Add a bit of paper pulp to your slip. Use a standard basic toilet paper or if you have easy access to cotton linter. That will aid in a strong bond and aid in stonger green ware and then on. Im having a hard time understanding how it broke. If you scored properly and added slip then it should of been firm. Maybe your slip is too watery and there isnt enough clay content. Maybe your scores were too simple and maybe just simple drag lines.
Dont recycle the pieces now. Get yourself some paper clay slip and rebuild then clean up.