I've tutored quite a few kids of varying ages over the years and in my experience, there's no harder group to teach than teenage girls - and it's doubly hard if

I've tutored quite a few kids of varying ages over the years and in my experience, there's no harder group to teach than teenage girls - and it's doubly hard if the kid in question is fairly popular and active in other areas. There are just so many things competing for a kid's attention that it makes the most sense to (most of) them to quickly memorize a formula, get the best grade possible with minimal effort, and move on to more enjoyable things. The best method I've found for tutoring teenage girls (and I'm saying this as a girl who hated math as a teenager in spite of a love of computers and economics) is to start off by finding out what they enjoy. Put the lessons aside, don't try to talk theory, and don't get all crazed trying to show her how awesome math is. Eyes will glaze over and you will have lost before you ever get started. You can't teach someone unless you first inspire an interest. What does she want to do as a career? What are her hobbies? What kinds of things interest her? At that age, she's probably thought about a lot of different careers, and in pretty much any career, you can tie things back to math (especially junior high and early high school math). If she enjoys cooking, you can talk about proportions and cross multiplication and show how you can use that to adjust the number of portions produced by a recipe. I know of one family where the parents had their daughter go on Pinterest and find recipes for a family meal, then scale them up to fit the size of their family. If decor is her thing, you can talk about floor plans and usable area. Make a diagram and figure out how much space an 8' circular rug will leave for a bed and desk...the swing radius of a door is generally 1/4 of a circle, and you can't put most things in that space. Mathalicious.com is a good source of more real world lessons. Take the time to walk through the logic and show how things relate back to her lessons. It's not efficient, but in most cases, you don't have to do this for every single concept. The goal is to (a) create interest, and (b) show how math is relevant to her life. Above all, be patient and understand that even with the best, most passionate instruction...she might still hate math. The world needs many different types of people, and not all of them have to have a deep understanding of math. She can still be happy and successful even if she never learns to like math.