Hi Eve,
A lot of our manager like the Working On Calendar that is in the Team area. This shows them in a visual way everything their people are working on. (For our more analytical managers, we use a Resource Grid report or they use the User Utilization report so they can see hours).
If you are looking for across teams though, that could get complicated. Reporting across teams is hard because users can belong to multiple teams.
If you only care about Home Team, I do have a report idea to help you out while you are figuring out an integration...
A dashboard using that three column layout. Each column would have an assignments report (so you can break down tasks with multiple assignees) with the name of the task grouped by Assignee's Home Team. Column one would have New tasks, column two would be In Progress, and the third one complete. You will have to do some text mode the grouping but I can help you out with that if you'd like.