(Actually, I often heard The William Tell Overture, too, which was the theme tune to the TV programme The Lone Ranger. But at the time I wasn't aware it was classical music.)
I suppose Sheep May Safely Graze was thought by the school authorities to be soothing.
It's probably a good piece of music - it's by a composer of colossal, almost super-human, power - but even now it fills my head with cotton wool and uneasy despair.*
Anyway, grazing. Do-it-yourself grazing will involve eating snacks all day, and grazing animals means keeping them somewhere where they can constantly eat grass.
In the USA grazing can mean eating food in a supermarket without paying for it, and in South Africa it can mean just plain eating (in South Africa a graze is a snack or informal meal).
If you graze TV Channels you're watching lots, but none of them for very long.
The image of animals gently shortening grass has given us the other meaning of graze, meaning to scrape against something with just enough force to harm its surface. It often involves young knees and tarmac, but bullets (at least in fiction) have a habit of grazing things, too.
I suppose being a sheep safely grazing sounds idyllic: but it's not for me.
The Lone Ranger did more good, after all - and he certainly had more fun.
Thing Probably Not To Do Today: graze. This word comes from the Old English grasian, from græs, grass.
*I fear the process of education has always involved discouraging original thought. Or even thought at all.