Today we problem solved using another Would You Rather...? These activities come from the website:
Today's problem was:
Would You Rather....
I was thrilled to find this problem! It connects back to the activities we performed with probability (Two Coin Toss and Dice Dilemma).
I began by asking the kids to think about the above problem and discuss their reasoning with their table group. After a few minutes discussion, they were to make a choice and explain their reasoning. Since this is the third or fourth time we have worked on a "Would You Rather," they are much more willing to write something that they may or may not change later.
Once we had our predictions, we began to find our theoretical probability (what SHOULD happen). We also mentioned that we had to take into account that luck is also involved.... you never know what will happen!
The information was the same for each class:
- Game A had a 50% probability of winning and the payoff was only $3 a win.
- Game B had a 55% probability of winning and the payoff was only $1 a win.
At this point, some minds were beginning to change.... but not everyone had a solid of idea of why.
So, now we moved on into our favorite part.... experimental probability (data gathering)! We began by working with Game A. We created a table to hold our data. I gave each student two pennies and we tossed them 10 times. Each time we logged our outcome on the table. We determined how much money we had won or lost. Then we compiled all of the classes data together to see how this game held up to our theoretical probability.
Theoretically we should have won 50% of the time:
|Johnson's class won 37% of the time|
|Dittrich's won 50% of the time|
Whitehead's class won 10% of the time!
We also discovered that if we won this game only 50% of the time, we would never break even.... we would lose $10!
Now, we needed to test Game B. We set our table up in the exact same way. We rolled the dice 10 times, logged our outcomes on our tables, and compiled the classes' data.
Theoretically, we should have won 55% of the time.
|Johnson's class won 60% of the time.|
Dittrich's class won 58% of the time
Whitehead's class won 55% of the time
Again, if we won only 55% of the time we would still lose about $2.
At this point, I asked the kids to write their new answer to "Would You Rather..." I explained that they did not have to change their game choice if they felt that they could mathematically prove their reasoning, but that their reasoning should have changed from just "because I think" to more of a "because I know".
After they chose the game they felt had a better probability of winning and, therefore, making them some money. I had each student create a new table for the chosen game, play the game 10 more times, combine the data with their first game and write a conclusion about their choice of game.