Posts Tagged ‘probability’

perfect match

By Kristina

Ahh, math in real life…but what about math in *reality* life?

Are You The One? castPhoto Credit: MTV Press

MTV’s Are You The One? unwittingly poses a mix of the old game standby Mastermind, probability, and reality-show intrigue.

mastermindPhoto Credit: Wikipedia

“If your perfect match was standing right in front of you, would you even know it? In the most ambitious dating experiment ever attempted, that question will be answered as contestants compete in a series of challenges designed to test the intelligence of their heart. “Are You The One” begins by selecting 10 beautiful single women from across the US. Using the most extensive matchmaking process ever seen, 10 men will be found and perfectly matched for these women. But the results aren’t revealed to them. Now all 20 people are living together in Hawaii where they share one objective: Find their PERFECT MATCH. Each week, the group will follow their hearts and lock in a choice of who they think is their PERFECT MATCH. If all 20 people find their perfect match within 10 tries, they’ll all split $1 MILLION!”

Each week, the group nominates one couple to go into the “truth booth,” which gives a definitive “yes” or “no” as to whether the couple is a match. That gives the group one data point. Then the group goes into a “matchup ceremony” where they pair up with another person and are told how many pairs are matches and how many are wrong.

Ideas for Math Questions

1) How many ways can they pair up?

2) If in the first truth booth, the couple is a match, how many ways can the remaining couples pair up?

3) If in the first truth booth, the couple is NOT a match, how many ways can the remaining couples pair up?

4) What strategies could the couples use when they receive their data from the matchup ceremony? For example, in the first week, the couples got 2 out of 10 matches correct. In the second week, they chose to go with completely different pairs and got 4 out of 10.

5) What is the probability that the group wins?

skunk & cookie dough

By Kristina

Yesterday we played Skunk in math class to explore chance. I chose this game because it’s simple, has the kids stand (fights against sleepiness in the morning), and can be altered to suit your teaching needs. I also added an incentive: the winner in each class would get a free cookie dough cupcake from our upcoming Valentine’s Day prom fundraiser bake sale.

cupcake Photo Credit: Little Miss Runshine

 I plan to bake the Little Miss Runshine cookie dough cupcakes and add a little cookie on top. This prize caused much clamoring for topping with cookie dough oreos and insisting that I price them at $30 per cupcake. I am sad to find out that the cookie dough oreos have received unfavorable reviews; I may have to make my own from Oh Bite It’s recipe.

middle 1 Photo Credit: Oh Bite It

To start the game each player makes a score sheet like this:

skunk1

Each letter of SKUNK represents a different round of the game; play begins with the “S” column and continue through the “K” column. The object of SKUNK is to accumulate the greatest possible point total over five rounds. The rules for play are the same for each of the five rounds.

At the beginning of each round, every player stands. Then, a pair of dice is rolled. (Everyone playing uses that roll of the dice; unlike other games, players do not roll the dice for just themselves.)
A player gets the total of the dice and records it in his or her column, unless a “one” comes up.
If a “one” comes up, play is over for that round and all the player’s points in that column are wiped out.
If “double ones” come up, all points accumulated in prior columns are wiped out as well.
If a “one” doesn’t occur, the player may choose either to try for more points on the next roll (by continuing to stand) or to stop and keep what he or she has accumulated (by sitting down).
Note: If a “one” or “double ones” occur on the very first roll of a round, then that round is over and each player must take the consequences.

As recommended, we played a practice round. I had a student up at the front call out the sum of the dice on each roll while I put the results on the whiteboard. Some students began articulating their strategies (e.g., one would always sit after the 3rd or 4th roll in a round, one tried to peek around at the others’ score sheets so he would know how much to bet). Another claimed that he could predict exactly what I would roll (which sometimes got creepy when he was right). The thing that made me the happiest: students asking if we could play again because “that was fun.”

We used Skunk to practice finding experimental probabilities (using the game results to show the probability of rolling a given number, or greater than a given number) and to review terminology like trials, outcomes, frequency, and relative frequency. I then used it to explain the concept of sample space (starting with sample space for rolling a die, then sample space for rolling two dice). I wish we had longer class periods so that we could spend more time discussing chance and strategies (from the NCTM prompts) in addition to doing practice IB problems. I may bring back Skunk again or switch to Pig.

I would love to get the original Skunk game (found via All About Fun and Games)!

skunkcoverskunkscore Photo Credits: All About Fun and Games