In this confirmatory factor analysis, factors previously identified to explain the variability in Middle School Mathematics Teachers’ perception of the Common Core State Standards of Mathematics were considered as factors hypothesized to effect high school math teachers’ perceptions of challenging math tasks (CMTs). The factor of student characterization (i.e., disposition, academic preparation, and student behavior) was additionally considered as a factor hypothesized to explain teachers’ perceptions of CMTs, as well as site-based variables (i.e., curriculum, assessment and evaluation, professional development, and collaboration). In addition, teachers’ understanding of the importance of the mathematical practice standards and teacher familiarity with enacting CMTs were factors considered in the model. The original septenary factor structure was modified and good model fit was achieved. In addition to the confirmatory factor analysis model which provides a structure for considering teachers perceptions of CMTs, descriptive statistics are presented from the survey developed that captured teachers’ perceptions of CMTs relative to their sites.