Bicycle Mechanics - Adding Gears

Is it possible to add a 3 or 5 speed freewheel cassette to a childs single speed bike? My daughter is a small 6 year old so she rides a 16inch wheel bike, if she was bigger she would be able to ride a 20inch bike with gears. It seems a bit daft but she is getting bored of singlespeed.
I am really after information concerning the cassette and spacing as the shifter and cable routing is not a problem.
Thanks

I don't think its possible. a derailleur needs a derailleur hanger bolted or welded onto the frame. some derailleurs (like the wal-mart type shimano tourney) have a "claw" that doesn't need a hanger...that might work.

keep in mind though, you will also need to redish (center) the rear wheel if you screw a freewheel on.

all in all, it really seem like more trouble then its worth. might be an interesting project, though.

Spread the frame and add an old 3 speed hub?

I am going to answer my own question here just in case anyone else is interested.
It should be possible for the 3 speed as I have just tried a 5 that was off a surplus bike and that was just fractionally too large to fit between the dropouts by the time I added washers to the axle. The derailleur would work as it is held on by the axle nuts and a screw that fits in the dropout. I called my LBS asking about a 3 speed freewheel, but sounding rather bemused he told me they stopped using them 25 years ago. I have seen suppliers for them on the web so someone is bound to have one for sale somewhere.

Tell her singlespeed and/or fixed gear is the in thing

I have just tried a 5 that was off a surplus bike and that was just fractionally too large to fit between the dropouts by the time I added washers to the axle.

If its just a few MM, spread the frame: http://www.sheldonbrown.com/frame-spacing.html (scroll down to "Frame Spacing Adjustment").

Read about that last night but with the frame being so small I am not keen on trying it. Thanks for the suggestion though, will try and find a 3 speed freewheel this week.

If that doesn't work, look around for a decent used bike. In the spring, I found a 10-year-old "mountain bike" on 20" wheels that had a 14" frame only. It used a wide 5-speed freewheel, but I replaced it with a 7-speed freewheel I had from a defunct bike so she could have lower gears. The change worked with minimal fiddling of the hub.

I bought it used at a store, so I had the store replace the tires with narrower slicks: 20 x 1.5 or 1.75". Not only it makes the bike easier to ride but it also lowers the bike by about 1".

Over the summer, the project evolved when I installed a set of road bars (easy to find narrow ones in 20-year-old stuff), brakes and a set of 8-speed bar-end shifters I had at home.

If you swap out the rear wheel for a geared hub, three or five speed. your going to need to add brakes to the bike. Unless you find one of the rare brake equiped hubs, I think Shimano makes a 7 speed hub with a roller cam brake.

As for spreading the frame, the frame is most likely built with plain steel tube, one step up from water pipe. A soft, heavy tube that will bend much more then the tubes used to build adult bikes.

6 is a bit young to deal with derailleur gear changing. It gets dirty, and the risk of de-chaining increases, esp if they try to back-pedal.
Hub gears are a much safer bet at that age. 3 speed are pretty low cost, but 5 speed are nicer.
If you get a decent hub, it is probably worth rebuilding it into a larger rim as she gets larger bikes.