Online educational games have been widely used to support students' mathematics learning. However, their effects largely depend on student-related factors, the most prominent being their behavioral characteristics as they play the games. In this study, we applied a set of learning analytics methods ("k"-means clustering, data visualization) to clickstream data from an interactive online algebra game to unpack how middle-school students' (N = 227) behavioral patterns (i.e., the number of problems completed, resetting problems, reattempting problems, pause time before first actions) correlated with their understanding of mathematical equivalence. The "k"-means cluster analysis identified four groups of students based on their behavioral patterns in the game: "fast progressors," "intermediate progressors," "slow progressors," and "slow-steady progressors." The results indicated that students in these clusters, with the exception of slow progressors, showed significant increases in their understanding of mathematical equivalence. In particular, "slow-steady progressors," who reattempted the same problem more often than other students, showed the largest absolute learning gains, suggesting that behavioral engagement played a significant role in learning. With data visualizations, we presented evidence of variability in students' approaches to problem solving in the game, providing future directions for investigating how differences in student behaviors impact learning. [This is the online version of an article published in "Educational Technology Research and Development."]