This is my favourite way to make a mug rug as there is no need to quilt it at the end.
You will need:
Backing fabric 11 x 9 inches
Wadding 11 x 9 inches (you may wish to use heat resistant wadding but do not use polyester wadding as it will melt onto your iron)
Five strips 8 x 2.5 inches
Binding 48 x 2.25 inches, folded and pressed in half with wrong sides facing.
Lay the wadding on top of the backing fabric.
Position the first strip, right side up, about one quarter of an inch from the right
hand edge.
Sew in place using a quarter inch seam through all three layers.
Turn the work so that the strip is positioned to the left.
Lay the next strip on top of the previous strip with right sides facing.
Sew a quarter inch seam through all layers down the right hand side of
the strip.
Lift the second strip and press towards the right.
Like this.
Place the third strip on top of the second strip with right sides facing.
Sew a quarter inch seam through all layers down the right hand side of
the strip.
Lift the new strip and press to the right.
Continue until all five strips are attached. Then sew down the right hand
side of the final strip.
Then sew along the top and bottom and trim all the way round to make a
rectangle.
Line up the raw edges of the folded binding strip with the edge of the mug rug.
Leave about 3 inches before starting to sew a quarter inch seam down the side.
Stop sewing one quarter of an inch before the first corner.
Pull the work away from the needle area of the machine. There is no need to
cut the threads. Turn the work to this position.
Lift the binding and finger press in this position. The fold should make a
45 degree angle and the raw edge should be in line with the right hand side
of the work.
Keeping the fold in place, bring the binding down in line with the next raw
edge of the work.
Continue to sew from the very edge of the work to the next corner and
repeat until all four corners are done. Stop sewing about three inches
before the finish.
Overlap the ends of the binding strip and cut so there is a half inch overlap.
This bit is quite tricky! Sew the ends of the binding, right sides together,
using a quarter inch seam.
Finger press the seam open then continue to sew the rest of the binding
to the mug rug. Turn the binding towards the back of the work.
Hand stitch the binding to the back, folding to make the mitred corners.
Ta-da!
Just testing 
I’ve also made table runners, toppers, cushion fronts and place mats using
the ”Quilt as you go” method. It also works well for small jelly roll strip quilts.
If you want some extra challenge….use diagonal strips, maybe of different
widths.
.
. I used nice thick wadding/batting to protect the screen.
. 
Oh Sew Tempting 