An appreciation of experimental design is an important aspect of introductory statistics teaching in a wide range of applied disciplines, including medical statistics. Understanding the impact of design decisions on the choice of analysis method and subsequent interpretation of results can help to embed the importance of statistical thinking in the experimental process. I discuss an interactive exercise, based on R.A. Fisher's celebrated "Lady Tasting Tea" experiment, that is intended to raise awareness of design issues as part of an undergraduate statistics module. The exercise used a discovery approach, with students encouraged to identify design issues and agree on solutions themselves via small group discussion, with only low-level prompting from the instructor. The value of this teaching style and possible extensions of the tea-tasting experiment to other related topics suitable for more widespread use are also discussed.