Linear to Quadratic Equations

This is an idea I picked up from an article in Mathematics Teacher.

After students get used to linear equations you have to ask what interesting things can we do with linear equations besides draw lines? What if we add two linear equations? Well, obviously you just get another line. Not too interesting. But what if we multiply two linear equations together?

Make a chart
x|y₁|y₂|y₁×y₂

(x,y₁) plots the first linear equation
(x,y₂) plots the second linear equation
(x,y₁×y₂) plots a new function

Now you can introduce the quadratic equation and look at how the y-intercept is the product of the b's in the linear equations and the x-intercepts are the opposite sign of each b in the linear equations.

After you've done all your quadratic work, try dividing a linear equation by another linear equation or try multiplying three linear equations. Both are interesting and essential topics in Algebra.

Geometer's Sketchpad makes a perfect platform for investigating these equations.

Welcome to Math 2.0

I have started this blog to document and share my journey into teaching math in a 2.0 world. I am reading ISTE's Reinventing Project-Based Learning and will be posting ideas as they come to me. I'm looking for ways to get the students more involved in the discovery of math and ways to incorporate technology into the classroom. For example, I teach my students to complete the square on quadratic equations to find the roots then, after they're comfortable with the procedure, I set them to completing the square on the standard form of a quadratic equation. They end up with the quadratic formula. This is how math was discovered in the first place. Rather than handing them the information prepackaged, I lead them through the same discovery processes mathematicians went through. I feel it gives the students a personal ownership of the math.

Please feel free to comment and collaborate as I can use all the ideas I can get.