Both partners should know how to do all of the homework problems in a given assignment. Let me suggest a couple of ways pairs might work together. One way is called "Pair Programming", where one student is the "driver" (at the keyboard) and the other student is the "navigator". The driver and navigator periodically switch roles. The entire assignment is worked out by the pair working together. We'll watch a short video in class that explains how Pair Programming works. Another way pairs can work is for each student in the pair to do the assignment individually, then meet with your partner, discuss the assignment, and decide whose solution to submit for credit for each problem (you may also, as part of your discussion, decide to rework some of the solutions before submitting them).
Whichever way you choose, you should not split up the assignment so that one partner does half the problems, and the other partner does the other half, because exam questions may come from any of the homework problems.
You may choose the person you want to work with. You will have the same homework partner for the entire term. If you do not choose your own partner, one will be assigned to you.