The trading stuff is what it sounds like: they get some kind of "currency" (you can go OTT and use play money from your own country, or design your own; you can make it a little simpler and use stickers or stamps in books) based on behavior in class, and then on a regular basis they can trade it in for stuff. I used this system in a couple of different ways.
1. They filled up a paper X number of stamps and then got a random prize, like a notebook or a pencil case or something. In class, everyone would get a sticker at the end of the day unless they had been naughty. Most EFL teachers do this by putting names on the board, and I did it this way too, but these days I question the wisdom of that method. Other times, we would cross off a sticker or two, so that they had to re-earn them.
2. Everyone started class with 3 "flamingo dollars" credited towards them, which they would receive at the end of class. Misbehaving took away a dollar, doing well could earn another dollar. There were a handful of incidents where a student had to pay ME a dollar or two because they had been so poorly-behaved in class, and generally the idea of having to finish class by LOSING money kept them from acting up.
Then, once a month we would stop the lesson early and everyone would count up their "flamingo dollars." They could either buy something from me at a certain price (stickers, pencils, pencil case) or they could opt to save up for a more expensive prize (for example, being able to have a pizza lunch with me and watch a movie, instead of eating regular lunch with everyone else).
There is an opportunity for bullying/thievery to go on in certain groups, but I never saw it happen. (You might want to keep your own account, just to be sure.)
It might take some groundwork to get going---I inherited the system from another teacher and just ran with it---but it's not entirely impossible to manage on your own. When I was doing this "flamingo dollar" project, it was only with one particular class and without too much support from the school (except that they granted me the use of a spare room and DVD for the pizza lunch).
3. In the third school I used this in, I was again the recipient of a previously-existing system, except that this one was school-wide. Every teacher, not just me, handed out stickers. All of the students had their own little laminated books, with X numbers of stickers per page. They tried to earn as many as possible and then twice a year, the whole school had a market day. There were no lessons; instead, the owners went out and bought boxes and boxes of cheap snacks and prizes and trinkets and things, and the kids spent all of the school time running around and buying whatever they could afford (at the beginning of the day, the stickers were traded in for play currency, to make shopping easier). It worked really well, but it's just impossible to have something that huge without the support of the school.
So there are a lot of ways to do it. I know other people who hand out prizes more frequently (and using points instead of currency), like every class, but that's because they're "visiting teachers" who only get one or two 20-minute classes with a particular group every week, and it's hard to manage long-term plans with small children when they see you that infrequently.
For me it would also depend on the whole context: what's the environment like in the whole school? are there are other classes they're freaking out about? are they talking about schoolwork from other classes or just chitchatting? is it getting in the way of accomplishing the task you've set for them? is the task at hand too challenging/not challenging enough? There are a lot of reasons young students don't focus on the task at hand, so it's hard to recommend a particular answer.
The other thing I did a lot was enforce a "No L1 (in this case, it was Korean)" rule. Not because I have any beef with mixing L1 and L2, but in some classes that was the magic bullet to keep them from getting distracted. L1 was regulated to a tool to use sparingly, usually to explain the rules of a game, and that was it. I didn't have to do it in every class---it depended on the group and whether they were prone to getting sidetracked or not.
If you're not playing any TPR/get up and move type games, you might want to try that. Not for a whole class, but as a break to get the wiggles out. There's a lot of simple ways to do that:
1. Split the board into 2+ sections (however many teams you want to have). Write unit/review vocabulary in each section (make sure each section has all of the same words); each team has one section and every round, you read one of the words. A representative from each team has to run and erase the right answer; first gets a point. You can make this more challenging and check for comprehension by describing the target word instead of just reading it. (You could even godmode and say the word in L1, if you know it, but that's a tricky gambit.)
2. The same, but instead the students run to the board and write.
3. Simon Says (which I always use as "please" just to teach manners)
4. Charades. Your little divas and hams will LOVE this.
5. A coworker of mine liked to play a game he called "Ing On Under." It's just a TPR game to review verbs and teach prepositions: you call out something like "sitting on the chair" "swimming next to the window" "sleeping on the table" etc. and everyone has to do the right verb at the right place. For added funsies, you can use feelings ("angry swimming next to the window").
6. The granddaddy of all the games I played was probably One Step. It's basically a way to review: you ask a question and the student who gets it right takes one step. There were a couple different ways I played this, depending on the classroom size and layout and the number and size of my students.
6a. It's a team competition, with a race from one end of the room to the other. (Adaptable: how many times can they get from one end to the other in X amount of time?)
6b. Team competition, but instead they try to tag out the members of the other team. (Think of it as like a slow-motion team version of "Tag" where there are two teams trying to get each other out.)
6c. Free-for-all PVP: every kid for herself. (Slow-motion tag where EVERYONE is "it.") (This might not be feasible with 40 kids at once, however.)
7. If you've got plenty of flashcards, you could also do a flashcard scavenger hunt. To get the point for the card found, they have to use the word in a sentence or describe where it was. ("The dog is under the chair." and stuff like that.)
I guess all of my advice for you is GAMES!, which is not always a productive choice. They can be a big help, though, if used correctly. Otherwise, try to make assignments and language objectives related to THEM. This is the rule in language teaching generally but I think it's especially important with kids: if you give them language tools they can use to talk about themselves, or to immediately use in their lives, they will be more interested in the lesson and more likely to use it.
NB I'm not any kind of early childhood learning expert. This is borne out of my own TEFL experience, but there might be better ways.