In this paper, we present a novel tool to measure engagement in people with dementia playing board games and interacting with a social robot, Pleo. We carried out two studies to reach a comprehensive inventory of behaviours accounting for engagement in dementia. The first one is an exploratory study aimed at modelling engagement in cognitive board games. The second one is a longitudinal study to investigate how people with dementia express engagement in cognitive games and in interactions with social robots. We adopted a technique coming from Ethology to mould behaviour, the ethogram. Ethogram is founded on low level behaviours, and allows hierarchical structuring. Herein, we present preliminary results consisting in the description of two ethograms and in their structuring obtained through thematic analysis. Such results show that an underlying structure of engagement exists across activities, and that different activities trigger different behavioural displays of engagement that adhere to such a structure.