But Would You Put Money On It?

I have felt one of two extremes every day this school year:

  1. My students aren’t learning anything meaningful, it’s impossible to do everything I need to do well, and my brain is on fire.
  2. Cheers!  My students had fun while making meaningful mathematical connections.

Today was the latter kind of day so I thought I’d take a few moments to embrace it.

I proposed this scenario to my non-AP probability and statistics class:

Doubles Dilemma (1)

I had students discuss their initial reactions.  Many of them mentioned specifics like “1 out of 6” and “36 possibilities” but for the most part, the students were willing to put their hard earned money on the line for a chance at avoiding doubles.  (To be clear, no actual betting went on in my classroom)

Then we rolled until we got doubles.  And rolled again and again and again.  I have one computer and a class set of TI-84s.  So, naturally, we made a class dot plot of our average number of rolls to get doubles.

wpid-1029151423-1.jpgwpid-1029150825-1.jpg

 

Now that our data was collected, I asked them again if they would take the bet.  Since $5 didn’t seem to be enough money for them to really consider the probability, I upped the wager to $100.  That seemed to be enough money for them to consider the results of the experiment and think twice about putting up $100 because they feel lucky.

Thanks to Chris True, Mathematics Professor at the University of Nebraska, who proposed this scenario at an AP Statistics training I attended this summer.

 

1 Comment

  1. Reading through this write-up, I am wondering about an approach that uses three different parts:

    a) What if Stella only gets one chance to roll the dice?

    b) What if Stella has many chances (say, 100) to roll the dice?

    c) If the answers for (a) and (b) are different, then after how many rolls does one change their thinking? (And why?)

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