Self-Shrinking Ice Cream Box

So I was downstairs scooping some ice cream after dinner earlier, and this was probably one of the last few helpings my box of cookie dough ice cream would give me.

The problem was getting the ice cream out, since its at the bottom, and maneuvering a scoop is very difficult. Also, my hands got all sticky from the sides.

And in the end, that left me with a bowl of ice cream in little chunky peices, a set of sticky hands, and a box with an inch of ice cream left on the bottom.

Thats where the shrinkable ice cream box comes in... Why not have the box push up so the ice cream comes out easier? Similar to one of those push-pop popsicle things, but instead in the regular quart or half gallon of ice cream. It would make scooping easier, as well as reduce space.. maybe having the bottom part rip off as it gets used.

First post btw.