Discovery Learning – Rational Expressions

November 17, 2010 at 12:48 pm Leave a comment

This week I tried something a little different in my Elementary Algebra class for simplifying rational expressions. Typically I walk through an example of simplifying a numerical fraction to lowest terms and try to extract the key ideas and apply them to rational expressions containing variables. Based on some things I had seen/heard at AMATYC, particularly about how WolframAlpha (W|A) will impact the way we teach, I decided to try a new approach.

At the top of the board I wrote Simplify: \frac{x^2+8x+15}{x^2-9}

At the bottom of the board I wrote \frac{x+5}{x-3}

Then I said to my class “The correct result for this problem is at the bottom of the board. How do we get it?”, and I gave them a moment to think about it. I could see the wheels spinning.

  • “How does x^2+8x+15 turn into x+5 ?”
  • “How does x^2-9 turn into x-3?”

And then it happened – someone said we need to factor the numerator and denominator. So many times I have taught this and told my students “This is how you do it.” It seemed that the process was more accessible to my students because it came from one of them instead of coming top down from the instructor.

After walking through a few examples, I introduced multiplication of rational expressions and later division of rational expressions in the same way. It might have been the easiest day I have ever had teaching these topics. This will definitely not be the last time I use this approach!


The idea is to give your students a problem and an answer, and see if they can find the path to get there. Do you use this approach in your classroom? Have you used WolframAlpha in a similar way? Please share any experience or opinions by commenting on this blog, or you can reach me through the contact page at my web site –


I am a math instructor at College of the Sequoias in Visalia, CA. Each Wednesday I post an article related to General Teaching on my blog. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website –


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