creation of an original idea that adheres to certain mathematical guidelines. The creation of a dartboard begins with a design idea, and the challenge for each student is to make their design fit the mathematical guidelines. This means working backward through a formula using a total area as starting point rather than an endpoint. For example, a certain design may require a circle of area 30 square centimeters in order to fill 25 percent of the board’s area and satisfy the 5-point area requirement. The student must then realize that 30 square centimeters is the solution to the area equation and he must use inverse operations, including square roots, to find the radius of the ideal circle. The rigor increases when the student decides to include a triangle overlapping part of his circle, and his 30 square centimeters now needs to represent the difference between the area of a circle and the partial area of a triangle. Because situations like this are common, each dartboard goes through several drafts and designs are often altered significantly throughout the process. In the end, each dartboard design is unique, yet each has correctly solved the math problem that was built into the assignment. The value of open-ended math work like this is that it allows students to use math skills not only to solve a problem, but also to solve it in a way that is entirely new. The student is the creator of a thing that has never existed before and is wholly different from the other things around it. He is not only incorrect or correct, but is the owner of both his method and his product. The dartboard challenge and other open-ended math investigations are a way in which Saint David’s boys experience this.? M Nick Reeb teaches Upper School mathematics at Saint? David’s School.
Below: A sample dartboard, created by Filippo Ravalli ’13.
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