If your wood scrap is larger than 17 inches long cut to size.
Find the center lengthwise of the wood (8.5 inches) and mark a straight line down the center, top to bottom.
Mark 1.25 inches down from the top and up from the bottom.
Using your ⅜ inch drill bit start drilling at the marks you just made inward (the point you marked will be the outermost side of the drill hole).
Drill two holes the same depth but DO NOT go all the way through the wood.
Make sure your dowels fit snugly into these holes. If they don't, you can add some wood glue to keep them in place.
Mark one inch increments from the center point outward for a total of 8 inches to the right and left of center.