One of the most efficient ways for elementary school students to gain exposure to computational thinking is when it is integrated into other disciplinary areas; however, elementary school teachers often lack the necessary resources to do this effectively. By leveraging the motivation force of narrative to engage students and the scaffolding affordances of block-based programming to support students, computationally-rich narrative-centered learning offers promise to address this need. In this work, we review design principles from prior work for engaging elementary students in computational thinking as well as results from initial pilot studies to investigate how computationally-rich narrative-centered learning in the context of science problem solving can support the integration of computational thinking into other disciplinary areas.