Relationships between mathematical giftedness and mathematical creativity have been widely studied, but few studies are available for primary school age. For an investigation in this age group, it seems appropriate to use a content area that not only has high relevance for mathematics and special potentials for creativity, but also requires only a little knowledge and is easily accessible. We therefore investigated whether mathematically gifted primary school students differ from non-gifted ones in high creativity in dealing with mathematical patterns and structures. This question was explored in an interview study in which 24 third graders were asked to invent as many different figural patterns as possible, which enabled creative mathematical activity also by combining arithmetic and geometric aspects. A detailed qualitative analysis of the data revealed among other results several types of flexibility concerning the invention of patterns. The selection of students ensured that all participants performed well to very well in regular mathematics classes and that 14 of them could additionally be assumed to be mathematically gifted based on a specific test. This allowed a comparison of both subgroups. Results indicate a high correspondence between mathematical giftedness and mathematical creativity concerning the invention of figural patterns.