How are you going collaborating with your buddy class? Here is another idea for some collaborating.
What games do you play at playtime and lunchtime? Are the same games played? What is different? At each school find out the most frequently played games. Compare to your partner school. Why are some games played at one school and not at another?
What is the most popular computer game played by the students at each school? Is it the same?
What could you teach each other about the games you play?