T cells play a central role in adaptive immunity by regulating immune responses and by targeted killing of antigen bearing cells. However, before T cells can carry out these functions they must become activated by antigen-presenting cells (APCs) bearing cognate antigen. Activation involves interactions between T cell receptors (TCRs) and antigen, in the form of peptide-major histocompatibility complexes (pMHCs), in a tight adhesion region between the T cell and APC. In this region, known as the immunological synapse, few pMHC molecules (~10) with weak reaction kinetics to TCRs are able to induce sufficient intracellular signaling to activate T cells. It was proposed and theoretically confirmed that the necessary signal amplification occurs by a single pMHC molecule serially engaging many TCRs. The theoretical work assumed a homogeneous distribution of diffusing TCRs. However, recent experimental data have shown the existence of many mobile micron-sized clusters of TCRs. We use mathematical modeling to explore serial engagement in light of these new data. We are able to obtain an analytical expression for the number of engagements in the case of a single mobile cluster of TCRs. In the case of a field of immobile TCR clusters, we use matched asymptotic analysis to obtain a solution in the limit when the clusters are small compared with the size of the adhesion region. Lastly, we show numerical solutions of the full mathematical model.