Fraction Remix...
I had about 20 minutes after a test today, and RIGHT before the test, a high school student in precalculus was confused about how to divide 2 fractions, and she couldn't remember the method: "do you multiply the top and bottom?" were words that came out of her mouth.
So. I thought I'd give the following short lesson on why the "flip and multiply" that they seem to spout works.
First I asked them the following questions:
Simplify: (7/3) / (4/5)
Then after they did that and checked, I asked them to discuss WHY it worked, and "my teacher said so" or some such thing wasn't an option.
Then we walked through the following 4 scenarios:
So to recap, it basically boils down to seeing how many groups of the denominator fit into 1 unit (that's where the "flip" comes from), and then how many 1's fit into the numerator, and then you combine the 2 numbers and MATH.
That is great math. I never took precalculus but I'm pretty sure I could learn a lot out of one of your classes. You break down the steps in an easy way to learn.
ReplyDeleteHi! I'm studying to become an elementary school teacher at the University of South Alabama. I loved this post and how you helped to make sense of fractions for your students. Fractions are so intimidating. I've even seen some of my current classmates freeze up when they see them. You did a great job of breaking it down for your students. I think that students could benefit from learning the "why" at an elementary/middle school level. I've never thought about why we "flip and multiply" (I called it "drop, change, flip"), but I will definitely teach my future students in this way to help them gain understanding of the concepts. Thanks!
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