In our research, we consider complex Game Based Learning (GBL) scenarios where both individual and collaborative learning are addressed. In order to support these scenarios, personal devices (tablets, mobile phones) co-exist with shared devices (collaborative tabletops). New learning usages emerge in these multi-device environments where learners can swap from individual to collaborative tasks. In this context, new problems appear when one wants to design new GBL activities. One major issue refers to the combination of personal and collective workspaces. This notion also known as “territoriality” has been addressed in the literature, particularly for Collaborative Tabletop Workspaces. However, we need to extend and reconsider this notion when designing multi-device activities. For instance, providing users with both private and shared devices raises information visualisation issues. In this work, we present several aspects to consider for the design of GBL activities in this context: territory arrangement in multi device environments; inter-territory actions to manage information; and contextual information visibility for objects involved in the learning tasks. We then detail a case study used to apply our proposal. We have designed and enacted a scenario of a collaborative game to learn French grammar. Individual and collaborative tasks co-exist and are supported with a multi-device environment. We describe how the experiment was carried out and the main results deduced from students' answers to questionnaires.