Ingrid, thank you for your speedy response to my question.
I was thinking of making it like a quilt, so I think I will indeed use a cotton backing and will tack it at the corners of the nine squares!
This should wash in the machine up just fine right? The yarn is Lion Brand woolese and I have made washable sweaters with it.
I recall my grandmother making a knitted blanket for my son 47 years ago when he was born and it too had a cotton backing and binding. Now I am making this blanket for that son's child to be.
Also, I remember YOU responding to my queries five years ago just as quickly. Then I was just beginning to teach myself to knit for two other grandchildren! (twins who are now six years old).
Thanks again so very much! Lynn