Preheat oven to 350 degrees Fahrenheit. Grease an 8-inch square baking dish (or a deep dish pie dish) and set aside.
In a large mixing bowl, combine apple slices, sugars, and cinnamon, mixing well to coat the apple slices with the sugars and cinnamon. Spread in the prepared baking dish.
In a medium bowl, combine flour, sugar, baking soda, and salt. Work in the butter with a pastry blender until the mixture is crumbly.
Sprinkle the crumbly topping over the apples, coating evenly, and press down gently to form a sort of crust.
Bake for 35-40 minutes, or until apples are tender and filling is golden.
Cool for 10 minutes before serving.