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Generative artificial intelligence (GenAI) shows promise in supporting middle school learning, yet students’ voluntary engagement and prompt patterns remain underexplored. This study examines how students interact with a GenAI-based teaching assistant (GenAITA) over a seven-week curriculum. Students voluntarily used GenAITA during weekly learning tasks. A total of 2,812 interaction logs from 126 students were thematically coded to identify prompt types, followed by correlation analysis and linear mixed models to examine temporal patterns. Engagement fluctuated across tasks, increased over time, and was sensitive to task design. Students produced both task-relevant and task-irrelevant prompts, with six identified subtypes. Prompt types exhibited co-occurrence within tasks and covariation over time. Findings inform the design of GenAI tools and learning tasks in K–12 classrooms.