http://www.youtube.com/watch?v=lvGQX6GhgO4
Here's what I THINK is going on, not entirely sure. It's all complete speculation.
Girl A (I can't figure out her name) likes Kenta, and ran after him when he impulsively left with the telescope, but was embarrassed when their classmates teased them with the chalk drawing. She composed a text message suggesting a date, but chickened out and didn't send it.
But Erina also liked Kenta, and asked Girl A to deliver a note to him. Because Erina had that courage that girl A didn't, Erina and Kenta began dating. Erina would send text messages to girl A about their dates, not realizing how girl A felt about him.
She felt angry that her popsicle stick said "winner," which was so ironic while watching the two of them together, throwing the stick down in disgust.
She didn't have the courage to sign up to go to the "Let's Go See the Summer Triangle!" festival that Kenta organized. She saw Erina had already signed up (with a little heart next to her name), and fantasizing about how she would feel seeing Kenta and Erina there together, she once again chickened out.
Kenta also seemed cold towards her, possibly trying not to get too involved because of his impending move to Tokyo, but finally at the end of the school year he did at least give her his address on the popsicle stick that he picked up after she threw it down.
Erina and Kenta said their goodbyes at the station, and none of them ever saw each other again.
The girl never wrote him, but kept the stick as a memento, until years later she revisited the area and finally threw it away.
Thanks for this, I reccon your spot on !