Combine the tapioca and the first amount of water in a 3.84-L/4-qt sauce pot. Bring to a boil over high heat while stirring with a wooden spoon. When it thickens, strain it through a fine-mesh sieve and rinse it under cool water. The objective is to strain the mucilaginous liquid that has formed from the tapioca starch.
Cook the tapioca in the second amount of water over high heat at a rolling boil. The tapioca will be completely cooked when the pearls are almost completely translucent, 20 to 25 minutes. Strain the pearls through a fine-mesh sieve and cool them under cold running water.
Combine the pearls with the maple syrup, maple sugar and salt, stirring to dissolve the sugar. Reserve in the refrigerator during service. The pearls should not be held after service. Tapioca goes from being nicely chewy to waterlogged (an undesirable texture) and crumbly when it is stored in a moist environment.