One time I was running a programming practical class. One of the students came up to me and said 'my computer isn't working'. I asked him to show me what was happening. Each time he ran his program it exited with an error message. I asked him to show me the program. It was something of a revelation to him that the problem might be his program. Anyway, I found the offending line quite quickly, he was dividing by zero.
I said 'there's your problem'.
He looked at it and said 'There's nothing wrong'.
I said look harder, he looked blankly, so I asked him what would be the value of the two variables. He correctly worked out that the divisor would be zero, but still couldn't see the problem.
'What do you get when you divide a number by zero?' I asked. Again, that blank look.
I asked him what you got when you divided 1 by 1. He knew that. Divided by 0.5. He got that. He followed it down to 0.01 gives 100. I hoped he was seeing the pattern, but I took no chances.
"See, the smaller that you divide the number by, the bigger the result", I said, "so what happens when you divide a number by zero?"
He looked completely blank, the suddenly a look of revelation came over his face. I thought he had got it.
He took his calculator out of his bag and entered "1÷0=", looked at the result, and said to me with a look of triumph on his face "e".