That's the generally accepted maximum ratio of students to teacher in learn to skate.
For tots it's 8 to 1; for the 3 and 4 year olds four to one.
Some municipalities base the ratio on statutory classroom ratios, some on their own metrics, and some just fill classes until no one else wants to sign up. In practice, most rinks will try to keep the ratio low, with multiple coaches on a single class.
Personally I like a higher student/teacher ratio. I find the class flows better when you have to deal with more kids. (I had 27 all by myself in a PreAlpha class once. That was a bit much.)
Multiple coaches are helpful not just to keep the student/teacher ratio reasonable, but also because if one coach can't be there on any given week due to scheduling conflicts or illness the students still get a "regular" coach rather than a sub. Back in the day, when coaching staffs were larger however, you'd sometimes get the agonizing phenomenon of 2 teachers on a class with only 4 or 5 kids.
It can be tricky to find a rhythm with a second teacher. There are rinks with rigid week-by-week syllabuses (syllabi?), but generally you're sort of making it up as you go along within the general constraints of the USFS or ISI curriculum.
So how do you "share" the class?
If I'm new to a program, or the other teacher is the 'main' teacher, I 'll let them set the stage. Just tell me what to teach, and for how long.
If I'm the main teacher, I'll sometimes tell the other teacher what to do, or just turn the class over to them for some period each week. (I'm really bad at this; I always want to jump in.)
When you've been on a staff for a while, you start to know the other coaches well enough to really develop a rhythm, and they know enough to trust you. This is the best way to share a class; where you understand each other's strengths, and know when you can jump in and when you should hold back.
Once the kids are skating, competent teachers, however many there are, will simply move from student to student and give personal advice. If I start to see common errors or questions, I'll stop the class and bring up the point for everyone to hear.
At rinks with serious student teaching programs, you get to teach the student teachers as well, letting them know when to jump in, when to help kids individually, and when to take over. I feel that from the stands, parents should not be able to distinguish student teachers from staff coaches by the level of involvement-- every coach on the ice should be engaged in the class.
Hang on, have to pick myself up off the floor, where I fell down laughing. You could actually sit down with your co-teacher and create a syllabus, although I've never seen this happen in the regular classes. (I actually do have syllabuses for every level through FS4, which I pull out mostly when I'm teaching a level I'm less familiar with, or when I have a class that's struggling.) In specialty classes like dance or power, however, this is fairly common.
Do the classes at your rink use more than one teacher per class? What successful (or failed) strategies have you used or observed?