IPS - Day 4

Today we continued examining the idea of random events with the goal to re-inforce that what we think looks random may not be and that true random events may appear to be not random.

To start this class I had columns that represented months of the year. Students wrote the day of their birth under the appropriate month. I then asked students to comment on the data. Their were different observations about the distribution. I mentioned we would need data on births by month to see if our data fit the overall patterns or not. I then asked about the probability of having two birthdays on the same day. Most students thought that it was unusual. I asked if we increased the number of people to fifty or so what they thought would happen. About a third of the class responded that they thought we would get at least one match.

The fun part for this lesson is going to different classrooms and seeing if we got matches. I ask different teachers if we can interrupt their class for a few minutes and then have students in the class call out their birthday. Any time there was a match the person with the matching birthday would call out match. In visiting 3 classes we had matches of 3, 2, and 1. In the post discussion, students were curious about why the matches were so frequent. I told them we would look at how to calculate the probabilities as we progressed forward.

We then explored random sequences of heads and tails. By this time students were engaged in the idea of randomness and actively trying to imaging random coin tosses. The length of sequences (consecutive heads or tails) were tallied. We then used a calculator to simulate coin tosses and counted the length of random sequences. These typically showed a wider dispersion of sequence length and longer sequences. I wrote two sequences on the board, one reflecting the imagined results and one reflecting the random results. In looking at these sequences, students agreed the imagined results looked random while the random result looked fake while in reality it was the other way around.

We'll continue exploring the idea of randomness before we start to move into a more formal look at simulations.

For a student's perspective on the lesson and slides for the day, visit the class summary page on the course web site.