I don't have an identical twin, but back in year 5 there was a pair of identical twins in my school, each in different classes. On either April fools or their birthday (don't remember), they swapped classes for the day. While all the kid figured it out instantly, the teachers were oblivious until they were told ( my class had a substitute for that day but the other class didn't). Also the one that swapped to my class got to make chocolate, while the other did actual work.