Fill the zippered, plastic package from a king-size bedding set or large sleeping bag with rolled bubble wrap or packing peanuts. This creates the soft, inner beanbag while recycling items that would otherwise be discarded in a landfill.
Measure the inner bean bag's height, width and circumference. Cut a piece of fabric whose length is the circumference of the inner bean bag, plus 4 inches, and whose width equals the height of the inner bean bag plus 2 inches.
Lay your fabric with the finished edges at your right and left hands and the long edge facing you, with the "wrong" side of the fabric facing the ceiling. The wrong side of a fabric not as smooth, bright or clearly-printed as the right side, according to the Reader's Digest "New Complete Guide to Sewing."
Fold each short end of the fabric 1 inch onto the "wrong" side. Press along the folds with a steam iron on cotton setting to create a crisp edge.
Position the fabric so that the long side is facing you. Stitch a straight seam, 1/2 inch from the folded edge, at each end of the fabric, beginning at the edge closest to your body and ending at the edge farthest from you.
Cut a length of plastic hook and loop tape the same length as the now-finished edges of your fabric. Separate the two pieces.
Secure the first piece of hook and loop tape along the left-hand, finished edge of your fabric, placing straight pins 2 inches apart. Pin the second piece of hook and loop tape along the right-hand, finished edge of the fabric. Use a zigzag stitch along the right and left edges of the hook and loop tape to secure it to your fabric. Stitch slowly, removing pins as you go.
Mark the center point of the fabric along the long edges. With the "right" side of the fabric facing the ceiling, fold the finished left-hand edge of the fabric to the center. Repeat with the right-hand edge, overlapping the left-hand edge. Run your hands along the hook and loop tapes to ensure that they are pressed together and that the closure they create is straight and flat. This will be the outer cover for the beanbag chair.
Place straight pins 2 inches apart along the top and bottom of the bean bag cover. Stitch across the top, removing pins as you go, 1/4 inch from the open edge. Stitch a second seam, 1/8 inch from the first. Repeat the double seam along the bottom. This double seam will make your beanbag chair cover more durable.
Separate the hook and loop tape, turn your beanbag cover right side out and insert the inner beanbag. Close the hook and loop tape and allow your child to field-test your efforts.