Problem sets
See also, "Students’ Perspectives on Homework and Problem Sets in STEM Courses," by Lea Marie Eaton, Sheri D. Sheppard, and Helen L. Chen, Stanford University. The advice about being excessively clear and making the connections visible is especially key for online learning.
Having students work together on problem sets in online courses has the added advantage of helping students get to know each other. If you want students to work together on problem sets as homework, you might want to create student groups by time zone. Depending on the specifics, you can use online problem set banks or create your own. Students might need to turn in pictures of handwritten work--they can do this by uploading images into Canvas. You might also want to use Gradescope for evaluating written work.
Structuring problem sets
Design problem sets that engage students with cognitive tasks that range from simple to complex. Bloom's taxonomy is a useful framework for understanding the range of cognitive tasks. From simple to complex, the taxonomy categorizes tasks as remembering, understanding, applying, analyzing, evaluating, and creating.
A problem set or questions within it might begin with simple recall tasks asking students to identify or define a term, then understand them by selecting examples. Then perhaps students will be asked to apply that knowledge by modifying or predicting. The problem sets then might build upon those earlier tasks by moving on to more analytical tasks such as diagnosing or optimizing. Even higher-level tasks might include validating or disputing. Finally, the student might formulate or design something of their own.
Designing problems sets that first establish a foundation of remembering and understanding before being moving up to higher-order tasks will help students to learn the material more effectively.
During office hours
If there are a large number of students attending office hours for additional help, put students into Zoom Breakout Rooms so they can work with one another on problems while you circulate and help each group as needed. Consider recording and uploading these sessions for students who are unable to attend office hours. Students may mute themselves if they would prefer to work independently.
Norming with TAs
Communicating among a teaching team is sometimes harder online. Considering setting up a shared Slack thread or Google Doc to make sure that grading is happening consistently across groups.