Lower Elementary:
Question: Charlie went on a fishing trip with his dad. Charlie caught 14 fish. His dad caught twice as many fish as Charlie did. How many fish did Charlie and his dad catch altogether?
Answer: 42 fish
Solution: First we need to find how many fish Charlie’s dad caught. His dad caught twice as many fish as Charlie did. Charlie caught 14 fish. 14 doubled = 10 doubled + 4 doubled = 20 + 8 = 28. Charlie’s dad caught 28 fish. Let’s add the number of fish they caught to see how many fish they caught altogether. 14 + 28 = 42. Charlie and his dad caught a total of 42 fish.
Upper Elementary:
Question: A library has to put away 650 books. 50 books are put on display at the entrance and the remaining books are evenly distributed on 4 shelves. How many books are put on each of the shelves?
Answer: 150 books
Solution: First we need to find how many books are being put on the shelf. There are a total of 650 books, and 50 of them are put on display outside. That means that there are 600 (650 – 50) books to be distributed on the shelves. There are 4 shelves and an equal number of books are put on each shelf. To find out how many books go on each shelf, divide the number of books to be put on the shelves by 4. 600 ÷ 4 = 150. 150 books are put on each shelf.
Middle School:
Question: One-half of the 800 students at Whitney High School are girls. One-tenth of the girls play in the school band, and one-fourth of those students play the flute. What percent of students at Whitney are girls who play the flute in the school band?
Answer: 1.25%
Solution: To find the percent, we need to find the number of girls who play the flute in the school band. Half of 800 is 400, so there are 400 girls at Whitney High School. One-tenth of the girls play in the school band. One-tenth of 400 is 40, so there are 40 girls in the school band. One-fourth of the girls in the school band play the flute. One-fourth of 40 is 10. There are 10 girls that play the flute in the school band. To calculate the percent, we divide the number of girls that play the flute in the school band by the total number of students. 10/800 = 1/80 = 1.25%
Algebra and Up:
Question: What is the sum of all of the even numbers from 0 to 100?
Answer: 2,550
Solution: One way to solve this problem is to list out the terms and see if there is a pattern.
0 + 2 + 4 + 6 + 8 +… + 92 + 94 + 96 + 98 + 100
Notice that 8 + 92 = 100, 6 + 94 = 100, 4 + 96 = 100, and 2 + 98 = 100. If we pair all of these numbers together, we see that we get 24 pairs of numbers that sum to 100. We also have the 100 at the end of the list, and the 50 in the middle that did not have a pair to add to 100. So, 2,400 + 100 + 50 = 2,550.
Alternatively, we can set up an arithmetic series. The first term is 0, the last term is 100, and there are 51 terms in the list. The formula for the sum of an arithmetic series is:
Sum = number of terms/2 (first term + last term)
Sum = 51/2 (0 + 100)
Sum = 51(50) = 2,550
The sum of this arithmetic series is 2,550.
