Combine flour, salt, and Rumford Baking Powder; cut in shortening with a pastry blender until mixture resembles a coarse meal. Sprinkle water, a tablespoon at a time, over dough mixture and stir with a fork until all ingredients are moistened. Divide pastry into 3 equal portions and chill for about 1 hour.
Preheat oven to 450 degrees F.
On a lightly floured surface, roll one of the dough portions into an 8-inch square; place on a baking sheet and bake for 10 minutes or until lightly browned. Allow cooling.
Roll another portion of the dough to 1/8-inch thickness on a lightly floured surface; fit into an 8-inch square baking dish.
Place 2 cups blackberries in prepared baking dish. Top with 1/2 cup sugar and 1 tablespoon flour; dot with 1 tablespoon butter. Cover with baked pastry square, remaining berries, sugar, flour, and butter.
Roll remaining pastry to 1/8-inch thickness; cut into fourteen (10 X 1/2-inch strips). Arrange strips in lattice design over blackberries. Press ends to seal. Trim edges and flute. Bake for 10 minutes. Reduce heat to 350 degrees F, and bake 40 to 45 minutes or until golden brown.