IPS - Day 7

Today was a continuation of the lesson on simulations. The focus on these lessons is to help students build a foundation for how to use random integers to simulate a physical entity.

The first simulation problem was to simulate drawing cards with replacement from a standard deck of cards. After some discussion, students came up with using 0-12 with 0 representing an ace or 0-51 with 0-3 representing an ace. The question of interest was "What is the probability of drawing an ace within the first 10 draws?"

Students ran 3 simulations to gain some practice using their calculators. For students without calculators I had them use a random number table. We accumulated our results and found a probability of approximately 45%.

The next problem involved simulating rock-paper-scissors using random digits. Students readily came up with the idea to use either 0, 1, 2 or 1, 2, 3 to simulate RPS. They struggled with simulating the physical activity itself. I discussed how a simulation is recreating the physical process using random numbers. The challenge in this simulation is to simulate two people playing against one another.

Students then started to use the idea of generating two values and comparing them. One student determined that there were 9 possible outcomes to the game with 3 outcomes each of tie game, player 1 winning, player 2 winning. Using this idea, the student used 0,1,2 to represent ties, 3,4,5 to represent player 1 winning and 6,7,8 to represent player 2 winning.

Finally, we returned to Sounding the Alarm (from NCTM's Navigating through Probability in grades 9-12) and started to look at the theoretical probability. Students worked through an associated worksheet which they are to complete for homework. We'll discuss the results next class.

Visit the class summary for a student's perspective of today's class and to view the lesson slides.