Science education reform efforts in the Unites States call for a dramatic shift in the way students are expected to engage with scientific concepts, core ideas, and practices in the classroom. This new vision of science learning demands a more complex conceptual understanding of student engagement and research models that capture both the multidimensionality and contextual specificity of student engagement in science. In a unique application of person-oriented analysis of experience sampling data, we employ cluster analysis to identify six distinct "momentary engagement profiles" representing different combinations of the behavioral, cognitive, and affective dimensions of student engagement in high school science classrooms. Students spend a majority of their classroom time in one of several engagement profiles characterized by high engagement on one dimension, but low levels on the others. Students exhibited low engagement across all three dimensions of engagement in about 22% of our observations. Full engagement, or high levels across all three dimensions, is the least frequent profile, occurring in only 11% of the observations. Students' momentary engagement profiles are related in meaningful ways to both the learning activity in which students are engaged and the types of choices they are afforded. Laboratory activities provided especially polarized engagement experiences, producing full engagement, universally low engagement, and pleasurable engagement in which students are affectively engaged but are not engaged cognitively or behaviorally. Student choice is generally associated with more optimal engagement profiles and the specific type of choice matters in important ways. Choices about how to frame the learning activity have the most positive effects relative to other types of choices, such as choosing whom to work with or how much time to take. Results are discussed in terms of implications for practice and the utility of the methodological approach for evaluating the complexities of student engagement in science classrooms.