I found these white boards on Amazon. I thought they would be a lot thicker, but they are more of a very heavy card stock. So I used 2 for each piece of fabric.
I feel so much better now. Oliver can no longer string my fabric all over the house. When my hobby room is finished, I will store these on some type of bookshelf.
On another note, why hasn't anyone told me about The Nate Show on FOX at 1:00 every day? I absolutely love it!!!