This is actually really simple. You have, I assume, a Dynamic Distribution Group set up for the staff and one for all the pupils.
Assuming this is right:
In each of the distribution group properties, within the tab Mail Flow Setting there is a Message Delivery Restrictions option.
In delivery restrictions you can setup who can and who can't email this distribution group. So if you only want teacher to be able to send to the students then go to the student distribution group and within the delivery restrictions select the radio button for only accept messages from - Only senders in the following list, click on add and either select the teachers you would like to be able to email the students or if you would like all the teacher you can simply add the Teachers Dynamic Distribution group. This way you won't have to remember to add a new teachers individually to this list, as long as the dynamic distribution group is working. The other thing to remember is that if you only allow the teacher distribution group then people from outside won't be able to email the distribution group.
Hope this helps.