Quantifiers

Your question is more complex than it appears at first glance, and it is always best to address these issues with a complete sentence -- not a fragment. Let's assume your first phrase is used in the following sentence -- A large number of students are failing English grammar.

We quickly discover that this is an exception to the general rule regarding subject-verb number agreement. In this sentence, large is an adjective modifying the sentence subject. Normally, the general rule says that number is the subject and of students is a prepositional adjective phrase that modifies number. Under the general rule, since number is singular (numbers is the plural), the verb should be the singular is. But that is not the case with a number of phrases. In an exception to the general rule, we must view the subject as the entire noun phrase number of students. Because the noun phrae is plural, we use the plural verb are. This exception follows a linguistic principle called synesis, which allows some contructions to contro properties such as number according to their meaning rather than strict syntactical rules. Garner's Modern American Usage (Oxford University Press, 2009) includes a very interesting discussion of this issue.

Okay, lets change the sentence to -- The large number of students planning to attend the concert is worrying for its organizers. When number of is preceeded by the definite article the, everything changes. We go back to the general rule and the verb must be singular to agree with the singular number.

Although Garner's does not specifically address a lot of, the British usage bible upon which Garner's is based  -- Fowler's Modern English Usage (Oxford University Press, 2004) -- puts the phrase in the same category as a number of.

A lot of this material is confusing. A lot of these memos are confusing.

Remember, these are exceptions to the general rule.

Thanks Jeff. Very comprehensive and clear. I posed this question because some grammar checkers like 'Ginger' accepted as grammatically correct the following sentences:

1.   There is a large number of birds in the park.

2.   There are a large number of birds in the park.

My studies have convinced me that most grammar experts are a bunch of intellectual snobs who look for ANY excuse to change or deny the rules! Also they use dirty tricks to 'prove' their point, such as comparing one example with a 'no count' noun to another using a 'countable' noun. "It sounds funny" is no excuse! The power of English allows you to rephrase until it IS right and it SOUNDS right.