Briefly knead a handful of your air-dry clay. Roll the clay about 1/4-inch thick on a piece of wax paper, moving the clay as you roll it out to be sure it doesn't stick to the wax paper. On a cutting mat to protect the surface beneath, measure and cut out two rectangles using the ruler and pizza cutter. The larger rectangle for the back here is 3 1/2-inches wide and 6 inches long. The smaller rectangle to form the pocket is 4 inches wine and 4 inches long.
Score the edges of both rectangles where they will be attached. Dab water along the scored edges. Gently press the edges of the rectangles together, tucking a small wad of wax paper in between to form the pocket.
With the straw, make a hole at the top of the back rectangle of clay. Let the wall vase dry very well, one to two days.
When dry, lightly sand the vase if there are any bumps (optional). Wipe the vase and paint, if using. If you will be using the vase to hold water, you must also use a spray sealant.