Every week while teaching, there will inevitably be a few moments that I see a student getting frustrated - or just plain bored - when working with a warm-up, exercise or piece of repertoire. Sometimes it's because what they're working on is at a difficulty level they feel is just beyond their reach. Sometimes they haven't done any practice. Sometimes they've just had a big ol' day and are exhausted on arrival.
Regardless, I don't think writing lessons off halfway through as not productive, not enjoyable or not important is helpful for anyone. Instead, I like to help reset the attitude, direction or general vibe of the lesson. There's not something that I've found works every time, but these are some of my favourite ways to do it:
1. Chat: If they've just finished a play-through/sing-through that wasn't great, sometimes I'll comment briefly and then, instead of giving feedback straight away, I'll just ask something about their day, or comment on something about mine. When they come back to the task they're often more focused immediately and ready for the feedback I have to give. If it feels strange starting a conversation out of nowhere, sometimes I busy myself writing something on their paper and talk while I'm doing that.
2. Make it smaller: If students can't get the whole page happening (even if they nailed it the week before), we'll try half a page. Or a single phrase. Or a bar. Or two beats of a bar. Whatever they can master, we'll do that and I'll let them play it way more times than they need to - and build it back up from there.
3. Move on (and come back): I usually have a few 'projects' I'm working on with students at a time - which means I may shift the lesson to work on for example three things in sequence (task 1, task 2, task 3, back to task 1, task 2, task 3). This halves the time students need to sit with the same task at once but doesn't diminish how much time they spend overall in the lesson, which is sometimes easier if they're having an impatient or fidgety day.
4. Leave them to it: I am sometimes the problem. Playing with my students, sitting and watching them, encouraging comments, are sometimes ALL MAKING THINGS WORSE. Confusing them. Making them more annoyed with themselves. It's ironic but 100% true. Sometimes the best thing I can do for my students is go away, stop talking and simply say "I'll give you a few minutes to just practice. Let me know if you want help." This has helped instantly lots of times for me.
5. Improv - always, improv: For vocals I wouldn't really use this one much, but on both guitar and piano (and I imagine any other instrument too) - it's a dream to shake out negativity mid-lesson. I love improvisation as a tool in general and will write about it in more detail at some stage, but even just improvising with one scale, five notes, two notes, ONE note, with a cool backing track or duet part played by a teacher is like playtime. There's no mistakes, no book to read and technique-wise, it's usually below the level they need to play if they're practicing a prepared piece.
++ I also have lessons where no amount of coaxing, jokes, questions or activities will work - but they're VERY few and far between. All I know how to do in these cases is be light, kind and ask questions as I usually would. If anyone's got any other suggestions they're much appreciated!
++ Overhauling lesson content for students who are becoming generally disengaged with lessons is a different issue, with its own intricacies, and not the intended focus of this advice :)