This article describes "Build It!--The Rectangle Game" task that uses the context of a game to develop mathematical generalizations based on strategy. The underlying mathematics in this game-based task is for students to discover factors and prime and composite numbers through 100. The playful use of "The Rectangle Game" supported student agency and identity. Students were able to explore the idea of factors, even without being proficient with multiplication facts, because the tool removed these barriers while still working toward the desired learning outcomes. The students did not feel like they were taking risks but instead they felt like they were just playing a game. Students giggled over mistakes and celebrated when they found mathematical generalizations.