Knowing that most children would not be too thrilled with knitting "practice squares" I have looked around the internet for simple projects. I found a couple of easy projects like earwarmer/hairbands and simple hats but there really isn't much available at the Brand New Beginner level. The usual "garter stitch scarf" seems too big and time consuming for that very first effort and a child's shorter attention span.
I have been designing a few simple little knitting projects for children. I felt that a simple bookmark could be a good teaching tool for Cast On, Knit, and Cast Off.
A "Mug Mat" or coaster, although much like a practice square, at least would have a purpose for being. It would be a good project for introducing purling and counting stitches.
And a little purse/bag takes a bit more effort and involves learning to decrease and make a button hole. I-cord for a handle is another easy to learn technique. This is a pattern that I adapted from one on the internet.
Maybe after getting a few quick to knit, near instant gratification projects under their belt the children would be ready for a full size scarf for themselves.