Ex girlfriend issues

Trinity
So I've been with my boyfriend for about 6 months and him his ex girlfriend ended on bad terms, she recently found out that me and him were dating before school started and it turns out she's in one of my classes because I'm in taking advanced courses and she's a year older, whenever I see her in class she gives me the nastiest looks and anytime I see her around school and I'm with my boyfriend she just looks away. Should I tell my boyfriend? Everytime she gives me a nasty look I smile at her trying to avoid trouble. Should I stop that and completely ignore her or keep doing that? Other people have noticed and her best friend told me that she doesn't like the fact that apparently I'm prettier then her and that her ex is doing better then her after the break up. Help??