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!

Simulations based on Game Shows

The PCMI Probability problems had a "Game of the Day", oftentimes related to the King of Game Shows - The Price is Right. I don't know about you, but as a kid, whenever I was home sick, I always loved watching TPIR. (Honestly, though, I miss Bob Barker....)

Anyway, one of the "Game of the Day" activities in the PCMI packet is the "Spelling Bee" game, in which contestants select cards and hope to spell the word "CAR". I plan to show a clip of the game from TPIR website and ask my students to figure out the proability of winning. Of course, the probability isn't the easiest one to calculate, especially right after a 2 week break, so it will be a natural lead-in to simulations. I found this worksheet/writeup online and plan to use it as a guideline. In their partners, the kids will run through the simulation several times, then combine their data with another pair of students to calculate the simulated chance of winning.

P.S. Like many people, my favorite TPIR game was Plinko. I really want this game board from Oriental Trading...Disc Drop Game

Real or Fake?

Yesterday I went through the PCMI probability problems from 2007 and found some really neat ideas to use over the next few weeks. I plan to use one of the activities to start us off on day 1 next week.

The basic idea is for groups to create two datasets of a coin flip. First, they will fake a dataset of 240 coin flips, then they will create a real dataset by actually flipping the coin. They will write these two datasets on index cards. Using their two datasets, they will discuss with a partner and come up with a way to determine if a new dataset is real or fake. I will then have them exchange their cards with another pair of students and use their "test" to determine which card has the real data and which card has the fake data. If time allows, there are some additional coin flip datasets in the PCMI packet that I will put up for discussion.

At some point after that - not sure if I'll do it the next day or a few weeks later - the PCMI packet went on to use an inference test to determine if a dataset was real or fake. By splitting the coinflips into sets of 2 (or 3 or whatever), you could keep track of how many HH/HT/TH/TT combinations there were and compare them to the expected 1:3:3:1 ratio. This would provide an interesting introduction to inference testing and p-values, as well as tying in to binomial expansion and pascal's triangle.

This activity should be a good way to get them back into the school frame of mind, thinking about the start of inference techniques, and drawing conclusions from data. If I'm really good this week, I'll get it together in a google form.... We'll see how that goes :)

Problem Sets and Probability

Winter break is halfway over - where, oh where, did it go?? :) Last week, I spent time cleaning house, reading novels, and in general, just enjoying the off time. However, all good things must eventually come to an end, so this week, I vowed to work at least one hour per day on school stuff. (wishful thinking?)

Probability is one of my weakest areas as a stats teacher. Prior to going on break, we had covered basic probability, disjoint events, independent events, venn diagrams, tables, trees, etc. Next week, when we go back, we'll do simulations and probability distributions. In the past, I've not been pleased with how this unit turned out, so I'm hoping to do it better this year. A few weeks ago I ran across this problem set from the 2007 PCMI and today I've been working through it. So far, I have some ideas I think will work, especially for simulations. I really like the Game of the Day activities and plan to use several of them to spark conversation in my class.