To "slip and score" means when you are connecting two pieces of clay together, you have to "score" it, or make scratches in the clay on the area that will be connected, and then put "slip" or muddy clay over the scratched area. This is important because it creates a place for the clay to lock together, as opposed to simply being pressed together, and keeps it from falling apart once it is fired.
My project is symmetrical in that the design around it is symmetric vertically from the center of the one part of the design that doesn't match. I also dealt with symmetry when my vase was lopsided at first, and I went back to make it even all the way around.
