While video games have become a source of excitement for educational designers, creating informal game experiences that players can draw on when thinking and reasoning in non-game contexts has proved challenging. In this paper we present a design principle for creating educational video games that enables players to draw on knowledge resources gained in-game to reason about non-game phenomena. Games that incorporate this design principle, which we call "constructible authentic representations," engage players in the construction of artifacts that are visually and epistemologically aligned to tools and representations utilized in the target domain. We illustrate this principle with a study of six children (ages 7-13) playing a racing video game of our own design. Players that struggled with a formal graphing task before playing the game showed improvement on the same task in post-game interviews creating qualitatively correct velocity versus time graph that incorporated key kinematic features such as moments of constant velocity and varying degrees of acceleration. An analysis of pre- and post-game clinical interviews also revealed that players more fluidly drew on a variety of knowledge resources when reasoning about the game, real world, and formal representations. We hypothesize that designing games to include constructible authentic representations may allow for the creation of educational video games that can survive in the non-school gaming ecosystem.