Continuous monitoring of complex activities is valuable for understanding human behavior and providing activity-aware services. At the same time, recognizing these activities requires both movement and location information that can quickly drain batteries on wearable devices. In this paper, we introduce Change Point-based Activity Monitoring (CPAM), an energy-efficient strategy for recognizing and monitoring a range of simple and complex activities in real time. CPAM employs unsupervised change point detection to detect likely activity transition times. By adapting the sampling rate at each change point, CPAM reduces energy consumption by 74.64% while retaining the activity recognition performance of continuous sampling. We validate our approach using smartwatch data collected and labeled by 66 subjects. Results indicate that change point detection techniques can be effective for reducing the energy footprint of sensor-based mobile applications and that automated activity labels can be used to estimate sensor values between sampling periods.