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Ensuring that all the teeth surfaces are adequately covered during daily brushing can reduce the risk of several oral diseases. In this paper, we propose the mTeeth model to detect teeth surfaces being brushed with a manual toothbrush in the natural free-living environment using wrist-worn inertial sensors. To unambiguously label sensor data corresponding to different surfaces and capture all transitions that last only milliseconds, we present a lightweight method to detect the micro-event of brushing strokes that cleanly demarcates transitions among brushing surfaces. Using features extracted from brushing strokes, we propose a Bayesian Ensemble method that leverages the natural hierarchy among teeth surfaces and patterns of transition among them. For training and testing, we enrich a publicly-available wrist-worn inertial sensor dataset collected from the natural environment with time-synchronized precise labels of brushing surface timings and moments of transition. We annotate 10,230 instances of brushing on different surfaces from 114 episodes and evaluate the impact of wide between-person and within-person between-episode variability on machine learning model's performance for brushing surface detection.