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Welcome to my math blog! The purpose of this blog is to help you stay informed about our learning and experiences that have taken place during our math class. I have also included links your child (and you) may want to use in order to supplement math learning in 5th grade.

Tuesday, February 4, 2014

Probability: Rock, Paper, Scissors (Is it a fair game?)

To begin, we revisited the 2 coin toss from last Thursday.  I wanted the classes to see the 5th Grade circle graph once all three classes' data was combined.  We had a total of 1734 coin tosses.  That meant we should have had 433 HH, 433 TT, and 866 HT.  Here is our data:

Our data and our circle graph came almost spot on with our theoretical data....AGAIN!  (Which is as it SHOULD be!)

Today we played!  We played the game "rock, paper, scissors."  However, our play had a purpose.  Before playing the game, I asked the kids if the game was a fair game.  We turned to mathematics to find out.  In order to determine if "Rock, Paper, Scissors" is a fair game, we needed to list all possible outcomes of the game.  We did this by using the three visual models that we used with the 2 Coin Toss (t-chart, branches, and a matrix).  Please watch the video:  Rock, Paper, Scissors to see the lesson.

Using these three visuals, we were able to determine that Rock, Paper, Scissors IS a fair game.  There are three ways to win, three ways to lose, and thee ways to tie.  

Now, we needed to determine the theoretical probability (what SHOULD happen) when we played the game.

We discovered that each of the events should occur 1/3 of the time.  Therefore, when we play the game, we should be able to gather our data and create a pie chart that is divided evenly into thirds.

Time to play.... I mean experiment!  We each grabbed a partner and played until we had reached the end of one row.  Once we finished the game we recorded our tallies in the form of fractions and compared our theoretical data with our experimental data.  For example, the game I played with a student SHOULD have had us winning, losing, and tying 8 times each.  Instead, I had 8 ties, 8 losses, and 15 wins.  Therefore, my theoretical probability and my experimental probability were not compatible.

However, when we combined the data from all the students in a class, our data and our graph was MUCH closer!

  • Mrs. Johnson's class had a total of 668 games.  Therefore, there should have been about 222 wins, 222 losses, and 222 ties.

  • Mrs. Dittrich's class had a total of 505 games.   Therefore, there should have been about 168 wins, 168 losses, and 168 ties.

  • Mrs. Whitehead's class had a total of 523 games.  Therefore, they should have had about 174 wins, 174 losses, and 174 ties.

Once again, the kids were thrilled to see that their graphs came out almost exactly as expected.....forgetting that this is what was SUPPOSED to happen!  I love it!

Once again, I will combine the three class's data at the beginning of class.  They can't wait to see if we have a perfect pie chart divided into three equal pieces!

To round out the day, I asked the kids if they have ever watched The Big Bang.  While most hadn't, I assured them that this would not hinder their exit ticket assignment.  I explained that one of the characters on the show does not play Rock, Paper, Scissors.... NO.... he plays Rock, Paper, Scissors, Lizard, Spock!

So for our critical thinking/writing today, I asked the kids to:

Evaluate the fairness of this game.
Justify your reasoning.

I asked them to use one of the visual models (t-chart, branching or matrix) to list all possible outcomes of this game.  Determine if the game is fair and JUSTIFY (or explain) how they have come to this decision.

HOMEWORK:  Countdown 3.7

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