With all this discussion of multiplication and division, I have begun to wonder which of the two operations "comes first".
Now, I understand that, in most classrooms, division tends to be taught only after teachers are confident that most students have demonstrated some understanding of multiplication. I also understand that, in the algorithms, division is often more "technically" challenging to "master" than is multiplication.
But what about in real life? I can picture a young child sharing something (such as m&ms) with friends. In the process of sharing, the child is demonstrating an ability to divide. I *think* this is a very common thing for young children to do. However, I'm having difficulty thinking of activities that the same child might do that would indicate an understanding of multiplication.
In other words, it just might be that, outside of school students encounter division before multiplication. But in school, they typically encounter the operations the other way around.
Unfortunately, my experience with the activities of young children outside the classroom is very limited. So, I would invite those with more experience to give me some examples where young children engage in activities that would demonstrate at least a basic knowledge of multiplication outside the classroom.