Learning to Count…

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Clemente’s College Algebra classes are currently in the throes of our unit on probability.  A fundamental part of calculating probabilities is being able to count the number of ways something can be done.  While seemingly simple, our Wildcats quickly found out that looks can be deceiving.  

This week, we viewed probability through the lense of the card game, Blackjack.  Students were asked to play the game and then consider the probabilities of both their decision, as well as the opposite of their decision.  While students initially had difficulty articulating  why they were making the choices they made, they soon were able link together more coherent and complex ideas whereby they could eloquently describe their decisions in terms of mathematical probability.  

The main lesson of the week involved counting the number of ways each value in Blackjack can be reached.  The students were simply asked “Given one deck of cards, what is the most common value that is dealt?”  Classes were left to figure out how to solve this question of probability.  While some students did not know where to start, others suggested they draw on previous lessons where students had to find out the most commonly rolled number using two 6-sided dice.  Further, they drew on the previous day’s lesson of calculating the number of ways Blackjack is dealt to help figure out the card combination counting.  

The seniors worked collaboratively to come up with educated guesses as to which number combinations to try; they then used lists of these numbers to come up with the card values for each  pair.  Students challenged and checked each other to ensure they were counting correctly.  Other students chimed in to fill in holes of certain card combinations that may have been missed.  Overall, the students did an excellent job of coming up with interesting ways of approaching this problem and demonstrated perseverance in solving it.  By the way, the most commonly dealt card value in one deck of cards in Blackjack is 20.