In recent years, new emerging application domains have introduced new constraints and methods in data mining field. One of such application domains is activity discovery from sensor data. Activity discovery and recognition plays an important role in a wide range of applications from assisted living to security and surveillance. Most of the current approaches for activity discovery assume a static model of the activities and ignore the problem of mining and discovering activities from a data stream over time. Inspired by the unique requirements of activity discovery application domain, in this paper we propose a new stream mining method for finding sequential patterns over time from streaming non-transaction data using multiple time granularities. Our algorithm is able to find sequential patterns, even if the patterns exhibit discontinuities (interruptions) or variations in the sequence order. Our algorithm also addresses the problem of dealing with rare events across space and over time. We validate the results of our algorithms using data collected from two different smart apartments.