Tumbling Mat

Sorry if this isn't the right forum; I don't know which one would be more appropriate.

My almost-three-year-old daughter loves to tumble. I am setting up my basement as a play area and have set aside a corner to be a tumbling play area. Naturally I don't want her to be on the bare concrete floor and would like to buy or build a large and collapsible/foldable tumbling mat for her to use. They have one at my local library which is excellent; it has a hard (plywood?) base and dense foam and is covered in some kind of thick durable fabric. Unfortunately nobody at the library has any information as to where it came from, who made it, or anything of that nature.

I casually looked around a few sporting goods stores and they all have those blue folding gymnastics mats but they all seem to be rather flimsy and not offering as much protection as I'd like. My daughter can (and has) fall pretty hard on the mat at the library and shrug it off; I'm not confident that she would be able to do the same with the mats I've seen so far.

So I'm thinking I need to build something but I know nothing about what kind of foam I should be looking at (closed cell? open cell? rubber? minicel? polystyrene?), what format it should be (roll? sheet? does it matter?), what kind (if any) of backing I should use (plywood? poly? linoleum? particle?), or what I should cover it with.

If anyone has any ideas I'd be most appreciative.

 

First thing that leaped to my mind was the soft rubber floor squares like these:

Home Sport and Play Mat
SoftTiles Interlocking Foam Floor Mats - Home
http://www.walmart.com/ip/Step2-Play...ci_sku=2603666

I don't know if they would provide the level of cushioning you would want, but possilby a double layer would solve that.