<p>I agree with the above posters. Have your English teacher reference the great paper in her letter, but I wouldn’t actually add it as a supplement. I’d say only add a writing supplement if it’s an important component of your application as a whole: that is, something like a published work, legitimate research, some sort of state or nationally recognized piece, etc. Otherwise you’re just trying to show off your writing abilities… and they already have the essays for that.</p>