This case study analyzes how and why student engagement differs across 581 classes in one diverse high school. Factor analyses of surveys with 1,132 students suggest three types of engaging teaching practices--connective instruction, academic rigor, and lively teaching. Multilevel regression analyses reveal that connective instruction predicts engagement more than seven times as strongly as academic rigor or lively teaching. Embedded case studies of five classes use interviews and observations to examine how various classes combine connective instruction, academic rigor, and lively teaching and how these practices individually and collectively engage students. Across these analyses, this study introduces a typology for thinking systematically about teaching for engagement.