Invite x Invitation

[Raymott]

"But in this case, my teacher changed for "invitation", not "inviting" :( "

Isn't the context an exam in which the OP was marked (apparently) incorrectly?
People can say 'invite' for 'invitation'. This sort of slang comes and goes, but 'invitation' will always - for the foreseeable future - be the correct noun; and the correct answer if given a choice between 'invite' and 'invitation' in an exam.
In fact, I'm not sure that there is a context in which 'an invite' would be better than 'an invitation.'

[shannico]

As a non-native speaker I felt my addition to what had already been said and written was needed. I also thought its premise was clear enough in saying that a word like invite depends on the context it's being used.

Fair enough invite is a verb, but learners shouldn't be surprised if they happen to hear or read "Thanks for your invite!".
As a teacher I think it's helpful to broaden learners views on different usages of the same word. That doesn't necessarily mean encouraging them to use ungrammatical expressions.
If anything I'd be delighted if a student of mine wrote on a quick note to a friend "Thanks for your invite!" and "Thank you for your invitation" in a thank-you card to their friend's mum. That would mean not only were they smart enough to know the difference between a verb and a noun, but they brought it even to a higher level: they understood various pragmatic usages of the same word.

p.s. BTW I looked up ain't on Dictionary.com and its usage is regarded as non-standard, which is very different to informal.
http://dictionary.reference.com/browse/ain't

[Raymott]

As a non-native speaker I felt my addition to what had already been said and written was needed. I also thought its premise was clear enough in saying that a word like invite depends on the context it's being used.

Fair enough invite is a verb, but learners shouldn't be surprised if they happen to hear or read "Thanks for your invite!".
As a teacher I think it's helpful to broaden learners views on different usages of the same word. That doesn't necessarily mean encouraging them to use ungrammatical expressions.
If anything I'd be delighted if a student of mine wrote on a quick note to a friend "Thanks for your invite!" and "Thank you for your invitation" to their friend's mum. That would mean not only were they smart enough to know the difference between a verb and a noun, but they brought it even to a higher level: they understood various pragmatic usages of the same word.

Yes, I don't want to argue with you over this. In Australia, our uptake of American (or British) novelties like this has a lag time of about 5 years. It's quite possible that there are enclaves throughout the world that use "invite" as a noun. But there remain many places in which it would be considered 'wrong'.
However, in no place at all in the English-speaking world is "an invitation" wrong. That's what (to me) makes it more correct. As another example, in AusE we don't generally use "gifting" as a verb. This is something that might or might not catch on.

There are some words which are in "the dictionary" simply because a minority of people use them that way, and the dictionaries are descriptive. If they're labelled informal, that probably means that these usages won't be understood or used everywhere in the English-speaking world. That is, they are not 'informal' everywhere. In some places they might have a formal status, and in others, they might not even be recognised as being correct at all.
I would interpret informal (in this case, and others I've notived) to mean "not used universally", rather than "used universally in an informal context".

I have noticed in learning Spanish that some words are used everywhere, and some are regional, or informal (but only in Mexico, for example). I'd like to think that the Spanish courses I'm doing are teaching me generally used words, unless thay are labelled as transient, trendy, regional, etc.

By the way, Australian novelty words take longer to reach the American dictionaries, but they occur too.

[shannico]

Neither do I want to argue. I was only giving my opinion from a different perspective: a non-native English teacher perspective.
Still, I don't think that the informal label in a dictionary is meant to indicate a local usage of a word.

informal:
1. not of a formal, official, or stiffly conventional nature: an informal luncheon
2. appropriate to everyday life or use: informal clothes
3. denoting or characterized by idiom, vocabulary, etc, appropriate to everyday conversational language rather than to formal written language
4. denoting a second-person pronoun in some languages used when the addressee is regarded as a friend or social inferior: In French the pronoun "tu" is informal, while "vous" is formal

Informal | Define Informal at Dictionary.com

Always a pleasure "arguing" with you!

[Raymott]

Neither do I want to argue. I was only giving my opinion from a different perspective: a non-native English teacher perspective.
Still, I don't think that the informal label in a dictionary is meant to indicate a local usage of a word.

informal:
1. not of a formal, official, or stiffly conventional nature: an informal luncheon
2. appropriate to everyday life or use: informal clothes
3. denoting or characterized by idiom, vocabulary, etc, appropriate to everyday conversational language rather than to formal written language
4. denoting a second-person pronoun in some languages used when the addressee is regarded as a friend or social inferior: In French the pronoun "tu" is informal, while "vous" is formal

Informal | Define Informal at Dictionary.com

Always a pleasure "arguing" with you!

Yes, I know what "informal" means. What I question is whether this is the best descriptor for these newly-formed and possibly ephemeral words. Maybe "experimental" would be better, or something that means "not quite integrated into the mainstream yet".