Number - Singular or Plural

Question

The  number  of toxins in the world's five oceans  is  increasing even more rapidly than even the most concerned researchers predicted.

^number is singular here

A  number  of my friends  are  going the movies.

^number is plural

I know that notional agreements exist here, however why is "number" plural in the 2nd sentence even though it is uncountable.

elegantm · Answer

Just remember, "The Number" is considered SINGULAR & "A Number" is considered PLURAL,

mansianand1234 · Answer

will there be any case when 'the number of X' is considered a plural subject 
and
a number of X : a singular subject?

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