Using a size 5 straight needle, cast-on 40(44) stitches. In a K2, P2 pattern knit the stitches onto each of 3 of the #4 DP needles dividing them into groups of 13(14), 13(15), and 14(15) stitches.
Knit around in the K2, P2 pattern for 6(6½)inches.
Divide for the Heel:
Half the stitches will be knit for the heel; the other half will be for the instep and temporarily on hold. Work the following two rows over 20(22) stitches until heel measures 2(2¼)inches. Row 1:(Wrong side) Slip 1, P1 across the row. Row 2: Slip 1, then knit the remaining stitches across the row.
Pick up 11 stitches along the right side of the heel. Knit across the 20(22) stitches of the instep. Pick up 11 stitches along the left side of the heel. Knit the next (6)7 stitches. Arrange the stitches on 3 needles as follows. Needle 1: 17(18)sts (left of center heel) Needle 2: 20(22) instep stitches Needle 3: 17(18) sts (right of center heel)
Row 1: Knit stitches on all 3 needles. Row 2: Knit the stitches on needle 1 up to the last 3 sts, then K2tog, K1. Knit all the stitches on needle 2. On needle 3, K1, SKP, then knit the remaining stitches on the needle.
Repeat these 2 rows, until there are (10)11 stitches on needles #1 and #3. Here you may have a stitch more or less, depending on whether the sock is for a wide or narrow foot. Just make sure you have an equal number on both #1 and #3 needles.
Continue to knit around the foot until the sock is 8"(9½") from the center back of the heel. If you know the length of the child's foot, this is a good place to customize, and you should knit until you are 2" short of the desired length of the sock.
Shaping the Toe:
Knit the stitches on needle #1 up to the last 3 stitches, then K2tog, K1. On needle #2, K1, SKP, knit up to the last 3 stitches then K2tog, K1. On needle #3, K1, SKP, then knit the remaining stitches. Continue every round in this way until there are 3 stitches each on needles #1 and #3, and 6 stitches remain on needle #2.
Weaving the Toe Stitches Together:
Slip the stitches from needles #1 and #3 onto the same needles. Break off the yarn leaving 12" and thread it onto the tapestry needle.
Holding the needles parallel to each other: Step 1: Run the tapestry needle (TN) knitwise through the first stitch of the front needle and slip it off. Run the TN through the next stitch on the front needles purlwise and do not slip it off. Step 2: Run the TN through the first stitch on the back needle purlwise and slip it off, then run the TN through the next stitch on the back needle knitwise and leave it on.
Repeat these two steps until there is only one stitch left on each needle. Then with the TN slip the stitch off the front needle knitwise and the stitch off the the back needle purlwise. Bring the remaining yarn to the inside of the sock. Secure the yarn and clip off the excess.