This one of 4 double side placemats I am making. How do I stop the gathering and puffing when sewing?

not pinned good enough? i would use spray basting on something that small maybe?
is the foot tension to tight? do you have a walking foot on?

All good ideas from watterstide. Also try using a little longer stitch

Walking foot? It has a normal foot that came on machine. pm me, please.

have you try lenghting you stitch on the sewing machine.

i did pm you..what machine do you have? when you have 3 layers of fabric..a walking foot, sort of "walks" on it..not pushing the fabric through..

My suggestion would be a walking foot. The thing that helped me avoid puckers was basting spray and a walking foot.

My advice exactly

here is a walking foot..why you need one, and how it works..

http://www.squidoo.com/walking-foot-quilting-with-jant

My suggestion is to quilt it before doing the binding.