There has been a steady rise in the support for games as learning environments. This support is largely based on the strong levels of engagement and motivation observed during gameplay. What has proven difficult is the ability to consistently design and develop learning games that are both engaging and educationally viable. Those in the game-based learning community contend the solution is to tightly integrate instructional objective(s) within the game's mechanics. In order to investigate whether or not intrinsic integration would aid in game design, an experimental study was conducted with 111 fourth and fifth graders in which three versions of a game were designed in order to determine which approach would have a more significant impact on conceptual understanding of the associative and distributive properties. It was found that those who played the intrinsic version of the game (properties mapped to game mechanics) had significant learning gains compared with those who played the extrinsic version. Perceptions of the game are also discussed, along with future directions.