The Best Practice in Mathematics Education project was funded by the Australian Office of the Chief Scientist, to examine promotion of students' learning, engagement and aspirations in this core learning domain. We draw upon cross-sectional survey data from 551 students in grades three to nine to examine how students' mathematics engagement relates to key dimensions of their learning climate (mastery or performance focused classrooms), teacher enthusiasm, and school caring. Engagement is known to be associated with positive school outcomes and influenced by environmental factors. Less known is whether, and the extent to which, students have different profiles of engagement across component dimensions (Fredricks, Blumenfeld, & Paris, 2004); and, how profiles may differ according to experienced environment dimensions. We first develop profiles of adolescents' behavioral, emotional, and cognitive engagement using multilevel latent class analysis, educing three profiles of "engaged", "compliant", and "disengaged" students, who systematically differed on experienced environmental factors. Mastery focused classrooms, enthusiastic teachers and caring school environment were experienced most by engaged, and least by disengaged students; performance focused classrooms were unrelated to engagement profiles. Identified patterns will be of particular use to teachers in understanding how class, teacher, and school influences together shape students' own engagement in mathematics.