'a job tutoring at Legacy Christian Middle School' - short answer

During my second week of high school I got a job tutoring at Legacy Christian Middle School. It was a simple job, meeting with a sixth grade girl to help her do her homework. The first month was awkward at best. She wouldn't focus and it was difficult to complete the simplest of assignments. Her approach to homework was completely different from my focused and determine work style. I thought I wasn't affecting her studies because her grades were not improving the way I thought they would. I contemplated quitting until one day, I showed up five minutes late. She was near tears, thinking I wasn't coming. That day I completely changed the way I approached our time together. I thought my job was to help this girl raise her grades, but in reality, my job was to be her friend. Once I stopped focusing on myself, we were able to connect. I cannot say I helped her drastically improve her grades, but I can say I helped a girl who needed a friend more than she need a tutor.

Please correct grammar and anything else you think I should change.

Wow, great great concept. However, your tone is very serious and presentation not as captivating as the touching message. Try showing more how this girl affected you perhaps, so it's kind of like a back and forth relationship.

That brings me to another point: try showing more than telling--maybe more imagery.
I did not notice any problems with the grammar.

I contemplated quitting; until one day, I showed up five minutes late.

And I would rewrite the second sentence as something like this:
It was a simple job: meet with a sixth grade girl to help her do her homework, but the first month was awkward at best.

(This is just a stylistic change so don't feel obligated to acknowledge it, the grammar was fine before, just a bit unwieldy.)

Other than this, your essay is really good right now. The prose and point are great, and I'm sure the college people will love it.

:)