"There is a number of" versus "There are a number of"

As a native speaker, this sounds correct:

There are a number of cows in that field.

whilst this sounds totally wrong:

There is a number of cows in the field.

But arguably the second form might be technically correct, because "a" indicates "a number" is singular.

Some examples support this hypothesis: "There is a collection of cows in that field."

Whilst others contradict it: "There are a lot of cows in that field."

Can you confirm which is correct, and is there a good justification which can be generalised to other situations?