Cognitive alertness decreases at night due to circadian rhythms with adverse effects on performance across domains and tasks, including real-world tasks like driving and flying. Additionally, the strategy used on a task may have a substantial effect on performance. However, little is known about whether and how circadian rhythms and strategy interact to affect performance. The current study investigates participants performance on an orientation task performed over a period of two weeks. Participants were assigned to simulated day or night shift conditions, and were trained to use one of two strategies for the orientation task. The results indicated that shift condition had little impact on a more declarative strategy for the task, but had a significant impact on a more spatial strategy. The results illustrate how different aspects of cognitive functioning may be affected differently by circadian rhythms, and point to some important implications for training and task performance in real-world contexts.