Many modern machine learning approaches require vast amounts of training data to learn new concepts; conversely, human learning often requires few examples--sometimes only one--from which the learner can abstract structural concepts. We present a novel approach to introducing new spatial structures to an AI agent, combining deep learning over qualitative spatial relations with various heuristic search algorithms. The agent extracts spatial relations from a sparse set of noisy examples of block-based structures, and trains convolutional and sequential models of those relation sets. To create novel examples of similar structures, the agent begins placing blocks on a virtual table, uses a CNN to predict the most similar complete example structure after each placement, an LSTM to predict the most likely set of remaining moves needed to complete it, and recommends one using heuristic search. We verify that the agent learned the concept by observing its virtual block-building activities, wherein it ranks each potential subsequent action toward building its learned concept. We empirically assess this approach with human participants' ratings of the block structures. Initial results and qualitative evaluations of structures generated by the trained agent show where it has generalized concepts from the training data, which heuristics perform best within the search space, and how we might improve learning and execution.