The UTeach Observation Protocol (UTOP) was designed to inform STEM teacher education. The instrument has been used in prior studies examining inter-rater reliability and relationships to teacher value-added scores. However, prior work has not shown examples of how rating with the UTOP works in practice nor has it discussed the instrument's strengths and limitations. Here, we describe how the UTOP draws upon theories and practices heavily emphasized in teacher preparation--including deep student engagement, classroom management, STEM content fluency, lesson structuring, and innovative instructional models. We then present the ratings of three sample elementary mathematics lessons on the UTOP. We show how the UTOP reveals important aspects of teachers' instruction, and discuss key strengths and weaknesses of the instrument. We find that the UTOP provides a broad view of instructional practice useful for informing systemic professional development, while also addressing content-specific teaching behaviors critical to STEM teaching. However, it may be cumbersome to consider so many teaching indicators simultaneously, and less emphasis is given to theory-driven indicators of the development of mathematical reasoning. This article provides a novel theoretical, empirical, and practical base of knowledge for using or making decisions about whether to use the UTOP for math classroom observations.