Now that's one smart cat.

As for the students, I suggest a change in some classroom rules or possibly some phone calls home. Depends on what you're dealing with. Also, to look on the bright side, it's halfway to March, which means only 4 1/2 months left of them! Hopefully next year will be better? Best of luck, OP.

Middle schoolers are at that awkward middle stage between childish elementary and savage high school

Well you did say the cat is senile. It just doesn't know enough to ignore you like the kids do.

Tell them that. Maybe they'll get the hint.

At least you have a well-behaved cat

Sounds like it time to go major Payne on those kids. Start by shaving their heads and see if they behave ( I'm kidding I thought that was funny to do to the kids in the movie).

Teachers, at least teachers in the US anyway, should get paid a lot more than they do. The crap they endure is almost on par with that of cops or prison guards, with the added risk of ignorant and unruly parents or the kids just making shit up about them that can ruin their lives, true or not. I respect the hell out of anyone with the patience to run four or five classes a day and not finish Friday afternoon by picking the worst one of them up by the ankles and using that one to beat the shit out of the rest of them. You're a teacher? You're a badass. Let no one say otherwise.

My sister insists that if you talk softly they will have to quiet down and listen hard (focus) to hear you. If they don't hear you and do as told/asked, there are consequences. ("it's your responsibility to pay attention and know what the rules/request/assignments/etc. Next time you'll make sure to hear me". Shouldn't take more than a couple of times and most will be "trained".

Try asking them what would engage them. I have teachers that just give lectures, and pass out worksheets. Try not to be them.