Take a skate board, and say hey, Im taking you to your first lesson of skate boarding. Even if you dont know how to skate board, you can do that.
You can take your bycicle and you can go on mountain trips together. Also, hiking is a good idea.
You can take your roller blades and you can go on a "sports" day. You can plan what you are going to do, maybe draw a map and tell her you are going on a search for a secret treasure.
Taking her out on "drinks" and other bullshit is ok, but I think if you have an activity you will get to know her much better. And also, you will build a lot more comfort.
I think I saw it the movie Hitch, when will smith playing hitch takes her with a water scooter.
Activity always works. Especially if she is a sports chick
Take care.
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