much / many / a lot of / lots of
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This is something I have to teach very often.. A subject that has to be taught at the same time as countable vs. uncountable nouns.
In general one can say that you use 'much' for uncountable nouns and 'many' for plural countable nouns. 'A lot of' and 'lots of' can be used for either.
However, the situation is a little bit more complex than this. You have to take into account if the sentence is positive or negative, or if it's a question.
This leads to the following table:
Plural countable nouns
Affirmative:
I have many books.
I have a lot of books.
I have lots of books.
Negative:
I don't have many books.
I don't have a lot of books.
I don't have lots of books.
Question:
Do you have many books?
Do you have a lot of books?
Do you have lots of books?
Uncountable nouns
Question:
Do you have much time?
Do you have a lot of time?
Do you have lots of time?
Affirmative:
I have much time.
I have a lot of time.
I have lots of time.
Negative:
I don't have much time.
I don't have a lot of time.
I don't have lots of time.