I have five children under the age of 9, and on Saturdays, when my husband is working, we are stuck in the house because of weather and finances. I want to do stuff together, but there is only one ...
I grew up with five siblings. I can assure you that there were times when we were "bored," but it was neither a terrible thing nor was it my mother's fault. Fortunately in large families there are always playmates available. They could probably come up with some sort of make-believe game on their own, but here's some of our favorite things to do, after Saturday chores were done:
Bake bread for the week. Or, bake bread and eat it or deliver to neighbors/relatives/someone in need of a smile. Also works for baking anything else.
Have Saturday morning projects: fix a shelf, paint a room, etc. Plan one thing each week that needs to get done, and do it! Teach the little kids how to help out
Plan simple science experiments. Check out a book full of them at the library. Most require simple household items, and they're fun.
Family band. If the older kids play the piano or another instrument, that's great. If not, pull out the pots and pans, make a wax-paper and comb kazoo, put some beans in a jar for a shaker and belt out your favorite songs. Or write a song.
This sounds lame, but we also loved to match socks. Every once in a while, Mom would pull out this huge pillowcase of single socks, and we'd go through and find all the pairs. We'd always try to find the most matches
Or things your kids could do themselves, if you need a break:
Put on a play (we'd either write our own or put on 'Little Red Riding Hood' or something. We'd also put on circuses all the time, but that's better for the outdoors)
Play school or house. We'd sometimes play "The Price is Right" (our favorite TV show) We even built the wheel to spin and plinko out of cardboard
Make our own art museum-- we'd pull out our crayons and modeling clay and whatever else and each make several pieces of art to display. Sometimes an older sibling would "judge" and give awards for most creative, best use of the color blue, etc.
Build blanket forts
Make things out of leftover cardboard boxes. Especially fun if you have really big cardboard boxes
Play with wooden blocks-- we'd make ramps to race toy cars down, or have contests of who could build the coolest or highest tower
Also, you could always set up playdates with another family. Invite the whole gang over, rather than just an individual child, so that there is still family bonding time, and come up with a large group game or just let the kids have fun