Lower Elementary:
Question: Reid had a long day and went to bed at 10PM and woke up at 6:30AM. He took a nap from 11:30AM and woke up at 1:15PM. How long did Reid sleep altogether?
Answer: 10 hours and 15 minutes
Solution: It is 2 hours from 10PM to 12AM, 6 and a half hours from 12AM to 6:30AM. So, the amount of time that elapsed from 10PM to 6:30AM is 8 hours and 30 minutes. It is 1 hour to go from 11:30AM to 12:30PM and it is 45 minutes from 12:30PM to 1:15PM. So, the time that elapsed from 11:30AM to 1:15PM is 1 hour and 45 minutes. If we add the times together, we have 9 hours and 75 minutes. However, there are 60 minutes in an hour. So, Reid slept for 10 hours and 15 minutes.
Upper Elementary:
Question: Bianca is buying beads to make bracelets. She bought 3 bags of beads, each containing 250 beads. She used 25 beads for each bracelet. How many bracelets did Bianca make?
Answer: 30 bracelets
Solution: One way to solve this problem is to find how many bracelets can be made from one bag of beads and then multiply by 3 to find how many total bracelets Bianca made. There are 250 beads in one bag. She uses 25 beads to make 1 bracelet. So, she uses 250 beads to make 10 bracelets. If one bag of beads contains enough beads to make 10 bracelets, then 3 bags of beads contain enough beads to make 30 bracelets.
Middle School:
Question: Mason spent 2 hours playing video games. He spent 1/3 of that time playing a racing game, 25% of the time playing a football video game, and the rest of the time playing an action-adventure game. How much time did Mason spend playing the action-adventure game?
Answer: 50 minutes
Solution: One way to solve this problem is to see how much time Mason spent playing the other games and subtract that from the 2 hours that Mason spent playing video games. 2 hours is the same as 120 minutes. 1/3 of 120 is 40, so Mason spent 40 minutes playing the racing game. 25% is the same as 1/4. 1/4 of 120 is 30, so Mason spent 30 minutes playing the football video game. Mason spent 70 minutes playing the other games, so he spend 50 minutes playing the action-adventure game (120 – 70 = 50).
Algebra and Up:
Question: A 20-sided die has the first 20 prime numbers as the numbers on the sides of the die. What is the probability of rolling a number that is greater than 35?
Answer: 9/20
Solution: First, we need to find the first 20 prime numbers to know what numbers are on the sides of the die. The first 20 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, and 71. There are 9 numbers that are larger than 35, so the probability of rolling a number greater than 35 on this die is 9/20.
Alternatively, when listing the primes, we see that 31 is the 11th number and 37 is the 12th number. If there are 11 numbers that are less than 35, then that means there are 9 numbers that are greater than 35. Therefore, there is a 9/20 probability of rolling a number greater than 35 on this die.
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