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There is little empirical research related to how elementary students apply computational thinking (CT) in problem-solving as well as appropriateness of integrated CT assessment design. The study utilized the cognitive interview technique to collect empirical evidence of students’ CT while they solved assessment problems in the areas of sequence, repetition, conditionals, and decomposition. Data collection took place during two periods after elementary students were taught eight Math-CT integrated lessons developed according to CT learning trajectories (LTs). Data analysis suggested that students demonstrated a range of CT competencies in the four areas and that students faced challenges particularly with word problems. The implications for elementary CT instruction and integrated CT assessment design were discussed.