Lower Elementary:
Question: Walter sent 7 emails on Monday, 4 emails on Tuesday, 9 emails on Wednesday, 3 emails on Thursday, and 6 emails on Friday. How many emails did Walter send this week?
Answer: 29 emails
Solution: To find the total number of emails, we need to add the total number of emails for each day. So, we need to add 7 + 4 + 9 + 3 + 6. Notice that 7 + 3 = 10 and 4 + 6 = 10. So, now we add 10 + 10 + 9 = 29. Walter sent 29 emails.
Upper Elementary:
Question: A swimming pool went from being half full to a quarter full in 45 minutes. At this rate, how long would it take for all of the water to drain out of the pool if it was full when you started?
Answer: 3 hours
Solution: Let’s find the fractional part that 45 minutes represents. The pool is half full and then it becomes a quarter full. 1/2 – 1/4 = 1/4. So, 45 minutes represents draining 1/4 of the pool. Therefore, if we count by 45, 4 times we will see how long it takes to drain the pool. 45, 90, 135, 180. It will take 180 minutes, or 3 hours, to drain the pool.
Middle School:
Question: A palindrome is a number that is the same when read forwards and backwards. For example, 12321 is a palindrome, but 54321 is not a palindrome. Powers of 11 are palindromes until what power?
Answer: The fifth power (161051)
Solution: To solve this problem, let’s find the powers of 11.
110 = 1
111 = 11
112 = 121
113 = 1331
114 = 14641
115 = 161051
So 11 to the fifth power is the first power of 11 that is not a palindrome.
Algebra and Up:
Question: What is the smallest whole number that is divisible by the first ten whole numbers?
Answer: 2,520
Solution: The first ten whole numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. One way to solve this problem is to find the LCM of smaller groups within ten numbers. For instance, because all numbers are divisible by 1 and if a number is divisible by 6, then it is also divisible by 2 and 3, which means that 1, 2, and 3 are all accounted for in any multiple of 6. In the same way, if a number is divisible by 8, then it is divisible by 4 and 2. If a number is divisible by 9, then it is divisible by 3. If a number is divisible by 10, then it is divisible by 5 and 2. Therefore, the problem simplifies to finding the LCM of 6, 7, 8, 9, and 10. One way to find the LCM of these numbers is to find the LCM of 2 numbers at a time and continue this method to reduce the list. The LCM of 6 and 10 is 30. So now we can find the LCM of 7, 8, 9, and 30. The LCM of 9 and 30 is 90. Now we need to find the LCM of 7, 8, and 90. The LCM of 8 and 90 is 360. Now we need to find the LCM of 7 and 360. Since 7 is prime and is not a factor of 360, the LCM is the product of 7 and 360. 360 • 7 = 2,520. 2,520 is the smallest whole number divisible by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
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