My child never discussed scores or grades with other kids. He was a National Merit Finalist at TJ, so it was clear he was doing well and had nothing to be embarrassed about, but he thought it was poor form to discuss such things. The kids did all talk about which college they chose to attend and wore college shirts one day in May to school. Before that, very close friends did talk about where they hoped to go, but it wasn't more generally shared.

OP, it only sets kids up for hurt. Let's say your dd has a perfect SAT score and perfect grades, but her top choice school picks a kid with lower grades/scores. She will feel bad and think it is unfair. But there are other factors that go into the decision. She should keep her ideas/scores private.