Crochet a chain of 37 stitches with the green yarn. Single crochet in the second chain from the hook. Single crochet in each chain stitch for a total of 35 single crochets.
Turn, chain one, single crochet in each single crochet across the row. Repeat Step 2 for a total of 14 rows. At the end of the 14th row chain one. Pull the top of the chain up to form a loop shape. Pull the right side up until it is taut. This will form a knot. Cut the top of the loop to make a 1/2-inch tail.
Change color by tying the end of the green yarn to the end of the gray skein. Tie the ends tightly. Pick up the crochet hook and make a chain one with the gray yarn to start the next row.
Single crochet over the two tails of knotted yarn and into each single crochet of the previous row. Turn, single crochet in each single crochet of the first gray row for the second gray row.
Change color back to green. Single crochet two green rows.
Change yarn to gray, crochet two rows of the lighter color.
Change yarn to green once more. Crochet 14 rows of green. Repeat Steps 4 through 6. Crochet 14 rows of green. Continue this process until the scarf is 60 to 65 inches long. Make a shorter scarf for a smaller person.
End with 14 rows of green single crochets.
Add a short fringe or leave the ends of the scarf plain. Hand sew an embroidered Slytherin logo patch to one lower side of the scarf.