Teaching is greatly about helping students to learn—by, for instance, sparking curiosity, fuelling imagination, and demonstrating relevance. We present material on number systems for catching and sustaining the attention of older pupils. This consists of a survey of the current legacies from various systems used historically, and some examples of how an understanding of number systems can aid in problem solving. The article offers a general appreciation of number‐systems, and concludes by introducing some basic results from number theory.