When two third-graders collaboratively manipulated a multi-modal, digital learning device called TouchTimes (hereafter, TT), that introduces multiplication through visual, tangible and symbolic means, their thinking about quantity shifted from being additive to being multiplicative. In this study, I examine the children's interactions around/with TT. My goal is two-fold: (1) to demonstrate the shift between the students' additive and multiplicative thinking; (2) to explain how their multiplicative thinking emerged around/with TT. The emergence of multiplicative thinking does not refer to the students' correct computations of multiplicative expressions as a response to verbal or number problems. Instead, drawing on an enactivist perspective, I identify the children's thinking as their effective bodily reactions to a given unitizing task using TT--and I distinguish their multiplicative and additive thinking based on various researchers' conceptions of multiplicative thinking. Data was created by video-recording the children's interaction around/with TT. A retrospective analysis of the data reveals that the children's effective action to solve the unitizing task developed through a history of recurrent interactions in this environment.