With any injury case, you need to be careful. Many people think that just because they injure themselves somewhere, then whoever is involved in maintaining the area or structure should be liable. But this is not the case. Lets face it, we all have accidents sometimes, especially children and that's a fact of life.
In order to prove that the is liable, you need to prove that they did something that was negligent. In this case, you are going to need to prove that either: the material they chose to lay for the surface of the playground was unfit or inappropriate, or that they failed to maintain it in a way that caused it to be come unreasonably slippery. What the court will look at here, is the reasonableness of of school's actions. Generally schools have policies and procedures in place to ensure that they act reasonably and that they avoid liability of this type.
As Edward B said, lawyers will be able to tell you whether or not you have a case, once they see your evidence or once they have had an expert evaluate the playground surface.
