This should be long term game for you because shes in your class and you have until the end of the school year to ask for the number.
You dont need to approach her or even say hi.
Work on getting eye contact with her.
This will let you know wheither she is interested, a girl keeping eye contact while smiling is as big of an IOI as they come.
It can be hard at the beginning because she will most likely avoid your eyes. She doesnt want to give herself away. Look at her and smile.
*****The best time to look at her and smile is right after you make a small wise crack during class. Why you ask? Because for a couple seconds after the joke everyone is looking at you. Everyone is smiling or laughing at you. Then bam, you look at her and laugh at your joke too. Both of you will be giving eachother eye contact and smiling. This lets her know that you may be interested. Of everyone in the classroom that you could of looked at, you looked to her for approval. She will pick up on this and encourage her to look at you more often.
-Give her eye contact when you enter the room
-Give her eye contact when something funny happens. When something funny is said, share the laugh with her by using your eyes.
-Give her eye contact when you see her in the halls
Be the mysterious boy who isnt afraid to look and smile but refuses to talk to her.
After a couple weeks of this be blunt and to the point. "hey lets hang out sometime girl."
-Get the number
-Call the number
-Get the date
-Fvck
-Done
It works because iv done it before and im currently doing it right now. Three girls in three different classes iv targeted and have been at it for a couple months now. The last week of school I make my move and get their numbers. I wait till the end of the year now because it can be potentially awkward depending on how things go and sucks when you have to see them in class the next monday.