There are two more stages, medium and large, available as a single in-app purchase.
For anyone curious as to what they look like here they are:
The smallest stage (11x6)
The medium stage (13x7)
The large stage (17x9)
Anyone playing on a device with buttons can use the left analog stick and face buttons to select which direction to move in. This is useful if you have trouble accurately tapping on the squares.