Distributed, highly coordinated activities for learning are becoming more and more important as we move further into the world of pervasive mobile computing. These activities can be explored and developed using GroupScribbles, a system to allow the easy creation and exchange of shared information. However, to have confidence in the efficacy of shared activities for learning at scale, we need to be able to model the relationship between the rules and tasks as communicated to the group, and individual behaviour and experience. Trace Theory is a formal modelling language that allows us to do this. We show how Trace Theory and GroupScribbles can be used to model and test different ways a jigsaw pattern of engagement can be implemented, with implications both for the design of emergent pervasive technologies and for acute thought about coordination and collaborative learning.