This winter my fad has been knitting scarves. (A couple of years ago, it had been knitting beanies.) They have got to be one of the quickest and easiest things to knit. If you're teaching your children to knit then I would start with scarves.
I wanted to teach my boys to knit but it didn't caught on with them. Here are a few pictures of them knitting. They look so tense! :D
For the blue and brown scarf above, the stitch used was garter stitch. It's the same stitch so children only need to concentrate on doing the same thing - that's why it's so easy to start your kids on knitting these scarves.
What makes it even easier and quick was the needle size and the yarn thickness. The thicker the yarn then the bigger the needle and the quicker the knitting will be finished.
The blue scarf used two strands of medium thick yarn knitted together and I casted on 20 stitches using 12mm needles. The brown scarf was a really thick yarn so I only needed to cast on 10 stitches using the 12mm needles. Then we knitted using garter stitch until the desired length.
Remember these beanies I'd made for my boys? Almost a perfect match for the scarves.