Thursday, January 5, 2012

All we do is play games...

After yesterday's mini meltdown, I was so glad to have a good day today! Overall, I'm very pleased with how this week's lessons have gone, so I thought I would share for another other stat teachers out there.

Tuesday - Fake it or Make it
I modified my original "Fake it or Make it" idea based on this document that I found online. I modified the handouts from the document so that I could fit two data sets on one page. On the front, I used the Heads/Tails check sheet, then on the back, I put the data tables for total heads and tails, the frequency table for cluster size, and a small graph for them to graph cluster size. The kids really enjoyed seeing if they could trip me up and it was fun to see if their graph matched the expected values given in the document. When I first read this document, it reminded me of Benford's Law, so I showed a quick video that @approx_normal found online and we had a class discussion about comparing our observed results to our expected results and what that means. I LOVE that this activity allowed me to plant some seeds for inference and hypothesis testing!! The kids loved that they learned how to not get caught if they embezzle money.... *sigh* :)

Wednesday - Spelling Bee Day 1
Also based on the PCMI probability packet, the Spelling Bee game went over very well. I created Spelling Bee cards based on The Price is Right game, then laminated and cut them out (yay for Netflix as I cut cut cut 16 sets of cards). We started class by watching a video from YouTube and I asked them to make a prediction on the chance of winning the car. Then I introduced the idea of a simulation and we started exploring the game using the game cards. Each pair of students played 20 games, recording the number of Cs, As, Rs, and CAR cards and whether or not they won. After they were done playing, they calculated the true proportion of each type of card and their personal proportion of each type of card in order to compare them. This actually opened up a discussion on the Law of Large Numbers. BONUS!

Thursday - Spelling Bee Day 2
Today, we continued with the Spelling Bee game. At the front of the room, I had a graph prepared for them and each pair of students put a dot (I <3 smiley face stickers) for their proportion of wins.

This allowed me to introduce the idea of a Sampling Distribution (MAJOR WIN!). We discussed that based on all of our results that a pattern was emerging that would allow us to make an educated guess (basic idea of a confidence interval). The students then came up with their educated guess for the true chance of winning the car based on the data gathered. In case you are wondering, the true chance of winning the Spelling Bee game is 73.5% :) From there, I asked the kids to pretend that I really DID have a life and therefore no time to cut out 16 sets of cards - what could we have used instead to run our simulation? Most kids immediately jumped back to the random number table or putting numbers in a hat (DOUBLE YAY!). This was a great intro to using the random number table for simulations, which is what we'll discuss tomorrow....

Friday - Random Number Tables
I'm still brewing some ideas for tomorrow, but I think one of them will be this problem from the PCMI probability set...
You get 1 point every time you flip heads. But anytime you flip tails you're in "danger". If you flip tails a section time consecutively, you "bust" and lose all your points (but continue playing).
This game is just begging to be simulated... :) I think we'll play it as a class together using a coin flipper program on the board, then turn to a simulation to figure out the average score and whether you can go without busting.

If you made it this far, thanks for reading :) It's been a fun week so far and honestly, this is the MOST fun I've had teaching probability ever!


Galamore said...

Could you possibly send me the answers to this activity? It sounds great and I want to use it but I am new at teaching statistics and want to make sure I have my answers correct.

druin said...

I'm not sure which activity you are referring to? None of the activities mentioned in this post have "correct" answers as they are all about simulation.