Today was our first day of full lessons. The goal of today's class was to get students used to the format of the class (away from being used to filling out worksheets) and have students begin to problem solve together.
We played a game of "Skunk" with one die. After the winner was declared, we discussed strategies used in the game. Most students identified that if a 1 hadn't occurred in 5 consecutive rolls, then they felt the need to step out of the round because a 1 was more likely to occur next. This lead to the introduction of the idea of theoretical probability. We defined theoretical probability and the idea of patterns that occur in the long run.
Students were then each given a die and asked to roll it 20 times recording the outcome of each roll. We collected this data as a group and noticed that though we should get each number rolled 3.3 times in 20 rolls, not a single student has this occur. However, when we summed out data together (instead of looking at 20 rolls at a time, we now were looking at 220 rolls) we saw that the distribution of rolls was closer to equal for each value.
Finally, students were randomly paired and asked to solve two problems on our VNPSs. The first problem was "The sum of 15 consecutive numbers has an average of 27. Find the average of the first five numbers." I was surprised at how quickly they came up with the answer of 22 but had some challenges explaining their thinking. We discussed how important it is, especially in a statistics based course, to ensure you are using the proper terminology.
The second question was "A band of 10 pirates are going to disband. They have divided up all of their gold, but there remains one giant diamond that cannot be divided. To decide who gets it the captain puts all of the pirates (including himself) in a circle. Then he points at one person to begin. This person steps out of the circle, takes his gold, and leaves. The person on his left stays in the circle, but the next person steps out. This continues with every second pirate leaving until there is only one left - who gets the giant diamond. Who should the captain point at if he wants to make sure he gets to keep the diamond for himself? What if there were 11 pirates?"
This second question was great because it was unique enough that it leveled the playing field for every student in the class - it was not based on past course material so students who may have a stronger math background did not have an advantage to solving this problem. There was lots of problem solving and collaboration in groups. Each group provided an answer (not all the same answer) and we will verify solutions as a group in our next class.
It was great first class and I hope it has set the stage for a great year!
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