Games are often used to foster student engagement and motivation to learn content, such as mathematics. Although digital games dominate game-based learning research, the table games commonly used in classrooms warrant investigation. Especially for mathematics learning, prior research has not taken into account content-specific frameworks. Integer arithmetic (i.e., calculations with negative numbers) is a difficult topic that is crucial for later mathematics. Thus, this study synthesized multiple theoretical perspectives to understand students' experiences playing games during an integer unit. A mixed methods design study was conducted to answer the primary question: How was student experience (motivation to learn and engagement) related to game features? Student perspectives about the three integer games they played and observations of student engagement during gameplay were analyzed using perspectives from game design and the Cognitive Demand framework for mathematical tasks. Overall, students positively perceived playing games, however, individuals' motivation and engagement varied in relation to game features. Students provided valuable insights for research and practice as to which game features were engaging or motivating and why. Speed-based synchronous games that exclusively used skill, rather than a chance-skill balance induced stress and decreased motivation for many students. Thus, a critical implication was to first do no harm by selecting or designing classroom games that have features of turn-taking and chance. We suggest recommendations for mathematics learning and provide the STEM Classroom Games Features Framework to benefit research and practice of any STEM content area.