in place. As teachers, we are often tasked with designing good playing fields – student projects that optimally balance rules and guidance with creative freedom. One project that strives to find this balance is the Seventh Grade dartboard investigation. Each year, Saint David’s Seventh Grade algebra students accept the challenge to create an updated version of the game of darts. Each student designs and constructs a dartboard that, while adhering to specific requirements for the area of the bulls-eye and the border, flies in the face of conventional wisdom about dartboard design. Students design functional dartboards in a shape of their own invention. Dartboards take the form of hot rods, Christmas trees, self-portraits, and abstract geometric patterns. Because of the area requirements, however, each dartboard represents a similar degree of difficulty. A dartboard must include a border worth 1 point representing 30 percent of its area, a chosen area worth 5 points representing 25 percent of its area, and a bulls-eye worth 10 points representing 10 percent of its area. The designer is free to assign his choice of point value to the remaining 35 percent of the dartboard area. Beyond these requirements, extra points are awarded to dartboard designs that include at least one type of symmetry, incorporate non-rectangular shapes, and include overlapping shapes. In the end, students explain their process and argue for the acceptance of their design in a letter to the Milton Bradley Company. The basis of this argument varies from letter to letter. One student this year highlighted the increased level of difficulty his dartboard presented due to the regions of negative point values he included. Another argued that his design was more kid-friendly than a traditional dartboard. A third presented his design as a holiday version of the dartboard, to be marketed seasonally. Each letter is assessed for its quality
Above and opposite page: Boys base the custom design of their dartboards on certain rules and boundaries, one of several math investigations in the Upper School.
“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.”
of writing and validity of the math processes involved, and each dartboard is ultimately evaluated on its mathematical accuracy, form, symmetry, and creativity. The dartboard investigation typifies the Saint David’s approach to mathematical problem solving. Within the math curriculum, emphass is placed on the individual’s voice in the problem solving process. Alternative solution methods are presented by teachers whenever possible, and are especially
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