Place apples in a large pot and cover with water. Bring water to a boil. Reduce heat, cover, and simmer for 5 minutes. Using a potato masher, crush apples and simmer for 5 more minutes. Transfer crushed apples to a sieve or piece of cheesecloth and press until all liquid has drained from the apple mash. Stir sugar into the juice and bring the mixture to a rolling boil, stirring constantly. Add pectin and boil for 1 minute, stirring constantly. Remove from heat and skim off excess foam with a metal spoon. Quickly pour the hot mixture into hot sterilized jars, leaving 1/4-inch headspace. Wipe the jar rims clean and cover immediately with metal lids, and screw on bands. Process in a boiling-water bath for 5 minutes. Carefully remove jars from water to cool.