Our study investigates how changing socioeconomic status (SES) composition, measured as percentage free and reduced priced lunch (FRL), affects students' math achievement growth after the transition to middle school. Using the life course framework of cumulative advantage, we investigate how timing, individual FRL status, and legacy effects of a student's elementary school SES composition each affect a student's math achievement growth. We advance research on school transitions by considering how changing contexts affect achievement growth across school transitions. Furthermore, we improve on school context research by measuring the ways that SES compositions across school transitions may be interconnected. Using state administrative panel data for third through eighth graders from 2009 to 2015, we use fixed effects to estimate math achievement growth by the end of eighth grade. Findings suggest that a student's elementary SES composition has a legacy effect on middle school achievement growth net of his or her own achievement growth and middle school SES composition. In addition, SES composition effects differ depending on the timing of exposure and a student's individual FRL status. Our study has important implications for both educational transition research and school effects research, which are discussed.