[Grammar] number, singular or plural

[sitifan]

1. A small number of children are educated at home.
2. A large number of invitations has been sent.
https://dictionary.cambridge.org/dictionary/english/number
In the above example sentences, #1 is plural, but #2 is singular. Why?

 

[tedmc]

I think the singular is used if the focus is on the number and the plural if the focus is on the subject.

 

[Tdol]

I'd honestly use the plural in both.

 

[Raymott]

I'd use 'are'. You need to follow the sense in these constructions. Sometimes it can go either way.
What's the small number? 5? So, "five children are ..." or "Five children is ..."
No one where I live would use the singular.