subject verb agreement - The number of books in economics that we need to buy (is/are) three

1) The number of books in economics that we need to buy (is/are) three.

or

2) A number of books in economics that we can buy for the course (is/are) available in the college book store.

Possible answers: a)is b)are

My approach:

I am confused here why is and are are used in the 1 and 2 sentence.

What they exactly mean according to subject verb agreement rules.