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Research on human-robot collaboration or human-robot teaming, has focused predominantly on understanding and enabling collaboration between a single robot and a single human. Extending human-robot collaboration research beyond the dyad, raises novel questions about how a robot should distribute resources among group members and about what the social and task related consequences of the distribution are. Methodological advances are needed to allow researchers to collect data about human robot collaboration that involves multiple people. This paper presents Tower Construction, a novel resource distribution task that allows researchers to examine collaboration between a robot and groups of people. By focusing on the question of whether and how a robot's distribution of resources (wooden blocks required for a building task) affects collaboration dynamics and outcomes, we provide a case of how this task can be applied in a laboratory study with 124 participants to collect data about human robot collaboration that involves multiple humans. We highlight the kinds of insights the task can yield. In particular we find that the distribution of resources affects perceptions of performance, and interpersonal dynamics between human team-members.