I seem to be all about knitting small things these days (okay, so not just these days but all days).
I made a hat from possum yarn in a beautiful fern-green colour that has been getting a lot of use already. It's the Rikke Hat pattern (free download on Ravelry) and it's a simple and quick knit in garter stitch.
You can make it quite slouchy or not and the best part of the design is the smaller-scale garter stitch band. I also learned the German twisted cast on for it, which is my new favourite method.
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Keira had been asking me to make her a cowl for ages ("something really soft to keep the wind off my neck") and I let her rummage through my yarn to choose something. She pulled out a half-finished project - a toddler's cardigan I was knitting for her but somehow lost interest in. Actually, I think I lost the pattern and it's been languishing at the bottom of a drawer ever since.
The yarn is Mirasol T'ika cotton (one label survived) and to make the cowl I cast on 108 stitches on a 4mm circular needle, knit 3 inches in rib, then 7" in stocking stitch, 3" in rib and cast off loosely.
.... just in case your 11 year old needs one too! .....