Trim both ends off your LED strip and pull it out of the silicone casing. Flip the strip over so you're looking at the back. Count out 6 copper pads from one end, and carefully cut through the middle of the pads.
Prepare your ribbon cable. For my project I estimated needing about 1/2m of 3-wire ribbon for each sunflower. Our 30awg wire ribbon is 1 m and has 4 wires, so, I cut the ribbon cable in half and stripped off one wire (do the one on the edge that is NOT striped).
Strip about 1/8" of shielding from each of the 3 wires and tin the ends of the wire.
Find the "in" end of the strip. For me, it's the end on the left if the writing on the front of the strip is right-side up.
Tin the pads on this end of the strip. Tinning both the wires and pads ahead of time will make it much easier to solder to the tiny pads -- all you need to do is re-melt the solder with the tip of the soldering iron to get a good connection.
Solder the striped wire to the pad marked 5V, the middle wire to the middle (Din) pad, and the remaining wire to the G pin.
Bend your strip around in a ring with the LED pixels facing outward. Use a piece of strong tape on the inside of the ring to secure the ends into a circle. Make sure the copper pads aren't touching or overlapping on the two ends of the strip.
Connect your alligator clips to the other end of the wire ribbon: red to striped, white to middle, and black to the remaining wire. Hook the alligator clips up to your Circuit Playground Bluefruit (once you've loaded the software) and test to be sure your ring lights up.
Make a ring for each of your sunflowers. My mobile has 5 sunflowers, which just about uses up my 1/2m strip of LEDs with a few extras left over in case I'm sloppy with my cuts.
Set the wired rings aside for now. We'll make the all flowers before soldering the other ends of the wire permanently to the Circuit Playground Bluefruit.
I used two strands of warm white fairy lights to add more interest and dimension to my mobile.
Cut the battery pack apart from the wire strand. If you cut through the lead wire you'll have a much easier time than if you cut through the copper wire closer to the lights.
Strip off about 1/4" of shielding from both wires. One of these wires will go to a G pin, and the other will go to pin A4. Using a digital in/out pin as our power connection will allow us to turn the fairy lights on and off in the software. Cool!
For testing purposes, gently press one of the bare wires to the 3v pad and the other to G. If the strand lights up, you've got them oriented right. If it doesn't, switch the wires around until you know which wire is which.
Repeat with any additional fairy lights strands -- my mobile uses 2 strands. Solder the power wire(s) from your strands to pin A4, and your ground wire(s) to G on the Circuit Playground.