Disclaimer: All Harry Potter characters herein are the property of J.K. Rowling and Bloomsbury/Scholastic. No copyright infringement is intended.
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The first time that Albus met Scorpius, they were both four years old. It was at Fortescue's that Ginny and Albus happened upon Astoria and Scorpius. The two women nodded politely to each other and made their way to separate tables, where they left their sons and their shopping bags and went over to the counter to pick up the ice creams. When they got back to their tables, they found the shopping bags intact and their sons missing.
They had a moment of the kind of heart stopping panic that only a parent can have before they spotted the two boys kneeling on a bench by the window on the other side of the store. They had their noses pressed against the window pane as they stared out into Diagon Alley. They were talking enthusiastically about something. Albus was waving his arms about, clearly describing something, while Scorpius listened with his eyes wide. Then Albus looked out of the window and laughed. He tapped Scorpius on his shoulder and pointed to something. Scorpius looked and then he laughed as well. Albus stared at the other boy for a moment and then he impulsively leaned forward and kissed him on his cheek.
Scorpius looked very surprised, but he smiled shyly at the other boy and then they went back to looking out of the window at the brightly lit and sometimes glowing display at Weasley's Wizard Wheezes across the road, ice creams and mothers forgotten in their absorbtion with each other. Neither of them remembered this meeting of course, but they were both fascinated with the story from the first time that they heard it.
So it was no surprise that when they ran across each other in the train on their first trip to Hogwarts, they were curious enough to make their way into the same compartment and attempt a conversation. By the time they reached Hogwarts a few hours later, they had decided that they were going to be best friends. They walked into the Great Hall for the sorting ceremony, hoping that they would end up in the same house.
"SLYTHERIN!" the sorting hat shouted the moment it touched Albus' head and that was that.