If your students are past caring about learning grammar, why not introduce one of Tim Bowen's word grammar articles to spice up a lesson?

Apart from its functions as a noun and an adjective, the word past has two other functions - as a preposition and as an adverb. As a preposition, it is used to mean 'after a particular time', as in 'It was past midnight by the time we arrived', and 'passing a person, place or thing', as in 'The thieves somehow got past all the alarms' or 'A policeman walked past'. It can also be used to mean 'further away than a particular place' in a similar way to after, as in 'Turn right a mile past the graveyard and you’ll see the church', and 'looking towards a point behind someone or something', as in 'I tried to catch his eye, but he stared right past me'. It can also be used to say that someone or something has passed a particular stage or point, as in 'He was past his prime as a player by then' or 'Unlike my sisters, I never got past the sixth grade at school'.

Past can also be used to say that your feelings have changed in such a way that you no longer think about something: 'I used to worry about him coming home late but now I’m past caring'. As an adverb, past is used to refer to time passing, as in 'The months went past and still no word from her or movement'. Past is also used in a couple of idiomatic expressions. If you are past it, you are no longer able to do what you used to do because you are too old, and if you wouldn’t put it past someone (to do something), you think they are capable of doing something bad, as in 'I wouldn’t put it past him to come up with a crazy stunt like that'.