Spread A Discovery Learning Buffet (aka "strewing" if the word doesn't bother you)
What it is, what it looks like in our home
One of the most important elements facilitating my children's math learning is the practice of strewing. "Strewing" fosters a math-rich environment in your home by making available a wide variety of materials to choose to learn from. There are many ways to do this, and it will look different in every home. This is what it looks like in ours.
In our living area I have baskets and shelves that are open and contain pattern blocks, legos, dominoes, Jenga and other blocks, snap blocks, Zome Tools, those magnetic balls and stick toys, K'nex, playing cards, dice, and Math U See base 10 blocks.
Then we have all your classic games, chess, checkers, Battleship, Connect Four, Chinese checkers, Pente, Othello, etc. We have a lot b/c my oldest is going on 14 and I've been accumulating games for years. Every Christmas and birthday is occasion to buy games :o) We don't have all of these Games, but a lot. I noticed this year that the educational math games like Dino Math Tracks and Sum Swamp have taken a back seat to the classic games, probably a function of the ages of my kids moving up.
I have math literature books on their own shelf next to the games, and these are still the most read books in my house, go figure, I keep thinking they'll be tired of them, and then I keep having to move a stack of MathStart readers to find a place to sit on my couch . . .
Because my girls enjoy activity books, I have baskets where these are stacked in the area they draw, color and do any table work in. Many times my youngest daughter will just pull one out and work it through without me even knowing it, I'll be cleaning up and see the entire book worked. Especially if there are dot to dots, thank you Bookcloseouts, LOL. On those desks (which are in between the kitchen and the living room so they are in plain view and constantly accessible) are pencils, colored pencils, crayons, markers, rulers, pencil sharpener, compass, protractor, calculator, etc.
I allow my kids full access to things like tape measures (this has provided hours of fun for all my kids, especially the metal kind that can be balanced up to the ceiling so you can see how high the vaulted ceilings are, LOL - yes, we cover safety and none have gotten hurt). When I'm sewing they help me measure and cut. When dh is in garage doing projects he involves them in how he does things. Then they imitate and I provide them any tools they need to imitate.
We have a "great room" style living / family / kitchen area so even a child sitting down at the piano can talk to me while I'm cooking . . . I can stop, go over and show them how the time signature and notes form fractional relationships . . . Up until this week my kids would just play around on the piano, only my oldest 2 were taking music lessons for violin and cello, but my girls have bugged me for piano lessons. I never noticed until a couple years ago how much math there is in the earliest music lessons in learning how to read note rhythms. In this book my daughter got this week, they exposed her to 4/4 time, 2/4 time and 3/4 time, so she learned to relate quarter notes to half notes, whole notes and dotted halfs - all strictly fractional concepts.
I hung an analog clock in our kitchen near their work area so they could see time in fractional ways.
Other essential strewing resource are tapes and video. We have the schoolhouse series, skip count tapes, my girls even ask to watch Mr. Demme's Math U See tapes and he's pretty hokey on those first series. I have baskets and shelves for these, they pick them out. Most of what I have has been picked up used on lists like Chris Brock's ReadItAgain yahoogroups list, it's not just for books. If you are patient and pick up things as they become available, it isn't as expensive.
I consider all of this "strewing." It's placing objects / materials / resources in plain view or easy access so they when they are browsing around they can land on something and investigate. And I'm not even mentioning the strewing I do for soc studies (rotating large maps under plastic on the kitchen table) language arts, etc.
I hope that gives a picture of how it works in our home.