Use Proportional Editing for whole faces not individual vertices

Question

I've made a tile grid where every face is disconnected from other faces ( no common vertices ). I would like to get a following effect:

But instead I get following:

How can use proportional editing for faces only, not vertices ?

Answer 1

First you need to extrude all the faces individually.

Then select all the bottom vertices and hide them using H button to leave visible only the top faces and use proportional editing to move the faces up.

Then select all the faces, change Pivot Point to Individual Origins and scale on Z axis to zero using SZ0 buttons.

Then unhide hidden geometry with Alt+H shortcut.