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On Division and Balloons

Number 1 is learning division.  We're working on two different techniques.  I'm not sure which is working better, here they are.

Method the first:
When presented with the problem 12/4, we tell her to think about having twelve things she has to divide evenly between herself, her sibs, (Number 2, and Number 3), and a friend.  The downside of this version, is she has to guess.  The whole thing becomes experimental, (which has value in and of itself).  Number 1 draws twelve balloons, (she invented the technique), and then tries different groupings of the balloons until she finds one that's fair to all the sibs and their friend.  The upside is that there's a reason to want to divide in the first place; there's an application.

Method the second:
When presented with the same problem, we ask her how many groups of four she can make out of twelve things.  One of the upsides of this method is that it's mechanical.  No. 1 once again starts with a drawing of balloons, but this time, she just counts off four balloons, (or what ever the number in the divisor is), at a time.  When she's done making groups of four, she has the answer: three.  Another advantage of this method is that it carries over into long division quite nicely.  The downside of this method is, of course, the converse of the upside of the first: there's no apparent application; it's a parlor trick.

What's your favorite?
We could always use another way to think about math problems.  What's your favorite method for teaching division?


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