Lower Elementary:
Question: A grandfather clock rings a bell in a pattern. When it is 1 o’clock, it rings the bell once. When it is 2 o’clock, it rings the bell twice. When it is 3 o’clock, it rings the bell three times, and so on. How many total times will the bell ring from 4 o’clock to 7 o’clock?
Answer: 22 times
Solution: At 4 o’clock, the bell will ring 4 times. At 5 o’clock, the bell will ring 5 times. At 6 o’clock, the bell will ring 6 times. At 7 o’clock, the bell will ring 7 times. Adding the bell chimes together, we have 4 + 5 + 6 + 7. We can add the 4 and the 6 first to make a group of 10. 10 + 5 + 7 = 15 + 7 = 22. The bell rings a total of 22 times from 4 o’clock to 7 o’clock.
Upper Elementary:
Question: Jake had a very busy day. In one day, he was asleep for 1/3 of the day, he worked for 1/4 of the day, he prepared and ate meals for 1/12 of the day, he exercised for 1/6 of the day, and then the rest of the day he watched TV. What fractional part of the day did Jake spend watching TV?
Answer: 1/6 of the day
Solution: To find a fractional part, we subtract the sum of the other fractional parts from the whole. In order to add the fractions, they need to have the same name.
1/3 = 4/12
1/4 = 3/12
1/6 = 2/12
1/12 = 1/12
All of our fractions now have the same name (twelfths). Now, let’s add the fractions.
4/12 + 3/12 + 2/12 + 1/12 = 10/12 = 5/6
Jake spent 5/6 of his day doing everything except watch TV. Subtract 5/6 from a whole to get the fractional part of the day Jake spent watching TV. 1 – 5/6 = 6/6 – 5/6 = 1/6. Jake spent 1/6 of his day watching TV.
Middle School:
Question: You have 2 sand-timers, one that is 7 minutes and one that is 5 minutes. Using these timers, how can you accurately measure 13 minutes?
Answer: Start the 7 and 5 at the same time. When the 5 runs out, flip it immediately. When the 7 runs out, start counting time. When the 5 runs out, flip it. When the 5 runs out again, flip it again.
Solution: One way to solve this problem is to start the 7 minute timer and the 5 minute timer at the same time. When the 5 minute timer runs out, flip it immediately. We now have 2 minutes left in the 7 minute timer (7 – 5 = 2). When the remaining sand in the 7 minute timer runs out, we have 3 minutes left in the 5 minute timer (5 – 2 = 3). We start measuring the time at this point. After those 3 minutes are up, flip the 5 minute timer. When that runs out, we are at 8 minutes (3 + 5 = 8). Flip the 5 minute timer again. When that runs out, we have 13 minutes (8 + 5 = 13).
Algebra and Up:
Question: What acute angle do the hands of a standard clock make at 8:30?
Answer: 75°
Solution: There are 360° in a circle. Since there are 12 numbers on a clock, each number represents 30° (360 ÷ 12 = 30). At 8:30, the minute hand is at the 6. The hour hand is halfway between the 8 and the 9 (since 8:30 is halfway between 8 o’clock and 9 o’clock). From the 6 to the 7 is 30°, from the 7 to the 8 is another 30°, and the halfway mark from the 8 to the 9 is 15° (since half of 30 is 15). Adding all the degrees together, we have 30° + 30° + 15° = 75°. The hands of a clock are 75° apart at 8:30.
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