As you know, I advocate for the teacher to have their ukulele amplified, if possible.  Of course, buying an electric ukulele is not always your best option - you'll pay a premium for that added pickup, and you really want it to sound best acoustic.  

Never fear, though...run to your local dollar store and buy that door alarm for a dollar, and you're on your way to making your own pickup!  The first video below is a quick demonstration & "summary" video with lots of sped-up video so you get the general idea.  A more complete tutorial is below that if you want to sit through that whole thing!

I generally recommend that a teacher have an acoustic-electric ukulele to teach with. It makes it easier for the students to follow you when you are playing as a class.

Many of us didn't purchase an electric as their first instrument, however.  Truly, this is probably a good thing for most of us, since you'll probably get a better instrument at the same price point if it doesn't have a pickup installed already.

In a pinch, you can put a pickup in your ukulele with a little (and I mean a LITTLE) craftiness and less than $5. All you need is a $1 door alarm from the dollar store of your choice (plus you get 3 of those little batteries your kids' hex bugs eat for breakfast!), a little soldering know-how (or have a friend, colleague, or music parent you can con...er...persuade to assist), a bit of wire, and an input jack. There's some a sundry items most can find laying around the house, too, but I'll give a more detailed tutorial later. (A bit of searching online can find the basics, especially at cigarboxnation.com, but you have to do some wading around to find the information you want...) 

Here's a basic video more to show that it CAN be done, rather than HOW to do it.  I'll put up a blog post of how to do it as soon as I find an instrument to do it to! (If for no other reason than there's  a misspelled word in this video, and it makes me twitch every time I see it!)