Monday, March 28, 2011

To LCD or Not To LCD

Is finding the LCD necessary?  I know that it makes the numbers smaller when adding fractions, but does it help conceptually?

Would teaching fraction addition like this:  $\frac{a}{b}+ \frac{c}{d} = \frac{ad+bc}{bd}$

and then reducing later make adding polynomial fractions like  $\frac{x}{x+2}+ \frac{3x}{x-3}$ a bit more intuitive?

Does teaching LCD make an already difficult concept more difficult?  Or does it help?

Here are a couple of applets that illustrate the point.  I'm wondering which one would be more helpful for 5th - 7th grade kids.

With LCD and without LCD.

If you want the original GeoGebra files:  LCD, NO LCD

6 comments:

Carlberg said...

I think this is a very interesting point, but I wonder if students could develop intuition for the non-LCD method without already knowing the LCD method.

martinandersongraham said...

I feel good about what we do with LCD because it really drills down into understanding factored form and common multiples, even if students don't express it that way. That is, I find harping on LCD helps them connect algebraic fraction to numerical ones.

However, my students know that finding a CD is more important than finding the LCD - we talk instead of efficiency.

misscalcul8 said...

I think Not To LCD because after the initial presentation of the concept, we basically skip to CD instead of LCD anyway.

Paul Hawking said...

I think fractions are such a beast for most students that they won't make the conceptual leap from using CD for numerical fractions to using CD for algebraic fractions. Meaning if you teach CD for numerical fractions, I don't think it will make it any easier when you teach CD for algebraic fractions. So I'd say do what works best for teaching numerical fractions--I like LCD because it avoids the calculator dependency issue of student's trying to simplify 56/98th and the like without a calculator--and expect the normal amount of challenge that comes when you get to teaching adding algebraic fractions.

Paul Hawking
Blog:
The Challenge of Teaching Math
Latest post:
How do you get students to practice without their notes?

hillby said...

When I review fractions with Algebra II, I don't mess around with the LCD. It's such a lame step when I just want them to not flip out about fractions.

Of course, I also tell kids that if you can't pull out a 2 or 3, I don't really care if it gets reduced.

gasstationwithoutpumps said...

I think that too much time on LCD detracts from understanding. The crucial concept is that a common denominator is needed—LCD is an efficiency hack. I would teach the general form of fraction addition first, since it is universally useful, and LCD only as a cool thing to do to save effort.

Incidentally, I mis-parsed the title when I saw it in my feed reader. If you can't find the Liquid Crystal Display, how can you read the blog post?