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Teaching the Addition of Fractions with Different Denominators

How and why I came up with this:.

I noticed working with college-age folks who really struggle with math that no matter how horrible they were at fractions, almost all of them remembered one thing - how to change a mixed number into an improper fraction.

Why on earth??? It's not as if that's easier to understand, and to be honest, some of them had **no idea** why they were doing it. That wonderful theory that "understand it and you'll get it, otherwise you're sunk" doesn't seem to apply here. Why could they do that, but not rememebr how to add 1/3 + 1/2?

One thing I did already know was that books don't spend enough time on the easy ones - you're supposed to do 1/3 + 1/2 and then they've got you doing 12/3 + 9/51 and 3/14 + 9/35. Oy! I wade through that slop, but I put in a daily review of the 1/3 + 1/2 kind of problem until it's automatic.

After the fifty-ninth time with those improper fractions, I noticed that everybody was doing the same thing. They would move their pencil over the numbers in the same way. The light bulb went on - it had become a 'motor memory' - like tying your shoes.

Ever since then, I've taught doing different denominator fractions the same way - emphasizing the visual-spatial elements and where your pencil goes, when. I encourage students to always do the steps in the same order until it's automatic, even though there are lots of different *possible* ways to do it and get it right. [Note: I don't force it. Nothing works for everybody.]