I have done miles and miles of the string piecing this way for borders, quilt blocks, etc...I use 3" wide paper and can when done, cut pieces for many many different patterns.
I like it sort of wonky rather than each piece cut exactly the same and sewn straight..but you can do either
I start with my paper in a box or in the pic you can see I use the thread holder...anything to keep it from rolling all over.
I cut my scraps anywhere from about 1" wide to 1 1/2" wide and about 3 1/2" long.
First you lay one piece right side up on the end of your paper...lay the next strip face down on that and sew as shown using 1/4" seam allowance.. Flip it back and finger press and then lay the next piece face down on that and repeat...I like to sew them at a little angle here and there to make them "wonky".....continue on as long as you like but I find normally I stopped at about 1 yard of the piecing and trimmed it as shown and then rolled it up and continued on...make sense?