Mining data streams has raised a number of research challenges for the data mining community. These challenges include the limitations of computational resources, especially because mining streams of data most likely be done on a mobile device with limited resources. Also due to the continuality of data streams, the algorithm should have only one pass or less over the incoming data records. In this article, our Algorithm Output Granularity (AOG) approach in mining data streams is discussed. AOG is a novel adaptable approach that can cope with the challenging inherent features of data streams. We also show the results for AOG based clustering in a resource constrained environment.