What are some suggestions for increasing fluency in addition and multiplication without rote, timed practice?

See Google Images "Montessori Addition" and "Montessori Multiplication" for my answer.

The following sites list fun math games, either online or "live" player: http://letsplaymath.net/ and http://www.homeschoolmath.net/online/ We play a derivative of the card game "War." Use a deck of cards for each player and remove the face cards. Instead of turning up one card, turn up two. The player with the highest sum (or I guess you could do it with multiplication too) wins that hand.

We just picked up a 4-player version of Shut the Box game at a thrift store and it seems to be doing the trick. The game is called the 4-Way Countdown.

A game of "Guess the number" works for my son, i.e. "I have a number in mind and if I add 5 to it, I get 9". Once he guesses, it's my turn to guess his secret number. I wasn't sure he'd like the game, but he does. We just started playing Battleships, so maybe I can give him hints as to where my ships are that are similar to the "guess the number" game and use number facts.

When my kids were young, my favorite math game was to [exchange story problems][1] we made up for each other. This promoted fluency and comfort with math that never left them. As they grew and we began doing semi-regular math workbooky stuff, we did almost everything orally, which developed mental math skills. I didn't push math facts at all (until about 4th grade, when I told them it was time to pin down any of the [multiplication table][2] that they hadn't picked up through use). We did play [number bond games][3] and [other math games][4] that I suppose would count as "drill"---but we did them for fun. [1]: http://letsplaymath.net/2012/05/14/tell-me-a-math-story/ [2]: http://letsplaymath.net/2011/09/06/how-to-conquer-the-times-table-part-2/ [3]: http://letsplaymath.net/2007/07/10/tens-concentration/ [4]: http://letsplaymath.net/2008/11/24/contig-game-master-your-math-facts/

Short answer: problems and projects. If you work with creative, non-routine problems and projects where a lot of multiplication (or any other technical skill) is used, the fluency of that skill will improve. For example, suppose you want to program a flight game in Scratch. There will be a whole lot of little tasks involving adding or multiplying coordinates of objects. To figure out algorithms, you will use - and practice - mundane skills. A family I know, back when people balanced checkbooks by hand, delegated the task to their eight-year-old, with some help from the parents. That was a lot of practice for fluency! "Just put the times tables where the kid can see" is a piece of folk wisdom from [this survey of how unschoolers use multiplication][1]. ![Ways to memorize][2] And this picture mentions another method: studying patterns. There are greatly many of them in the multiplication table. For example, the first digit of times nine being one less than the number. [1]: http://naturalmath.wikispaces.com/Child-Led+Multiplication+Study [2]: http://naturalmath.wikispaces.com/file/view/Multiplication-table.jpg/157696971/Multiplication-table.jpg