This study investigates the nature and role of common ground in group learning of mathematics by means of the analytical constructs of "focal projects" and "contextualization." The analysis investigates two students (12-13 years old) playing a dice game, where their task is to distribute a set of markers based on the total of two dice. The analysis shows how consistency between the students' focal projects became crucial in their progression from a uniform to a non-uniform distribution of the markers used in the game. The task system and concrete manipulatives became important in furthering the students' explorations. In the frame of a frequency context, we also discuss how a contextualization may restrict certain aspects of probability from coming into play during such explorations.