My father's mother was known as Gramma Cookie, and she passed away about 12 years ago. She was a nurse, and she also sewed and crocheted. She wasn't around when Knit A Square was formed, but I know that she would have sent a square or two to South Africa to help the AIDS orphans and vulnerable children there.
This granny square design is in her honor, with the sample square done in her favorite color, purple. I'll add a step by step photo tutorial later. This one works up really quickly - you can bang out a few of these a day, if you have the time.
Love you and miss you, Gramma Cookie! XXXOOO
Gramma Cookie's Solid Granny Square
See the free pattern at the KnitASquare forum.
You can personalize the pattern by alternating stripes of color around, or even using different variegated colors to make it super colorful. You could also switch up the stitches each round by switching between dc, hdc, and sc. I would not make any stitches longer than dc, to keep it tight and warm for Knit A Square.