someone had better/I'd better/you'd better and so on

[yes.one]

I need some help on finding the best way to show my students that when I say You'd better leave now, that is the contraction of had and not would as they tought. I believe saying it would be better for you to leave or you'd better leave is the same , is that correct? And how can I explain them that?
PS: They all speak Portuguese.

[Tdol]

It's such a strange expression, that it's just a matter of learning it and being aware that it is tested with tedious frequency in exams. It has a meaning similar to that you say, but might that not reinforce their incorrect idea. Why not say it's like a strong form of 'should'?

[jahlove]

the last time i visited this site i came across a test called"test your crazy people vocabulary"now i really need it ,i don t know where to find it again.
could anyone help me. i promised to work on it with my students.
now i don t know what to do.

please helpe me.

jahlove