This pattern will fit a smaller baby with the brim folded up and will ‘grow’ with the baby by folding the brim down, as modeled by the balloon. Mother and baby-tested and approved! Stays on well, too.
Start with soft washable yarn.
Take the stitch gauge of your yarn per inch (i.e. 5 stitches per inch for worsted weight) and multiply by 12 for a term baby hat, by 10 for a roughly 34-week preemie hat. (Probably by about 15 for a 6-month-old.) Round off to the nearest multiple of 6. Cast on stretchily that number of stitches (I use long tail cast on for this). Join to knit in the round, using whatever needle configuration you prefer and whatever size you need to get gauge. Note: A looser, more drapey knitted fabric will stretch better and fit longer; a denser knitted fabric will be suitable for an outdoor cold-weather hat. Place marker at beginning of round if desired.
Knit two rounds, purl two rounds. Repeat the sequence twice for a total of12 rounds.
Now knit every round. Knit for 4 inches total length (including brim) for a preemie, 5 inches for a newborn term baby, 6 inches for a 6-month-old.
Decrease rounds: My favorite decrease for hats is to decrease 6 stitches every other round until you have half or less than half the original number of stitches on the needle. Then decrease every round until you have 6 stitches left; break yarn, draw through remaining 6 stitches and bring yarn to inside; knot once and weave in ends. You may pom-pom if you wish, but it’s not necessary. This gives a neat, nicely rounded crown.
More detailed decrease instructions if you need them: Divide the number of stitches by 6 (you have a multiple of 6, remember?). For example, if you have 66 stitches, you will have 11 in each decrease section. Knit until two stitches before the end of the section (knit 9 in our example), then knit 2 together. Place a stitch marker if desired. (When you read your knitting, you may not need the marker, but it helps at first.) Repeat 5 times to the end of the round. Then knit one round plain. Next round: knit to 2 stitches before marker (8 in our example), k 2 tog, repeat around. Knit one around. Continue to decrease every other round until you have half, or a little less than half, the original number of stitches; in our example, half of 66 is 33. You would end up decreasing until you had 30 stitches, since 33 won’t end up as a number of stitches in a round. After knitting the decrease round in which you hit the magic number of stitches, then decrease every round until 6 stitches are left as above.
(I made the stripe pattern on the blue hat above by doing the last 2 sets of 2 purl rows in a different color, I believe.)