I'm not sure if it matters, but you may need to alter the sequence of joins to something like the following, so that you are not starting out the joins by trying to join two tables that have not yet been referenced in any way.
SELECT COUNT (*) AS c
FROM ChildAssignments
JOIN NoticeChild ON NoticeChild.Children_Id=ChildAssignments.Child_Id
JOIN Notices ON Notices.Id=NoticeChild.Notices_Id
JOIN Locations ON ChildAssignments.Location_Id=Locations.Id
WHERE Child_Id=NULL