Build a Scratching Post
Find center on the plywood by taking a level and making a mark from corner to corner on each side, creating an X. Do the same thing on the bottom of the post. Put a piece of tape along the outside edges of the wood. Fold the carpet over on each side. Secure with staples. Take a screw and put it in the center of the bottom of the plywood, leaving some of it sticking out through the carpet side.