I think I'd need to see the context, but neither of them sounds natural. Without any other information, I'd say "the number of construction sites."

I don't think you need a quantifier to describe the 'number of sites'. you could rather express it this way: "there are six construction sites all in all." "the total construction sites to be excavated within the month would be six." or: "there are LOTS of construction sites to be excavated." :)

Amount or Quantity is used when talking about a total that can be added to (or subtracted from). Think of a pile of coffee or beans or rice. Quantity (but not Amount) is also used when you are talking about a number of items, each one of which can be considered as a whole or complete thing. So you could have a quantity of sites, but not an amount of sites. To help remember, think of a pile or a MOUNTain of coffee or rice. You can add to or subtract from this aMOUNT.

3. a number of construction sites. To use "amount" or "quantity" you need another word: a large amount; a large quantity; a small quantity; a small amount; etc