This business of pooping/peeing outside the designated area isn't limited to cats (see blog entry below). My wife teaches kindergarten, and every year she has one or two kids who go in their pants.
My own experience when I was that age was a little different. I was a puker. One time in the middle of reading time, I scooted off to the side and yacked into a wad of tissues, which I stuffed back in my pocket.
You can hide the physical evidence, but not the smell. The teacher politely asked if anyone got sick, but I denied any knowledge of this alleged sickness.
I tossed my pukey wad of tissues in the trash when no one was looking.