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This study uses survey data to examine how high school students' self-reported usage patterns of AI chatbots relate to their levels of engagement, sense of belonging, perceptions of homework, and selected character strengths. Using factor analysis, we found their usage patterns differ from their perceptions of acceptable use for most academic tasks, with two exceptions: students who believe AI should write entire papers or explain concepts are likely to use them accordingly. Through K-means clustering, we identified that students with low engagement, diminished belonging, negative homework perceptions, and lower character strengths are significantly more likely to use AI for writing entire papers. These findings inform targeted interventions addressing academic and social-emotional factors for students who use AI for different purposes.