In a small saucepan, bring 2 cups water to a boil. Stir in 1 teaspoon sugar until it dissolves. Toss in the pearl tapioca. Cook for about 20 minutes. Rinse, drain, and refrigerate until chilled.
Pour tea, milk, and 4 teaspoons sugar into a cocktail shaker. Stir until the sugar has dissolved and the milk is well mixed in. Add the ice cubes, and shake so the whole drink can get cold. Pour into a glass, and add tapioca.