Teacher Tales: Trinomial Factoring in Algebra I

by David Wright, Algebra 1 and 2 teacher at Jesuit Dallas

About Me: I’ve been teaching for 20 years and currently teach algebra I and II at Jesuit Dallas, a one-to-one iPad school. Last year, I ran across an article in the paper about a revolutionary, free, web-based calculator called “A Better Calculator.” I googled it and found Desmos. Desmos has transformed my classroom. This is a lab I created and wanted to share with everyone. Please feel free to copy and use it.

I introduce my students to factoring through finding the GCF - both monomial and binomial factors. First, I go through the process of factoring a trinomial. After introducing this and going through the monotony of factoring multiple problems in homework, I use Desmos to re-energize my students. Desmos eliminates the abstractness that comes with mathematical processes and allows the students to play with the numbers. With Desmos, the students can see something tangible happen to the corresponding graph, and I can guide them in the direction I want to take them.

In this lab, I’m looking for the students to see the connections between the factored trinomials and the points where the parabola crosses the x-axis. Even though we’re discussing factoring, I get to introduce the concept of the zeros of the function and I can even incorporate the idea of the double root. We use previous homework problems, which have already been checked in class, to develop a hypothesis about the zeros of the function with the corresponding binomial factors. The students recognize the connection between the standard form of a quadratic function and the factored form for the function. They see this connection as a way to check their work. However, I see it as a way to pull together mathematical concepts that will be discussed in later chapters (solving quadratic equations and finding the x-intercepts when graphing a quadratic function). It also reduces the numbers of students who ask, “Why do I need to be proficient in factoring?” or “Will I really need to do this in subsequent chapters?”

One pleasant surprise this year was that my super-star students wanted to take the concepts further. I didn’t want to expand this topic beyond its scope because I didn’t want to overwhelm the other students. However, they began discussing the possibilities of the graph not touching the x-axis or having more than 2 places where the graph touched. It was very insightful on their part. With Desmos, I could still engage those students while I was working with others who were struggling.

I hope you take the time to look through the lab (here) and give it a try with your students. Please feel free to send feedback to me at dwright@jesuitcp.org!

Interested in sharing your classroom experiences? Email us at calculator@desmos.com