You can create multiple announcements and have them sent to different classrooms, but to have them sent at different times you would need to create one announcement at a time and specify the date and time for each one.
Below are the steps for creating announcements and multiple announcements for various classrooms and adding a Google Document to an announcement.
First, watch this helpful video showing you how to create an announcement:
This video shows you how to create multiple announcements for various classrooms:
You can even attach documents from your Google Drive to your announcements:
NOTE: All documents uploaded via Google Drive will also be added in the "Library" with an option to filter these documents only.