Making Connections with Quadratics

Quadratic Equations — The Core of Algebra 1 

How do you teach quadratics in Algebra 1?

Quadratic equations are inescapable in high school math. Algebra 1 is typically a student’s first brush with them, and how that goes can have lasting impacts on how a students performs in all high math classes.

So you know, no pressure. 😉

Algebra 1 teachers have a big task. In most curricula, they need to teach students at least 3 basic methods of solving quadratic equations – graphing, factoring, and the quadratic formula. In some courses, you can add completing the square to this list. In addition, Algebra 1 teachers usually have to teach what a quadratic equation is, what a parabola is, how to graph them, and how to find the axis of symmetry and roots. Not to mention how to factor.

Yikes. This is a doozy of a unit for most teachers and students alike. So what can we do as math teachers to make our students better appreciate these powerful equations?

My first few years of teaching, I would have followed what I think is a pretty standard sequence.
1) Graph quadratics, identifying roots2) Solve quadratics by factoring3) Solve quadratics by quadratic formula4) Review5) TestI celebrated as my students demonstrated mastery of each topic at the end of class, moving right along through the various solution methods.Then I’d carefully write a test that closely aligned to my daily exit tickets, create a fun review game to help my kids practice, and prepare for a classroom full of As.
Not what happened. 
Instead, I would grow increasingly more despondent as I graded test after test, marking mistakes that students simply did not make on their daily exit tickets. I was stumped. Why weren’t my students able to translate their classroom learning in a test setting? Was it that they didn’t study enough? Did I not give enough homework? Was the review game too goofy?

The solution popped into my head one day when I was watching my students work on a practice sheet. The instructions said to solve by factoring, because that was the day’s learning target. I watched a student make a factoring mistake –  mixing up the signs, an error math teachers know all too well –  and as I was about to point it out to her, a student at her table beat me to it. He held up his graphing calculator and said “you factored wrong, I can tell because I solved this question by graphing and I can see that the roots I got are different from yours.”

Eureka!

In my quest to have each student master the three methods of solving quadratics one at a time, I had never given them time to practice the methods all at once. Therefore, most of my students saw them as totally unrelated skills. What a waste! The beauty of algebra is that it is a set of overlapping tools, and that every problem can be tackled from different angles. I guess I thought my students would figure that out on their own. Some had, as evidenced by my student’s intrepid graphing calculator use. But many of my students thought that they were somehow breaking my rules if they explored other methods. Other students just never thought of it.

Enter this silly little worksheet. I decided that instead of a review day, I would spend time in class asking my students to use EVERY method to solve the SAME problem. This would allow them to see the parallels between the methods, and to understand that each method was just a different tool to solve the same problem. It also naturally opened up a discussion about the pros and cons of each method.

Following the introduction of this extra day, my students performed much better on both formative and summative assessments on solving quadratic equations.

If you’d like to purchase a copy of this resource for your students, click here!