Carnival Day in Math Class

By Lynn K. McMullin

Often, I have mentioned the importance of 21st century skills and real-world applications in classroom learning.  I’m sure everyone is familiar with the concept that knowledge is expanding astronomically. We’ve all read or heard that knowledge doubles at some “fill-in-the-blank” rate, whether that rate be every 8 days … or every 8 months … or some other frightening statistic.  But, the point remains: change happens in content knowledge so quickly that what a person knows is becoming secondary to what a person is able to do.

We hear that students in other countries are now achieving much more than our own students do.  Studies show that the countries with the highest achievement teach fewer topics more deeply. They teach less content knowledge and more reasoning and application skills.  In order to compete in the global economy, the United States will need students who can communicate, collaborate, and problem solve, not recite.  Our students will work with ‘just-in-time’ specifics by researching and analyzing information just as they need it for the particular problem and proposal their boss has assigned.  They need to be innovative, analytical, and persistent.

This week, in two high school math classes, students participated in Carnival Game Day. The task was this: work collaboratively in a small group to develop a carnival game that favored the house, but looked ‘winnable’ to the potential client.  There were a lot of parameters.  Students had to use a combination of at least two spinners, coins, dice, or cards. They needed to write-out the ‘game-play” rules, test the probabilities for profit vs. payout, and calculate the mathematical expectation of their games.

On “Carnival Day" itself, the students were given $48 in play money and were required to visit each game a minimum of three times.  In the end, the tables had to calculate their profits; and the contestants, their winnings.  Keep in mind, the students could go back as many times as they wanted to the games that seemed the “loosest” to them.



Lollipalozza -- what row you spin, what side you flip,
which lollipop you choose determines whether you win --
nothing, the lollipop, or $4.

 Lollipalozza was both enticing and interesting. It cost $3 to play. First, you spun for a color: 33.3% of the wheel was red (the bottom row) and 8.3% of the wheel was yellow (the top).  If you spun blue, green, or yellow, you knew you walked away with at least a lollipop; so if you didn’t mind a $3 price tag for the lollipop, you could call yourself a winner at that point!  Next, you flipped a coin.  Heads got you a pick from the left side; tails from the right.  Now, you got to select a lollipop from the colored row and side you had won.  If the dot on your lollipop stick matched the color of the row, you won $4… and the lollipop!

In Probability Roulette, you paid $3 to play. You had to spin the wheel and roll the dice simultaneously.  If your die landed on a pink triangle, you won the show of the die, anywhere from $1 - $6.  If your die landed on a green triangle, you lost.

I really enjoyed seeing what the kids had created, but I didn’t count my money on the way out.  I did hear one student complain to Mrs. Gabrielle Aitchison, their math teacher and the department chair, “I don’t get it. The probability of winning our game is minimal, but everyone keeps winning!”

The final part of this activity is that the students each write a self-evaluation based on the game they invented and the games they played.  Which game was the best performer and why?  Remember, a game had to both make money and attract customers. What would you do to improve your own game now that you saw how it performed?  Explain why your game’s performance did or did not match your mathematical prediction?  Students learned a little bit about odds and gaming at the same time, knowing how games can be built to favor the table and still look attractive.



Spin the roulette wheel and throw the die into the spinning wheel --
land on pink, you win the face value of the die.



Will this kind of collaborative, problem-solving activity make a difference?  I think so, especially since self-reflection is an important final component of the process.  Students still had to “know” things about probability and math to write their game proposals and resolve their problems.  But, they also had to put what they knew to the test, and then they had to be critical of their results. 

What do I see next?  I’d love for this kind of activity to move into the technology realm, with the kids designing their game components on computers and testing their results over the broad spectrum of their many peers through their ready access to ‘social networking.' Posting links to their games and collecting the results might even be one example of putting the Internet to work for them.

The Carnival Day assignment was designed by Mrs. Gabrielle Aitchison, (in red)
who grades students on every facet ... from the project proposal to the visual display ... from the "fairness" of the payout description to their grammar and spelling.