An important aspect of a memory is whether it is representing a specific event or whether it is a representation of knowledge extracted over multiple episodes. To investigate this difference, we developed a new multi-trial behavioral task that can assess memory accumulation in rodents. It makes use of rodents' innate drive to explore novelty and allows for later recordings (e.g. electrophysiology) and interventions. The task consists of three distinct conditions (stable, overlapping, random) that can be repeated within animals. Rodents are exposed to multiple sample trials, in which they explore objects in specific spatial arrangements. In the stable condition, the locations are constant during all sample trials, and one object's location changes during test. In the random condition, object locations are presented without a specific spatial pattern. In the overlapping condition, one location is shared (overlapping) between all trials while the other location changes during sample trials. We show that in the overlapping condition, instead of only remembering the last sample trial, rodents form a cumulative memory of the sample trials. We adapted the task so that it can be learned by both rats and mice, making it suitable for investigating this aspect of memory across species and using a wide array of methods to measure and perturb the neural basis of memory.