 98 = 482 cm. Regroup the result into m and cm.

Kilometers

Prerequisite

  1. 4 m 52 cm — Exchange one m for 100 cm, then subtract: 525 − 73 = 452 cm. Regroup the result into m and cm.
  2. 4 m 91 cm — Exchange one m for 100 cm, then subtract: 565 − 74 = 491 cm. Regroup the result into m and cm.
  3. 4 m 88 cm — Exchange one m for 100 cm, then subtract: 525 − 37 = 488 cm. Regroup the result into m and cm.

Understanding checks

  1. 2,040 m — 2 km = 2,000 m; add 40 to make 2,040 m.
  2. 5 km 55 m — Partition 5,055 into 5 full groups of 1,000 plus 55.
  3. 6,040 m — 6 km = 6,000 m; add 40 to make 6,040 m.

Guided

  1. 2,875 m — 2 km = 2,000 m; add 875 to make 2,875 m.
  2. 4 km 20 m — Partition 4,020 into 4 full groups of 1,000 plus 20.
  3. 4,375 m — 4 km = 4,000 m; add 375 to make 4,375 m.
  4. 2 km 375 m — Partition 2,375 into 2 full groups of 1,000 plus 375.
  5. 6,480 m — 6 km = 6,000 m; add 480 to make 6,480 m.

Independent

  1. 4,875 m — 4 km = 4,000 m; add 875 to make 4,875 m.
  2. 4 km 125 m — Partition 4,125 into 4 full groups of 1,000 plus 125.
  3. 7,480 m — 7 km = 7,000 m; add 480 to make 7,480 m.
  4. 6 km 650 m — Partition 6,650 into 6 full groups of 1,000 plus 650.
  5. 5,375 m — 5 km = 5,000 m; add 375 to make 5,375 m.
  6. 5 km 375 m — Partition 5,375 into 5 full groups of 1,000 plus 375.
  7. 5,480 m — 5 km = 5,000 m; add 480 to make 5,480 m.
  8. 8,250 m — 8 km = 8,000 m; add 250 to make 8,250 m.

Challenge

  1. 1 km = 1,000 m — Each of the 3 kilometers contains 1,000 meters. The unit changes, not the distance.
  2. 2 km 750 m — Rename as 2 km 1,200 m, then subtract 450 m to get 2 km 750 m.

Exit

  1. 5,875 m — 5 km = 5,000 m; add 875 to make 5,875 m.
  2. 4 km 55 m — Partition 4,055 into 4 full groups of 1,000 plus 55.
  3. 3,065 m — 3 km = 3,000 m; add 65 to make 3,065 m.

Subtracting from Kilometers

Prerequisite

  1. 2,375 m — 2 km = 2,000 m; add 375 to make 2,375 m.
  2. 2 km 875 m — Partition 2,875 into 2 full groups of 1,000 plus 875.
  3. 6,480 m — 6 km = 6,000 m; add 480 to make 6,480 m.

Understanding checks

  1. 3 km 950 m — Exchange one km for 1000 m, then subtract: 4055 − 105 = 3950 m. Regroup the result into km and m.
  2. 2 km 878 m — Exchange one km for 1000 m, then subtract: 3055 − 177 = 2878 m. Regroup the result into km and m.
  3. 2 km 998 m — Exchange one km for 1000 m, then subtract: 3650 − 652 = 2998 m. Regroup the result into km and m.

Guided

  1. 2 km 445 m — Exchange one km for 1000 m, then subtract: 3375 − 930 = 2445 m. Regroup the result into km and m.
  2. 2 km 279 m — Exchange one km for 1000 m, then subtract: 3125 − 846 = 2279 m. Regroup the result into km and m.
  3. 7 km 474 m — Exchange one km for 1000 m, then subtract: 8020 − 546 = 7474 m. Regroup the result into km and m.
  4. 1 km 415 m — Exchange one km for 1000 m, then subtract: 2065 − 650 = 1415 m. Regroup the result into km and m.
  5. 4 km 788 m — Exchange one km for 1000 m, then subtract: 5375 − 587 = 4788 m. Regroup the result into km and m.

Independent

  1. 2 km 960 m — Exchange one km for 1000 m, then subtract: 3125 − 165 = 2960 m. Regroup the result into km and m.
  2. 1 km 489 m — Exchange one km for 1000 m, then subtract: 2125 − 636 = 1489 m. Regroup the result into km and m.
  3. 1 km 980 m — Exchange one km for 1000 m, then subtract: 2875 − 895 = 1980 m. Regroup the result into km and m.
  4. 4 km 192 m — Exchange one km for 1000 m, then subtract: 5055 − 863 = 4192 m. Regroup the result into km and m.
  5. 4 km 740 m — Exchange one km for 1000 m, then subtract: 5650 − 910 = 4740 m. Regroup the result into km and m.
  6. 4 km 870 m — Exchange one km for 1000 m, then subtract: 5040 − 170 = 4870 m. Regroup the result into km and m.
  7. 1 km 629 m — Exchange one km for 1000 m, then subtract: 2020 − 391 = 1629 m. Regroup the result into km and m.
  8. 3 km 658 m — Exchange one km for 1000 m, then subtract: 4650 − 992 = 3658 m. Regroup the result into km and m.

Challenge

  1. 1 km = 1,000 m — Each of the 4 kilometers contains 1,000 meters. The unit changes, not the distance.
  2. 3 km 750 m — Rename as 3 km 1,200 m, then subtract 450 m to get 3 km 750 m.

Exit

  1. 3 km 41 m — Exchange one km for 1000 m, then subtract: 4040 − 999 = 3041 m. Regroup the result into km and m.
  2. 2 km 567 m — Exchange one km for 1000 m, then subtract: 3250 − 683 = 2567 m. Regroup the result into km and m.
  3. 1 km 866 m — Exchange one km for 1000 m, then subtract: 2375 − 509 = 1866 m. Regroup the result into km and m.

Liters and Milliliters

Prerequisite

  1. 1 km 953 m — Exchange one km for 1000 m, then subtract: 2650 − 697 = 1953 m. Regroup the result into km and m.
  2. 3 km 770 m — Exchange one km for 1000 m, then subtract: 4375 − 605 = 3770 m. Regroup the result into km and m.
  3. 5 km 394 m — Exchange one km for 1000 m, then subtract: 6375 − 981 = 5394 m. Regroup the result into km and m.

Understanding checks

  1. 8,480 mL — 8 L = 8,000 mL; add 480 to make 8,480 mL.
  2. 6 L 375 mL — Partition 6,375 into 6 full groups of 1,000 plus 375.
  3. 5 L 875 mL — Partition 5,875 into 5 full groups of 1,000 plus 875.

Guided

  1. 2,250 mL — 2 L = 2,000 mL; add 250 to make 2,250 mL.
  2. 4 L 875 mL — Partition 4,875 into 4 full groups of 1,000 plus 875.
  3. 7,065 mL — 7 L = 7,000 mL; add 65 to make 7,065 mL.
  4. 5 L 250 mL — Partition 5,250 into 5 full groups of 1,000 plus 250.
  5. 2,020 mL — 2 L = 2,000 mL; add 20 to make 2,020 mL.

Independent

  1. 7,480 mL — 7 L = 7,000 mL; add 480 to make 7,480 mL.
  2. 5,875 mL — 5 L = 5,000 mL; add 875 to make 5,875 mL.
  3. 3 L 375 mL — Partition 3,375 into 3 full groups of 1,000 plus 375.
  4. 8,125 mL — 8 L = 8,000 mL; add 125 to make 8,125 mL.
  5. 4 L 375 mL — Partition 4,375 into 4 full groups of 1,000 plus 375.
  6. 5,125 mL — 5 L = 5,000 mL; add 125 to make 5,125 mL.
  7. 7 L 125 mL — Partition 7,125 into 7 full groups of 1,000 plus 125.
  8. 6,040 mL — 6 L = 6,000 mL; add 40 to make 6,040 mL.

Challenge

  1. 5,250 mL — Each L is 1,000 mL. Add the remaining 250 mL.
  2. 5 L 125 mL — There are 5 full groups of 1,000 mL and 125 leftover mL.

Exit

  1. 8,040 mL — 8 L = 8,000 mL; add 40 to make 8,040 mL.
  2. 4 L 125 mL — Partition 4,125 into 4 full groups of 1,000 plus 125.
  3. 7,125 mL — 7 L = 7,000 mL; add 125 to make 7,125 mL.

Kilograms and Grams

Prerequisite

  1. 8,480 mL — 8 L = 8,000 mL; add 480 to make 8,480 mL.
  2. 7 L 40 mL — Partition 7,040 into 7 full groups of 1,000 plus 40.
  3. 6,875 mL — 6 L = 6,000 mL; add 875 to make 6,875 mL.

Understanding checks

  1. 6 kg 480 g — Partition 6,480 into 6 full groups of 1,000 plus 480.
  2. 3,480 g — 3 kg = 3,000 g; add 480 to make 3,480 g.
  3. 8 kg 40 g — Partition 8,040 into 8 full groups of 1,000 plus 40.

Guided

  1. 2,065 g — 2 kg = 2,000 g; add 65 to make 2,065 g.
  2. 4 kg 250 g — Partition 4,250 into 4 full groups of 1,000 plus 250.
  3. 3,125 g — 3 kg = 3,000 g; add 125 to make 3,125 g.
  4. 3 kg 375 g — Partition 3,375 into 3 full groups of 1,000 plus 375.
  5. 3,020 g — 3 kg = 3,000 g; add 20 to make 3,020 g.

Independent

  1. 7,375 g — 7 kg = 7,000 g; add 375 to make 7,375 g.
  2. 7 kg 650 g — Partition 7,650 into 7 full groups of 1,000 plus 650.
  3. 7,065 g — 7 kg = 7,000 g; add 65 to make 7,065 g.
  4. 5 kg 375 g — Partition 5,375 into 5 full groups of 1,000 plus 375.
  5. 7,250 g — 7 kg = 7,000 g; add 250 to make 7,250 g.
  6. 3 kg 55 g — Partition 3,055 into 3 full groups of 1,000 plus 55.
  7. 7,875 g — 7 kg = 7,000 g; add 875 to make 7,875 g.
  8. 7 kg 875 g — Partition 7,875 into 7 full groups of 1,000 plus 875.

Challenge

  1. 6,250 g — Each kg is 1,000 g. Add the remaining 250 g.
  2. 6 kg 125 g — There are 6 full groups of 1,000 g and 125 leftover g.

Exit

  1. 7,125 g — 7 kg = 7,000 g; add 125 to make 7,125 g.
  2. 8,650 g — 8 kg = 8,000 g; add 650 to make 8,650 g.
  3. 4 kg 875 g — Partition 4,875 into 4 full groups of 1,000 plus 875.

Word Problems

Prerequisite

  1. 2 kg 20 g — Partition 2,020 into 2 full groups of 1,000 plus 20.
  2. 4,125 g — 4 kg = 4,000 g; add 125 to make 4,125 g.
  3. 8 kg 40 g — Partition 8,040 into 8 full groups of 1,000 plus 40.

Understanding checks

  1. 2 km 792 m — The route is 3065 m. Subtract 273 m to get 2792 m; regroup into kilometers and meters.
  2. 1 km 529 m — The route is 2020 m. Subtract 491 m to get 1529 m; regroup into kilometers and meters.
  3. 3 km 169 m — The route is 6020 m. Subtract 2851 m to get 3169 m; regroup into kilometers and meters.

Guided

  1. 6 km 475 m — The route is 7480 m. Subtract 1005 m to get 6475 m; regroup into kilometers and meters.
  2. 4 km 552 m — The route is 4650 m. Subtract 98 m to get 4552 m; regroup into kilometers and meters.
  3. 2 km 800 m — The route is 3065 m. Subtract 265 m to get 2800 m; regroup into kilometers and meters.
  4. 1 km 698 m — The route is 2020 m. Subtract 322 m to get 1698 m; regroup into kilometers and meters.
  5. 1 km 77 m — The route is 2055 m. Subtract 978 m to get 1077 m; regroup into kilometers and meters.

Independent

  1. 4 km 3 m — The route is 4480 m. Subtract 477 m to get 4003 m; regroup into kilometers and meters.
  2. 2 km 74 m — The route is 2375 m. Subtract 301 m to get 2074 m; regroup into kilometers and meters.
  3. 1 km 880 m — The route is 2480 m. Subtract 600 m to get 1880 m; regroup into kilometers and meters.
  4. 5 km 745 m — The route is 8375 m. Subtract 2630 m to get 5745 m; regroup into kilometers and meters.
  5. 6 km 346 m — The route is 7875 m. Subtract 1529 m to get 6346 m; regroup into kilometers and meters.
  6. 3 km 372 m — The route is 3480 m. Subtract 108 m to get 3372 m; regroup into kilometers and meters.
  7. 1 km 107 m — The route is 2065 m. Subtract 958 m to get 1107 m; regroup into kilometers and meters.
  8. 1 km 629 m — The route is 2055 m. Subtract 426 m to get 1629 m; regroup into kilometers and meters.

Challenge

  1. 1 km = 1,000 m — Each of the 7 kilometers contains 1,000 meters. The unit changes, not the distance.
  2. 6 km 750 m — Rename as 6 km 1,200 m, then subtract 450 m to get 6 km 750 m.

Exit

  1. 2 km 996 m — The route is 3040 m. Subtract 44 m to get 2996 m; regroup into kilometers and meters.
  2. 2 km 916 m — The route is 3125 m. Subtract 209 m to get 2916 m; regroup into kilometers and meters.
  3. 4 km 228 m — The route is 6875 m. Subtract 2647 m to get 4228 m; regroup into kilometers and meters.

Practice

  1. 5 m 20 cm — Partition 520 into 5 full groups of 100 plus 20.
  2. 6 m 93 cm — Exchange one m for 100 cm, then subtract: 750 − 57 = 693 cm. Regroup the result into m and cm.
  3. 2 km 20 m — Partition 2,020 into 2 full groups of 1,000 plus 20.
  4. 3 km 646 m — Exchange one km for 1000 m, then subtract: 4040 − 394 = 3646 m. Regroup the result into km and m.
  5. 4 L 65 mL — Partition 4,065 into 4 full groups of 1,000 plus 65.
  6. 5 kg 20 g — Partition 5,020 into 5 full groups of 1,000 plus 20.
  7. 4 km 701 m — The route is 4875 m. Subtract 174 m to get 4701 m; regroup into kilometers and meters.
  8. 875 cm — 8 m = 800 cm; add 75 to make 875 cm.
  9. 5 m 51 cm — Exchange one m for 100 cm, then subtract: 650 − 99 = 551 cm. Regroup the result into m and cm.
  10. 6,125 m — 6 km = 6,000 m; add 125 to make 6,125 m.
  11. 4 km 553 m — Exchange one km for 1000 m, then subtract: 5375 − 822 = 4553 m. Regroup the result into km and m.
  12. 4,020 mL — 4 L = 4,000 mL; add 20 to make 4,020 mL.
  13. 8,250 g — 8 kg = 8,000 g; add 250 to make 8,250 g.
  14. 2 km 962 m — The route is 5375 m. Subtract 2413 m to get 2962 m; regroup into kilometers and meters.
  15. 7 m 65 cm — Partition 765 into 7 full groups of 100 plus 65.
  16. 2 m 69 cm — Exchange one m for 100 cm, then subtract: 365 − 96 = 269 cm. Regroup the result into m and cm.
  17. 6 m 50 cm — Exchange 1 m for 100 cm: 6 m 120 cm − 70 cm = 6 m 50 cm.
  18. 660 cm — There are 100 centimeters in one meter, so 6 m 60 cm equals 660 cm, not meters.

Chapter Review

  1. 8 m 40 cm — Partition 840 into 8 full groups of 100 plus 40.
  2. 1 m 68 cm — Exchange one m for 100 cm, then subtract: 220 − 52 = 168 cm. Regroup the result into m and cm.
  3. 4 km 250 m — Partition 4,250 into 4 full groups of 1,000 plus 250.
  4. 1 km 55 m — Exchange one km for 1000 m, then subtract: 2020 − 965 = 1055 m. Regroup the result into km and m.
  5. 3 L 875 mL — Partition 3,875 into 3 full groups of 1,000 plus 875.
  6. 6 kg 65 g — Partition 6,065 into 6 full groups of 1,000 plus 65.
  7. 4 km 156 m — The route is 5375 m. Subtract 1219 m to get 4156 m; regroup into kilometers and meters.
  8. 275 cm — 2 m = 200 cm; add 75 to make 275 cm.
  9. 1 m 96 cm — Exchange one m for 100 cm, then subtract: 280 − 84 = 196 cm. Regroup the result into m and cm.
  10. 6,375 m — 6 km = 6,000 m; add 375 to make 6,375 m.
  11. 4 km 743 m — Exchange one km for 1000 m, then subtract: 5125 − 382 = 4743 m. Regroup the result into km and m.
  12. 6,875 mL — 6 L = 6,000 mL; add 875 to make 6,875 mL.
  13. 4,040 g — 4 kg = 4,000 g; add 40 to make 4,040 g.
  14. 3 km 708 m — The route is 5020 m. Subtract 1312 m to get 3708 m; regroup into kilometers and meters.
  15. 8 m 55 cm — Partition 855 into 8 full groups of 100 plus 55.
  16. 3 m 92 cm — Exchange one m for 100 cm, then subtract: 480 − 88 = 392 cm. Regroup the result into m and cm.
  17. 4 km 55 m — Partition 4,055 into 4 full groups of 1,000 plus 55.
  18. 7 km 472 m — Exchange one km for 1000 m, then subtract: 8375 − 903 = 7472 m. Regroup the result into km and m.
  19. 8 L 875 mL — Partition 8,875 into 8 full groups of 1,000 plus 875.
  20. 3 kg 20 g — Partition 3,020 into 3 full groups of 1,000 plus 20.
  21. 5 km 209 m — The route is 7055 m. Subtract 1846 m to get 5209 m; regroup into kilometers and meters.
  22. 250 cm — 2 m = 200 cm; add 50 to make 250 cm.
  23. 2 m 68 cm — Exchange one m for 100 cm, then subtract: 355 − 87 = 268 cm. Regroup the result into m and cm.
  24. 8,020 m — 8 km = 8,000 m; add 20 to make 8,020 m.
  25. 4 m 50 cm — Exchange 1 m for 100 cm: 4 m 120 cm − 70 cm = 4 m 50 cm.
  26. 450 cm — There are 100 centimeters in one meter, so 4 m 50 cm equals 450 cm, not meters.

Practice Exam

  1. 2 km 858 m — The suggested answer is not correct. Exchange one km for 1000 m, then subtract: 3375 − 517 = 2858 m. Regroup the result into km and m. (3 points: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.)
  2. 6 m 50 cm — Partition 650 into 6 full groups of 100 plus 50. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  3. 3 km 538 m — Exchange one km for 1000 m, then subtract: 4480 − 942 = 3538 m. Regroup the result into km and m. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  4. 1 m 72 cm — Exchange one m for 100 cm, then subtract: 225 − 53 = 172 cm. Regroup the result into m and cm. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  5. 3 m 75 cm — The suggested answer is not correct. Exchange one m for 100 cm, then subtract: 450 − 75 = 375 cm. Regroup the result into m and cm. (3 points: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.)
  6. 3 km 971 m — The route is 4250 m. Subtract 279 m to get 3971 m; regroup into kilometers and meters. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  7. 4,250 m — 4 km = 4,000 m; add 250 to make 4,250 m. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  8. 2 kg 875 g — Partition 2,875 into 2 full groups of 1,000 plus 875. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  9. 520 cm — The suggested answer is not correct. 5 m = 500 cm; add 20 to make 520 cm. (3 points: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.)
  10. 2 L 480 mL — Partition 2,480 into 2 full groups of 1,000 plus 480. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  11. 6,055 g — 6 kg = 6,000 g; add 55 to make 6,055 g. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  12. 4,125 m — 4 km = 4,000 m; add 125 to make 4,125 m. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  13. 6 m 86 cm — The suggested answer is not correct. Exchange one m for 100 cm, then subtract: 775 − 89 = 686 cm. Regroup the result into m and cm. (3 points: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.)
  14. 7,480 g — 7 kg = 7,000 g; add 480 to make 7,480 g. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  15. 4 L 20 mL — Partition 4,020 into 4 full groups of 1,000 plus 20. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  16. 4 km 480 m — Partition 4,480 into 4 full groups of 1,000 plus 480. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  17. 3 km 799 m — The suggested answer is not correct. The route is 6375 m. Subtract 2576 m to get 3799 m; regroup into kilometers and meters. (3 points: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.)
  18. 8 m 75 cm — Partition 875 into 8 full groups of 100 plus 75. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  19. 5 m 78 cm — Exchange one m for 100 cm, then subtract: 665 − 87 = 578 cm. Regroup the result into m and cm. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  20. 2 km 658 m — The route is 3480 m. Subtract 822 m to get 2658 m; regroup into kilometers and meters. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  21. 7,065 mL — The suggested answer is not correct. 7 L = 7,000 mL; add 65 to make 7,065 mL. (3 points: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.)
  22. 8 m 50 cm — Partition 850 into 8 full groups of 100 plus 50. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
  23. 2 m 50 cm — Exchange 1 m for 100 cm: 2 m 120 cm − 70 cm = 2 m 50 cm. (3 points: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.)
  24. 650 cm — There are 100 centimeters in one meter, so 6 m 50 cm equals 650 cm, not meters. (3 points: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.)