Agree with Lion, with CMU partition walls we always use thickened slab footings. For cantilevered CMU walls where you cannot brace the top like Lion explained, such as with a toilet partition, you have to design vertical reinforcing in grouted cells for 5psf lateral which with something like 4" CMU can be harder than you would think. You may be able to tie perp. walls together and use a bond type scheme as well...
If you have to support the walls on plain concrete slabs there are some good design methods in Army/Navy publications, I can look it up later if you cannot easily find this online.