I cut each square into two pieces, about 3.5" from one edge, then added a one inch strip of the striped fabric in the middle (resulting in a 10" square again). When the block was reassembled, I cut the block again, this time in half. I then swapped the half blocks with other half blocks other colors and reassembled, alternating the striped piece to the top on one side and the bottom on the other. I had to trip the block to 9.5" to make it square; I took a quarter inch off the top and the bottom. The finished block was 9", and the finished blanket was 36". I then used the striped material for the binding. I could have made the blanket bigger by using all 20 blocks, but some of the colors were very pale and I wouldn't have had enough striped fabric for the binding. Like I said, it was less than a yard, probably closer to a half yard, and I wanted to make the best use of it.
I backed it with white flannel, as nothing else really worked and the white made the background of the striped material pop. It turned out really cute and cheery, perfect for the baby shower my daughter attended for a coworker. I will keep this in mind for future irresistible striped scraps that make their way into my stash!