How can I ask a teacher for a good recommendation without reusing an old one that she already wrote?

I’m a junior wanting to apply to very competitive schools (MIT, Caltech, CMU, Cornell etc). Most likely, my math teacher will write one of my recommendations. This year (as a junior), I’ve applied to several competitions, scholarships, and summer programs (5-6), all of which require a teacher recommendation. Since I’m one of her favorite students, I asked her to write me a letter, which she did gladly. For all of these programs, I told her it would be fine if she just reused the same letter for each application.

The thing is, I’m worried she’ll reuse the same letter for my actual college application. (I don’t really want her to because the letter she wrote this year was focused more on my personal qualities than my character and personality as a whole.) I plan on giving her a “brag sheet” with a list of most recent accomplishments and activities for her to include in the letter, but I’m just worried she won’t fully incorporate these into the letter because she’s somewhat lazy when it comes to these things and/or may not put in the effort to modify the recommendation. One of my friends who asked her for a recommendation said that she told him she was “too busy”, so that’s another reason I’m worried.

How can I ask her for a new recommendation without reusing the old one?

It is perfectly OK for you to discuss the new letter with her. Ask her what kinds of updates (like the brag sheet) she needs to have in order to write the letter(s). She knows that a LOR for college is a bit different from one for a summer program.

Or you can ask a different teacher.