MDM4U - Activity: introducting non-uniform probability distributions

Students were given time to play "Crossing Toronto Harbour". In my de-cluttering of my filing cabinet this summer, I re-discovered a few past editions of the OAME Gazette and found this activity by Kelly Young in the June 2010 Edition.

The main idea: students are paired up and each given 10 "boats" and a 2 dice. Each student rolls the dice and if they have a boat in the dock with that sum, they get to cross their boat to the other side. If that dock is empty, they do nothing and pass the dice to the other player. The game continues until the first player has crossed all their boats to the other side.

My challenge was to find enough items of different colours for students to use as "boats" that were cheap to find but small enough to fit on the game board. I was at the dollar store this weekend and found these packages of decorative pompoms to use.

Students quickly discovered boats in the #1 dock would never cross and that sums of 6, 7 and 8 occurred most frequently.

This lead nicely to a discussion of that the probability of any event lies between 0 and 1 and that not all events have the same probability of occurring. Unlike a standard die that has a uniform probability, looking at the sum of two dice has a probability distribution where a sum of 2 and 12 are least likely to occur while a sum of 7 has the highest probability of occurring. Students were introduced a probability distribution chart where all outcomes are listed along with their probabilities. A histogram or bar graph could be used to graphically display a probability distribution depending on the event used.

I also asked students to keep track of what numbers they rolled so that we could continue to distinguish between theoretical probability and experimental probability. Here is a chart of the outcomes rolled in this class:

We will refer to this data to start next class to chat about why it is not an identical match to the theoretical probability distribution.
Homework was assigned from the question bank focusing on probability distributions as well as determining the probability of different sums when rolling 2 dice.