That sounds like a great idea, Cindy.
potatoes don't produce tubers below the part you plant, but they don't get many nutrients above that, so they mostly just make tubers above. They'll produce in nothing but straw layered above the "eye" portion, so if you don't have soil to spare, you can use only straw, or a soil/straw mix.
You can begin to pick the small "new
potatoes" after they begin to blossom...that's the sign that tubers are forming.