The Fractions


I'm teaching math this year for the first time in a billion centuries. The program I'm using is innovative and progressive, but sometimes stupid. Today I was supposed to introduce division of fractions with this weird picture drawing activity. I showed the kids one picture instead of a trillion and then said, "Okay, now here's how you really do it." I even introduced cross factorization to their complete amazement. They were thrilled and all were dividing fractions in no time. We don't really understand why flipping over the second fraction and multiplying works, but do we really have to know why? I say no.
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Comments

KC said…
i have never understood why that's how you divide fractions.
9:23 PM
Anonymous said…
Just think of it like, multiplication is the oppposite of division, and the reciprocal is the opposite of the original fraction. It's the same reason that to find one-half of something, you divide by two.

Not looking forward to today much. Maybe it will surprise me. April is the cruelest month.

Love
TD
6:33 AM
Anonymous said…
When does one ever multiply or divide fractions in the real world?

What math program are you using?

Jeff
7:54 PM
Anonymous said…
There is a simple way to teach this stuff. The key idea is to observe that a fraction is not only a number but also an operation. For instance, 2/3 is the the NUMBER two thirds, but it can alternatively be thought of as the OPERATION of multiplying by two and dividing by three. Once you grasp this, fraction multiplication and division is obvious. Isn't it?
11:04 PM
Undomestic said…
I think I like your explanation the best lh!
11:55 PM
KC said…
ros, i think i remember something about reciprocol. sounds familiar. i think the problem is really my 9th grade math teacher. he liked to turn on a strobe light and throw a tennis ball in front of it and repeat "parabola. parabola" over and over again.
7:38 AM
Anonymous said…
I've heard that Peter uses strobe lights and tennis balls with his classes as well.
8:41 AM
Anonymous said…
The strobe light, the tennis ball
and of course the disco ball all
are standard pedagogical tools, as
any educational theorist will tell you. We all use them, right?

Regarding the whole fraction discussion, I say, "Let confusion reign."

-P.
7:03 AM
Julie Anna said…
After talking about this with the big math heads at FOTD, I still was not getting the mathematical reasoning behind multiplying by the reciprocal, and was falling back on "Because I said so, that's why." But I just read anon's description of it being an operation, and the whole thing became clear in my head. If you are dividing 3 by 6 (3/6) then you immediately see that 3 * 1/6 gives you the right answer. So if you divide 1/2 by 3/4, then by the same reasoning, 1/2 * 4/3 should give you the right answer. An AHA! moment folks. Few and far between these days.
2:03 PM
LH said…
We're on to AREA of prisms and rectangles now. And plotting pairs of numbers on graphs. Our plotted points make sailboats and turtles. kind of dumb, but w/e.
6:36 AM
Anonymous said…
Regarding the division of fractions, I have heard the saying, "Don't ask why, just invert and multiply."

See how your sixers like that!
5:32 AM
LH said…
Yes, anon, that will now be part of my teaching repertoire for the rest of my life. thanks a gazillion. love it.
6:47 PM
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