The sensor networks, web click stream and astronomical applications generate a continuous flow of data streams. Most likely data streams are generated in a wireless environment. These data streams challenge our ability to store and process them in real-time with limited computing capabilities of the wireless environment. Querying and mining data streams have attracted attention in the past two years. The main idea behind the proposed techniques in mining data streams in to develop efficient approximate algorithms with an acceptable accuracy. Recently, we have proposed algorithm output granularity as an approach in mining data streams. This approach has the advantage of being resource-aware in addition to its generality. In this paper, a model for mining data streams in a wireless environment has been proposed. The model contains two novel contributions; a ubiquitous data mining system architecture and algorithm output granularity approach in mining data streams.