Clarity

Some of my students struggle with division.  I have taught a strategy called flexible division to see if they would find it easier.  It is essentially using the multiplication of friendly numbers and “keeping track” of these numbers on the side of your division problem.  For example, if you are dividing 85 into 2 groups, we would look at how many times 2 can fit into 85.  If we know 2 x 10 (because 10 is a very friendly number, or any multiple of 10 for that matter) equals 20, we would write the “10” on the side of the problem to remind us that we multiplied 2 by 10, and then write the “20” underneath the 85 and subtract it.  I tell the kids that it is like picking away at the “ice chunk number” – using the multiplication of friendly numbers until we whittle away at the big number until there is nothing left to whittle away – or, until we have “ice cubes” (remainders) left.

One of my students had an A-Ha moment this afternoon when we were going through Flexible Division once again as a class.  He had always said that he didn’t get it, but couldn’t articulate exactly what about the strategy he didn’t get, so he would go back to his drawing pictures strategy (and there’s nothing wrong with that!).  Well, today he actually came up with a very profound question, and we got to the bottom of his confusion – he asked, “How do you know which number you use for the multiplication part?”  I was ecstatic.  It apparently doesn’t take much!  I explained, with the help of my other students, that it was any “friendly” number (such as 5, 10, or any other multiple of 10) you pulled out of the air, as long as the product didn’t go over the dividend (the number being divided)!  It could be any number you are comfortable multiplying by the divisor (the number you are dividing the dividend by), and all you are doing is making that divisor smaller and smaller.  It was a nice breakthrough moment for him, and it really showed the power of asking questions in Math, and the clarity that (hopefully) comes as a result. 🙂

Here is an example of a Division Lesson from Ontario’s Guide to Effective Instruction (Gr. 4-6) that includes a visual of the flexible division strategy.

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