Math Bytes – March, 2017
How do you spell math? F-U-N! Let’s have some fun with math, can you solve this riddle?
There are two rookie baseball players, Bluto and Popeye, who started the season on opening day and made a wager as to which one would have the best batting average at the end of the season.
The last day of the season arrives, and not much is going to change–especially considering that neither one of them is in the starting lineup.
Bluto says, “Hey, Popeye, what did you bat for the first half of the year?”
Popeye answers, “I batted .250.”
Bluto responds, “Well, I got you there. I batted .300. How about after the All-Star break?”
Proudly, Popeye pipes up, “I batted .375.”
Bluto says, “Pretty good, but I batted .400. Fork over the 20 bucks that we bet.”
The bat boy, Dougie, saunters over and says, “Don’t pay the 20 bucks, Popeye. I think you won.”
How could Popeye have won?
Justify your answer by emailing Marty Lessman today!
Or read the answer below:
The first standard of mathematic practice asks students to make sense of a problem and persevere in finding the solution. Finding an entry point into the problem often times is tricky enough. Problems in which solutions do not readily present themselves have a tendency to lead to student fatigue. It is here we need to encourage students to push for further understanding of the problem. Creating sketches, models, using algebra, higher levels of math, guess and check, and hands on activities should all be encouraged when a tiresome math problem presents itself. The above riddle offers many entry points into the problem. I encourage you to have students explore, come up with an answer, and share the thought process behind HOW they got the answer.
Answer: Taking averages of averages is a mathematical no no. Popeye could have won, even after having a worse batting average for both portions of the season, contingent on the number of times each batted for each portion of the season.
One example of the season could be: Popeye bats 20 times in the first half of the season and gets 5 hits (.250 avg). Second half of the season Popeye bats 200 times and gets 75 hits for a .375 average. For the season he bats .363 (80/220). Bluto batted 100 times in the frist half and had 30 hits for a .300 average, and the second half only batted 5 times with 2 hits for a .400 average. For the season he bats .304 (32/105). Thus, POPEYE WINS!!!!
This riddle was brought to you by Car Talk.