Factoring Monic Quadratics (when a = 1) Practice Activity

In the Oklahoma math standards, students are first exposed to factoring quadratics in Algebra 1. However, they are only exposed to factoring quadratics where the leading coefficient is 1. These are called monic quadratics.

Image Source: Oklahoma Algebra 1 Standards

Thus, my Algebra 2 students should already be fluent with factoring monic quadratics as we begin to factor more complicated quadratics. But, this is not always the case. For one thing, it's usually been about a year and a half since students have had to factor in Algebra 1. Secondly, the Oklahoma standards are weird in that students factor quadratics in Algebra 1 but don't really do anything else with them. They don't graph quadratics. They don't solve equations with quadratics. This leads to factoring being taught as a sort-of one-off topic that doesn't get practiced over and over throughout the course .

I say all this to explain why I'm spending time on factoring monic quadratics in Algebra 2. Most would use this as an Algebra 1 activity.

Pairs of students were given a Factoring Monic Quadratics Mat which featured six different quadratics to be factored. Ideally, I would have laminated these, but I was running out of time.



I did laminate the factors that students had to choose from. I printed them on colored paper to make them stand out on the mat.



For example, the first quadratic could be factored as (x - 1)(x - 2).




If I were to do this activity again, I would make multiple factoring mats that used the same set of factoring cards. Then, when a group finished early, I could automatically give them some new challenges to complete.


I'm currently planning for a new prep for next year, so this isn't at the top of my to do list. Bill Carrera shared some sets he created on Twitter after I posted some photos of my students completing this activity. Be sure to check them out! 


It was interesting to see my students take different approaches to these puzzles. Some tackled the puzzles in order. Others jumped around. A surprising number of them fell for my distractor choices which told me two things. First, I picked good distractors. Secondly, it was a very good thing we were spending time practicing these factoring problems in class.