Is it normal for my rabbit's teeth to break off?

Last week I noticed my rabbit' teeth were really long. They overlapped by a lot and were kinda crooked. I didn't know if that was okay since I've never really seen what a rabbit's teeth are supposed to look like. My mom told me not to think anything of it because he was still eating the same and didn't seem in any pain of uncomfortableness. Today I was cleaning his cage and found what looked almost like a plastic fang from my clip so took it out thinking he would accidently swallow it. But when I touched it I realized that it was his tooth. I checked his mouth and sure enough the teeth were much shorter. I'm kinda of freaked out! I don't know if its normal like the way humans loose and grow back teeth when their young. I keep trying to look at his mouth but he won't let me. I even see one behind the tooth that looks like a little sliver. I've heard that rabbits need to chew on wood and things like that to keep their teeth short, whick i've given him but he never seems to get it.