Every school is different - and every class is different.

I had some classes in middle school which were horrible - I also had same horrible classes in high school - but there were also some excellent classes at all levels.  I would say that students' discipline is most consistent at the elementary schools and after that it's a bit closer to a lottery. 

By the way, have you tried sleeping elephants?  It requires students to be quiet - and also work in groups after they 'wake up' - I've never tried it at the high school level (didn't know this game back then), but I imagine it should work quite well.

How big is your class anyways?

One game which always worked in high school - even in the horrible classes - 'guess the celebrity'.  It consisted of me picking a card with celebrity's picture.  Students had to ask questions 'is it a woman/man; is he/she American/Korean/Chinese; is he/she a singer/actor/etc; is he/she beautiful/tall/etc....

After I'd play this game with the whole class, I'd give same cards to students in groups - and they'd do the same thing amongst each other.  But yeah - that's just one game.

You need to find an activity for every English skill.  For example, sleeping elephants/find a mistake/ for reading/writing (you need to give white board/marker to each group for these).  Elimination game for reading (get the template with sounds - but this activity doesn't always work).  Charades for speaking/reading (I've recently uploaded a template for that - it's very good - works in groups).  For listening - try snatch game or cowboy game - they are really good.

There is no doubt that for teaching numbers, there is nothing better than the nintendo DS 'brain academy' it has 2 great activities - one is count the boxes (it's harder than it sounds and is great for students who cannot read) and calculate the answer (the questions are written in English 'one plus one is', seven times seven is' etc) (btw - when it comes to the DS brain academy, they have one minute to come up with as many answers as they can).  BTW - I've already written about this nintendo DS bit here - and how to get it working on computer a while back.

Also try to engage their interests - get them to review their favorite movie/game/book.  I've also done a bit on music - showed them videos of different music genres (rap/hip hop/rock/classical/etc) and got them to talk about their favorite singers and describe their music style. 

Have you tried K-pop quiz?  There were bunch of k-pop quizes here - and they featured tons of k-pop video bits - although I think k-pop quiz is a waste of time in terms of educational value, it does get students' attention. 

Otherwise,you can also use horror themes, because students do like those.  When teaching directions, I'd use scary maze.  At first students didn't know what it was, and the initial reaction was good.
There's also a pretty cool 'horror adventure' template here -


In each case, I made it clear that they had to use English in order for us to continue with the game/activity. 

Games is probably the way that I would go.

Maybe do something with music videos. Have the lyrics on a PPT, and the students need to fill in the blank.

A "What happens next?" quiz.

The Price is Right game.

http://lyricstraining.com/

Great website for getting the kids to do 'fill in the blanks' to English songs.

I split the kids into teams of 4, each team has a whiteboard / marker / eraser. Play each line twice, then get them to show their answers. I've not used it many times, but each time I have it has worked well.

If you do use it, be sure to check that the lyrics are school friendly before doing so.

My students had a great time playing the speed quiz game last week (it's basically hot seat, but the students are familiar with the name speed quiz). There are a number of versions here on waygook, for example: http://www.waygook.org/index.php?topic=58356.0
However, you can easily make your own using pictures and whatever words or expressions you want the students to use.

I split the class into 3 teams (~6 people each) and gave them 1-2 minutes per turn depending on whether they were doing speaking only, actions only, or both (I made each round of turns different). I also had them change the player in the 'hot seat' after each correct answer. All of the students, from high level to low level, really enjoyed it, especially during the action only round because it completely leveled the playing field and was also hilarious to watch!

I've also had success with my lower classes using the K-pop twist game, k-pop slam (lyrics) game, and the guess the celebrity game that someone else mentioned earlier (I demo one or two with the whole class, and then tape a celebrity name on each student's back for them to try playing - some class favourites were Park Geun Hye, Hello Kitty, Pororo, and cast members from Infinity Challenge and Running Man).

The comment about your class having a contribution to their final grade is good. In my high school class I get the students to do a project towards their final grade. They have about 10 options to choose from so can always find something that they find interesting. You can make the ideas practical and interesting, like cooking in English or singing an English song. Students can work on their project every other or every third week and present it at the end of their semester.

Produce a detailed plan with the benefits for your co-teacher to see. In my school the work is presented around school so looks good on the English department.

I used to work in one of the worst high schools in Korea. When students dropped out and come back they came there. When other schools kicked them out, they came there. If a teacher was caught with a DUI the punishment was they had to go teach there!  I spend a year there and the suggestion of move the two or 3 that care up front and ingore the rest is what I did. In the classes where no on cared, I tutored my co teacher and let them have at it. Eventually the students  started downloading English movies and bringing them to class. It was a great gig!  I miss it.