Querying and reasoning over RDF streams are two increasingly relevant areas in the broader scope of processing structured data on the Web. While RDF Stream Processing (RSP) has focused so far on extending SPARQL for continuous query and event processing, stream reasoning has concentrated on ontology evolution and incremental materialization. In this paper we propose a different approach for querying RDF streams over ontologies, based on the combination of query rewriting and stream processing. We show that it is possible to rewrite continuous queries over streams of RDF data, while maintaining efficiency for a wide range of scenarios. We provide a detailed description of our approach, as well as an implementation, StreamQR, which is based on the kyrie rewriter, and can be coupled with a native RSP engine, namely CQELS. Finally, we show empirical evidence of the performance of StreamQR in a series of experiments based on the SRBench query set.