Both storytelling and learning by teaching approaches have shown to be beneficial separately when integrating robots into learning settings. This paper discusses how to combine them, based on principles found in the literature, and presents the design and implementation of a playful robot application for second language (L2) learning targeted at primary school children. Our first tests showed that the robot kept the children engaged throughout the learning activity. It appears to be a promising approach as some vocabulary gain is observed in children, but there can be several factors involved that were not controlled in the trials and that will require further work.