This is what I've been teaching the girls to do while I crochet. I'm a firm believer in children not doing "busy work", but rather learning the skills they need to complete the craft/skill later in life. Admittedly, not every activity has to teach a lesson, but if it does- why not??
This is very simple- my daughters are 8, 6, 4 and 4 and they are all sitting in the living room watching Veggie Tales doing this without even looking at their hands. They learned about an hour ago so that should tell you how simple it is!
First, simply lay out your hand. Right handed- lay out left hand. Left handed- lay out right.
Place the ball of yarn you will be using to the right of your pinkie finger (lefties, just reverse all of these directions) and pull a strand across your palm with the beginning end laying between your thumb and forefinger.
Now, take the yarn by your pinkie and weave it under your pinkie, over your ring finger, under your middle finger and over your pointer finger.
Loop the yarn under your pointer finger and weave back through your fingers: under your pointer, over your middle finger, under your ring finger, over your pinkie.
You are going to start at your pinkie finger and lift the yarn over the strand that is laid flat AND the tip of your finger, off the hand.
The yarn that is now on your finger is the piece that was laying flat. Repeat with all 3 other fingers. Your hand should look like this now.
Loop the yarn around your hand, and lay it along your fingers again. No more weaving in and our of fingers. Just lay the next round of yarn on top of your fingers.
And move the loops off of your hand again! Repeat as many times as necessary to get the length that you need. The looser you make your loops, the looser your finished project will be and alternately, the tighter they are the tighter it will be.
If your children want to make a wider scarf, one of them can volunteer their hands and the other can weave and knit off of both hands outspread before them. You'll be working on 8 fingers that way instead of 4. It's the same concept, just worked in a larger piece.
To finish the knitting off, cut the end coming out of the ball of yarn off, leaving a nice long tail. Weave the tail through all of the finger loops and tie it off in a secure knot. Weave the end in a ways and snip it off if need be.
This is a fun and practical project. If your children like to do it, you will probably end up with a scarf for every person in your family. Right now my girls are happy just knitting like this, but if they tire of it there are a lot of websites and YouTube videos out there on different things you can make finger knitting. I'm sure I'll be looking for something in the future, so I'll add nice links I find to this post for everyone to benefit from :)