Do you remember how to divide fractions?
That’s what I taught last week in math, and it is a great example of why I love the Common Core.
If you’re like me, when you learned how to do this, somebody taught you to flip the second fraction and multiply them.
It seems like a magic trick. You’re dividing two numbers, but you never divide. You do something else.
Did you ever ask why that’s how you do it? You probably didn’t. We didn’t ask those kinds of questions. That’s how math is done. Every kind of problem has a set of steps, and you memorize and do them. We didn’t ask why in math. Math is something you DO, not something you UNDERSTAND. Dividing fractions has a different set of steps from multiplying fractions, which has a different set of steps from adding or subtracting fractions. Dividing fractions also has a separate set of steps from dividing decimals, which is different from multiplying decimals, which is different adding and subtracting decimals. Oh, and negative numbers all have different sets of steps to pile onto that, too.
Students learned WHY that one got carried, by learning a variation like this:
And everybody got real upset about that.
Except for the kids who forgot which set of magic steps goes with this kind of problem and had something to fall back on that didn’t require memorizing. This week, I taught my class the set of steps to divide fractions, like I showed you above (YES  the Common Core still teaches the magic steps  it just teaches you how to understand them first. Weird, I know.). Within a month, about ¼ of them will have forgotten that set of steps all together. Another ¼ will not remember if dividing is the operation where you flip one of the fractions, or which fraction you flip, or if you just flip the division sign to multiplication. Another ¼ will not remember whether dividing fractions is one of the operations where you need a common denominator or not.
They learn to see it visually, like this:
Pretty logical, huh? Since I know they learned how to divide whole numbers like that in 3rd grade, I can show them how to use the same logic to divide fractions that way:
Additionally, in 3rd grade, they also learned to divide using “repeated subtraction:”
Knowing that, I could show them that the same idea applies to dividing fractions:
And now, a month from now when ¾ of the class has forgotten the “magic trick” for dividing fractions, they have TWO strategies to fall back on, both of which make sense, don’t need memorizing, and that relate back to how they’ve known to divide every other kind of number for the last four years.
(Note: for anyone interested in understanding how the Common Core unfolds mathematical concept, I highly recommend this extraordinary video series by Graham Fletcher: https://gfletchy.com/progressionvideos/)
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About MeI'm an awardwinning teacher in the Atlanta area with experience teaching at every level from elementary school to college. Categories
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