Thanks for your help. I went back to the same JoAnn's that had never heard of the Invisigrips backing and they had it. I have used the Nexcare tape and it works well. I did not like the way it works on smaller rulers, though.
The rulers that I bought at the quilt shop that work so well are called Creative Grids. I have a large square up ruler by them that works very well and doesn't slip. (I haven't made that log cabin yet, so I haven't used that one.) When I went back for a smaller square up ruler, they didn't have a creative grids in that size.
So now, I have the invisigrip for those rulers that don't have a non-slip back.
Thanks again.
bkay