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Sleep Cycle worksheet

Grades 3–4 · CCSS 4.MD.A.2, 3.MD.A.1

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- I want to: Go to bed at a set time
- Bedtime: 17:32
- Time to fall asleep: 20 min
- Sleep cycle length: 100 min
Find: Wake up at (5 cycles, 8 h 20 min of sleep)
Answer
2.
Problem 2.
- I want to: Wake up at a set time
- Wake-up time: 06:53
- Time to fall asleep: 11 min
- Sleep cycle length: 75 min
Find: Go to bed at (5 cycles, 6 h 15 min of sleep)
Answer
3.
Problem 3.
- I want to: Wake up at a set time
- Wake-up time: 03:55
- Time to fall asleep: 13 min
- Sleep cycle length: 80 min
Find: Go to bed at (5 cycles, 6 h 40 min of sleep)
Answer
4.
Problem 4.
- I want to: Go to bed at a set time
- Bedtime: 19:26
- Time to fall asleep: 18 min
- Sleep cycle length: 80 min
Find: Wake up at (5 cycles, 6 h 40 min of sleep)
Answer
5.
Problem 5.
- I want to: Wake up at a set time
- Wake-up time: 04:30
- Time to fall asleep: 15 min
- Sleep cycle length: 75 min
Find: Go to bed at (5 cycles, 6 h 15 min of sleep)
Answer
6.
Problem 6.
- I want to: Wake up at a set time
- Wake-up time: 11:54
- Time to fall asleep: 15 min
- Sleep cycle length: 104 min
Find: Go to bed at (5 cycles, 8 h 40 min of sleep)
Answer
7.
Problem 7.
- I want to: Go to bed at a set time
- Bedtime: 20:27
- Time to fall asleep: 20 min
- Sleep cycle length: 100 min
Find: Wake up at (5 cycles, 8 h 20 min of sleep)
Answer
8.
Problem 8.
- I want to: Go to bed at a set time
- Bedtime: 19:08
- Time to fall asleep: 12 min
- Sleep cycle length: 98 min
Find: Wake up at (5 cycles, 8 h 10 min of sleep)
Answer
9.
Problem 9.
- I want to: Go to bed at a set time
- Bedtime: 02:03
- Time to fall asleep: 11 min
- Sleep cycle length: 80 min
Find: Wake up at (5 cycles, 6 h 40 min of sleep)
Answer
10.
Problem 10.
- I want to: Wake up at a set time
- Wake-up time: 03:12
- Time to fall asleep: 10 min
- Sleep cycle length: 80 min
Find: Go to bed at (5 cycles, 6 h 40 min of sleep)
Answer

Answer key: Sleep Cycle worksheet

1. Wake up at (5 cycles, 8 h 20 min of sleep): 2:12 AM
1. Time from bedtime to waking: cycles × cycle length, plus the time it takes to fall asleep
  $5 \times 100 min + 20 min$ $= 520 min$
2. 6 cycles (10 h of sleep): count forward 620 minutes from 5:32 PM
  $5:32 PM + 620 min$ $= 3:52 AM$
3. 5 cycles (8 h 20 min of sleep): count forward 520 minutes from 5:32 PM
  $5:32 PM + 520 min$ $= 2:12 AM$
4. 4 cycles (6 h 40 min of sleep): count forward 420 minutes from 5:32 PM
  $5:32 PM + 420 min$ $= 12:32 AM$
2. Go to bed at (5 cycles, 6 h 15 min of sleep): 12:27 AM
1. Time in bed for each option: cycles × cycle length, plus the time it takes to fall asleep
  $5 \times 75 min + 11 min$ $= 386 min$
2. 6 cycles (7 h 30 min of sleep): count back 461 minutes from 6:53 AM
  $6:53 AM - 461 min$ $= 11:12 PM$
3. 5 cycles (6 h 15 min of sleep): count back 386 minutes from 6:53 AM
  $6:53 AM - 386 min$ $= 12:27 AM$
4. 4 cycles (5 h of sleep): count back 311 minutes from 6:53 AM
  $6:53 AM - 311 min$ $= 1:42 AM$
3. Go to bed at (5 cycles, 6 h 40 min of sleep): 9:02 PM
1. Time in bed for each option: cycles × cycle length, plus the time it takes to fall asleep
  $5 \times 80 min + 13 min$ $= 413 min$
2. 6 cycles (8 h of sleep): count back 493 minutes from 3:55 AM
  $3:55 AM - 493 min$ $= 7:42 PM$
3. 5 cycles (6 h 40 min of sleep): count back 413 minutes from 3:55 AM
  $3:55 AM - 413 min$ $= 9:02 PM$
4. 4 cycles (5 h 20 min of sleep): count back 333 minutes from 3:55 AM
  $3:55 AM - 333 min$ $= 10:22 PM$
4. Wake up at (5 cycles, 6 h 40 min of sleep): 2:24 AM
1. Time from bedtime to waking: cycles × cycle length, plus the time it takes to fall asleep
  $5 \times 80 min + 18 min$ $= 418 min$
2. 6 cycles (8 h of sleep): count forward 498 minutes from 7:26 PM
  $7:26 PM + 498 min$ $= 3:44 AM$
3. 5 cycles (6 h 40 min of sleep): count forward 418 minutes from 7:26 PM
  $7:26 PM + 418 min$ $= 2:24 AM$
4. 4 cycles (5 h 20 min of sleep): count forward 338 minutes from 7:26 PM
  $7:26 PM + 338 min$ $= 1:04 AM$
5. Go to bed at (5 cycles, 6 h 15 min of sleep): 10:00 PM
1. Time in bed for each option: cycles × cycle length, plus the time it takes to fall asleep
  $5 \times 75 min + 15 min$ $= 390 min$
2. 6 cycles (7 h 30 min of sleep): count back 465 minutes from 4:30 AM
  $4:30 AM - 465 min$ $= 8:45 PM$
3. 5 cycles (6 h 15 min of sleep): count back 390 minutes from 4:30 AM
  $4:30 AM - 390 min$ $= 10:00 PM$
4. 4 cycles (5 h of sleep): count back 315 minutes from 4:30 AM
  $4:30 AM - 315 min$ $= 11:15 PM$
6. Go to bed at (5 cycles, 8 h 40 min of sleep): 2:59 AM
1. Time in bed for each option: cycles × cycle length, plus the time it takes to fall asleep
  $5 \times 104 min + 15 min$ $= 535 min$
2. 6 cycles (10 h 24 min of sleep): count back 639 minutes from 11:54 AM
  $11:54 AM - 639 min$ $= 1:15 AM$
3. 5 cycles (8 h 40 min of sleep): count back 535 minutes from 11:54 AM
  $11:54 AM - 535 min$ $= 2:59 AM$
4. 4 cycles (6 h 56 min of sleep): count back 431 minutes from 11:54 AM
  $11:54 AM - 431 min$ $= 4:43 AM$
7. Wake up at (5 cycles, 8 h 20 min of sleep): 5:07 AM
1. Time from bedtime to waking: cycles × cycle length, plus the time it takes to fall asleep
  $5 \times 100 min + 20 min$ $= 520 min$
2. 6 cycles (10 h of sleep): count forward 620 minutes from 8:27 PM
  $8:27 PM + 620 min$ $= 6:47 AM$
3. 5 cycles (8 h 20 min of sleep): count forward 520 minutes from 8:27 PM
  $8:27 PM + 520 min$ $= 5:07 AM$
4. 4 cycles (6 h 40 min of sleep): count forward 420 minutes from 8:27 PM
  $8:27 PM + 420 min$ $= 3:27 AM$
8. Wake up at (5 cycles, 8 h 10 min of sleep): 3:30 AM
1. Time from bedtime to waking: cycles × cycle length, plus the time it takes to fall asleep
  $5 \times 98 min + 12 min$ $= 502 min$
2. 6 cycles (9 h 48 min of sleep): count forward 600 minutes from 7:08 PM
  $7:08 PM + 600 min$ $= 5:08 AM$
3. 5 cycles (8 h 10 min of sleep): count forward 502 minutes from 7:08 PM
  $7:08 PM + 502 min$ $= 3:30 AM$
4. 4 cycles (6 h 32 min of sleep): count forward 404 minutes from 7:08 PM
  $7:08 PM + 404 min$ $= 1:52 AM$
9. Wake up at (5 cycles, 6 h 40 min of sleep): 8:54 AM
1. Time from bedtime to waking: cycles × cycle length, plus the time it takes to fall asleep
  $5 \times 80 min + 11 min$ $= 411 min$
2. 6 cycles (8 h of sleep): count forward 491 minutes from 2:03 AM
  $2:03 AM + 491 min$ $= 10:14 AM$
3. 5 cycles (6 h 40 min of sleep): count forward 411 minutes from 2:03 AM
  $2:03 AM + 411 min$ $= 8:54 AM$
4. 4 cycles (5 h 20 min of sleep): count forward 331 minutes from 2:03 AM
  $2:03 AM + 331 min$ $= 7:34 AM$
10. Go to bed at (5 cycles, 6 h 40 min of sleep): 8:22 PM
1. Time in bed for each option: cycles × cycle length, plus the time it takes to fall asleep
  $5 \times 80 min + 10 min$ $= 410 min$
2. 6 cycles (8 h of sleep): count back 490 minutes from 3:12 AM
  $3:12 AM - 490 min$ $= 7:02 PM$
3. 5 cycles (6 h 40 min of sleep): count back 410 minutes from 3:12 AM
  $3:12 AM - 410 min$ $= 8:22 PM$
4. 4 cycles (5 h 20 min of sleep): count back 330 minutes from 3:12 AM
  $3:12 AM - 330 min$ $= 9:42 PM$