I've done this for the past couple of years. Both classes enjoy the experience. Here are a few of the things we have done during our 30 minutes once a week.
First grade reads their familiar books to their buddy.
Fourth
grade reads their familiar books to their partner.
Work crossword puzzles as a team. The fourth grader figures out the word, the first grader writes in the letters for writing practice.
Write and reply to each other in a journal.
Create a graph together. We had each team eat an apple and count the seeds, then write down the number and place it on a classroom graph.
Fill in
a Venn diagram together about two books both classes have read, or about two different objects we have scrutinized.