This study investigated students' modeling progress and strategies in a problem-solving simulation game through content analysis, and through supervised and unsupervised lag sequential analysis (LSA). Multiple data sources, including self-report models and activity logs, were collected from 25 senior high school students. The results of the content analysis found that the problem-solving simulation game helped most of the students to reflectively play with the science problem and build a workable model to solve it. By using the supervised LSA, it was found that the students who successful solved the game frequently linked the game contexts with the physics terminologies, while those who did not solve the problem simply relied on the intuitive knowledge provided in the reference materials. Furthermore, the unsupervised LSA identified four activity patterns that were not noticed in the supervised LSA: the fragmented, reference material centered, reference material aided modeling, and modeling centered patterns. Each pattern has certain associations with certain problem-solving outcomes. The results of this study also shed light on the use of different analytics techniques. While the supervised LSA is particularly helpful for depicting a contrast of activity patterns between two specific student groups, the unsupervised LSA is able to identify hidden significant patterns which were not clearly distinguished in the pre-defined student groups. Researchers may find these analytics techniques useful for analyzing students' learning processes.