Matting or floor covering to dampen acoustics in kitchen

[AngelDog]

Our kitchen/diner has terrible acoustics - really echoey. It is an enormous open-plan area with acres of hard floor tiles laid on top of floorboards. I want to find some kind of floor covering for some of it to dampen the acoustics a bit.

We don't want to lay carpet as we have small children who still throw half their food on the floor and we don't want rugs because of the fumes they give off (my kids have issues with airborne chemicals). Is there any other type of non-permanent floor covering which we could put on parts of the floor to dampen the sound a little bit?

(Adding soft furnishings hasn't helped as much as I'd hoped - the room contains 12 full-length lined curtains, 2 half-length curtains, a bookcase full of books, 2 rugs, 2 armchairs, a table and soft-covered dining chairs and the echo is still terrible, though better than it would have been without them.)