You might want to wear cute teaching attire, like melodias and a tie top, and some funky earrings.
Don't be a stickler for technique, of course . Maybe have them do some sort of stupid little contest or game at the end - women at my parties always like to see who can outshimmy one another. If you have hip scarves, bindis or whatever to give out as a "swag bag" to the winner, even better!
If you're not doing a performance along with the mini lesson, I'd just wear slightly glammed up class wear. Make sure your hair and makeup look nice, but not stage worthy. Wear a cute top, some good yoga/dance pants and a pretty hip scarf. Add some dangly earrings and maybe a necklace or bracelet.
As for making it fun, I think if I knew nothing about dance and was getting a private mini lesson at a party I'd probably want to come out of that with something "put together." A super simple combo set to music will make your clients feel like they accomplished something they can show off to other friends.
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I do a lot of these types of gigs. Really like them. Here's what I usually do it:
Go in costume. Depending on the venue, maybe not your best but a nice one.
Make a 30 minute CD starting with a song to perform to, followed with music to teach to. I like to use Egyptian pop for this because the rhythm is pretty consistant throughout.
At the Venue:
Do an upbeat 3-5 minute routine
Teach them 3 or 4 basic moves (keep it bubbly and fun)
Teach them a short routine based on what you showed them. Repeat a few times. Hurray you did it!
Smooches -thanks -hand out your business cards -collect fee -go home.
I do this somethimes for bachelorette parties.
A fun thing to do at the end is dance in a circle and have them show each other what they've learned (the others copy)
And of course the partypig (I'm sorry don't know if you say it like this in english lol) gets extra time to shine in the circle ;-)
No performance but teach in costume? They just want to see a costume up close, I guess. As long as you don't mind getting in full regalia & are charging appropriately for it, why not? Be prepared, however, in case they ask you to perform anyway since you'll be in costume. Oh, and make sure the goodie/prize bag is built into your price, too.
Teach a few basic moves, then show how to combo a couple. Then put those movements & couple of combos to music so they can do a little dance. End party game could be best shimmy contest, award the prize (or if you have one 'big' item give that out & everyone else gets a bindi so then everyone's a winner yay), kisses you're all the best evah here's my card you should sooo come take lessons from me, collect $$ & bye bye.
30mins goes by *fast* so try to have it all down pat before you get there & keep whatever you teach simple & short. It'll be great
Like everyone else said, keep it very light and fun. Teach good technique but don't be a stickler or the 30 minutes will be gone before you've even taught a single move. Don't bother correcting too much unless they either a) aren't even in the neighborhood of the move or b) are doing something that could cause injury.
If you teach regular classes, make sure you bring lots of cards and mention that if they thought this little taste is fun, they should think about taking a whole session. I've actually gotten several students from these types of parties - some of them get hooked right away!
When I'm booked for a full performance/mini-lesson package in costume, I change into pants that match my bedlah or bra in between the performance and the lesson. I prefer not to teach in a skirt because I'm constantly having to pull it up so they can see my legs and feet.