I work really hard to make sure that my children get a heavy dose of math in their lives. I feel that math as a mental skill is extremely undervalued; the emphasis is either on rote memorization or solely on application (cooking, measuring, etc.). These things are important, but they tend to lack the element of critical thinking that truly is the entire foundation of math. The art of mathematics can truly be so much more than we (and that includes me) give it credit for.
To that end, I'd found ways over the years to sneak a few challenges into our homeschooling adventure that have driven my children insane ... and taught them how to reason, to problem solve and to think outside of the box. My favorite method-which I've recently resurrected--is the puzzle tray.
At one point, this was actually a puzzle box: a small recipe card holder-type box with a few ziploc baggies that contained individual puzzles of various types. Many were of the toothpick variety. A few were tangrams or the like. All were geared toward my 3rd grade-and-under crew and all could be completed with just the materials provided in the baggie.
Nowadays, I've opted for the Montessori-inspired tray approach. Using primarily puzzles I've printed from my favorite spots over the years, I slip the instructions into a page protector and leave any necessary manipulatives (coins, toothpicks, bingo chips, paperclips, etc.) in a small bowl on the tray. The kids take turns working the puzzles, sometimes in pairs, sometimes carting the tray off to their rooms for a little privacy.
When the kids were little(-r), I kept a prize box going that they could tap into once they'd accumulated so many "points." Each baggie was assigned a number of points based on difficulty, and a running tab inspired them to either master as many of the easier puzzles as they could handle or stretch to conquer a big ten pointer and get into that box in one fell swoop. The prize box had pencils, those little Dover sticker books, fancy erasers and the like. It was a nice motivator to get reluctant learners into the mode of brain teasing.
Today, the reward is being able to report back--and demonstrate--how you solved a puzzle. Many of our favorites have multiple ways to get tot he correct answer, and sharing how you did it in the least number of steps, or the fastest, or with the most finesse is a high point in our days. That was my ultimate goal all along--making the art of the solution a reward in and of itself. It just took a few years to get that far!
This doesn't replace our normal math instruction. It's all part of what I see as a well-rounded environment. As a writer, I don't have to work very hard to make sure that our homeschool is print-rich. But math ... well, that takes a little more effort!