The copolymerization of ethylene and propylene by a heterogeneous Ti/MgCl2 Ziegler-Natta catalyst is studied with density functional theory calculations. One particular model of an active site, the so-called "TiCl3-based slope site", is looked at in detail. The influence of the previous monomer insertion is allowed for by examining sites where the growing polymer chain is modeled by a methyl, propyl, isobutyl, and 2-butyl group. Propylene is found to form a more stable pi-complex with the active site than ethylene. Propylene is also found to have a lower barrier to insertion into the Ti-C bond than ethylene in most instances and to prefer to insert in a 1-2 orientation rather than a 2-1 orientation. The relative height of the insertion barriers of ethylene and propylene is in contradiction to experimentally observed copolymer compositions. Increasing steric bulk of the polymer chain disfavors propylene insertion relative to ethylene insertion and 1-2 propylene insertion relative to 2-1 insertion. Some of the insertion reactions examined are shown to be significantly stereoselective due to the interaction of propylene and the growing polymer chain. Despite these stereoselective reactions, the active site modeled here will not produce tactic polymer except under some special circumstances which are outlined.