In this paper, we investigate the mathematical, social and affective nature of children’s engagement with TouchCounts, a multitouch application for counting and doing arithmetic. In order to study these dimensions of engagement in a way that recognizes their fundamental intertwinement, we use rhythm as a primary unit of analysis. Drawing on over 8 hours of research sessions with children aged 6, 7 and 8 years old, we show how various rhythms emerged from their interactions and how these rhythms changed over time—moving from the particular to the more general. We also show how important rhythm is to children’s carrying of activity, which relates to aspects of interest and motivation.