Wearable construction toolkits have shown promise in broadening participation in computing and empowering users to create personally meaningful computational designs. However, these kits present a high barrier of entry for some users, particularly young children (K-6). In this paper, we introduce MakerWear, a new wearable construction kit for children that uses a tangible, modular approach to wearable creation. We describe our participatory design process, the iterative development of MakerWear, and results from single- and multi-session workshops with 32 children (ages 5-12; M=8.3 years). Our findings reveal how children engage in wearable design, what they make (and want to make), and what challenges they face. As a secondary analysis, we also explore age-related differences.