Lower Elementary:
Question: Taylor arrives home from school at 3:30PM. He practices basketball for 55 minutes, plays video games for 40 minutes, and then takes 5 minutes to freshen up for dinner. What time does Taylor eat dinner?
Answer: 5:10PM
Solution: One way to solve this problem is to find the total time that passed for Taylor to do his activities. Let’s add the times for each of the activities. When adding elapsed times, it’s helpful to add times that add to 60 since there are 60 minutes in an hour. 55 + 40 + 5 = 60 + 40 = 1 hour and 40 minutes. Taylor arrives from home at 3:30PM, and it takes him 1 hour and 40 minutes to do his activities. One hour past 3:30PM is 4:30PM. 40 minutes after 4:30PM is 5:10PM. Taylor eats dinner at 5:10PM.
Upper Elementary:
Question: Wendy has a 20 inch by 15 inch piece of paper. She cuts out a 10 inch by 10 inch square from the corner of the paper. What is the area of the remaining paper after the square is cut out?
Answer: 200 square inches
Solution: One way to solve this problem is to find the area of the piece of paper before it was cut and subtract the area of the square that is cut out. The area of the piece of paper before it was cut is 20 × 15 = 300 square inches. The area of the square that is cut out is 10 × 10 = 100 square inches. So the area of the remaining paper after the square is cut out is 300 – 100 = 200 square inches.
Middle School:
Question: Jessica and Kelly take turns babysitting for the Masons. Jessica babysits for 4 hours and Kelly babysits for 3 hours. Altogether, the Masons pay them a total of $84. How should Jessica and Kelly split their pay so that they each get their fair share according to how many hours they worked?
Answer: Jessica: $48, Kelly: $36
Solution: Jessica and Kelly worked a total of 7 hours (4 + 3 = 7 hours). They got paid a total of $84. To find out how much they should be paid for one hour, divide the total they earned by the number of hours worked. 84 ÷ 7 = 12. They earned $12 for every hour they worked. Since Jessica worked for 4 hours, she earned $48 (12 × 4 = 48). Kelly worked for 3 hours, so she earned $36 (12 × 3 = 36).
Algebra and Up:
Question: How many different arrangements are there of the letters in the word “calculus?”
Answer: 5,040
Solution: Notice that this is a permutation with repeated outcomes. To find the number of arrangements, we need to find the total number of letters in “calculus.” There are 8 letters in the word. The number of arrangements of those letters is 8!. However, we have 2 c’s, 2 l’s, and 2 u’s. That means we need to divide by 2!•2!•2! to take into account these repeats.
8! / (2!•2!•2!)
Expand the factorials:
8•7•6•5•4•3•2•1 / (2•1•2•1•2•1)
Multiply the denominator.
8•7•6•5•4•3•2•1 / 8
Cancel the 8s.
7•6•5•4•3•2•1 = 5,040
There are 5,040 different arrangements of the letters in the word “calculus.”
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