Almost a half century ago, my teacher taught a math lesson that I still remember today. We were learning how to add and subtract fractions, and she explained how to make equivalent fractions in order to have a common denominator. She started by asking us to multiply 1/2 by 1, 3/4 by 1, 5/6 by 1, etc. Then she wrote several names for 1 on the board - 2/2, 6/6, 10/10, etc. She explained that we could multiply the numerator and denominator by the same number without changing the value of the fraction because we were really multiplying by 1. I realize now that she was teaching us both the how and why in math, and I think that is why I still remember the lesson and have been able to manipulate fractions ever since.
Whenever I help students learn to make equivalent fractions, I always try to replicate my teacher's lesson. This week, I came across a great visual in a
Wikiversity article and decided to make a laminated version on 4 x 6 cards,
so students could use them with dry erase markers. I think this will help them understand what they are doing and why they are doing it.
February 2011 - Last week I started making the cards reversible by changing from multiplication to division, so they can also be used to reduce fractions to lowest terms by dividing by a form of one. Students have had very positive responses to these cards.
I want one of those. Way cool idea!
ReplyDeleteRock on!
ReplyDeleteI draw this on the board and call it the BIG FAT ONE. I've done it so many times that my BIG FAT ONE looks pretty good and I can do it super-way-fast.
Here's a pix: https://twitter.com/#!/MathPsych/status/180419316276146176/photo/1
I love the idea of doing a ton of them, too. I've never done that.
Thanks, Sue!
Bon - You make a great looking BIG FAT ONE!
ReplyDeleteThis is nice article for equivalent fractions . nice work u are the best article writer . . . . cheers
ReplyDeleteThank you for the nice compliment. I was lucky enough to be allowed to learn math in a way that made sense to me. I try very hard to help students learn math in a way that makes sense to them.
ReplyDeleteI love how visual aids like this make learning math concepts more engaging and understandable.
ReplyDeleteYour teacher's insistence on the 'why' — multiplying numerator and denominator by the same number is just multiplying by 1 — is exactly the seed that lasts a half century. Laminated dry-erase cards are a smart, low-tech way to make that rehearsal tactile, and the reversible cards bridging multiplication and division tie reducing to lowest terms back to the same idea. Bon's 'BIG FAT ONE' from the comment thread is another gem. I run factorcalculator.org, a free math tools site, and I share your view that understanding the 'why' first is what makes skills stick.
ReplyDelete