Probability Carnival Brings Grades Together

Edward Pertcheck, Seventh Grade Math Teacher
Seventh graders used their mathematics creativity to put on Live Oak's annual Probability Carnival, which applies their growing knowledge of fractions into a collection of interactive games for third, fourth, and fifth graders. 
The Probability Carnival Project is an annual tradition at Live Oak and the culminating experience for the seventh grade math unit covering fractions and probability.
During the second unit in math, students review fractions and practice operations (addition, subtraction, multiplication, and division) with fractions and practice converting between fractions, decimals, and percents. These are all skills from previous years and we review them before moving on to probability. Probability is represented with fractions, decimals, and percents, so it is important to have these concepts in mind.
To learn and experience probability, students complete a series of activities involving dice, playing cards, coins, and spinners. We make predictions based on the expected (theoretical) probability before rolling dice, choosing cards at random from a deck, flipping coins, and spinning spinners. We then compare the theoretical probability with our experimental probability. (Experimental probability is the probability that something actually occurs in your experiment or trial.)
Looking deeper into probability, students asked questions about the odds of two different events both occurring. Some events are possible at the same time, such as rolling a four on a die and flipping heads on a coin. Others are not possible at the same time, such as getting both a three and a four on one die roll. These questions lead to using fractions to represent these different probabilities, and figuring out which operations (such as addition and multiplication) could help calculate probability.
With this knowledge, the Probability Carnival Project tasked the seventh grade mathematicians with designing and creating a game of chance. Their games were required to incorporate compound probability. Students first sketched out ideas for their games and then headed to the ChangeMaker Lab. After an orientation about safety and expectations in the ChangeMaker Lab with Victoria Cheng, we had two class periods in the ChangeMaker Lab to construct our probability games. Students worked diligently to create all sorts of games that included rolling dice, spinning spinners, and pulling numbers out of a hat. Students also created signs for their games to advertise the games to the other students who would come to play them. 
The project ended in a Probability Carnival that the seventh graders hosted for younger students during our math class. We invited students from third, fourth, and fifth grades to come to the carnival and play the games. The younger students had fun attempting to win the various games while the seventh graders kept track of how many people won and lost their game.
Students finalized and submitted their game directions along with their calculations for theoretical and experimental probabilities of their games. This week, students are wrapping up the project by completing a reflection. They will record what they have learned and how they would modify their games to improve them if they had another iteration.
Students enjoy and benefit from the hands-on nature of this project where they experience probability through games. They demonstrate their resourcefulness and the depth of their mathematical knowledge during the construction process. It’s great to see how they are able to apply skills of probability and other areas of math to making a successful, usable product.


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