Preheat oven to 300 F., you will use it to keep the sugar mixture warm so you can mold it into lollipops. If you are using candy molds or doing small, non - spiraled lollipops then you can skip this step.
In a heavy bottomed pan, add sugar, corn syrup, water and cream of tartar.
Attach a candy thermometer to the side of your pot and bring mixture to a boil, stirring occasionally.
When sugar mixture's temperature gets to 300 F. or hard crack stage (see ice water test below if working without a candy thermometer) add in your kool aid all at once if using the same color and flavor for the whole lollipop, along with a teaspoon of water, or if using different colors and flavors, divide mixture into 3 pots or heat proof bowls and quickly stir in your kool aid packet with a 1/2 teaspoon of water, this water should steam out quickly and candy should stay at hard crack stage, stir until the kool aid is mixed in then pour your hot sugar onto a parchment paper lined heat proof counter or cookie sheet or if using candy or sucker molds then pour into them now and skip the remaining steps.
If using molds, place sucker sticks in the designated space and pour the hot sugar into molds. If doing non-spiraled suckers then spoon out about 1-2 tablespoons hot sugar mixture onto a piece of parchment paper then insert and bury the sucker stick in the hot sugar mixture. When sugar is cooled , enjoy. (If doing this, skip the remaining steps, those steps are for rolling up a spiraled lollipop).
Let mixture cool until you can pick up the side of the parchment paper and the sugar peels away naturally but it is still warm and moldable. The sugar will still be hot so be careful, use heat proof gloves if you have them or try to maneuver the hot candy with the help of the parchment papers edge.
Roll or form the sugar mixture into a cylinder the best you can.
Once you have done this with all pieces of sugar, lay them side by side.
If sugar mixture has started to cool too much, place into the warmed oven until it becomes pliable again.
When the sugars are side my side and sugar is moldable, pull and stretch the sugar cylinder out so it's a long rope, you can cut this rope into a few pieces when it gets too long, I ended up with 5 separate ropes.
If sugar gets too hard to handle, place back into the oven again then repeat until you get about a 1 inch thick rope.
Roll rope pieces into a spiral, you can make these lollipops any size you want so you can roll the whole rope for one or cut the sugar rope with a knife when you feel you have enough, we will press these lollipops down so don't worry about them being too thick at this point.
Once lollipops are rolled, place back into the oven to make the sugar soft again.
Remove from oven and insert your popsicle stick into the bottom center and about half way up through the sucker.
Next we will press the lollipop so it's not too thick, reheat the lollipop in the oven if it's too cold to press, then remove from oven and use a piece of parchment paper over the top of the lollipop. Then use a pot or pan or anything with a smooth bottom and press down hard on the warm sugar to press out the lollipop to your desired thinness, Mine are around 1/2 an inch thick.
If you want a smooth surface on your lollipop, place in the oven again for a minute and it will get a shine to it, if you don't mind then just allow it to cool and enjoy when it's cooled and firm.