My 2 1/2 yr. old grandson is fascinated watching me knitting. I gave him some big needles and some yarn, but as smart as he is 
, he, of course, can’t do much with them. Any suggestions would be greatly appreciated. Thanks.
I’m not sure a child that age has the ability to do a “pattern” of any sort. Maybe you could attempt to just show him how to make a knit stitch and tell him he’s making a “scarf”. :lol:
Or if he has a favorite stuffed animal, a blanket for it.
I keep an ice cream bucket with Maddi’s “knitting”. She delights in rolling the short, fat, bamboo circulars and likes to “knit”. What I did was cast on enough stitches of her favorite colored yarn; pink and knit several rounds so that she feels like she’s actually getting somewhere with it. When she’s gone home, I’ll knit a couple more rounds and I quite often use her WIP to test stitches and stitch patterns. Now, you and I know she’s not knitting it but at 3, I don’t think it’s harmful for her to pretend.
I think it’ll be something she’ll remember when she’s older. Knitting with grandma (or Aunt Mary or whoever you are to her). 
A knitting book I have talks about a mother who goes back over the kid’s work chasing loose stitches out while the kid is asleep.
It keeps the kid’s enthusiasm up so she sticks with it and by sticking with it she’ll get better where she doesn’t have loose stitches.
This post caught my eye. My 4 yr old daughter has her own needles and yarn, but as of yet hasn’t quite got the hang of it all. I love the idea of adding to her work so she see progress. She wants to make a hat…Mom’s still got to figure that out yet! I’m still in scarves. 
Have you thought of trying a small loom? That’s how I did my first-ever hat. I started with a small one and made a little hat just right for a small stuffed bear.
Sewing cards are great, too! You can just glue a picture to a piece of cardboard, punch holes around the image. Take an old or discarded, wooden knitting needle (smaller than the holes), drill a hole in the dull end to simulate a needle, thread some yarn through it and give it to the little one. Maddi can sit for at least an hour, working on something like this. She’s actually pretty easy to occupy.
I taught a 3-year old to "finger knit."
It’s just pulling one loop through another like a crochet chain.
She made bracelets, necklaces and belts for her sister, her mother, herself and me.