Young children in the United States are widely using technology at ages 3 and 4, but to date there are no well documented participatory design methods for including this age group in the development of technologies. A few attempts at using methods designed for older children were unsuccessful. To address this gap in methods, this research developed Play-based Design, a novel participatory design method inspired by make-believe play in the style of Tools of the Mind, an evidence-based preschool curriculum. Play-based Design first sets the context for play and design through stories. It then enables children to plan play by selecting roles and contribute their ideas as they act and speak during make-believe play activities in which they interact with other children, voice agents, adult facilitators, and generic props. This research includes four sets of design sessions with 3-4 year old children. The first provided the design of StoryCarnival a web-based app to set up Tools of the Mind style play. The second set of design sessions led my research team through the development of voice agents to support Tools of the Mind style play as it happens. These two sets of sessions provided inspiration and insight for using StoryCarnival combined with voice agents to support design activities for technologies with physical and social components. The last two sets of sessions gave me an opportunity to understand whether Play-based Design could be applied to obtain design requirements from children for technology unrelated to make-believe play by focusing on obtaining ideas for Internet-of-Things applications in the home. The research presented in this dissertation required an interdisciplinary journey through child development theories, storytelling for children, graphic design, qualitative methods, software development, and related approaches from the literature. Participant observations, group discussions, and video analysis were used to collect and analyze data. Results from the last two sets of design sessions focused on obtaining ideas for Internet-of-Things technologies to provide evidence that Play-based Design can enable 3-4 year old children to contribute their ideas to the design of technologies. More specifically, in this dissertation, I provide supporting evidence for my thesis statement: “When applied to participatory design sessions with young children, Play-based Design can: (1) allow young children to express their ideas through make-believe play, which is a developmentally appropriate activity; (2) enable children to act out design ideas or verbally express them by conversing with researchers or voice agents; (3) support fluid communication between adult researchers and children; and (4) inform the design of technologies that facilitate activities that have social and physical components (e.g. tangible user interfaces, voice agents, IoT).”