Decomposition is a foundational computational thinking construct that is often introduced early as students are learning computer science in the elementary grades. Although decomposition is often described in early computational activities, little research exists about students’ understanding of decomposition. In this mixed-methods research study, 173 third-grade students from eight elementary school classrooms in the Midwest participated. These learners were taught eight computational lessons that were integrated into their mathematics instruction. They completed a computational thinking assessment after the first four lessons and again after the second four lessons. Analyses included the distribution of correct decomposition item responses, confirmatory factor analysis and item-level error analysis. Results indicate wide variability in students’ performance on the decomposition assessment items as well as in performance on items contextualized within mathematics. This study highlights the need for additional considerations about assessing computational understanding, implications for assessment within integrated contexts, and the use of paper-and-pencil tests compared to embedded assessments.