One way to solve this problem in an elegant and unobtrusive way, is to add a "Load more" or "View more" link or action button at the bottom of the display area in each grid. Check out the mockup below.
The user can click/tap on that footer link to load/fetch more records. (Display a "loading.." message to provide feedback to the user on what's going on while you fetch the data in the background. This is what makes it unobtrusive).
Finally, just display the new set of records at the bottom of the existing set to make sure the user doesn't lose the previous set. So every time the user clicks/taps "View more", you can just keep appending to the already displayed set of records.
UPDATE: Based on the comment below, I've changed the design a little bit to ensure the size of the grid remains the same. Check out the mockup below.
The user can view only a specific number of records at any given time. He can hit the link at the top to see the previous "n" records or the link at the footer to see the next "n" records. (I've added the arrow icons for visual indication of previous and next set).
Hope that helps.