I have a bright, busy almost-4-year-old son who's at home with me full-time. I also have twin, special-needs sons in high school and a son in middle school who requires some special attention in his own right...plus a husband and a puppy. And it's winter.
SO...especially on school nights when the older 3 boys are home and need help with school work, PLUS I need to make dinner, etc...I need ways to keep the little one occupied somewhat independently (aside from TV and computer games).
I don't frequent this forum, so sorry if this post is repetitive, but let's share one or two favorite ideas for keeping a kid this age busy while you do housework. Let's try to stick to things a little more out-of-the-ordinary than puzzles and coloring books, since I'm sure we all know about those, already.
Here's mine (kooky as it sounds): Since my son was a young 3, when I'm doing something sedentary (like sewing, or working on the computer), I'll let him sit near me and give him my tomato-style pincushion. He likes to organize the pins by color and size and clean/sharpen them, with the little strawberry sand-bag that's attached. It's actually a great fine-motor skill, if your little one is calm enough not to hurt themselves. If I can sit on the bed or a couch (as opposed to a table), he'll stick the pins into the cushions or mattress, to make a shape or letter, then put them back in the pincushion. I can consistently get a good 20-30 minutes, out of this.