Combine halved strawberries and 1/4 to 1/2 cup sugar, stirring gently; chill 1 to 2 hours.
Combine flour and salt in a large mixing bowl; cut in shortening with a pastry blender until mixture resembles coarse meal. Sprinkle ice water evenly over surface; stir with a fork until dry ingredients are moistened. Divide dough into three equal portions, shaping each portion into a ball.
Place each ball on a lightly greased baking sheet. Roll each into a 9-inch circle 1/4-inch thick; trim edges, and prick with a fork. Bake at 450° for 10 minutes or until lightly browned. Cool on baking sheets 5 minutes; carefully transfer to wire racks to complete cooling.
Beat whipping cream until foamy. Gradually add powdered sugar, beating until soft peaks form.
Place 1 shortcake layer on serving plate. Arrange one-third of halved strawberries on layer, and spoon one-third of whipped cream over strawberries. Repeat procedure with remaining shortcakes, strawberries, and whipped cream. Garnish top of cake with whole strawberries.