IPS - Day 6

Today we continued to look at simulations. We started by estimating that at least one alarm would sound. We accumulated all of the class responses and found 539 out of 560 simulations had at least one alarm sound, resulting in a .96 probability.

We then discussed how the distribution of each individual's 20 simulations could be summarized. I do this as an assessment of what students already know. Students felt comfortable with creating bar and pie graphs for the categories of no alarms and at least one alarm. I briefly discussed how a histogram could be made from the data and explained the difference between a histogram and bar graph. By a raise of hands, most students did not feel they knew how to construct histograms. Students also mentioned calculating the average number of alarms that sounded.

The next task was developing a simple simulation. In this case, representing an 80% success rate and 20% failure rate. A trial consisted of generating 10 values. The question of interest was what would be the probability of seeing 10 successes.

I allowed time for students to consider how to simulate this situation using random numbers and to discuss their ideas in groups. About half the groups came up with ideas that reflected a 50% - 50% success/failure rate. I put these ideas on the board along with some ideas using either digits 0-4 or 0-9 with successes being the digits 1-4 and 2-9, respectively. In the discussion that ensued I focused students on how the 80% success rate was being modeled. Students realized they needed an 80-20 split on values and provided some additional examples.

I then had students run 5-10 simulations and had each group estimate the probability of seeing 10 successes in a row. Results varied from 0% to 20%. We gathered up the class data and had 6 out of 83 simulations show the 10 successes in a row, for an estimated probability of 7%.

I then had students write down things they wanted to remember when trying to simulate a situation.

Go to the day's summary page to see a student's perspective and the lesson slides that were used.