Mr. T is a middle school math teacher who dreads his unit on probability and statistics. The students don't seem interested and, though he has tried to use both humor and relevance to make his worksheets more interesting, it still seems to be one of his least engaging units. In the teachers room that afternoon, Mr. T was discussing the upcoming school carnival with the principal and a couple of other teachers. Last year, several of the games that were created by the parents turned out to be far too easy to win and, as a result, the carnival made little money. As they spoke it dawned on Mr. T, this is a probability issue! He decided that he would get his kids involved.
Mr. T. asked the principal to speak to his classroom the following week, describing the profitability problem and asking the students for their help with this year's carnival. When the principal left, Mr. T broached the problem to his students, "How can we accurately predict the amount of profit that carnival games will make?"
Rather than directly teaching students a strategy, Mr. T. assigned them to groups and asked each group to identify a strategy. He allowed students to access the Web on their tablets and smartphones as they explored and discussed, but asked each group to summarize their strategy in a Google Doc. One member used a laptop to enter the team's strategy into the Google Doc while the others viewed the Doc through any available device. He used a single document that had a section marked for each team. This allowed teams not only to review their team's work, but to learn from the progress of the other teams as well. After each team had devised a strategy, a quick classroom discussion identified that best of those strategies and they created a formula to guide their process:
Profit = ((Number of Students Playing X The Cost of the Game) - (Number of Students Playing X The probability of winning) X The Cost of the Prize)) - The Cost of the Game.
Several of the groups had even gone further and replaced the (Number of Students Playing X The Probability of Winning) with a more complex formula that recognized that different subgroups, grade levels for example, might have different probabilities of winning. Mr. T was almost as amazed at the sophistication of their solutions as he was at the level of engagement among even the most reticent learners!
Each of the teams either adopted a game from the previous year or created a proposal for a new game. Searching on their tablets and smartphones, students quickly located a host of Websites that featured ideas for carnival games that could be adopted or adapted. Together, the class decided that the final product would include:
While students were invited to model their games in any technology-based format, most found the tablets to be the best tool given the freedom from a mouse or other input device. They locate tools such as Sketcher 3D Lite or Kids Sketchup Lite to do the job.
Each team contributes an image of their game with a brief description. Using a laptop, these are assembled by a cross-team group into a survey in SurveyMonkey and, tablets in hand to displey the choices in the SurveyMonkey list, students fan out in the halls before and after school and at passing times to gather preference data regarding the games. They stop passing students, ask them to look briefly at each of the games on the tablet, and then mark their top three selections for games that they would like to play. It reminds Mr. T of the preference surveys that were conducted in supermarkets in his youth, but without the paper!
On testing day, students randomly select a test population from each grade and set up stations in the hall and, using tablets running either Google docs or Datadroid Forms lite to capture live data on both probabilities of winning and additional student reaction data.
All of the data and images are sent to team laptops where the final proposal is assembled both as a print document and as a presentation. On presentation day, each team presents their game proposal to the school carnival planning committee made up of PTA leaders, the school principal and the district math coordinator. Mr. T is impressed with both the quality of the proposals, particularly the mathematics, as well as the earnestness of the presenting students. He is pleased when all of the games are accepted by the committee!