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The WPI approach to engineering education has as its outcomes team projects which work on problems of contemporary significance in both engineering and society. This approach has been highly successful since its inception in the 1970s. In terms of curriculum, the implementation of this approach has been done in a top-down manner. This paper is concerned with how a mathematics course-linear algebra-taken at the freshmen level might be modified to be consistent with the WPI educational philosophy while still maintaining traditional mathematical goals. After several years of doing this, it seems possible to achieve these goals. Final exam data is provided to substantiate these claims.