Today, I posed a "Would You Rather" question. I found this activity, originally called "The Million Dollar Dilemma," in the January 1993 edition of the AIMS Education Foundation.
Basically, the kids are asked whether they would prefer to take $1,000,000 at the end of 31 days, or take a penny doubled daily. Of course, most of my classes chose the million, but I never make it that easy.... we have to prove our answers! So, we filled out a table that showed us doubling a penny daily for 31 days AND finding out the total amount of money we could make cumulatively!
My kids are always surprised by the final results! Up to day 27 they are convinced that taking the million is the way to go, but once we surpass the million they are taken aback by the both the day's pay and the final total pay.
While working on this activity, I asked the kids to find patterns. These are some of them:
- the day's pay always ends in 2, 4, 8, 6 and repeats that pattern then entire time (excluding the first penny)
- the total pay always ends in 1, 3, 7, 5 and repeats that pattern the entire time
- the day's pay is always $.01 greater than the previous total pay
- you can find the next total pay by multiplying the previous total pay by 2 and adding $.01.
To finish the activity, I asked the kids to explain which option they would choose now. I did specify that I expected more of an explanation other than "it was more."
To see a mathematical explanation for this activity, go to:
HOMEWORK: Countdown 7.2