Prepare the apples by slicing, coring, and peeling them. I recommend teaching your children how to use a vegetable peeler. It makes this whole process much more pleasant for everyone. (It’s a lot of work for one person to do all that chopping and peeling.)
In a 9x13 inch pan (or similar), pour 3 cups of water and 2 tablespoons of lemon juice. Add the peeled apple sections to the lemon water as you’re working. This will keep the apples from turning brown.
Once all the apples are ready, place them in a large, heavy-bottomed pot. Add the maple syrup and cinnamon sticks. Also add about 2 cups of water so the apples don’t stick to the bottom of the pan during cooking.
Cover the pot and bring the water just to a boil. Lower the temperature to low and simmer for about 20 minutes, or until the apples are very tender. The time will vary according to what type of apple you’re using. Stir periodically when simmering the apples.
Remove the cinnamon sticks and mash the apples to the thickness you desire. If you want it very smooth (like store-bought applesauce), you can puree it in a food processor. I do it by hand with a potato masher.
After mashing, return the cinnamon sticks to the applesauce and simmer gently (uncovered) for 5 more minutes. You want to cook off some of the excess water.
If you want to can the applesauce, it should be done in a hot water bath for 20 minutes with 1/2 inch headspace. See the Ball applesauce recipe noted below for details.
This will keep for up to 2 weeks in the refrigerator if you don’t can it. The canned version will keep for many months.