Tracking events, registrations, activities

In an event management solution...

There are many events, each attended by many teachers. And each teacher can attend many events. So far, so good -- I created a join table called 'registration' between 'events' and 'teachers.'

Now I need to add a layer of complexity and track activities. To keep it simple, let's track meals. Each event includes several meals. Each meal will be attended by many teachers (obviously the teachers in the 'registration' table for this particular event).

I don't know where to connect up the meals so I can show the teachers eating each meal or conversly, the meals each teacher attended.

If the relationships are:

event and teachers are related through 'registrations' where event (1) > registrations < teacher (1). Do meals relate directly to events (1 event > many meals)? Should meals relate to 'registrations' which already joins events and teachers?

Neither one seems to work, at least not the ways I've tried to set them up and the bruises from beating my head against the wall are beginning to attract unwanted attention.

Would someone please point me in the right direction? I hope I’ve been clear enough that you can all follow what I’ve done. I've attached an image of the relationship graph showing my 2 possibilities.

Thanks.