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Design is a distinct discipline with its own practices, tools, professions, and areas of scholarship. However, practitioners from other fields often leverage aspects of design in their own work, leading to subfields like engineering design and architecture design that are neither wholly design nor wholly the intersecting discipline. Similarly, design and computing are known to intersect in educational contexts. Unfortunately, we do not yet have a clear understanding of how to characterize the kinds of design that may accompany computing topics, resulting in challenges to teaching and learning. This gap is particularly prevalent in K-12 computing education, where design is often used to promote student engagement but rarely studied as its own disciplinary phenomenon. Toward the goal of better understanding the nature and role of design in computing education, this article motivates and describes two qualitative, exploratory analyses of how design skills manifest in popular K-12 computing education curricula and activities. We find evidence to suggest two types of design within existing computing education curricula and standards: nondisciplinary "problem-space design," which deals with defining software requirements, and disciplinary "program-space design," which deals with choosing how best to meet those requirements. We find that these two types of computing design may exist independently, but they often overlap, creating an intriguing intersection of discipline-specific computing design educational activity. Finally, we discuss the practical implications of proceeding with research and educational practice in light of these results, highlighting the need for further exploration into the unique overlap of design and computing education.