Place apple juice concentrate, cranberry juice, apple chunks, and cinnamon in a blender, cover, and blend on HIGH speed until smooth. Add ice cubes, 1 cup at a time, covering and blending on high setting after each addition until smooth and icy. Serve with a straw or a spoon.

Freeze leftovers in 1-cup servings in small airtight microwave-safe containers. To serve, microwave each serving for 15 seconds then stir. Continue microwaving in 10-second increments until slushy.