One of the major open problems in sensor-based Human Activity Recognition (HAR) is the scarcity of labeled data. Among the many solutions to address this challenge, semi-supervised learning approaches represent a promising direction. However, their centralised architecture incurs in the scalability and privacy problems that arise when the process involves a large number of users. Federated Learning (FL) is a promising paradigm to address these problems. However, the FL methods that have been proposed for HAR assume that the participating users can always obtain labels to train their local models (i.e., they assume a fully supervised setting). In this work, we propose FedAR: a novel hybrid method for HAR that combines semi-supervised and federated learning to take advantage of the strengths of both approaches. FedAR combines active learning and label propagation to semi-automatically annotate the local streams of unlabeled sensor data, and it relies on FL to build a global activity model in a scalable and privacy-aware fashion. FedAR also includes a transfer learning strategy to fine-tune the global model on each user. We evaluated our method on two public datasets, showing that FedAR reaches recognition rates and personalization capabilities similar to state-of-the-art FL supervised approaches. As a major advantage, FedAR only requires a very limited number of annotated data to populate a pre-trained model and a small number of active learning questions that quickly decrease while using the system, leading to an effective and scalable solution for the data scarcity problem of HAR.