Preheat oven to 400 degrees. Lightly grease a baking sheet; set aside. In a medium bowl combine flour, 1/4 cup sugar, baking powder, baking soda, and salt. Using a pastry blender, cut in butter until mixture resembles coarse crumbs.
Drop dough into eight mounds onto prepared baking sheet. Bake for 12 to 15 minutes or until golden. Transfer to a wire rack; let cool.
Meanwhile, combine 4 cups of the strawberries and the 3 tablespoons of sugar. Using a potato masher, mash berries slightly; set aside. To serve split shortcakes in half; fill with strawberry mixture and whipped cream. Top with remaining sliced strawberries.