This article builds on prior work that aims to measure computational learning (CL) during middle school. Since game computational sophistication (GCS) has been used as a proxy for a student's engagement in CL we build on their model to more completely describe the relationship between different types of building blocks of computer games and GCS. In doing so, we present a single quantitative measurement for GCS. Our model, called GCS 2.0, has face validity for 39 games, each programmed by a pair of middle school children. We choose four of these games, two with high GCS and two with low GCS, and discuss the computational building blocks found in each game. We do this to help the reader better understand our measurement of GCS and its relationship to CL.