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This study investigates how the open-ended design of TouchCounts, a multi-touch app for early numeracy, shapes affective dynamics in parent–child interactions during family math activities. Grounded in inclusive materialism and affect theory, affect is defined as a relational, unfolding force entangled with interactions among parent, child, and technology. Using micro-scale qualitative analysis of two excerpts selected from five participating pairs, the study explores how the app’s two sub-environments—Enumerating World and the Operating World—shape affective engagement. Findings show that affect both drives and arises from mathematical encounters, through gesture, dialogue, and embodied action. The distinct affordances of the app support affect-rich interactions that reflect diverse mathematical thinking and communication.