Why? Because I deeply believe students in the fourth grade should know how the traditional algorithms for addition and subtraction work. But more importantly they should know why they work. And for that I have a secret weapon: Foursville.
I learned about chip trading at Dana Hall math camp. If you've never been, run, don't walk to sign up this summer. I didn't fully appreciate the beauty of our base 10 number system until Dana Hall but ever since then I have been in love.
We start Foursville as a game. For fourth graders trading chips is hard work. They really have to think and work together.
It sounds easy enough. 1 on the die means one yellow chip. 4 yellow chips = 1 blue chip. 4 blues = a green. 4 greens = a red. One red and you win. In the subtraction game you start with a red and see if you have anything left after passing through a few tolls. It's all the same idea as "carrying" and "borrowing" in our base 10 system but it blows their minds.
Early ah hah moments are when they roll a 4 and just take a blue. Or figure out 1 red is worth 64. The advanced students just do the subtraction in their heads translating the amount needed into Foursville chips. Meanwhile we are reviewing the algorithms learned in 3rd grade but now we can write them in expanded notation and see what all of that crossing out and regrouping really means. We ask ourselves questions and try to make connections.
Soon students are realizing we could play Fives or Sevensville because there is pattern. Boom! Base systems of numbers.
I feel good when students see why our society thinks the algorithms are a good way to do some math problems. They also know lots of efficient ways to do these problems mentally. The important thing is that they can make choices and are learning how to decide when to whip out pencil and paper and when it isn't necessary.
We finished Foursville by noticing the place value patterns of all base systems. In Foursville the green is 4x4x4. In Tensville it is 10x10x10. In Fivesville it is 5x5x5.
We'll see if they can think it through on Monday. I might still find time to show them Mayan math in base 20, but even if not, man it was a good week.