I remember when I was in fifth grade, my math teacher was teaching us the formula of triangle area. Originally very harmonious, but the teacher suddenly said:
My first reaction was: no, it should be doubled! So I told my teacher what I thought, but the teacher still refused to admit it, and said it was twice as big, which puzzled me.
In my understanding, expanding by n times does not mean multiplying by several times. I think it should mean this: expansion means adding a certain number on the original basis, and how many times refers to n times the original number. In other words, if this number is x, the number multiplied by n times should be: X+X×n, which is X(n+ 1). Because I think multiplying by several times means increasing the number by several times on the original basis, not simply multiplying.
The above is just my guess, and I can't 100% be sure that it is correct. However, there are indeed many people who expand according to the above standards. If the expansion is how many times, it really means how many times, then how to explain our common doubling? I don't think anyone will deliberately say that it will double because the number of a certain number or an object has not changed. I hope my friends can guide me on the right path!
Do you think my inference is right or what the teacher said is right?