<p>One approach to inquiry-based science learning has emphasized hands-on engineering design projects that encourage open-ended exploration, tinkering and building. Another involves more structured scientific inquiry activities where students make predictions, observe experimental results, and interpret and explain those results. Little is known about whether learning from open-ended engineering activities and from scientific inquiry support each other and, if so, in which directions. Should students do open-ended engineering to motivate their scientific inquiry and/or should they do scientific inquiry as preparation for more effective open-ended engineering? We explored this question of transfer between open-ended engineering and scientific inquiry activities in the context of an AI mixed-reality system. Our results reveal that learning from scientific inquiry activities transfers to learning on engineering activities but not the other way around. Children who engage in scientific inquiry first, produce better engineering outcomes later on and also engage in more relevant scientific conversations during engineering activities than students who start with open-ended engineering. In contrast, children who engage in open-ended engineering first do not produce better scientific inquiry or conversations later. These results suggest that science curricula may better enhance Science, Technology, Engineering and Math (STEM) outcomes if they sequence scientific inquiry activities before open-ended engineering activities, encouraging transfer of scientific principles learned from guided inquiry to use during engineering.</p>