Focus at mat time, plus a funny handwashing song

Today I walked into a preschool I'd never been to before.  I asked the staff my usual questions about the kids- how old the children were and what their names were, who had special needs, who would need help to focus at mat time and so on.  I was told that mat time was something of a problem, as several children simply wouldn't sit still and ran around the room, distracting all the others, and that the staff were wondering how best to deal with this.

By the time 'mat time' actually happened a couple of hours later, I'd done some pretty intensive preparation by learning all the children's names and trying to form some basic relationships, particularly with the children who had been identified as needy or 'difficult'- and just as well, because I ended up running that mat time by myself.

How did I form relationships with 18 kids I didn't know in a few hours?