I took a class for statistics about 1.5 years ago and I asked for a letter of recommendation. I'm kind of lazy so I'm just going to copy/paste what I wrote in an email. I also left a voicemail with a similar message to make sure she got the request.
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Dr. ABC,
Hello! My name is Situational. You may or may not remember me; I was enrolled in the hybrid "Introduction to Statistics" course in the Fall Semester of 2012. I know you are on your summer break and would prefer not to be hounded by requests from current/former students in your time off from school, but I was wondering if you were willing to consider to write a letter of recommendation.
The reason I was taking the statistics course was because it was a prerequisite for a graduate program. I am looking to apply to Doctor of Physical Therapy programs across the country this coming application cycle, which starts in July. I felt a letter coming from academia from one of the DPT prerequisite courses, especially a class which, during its sessions, focused on working together as a group (social interaction is a big deal as a DPT), would be a wonderful addition to any application.
I also felt I would be a good candidate to receive a letter of reference from you. My memory is hazy at this point, but I believe I received over 100% in your class (for the last several exams, you omitted a question or two). I was a large participant during the group sessions before quizzes going over the material as well.
Thank you very much for your time and consideration! I hope this message reaches you soon, as I discovered you do not teach during the summer, and may not check your email as frequently as when your hybrid classes are in session. If you need to contact me, you can contact me at either email at XYZ or by phone WXYZ.
Sincerely,
Situational
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When she agreed to write me a letter, I then dropped by her office hours and dropped off everything about me, my transcripts, my personal statement and secondary essays, etc, just so she can get to know me better before writing the letter of recommendation.
Hope this helps!