Health monitoring applications using smart devices are becoming increasingly popular due to an expanding number of new devices available and growing affordability of such devices. Smartwatches provide a new way to acquire data for heart rate and activity levels via accelerometers, gyroscopes, and other builtin sensors, which can enable a full range of health applications to improve users' lives. However, continuous heart rate monitoring can significantly reduce the operating time of a smartwatch, reducing the applicability for continuous monitoring. We propose GreenMonitor to extend the operating time of a smartwatch while maintaining accuracy of heart rate monitoring by leveraging the correlation between heart rate and activity level changes indicated by the accelerometer data. Through detailed implementation and evaluation we show that GreenMonitor can save 26% energy, on average for our traces, while maintaining accurate physical activity tracking and evaluation.