A Teacher's Guide to Teaching Factoring (Part 2): Planning your instruction of factoring quadratic expressions

 In my last blog post (A Teacher's Guide to Teaching Factoring (Part 1): Defeat the Dread & Ditch the Gimmicks), I wrote about why I DREADED teaching factoring quadratic expressions in my first few years of teaching Algebra 1 & 2.  

I shared that my dread was fueled by 3 main truths:

😫 Factoring quadratic expressions is a complex process!  There's a wide variety of special "shortcuts", and -believe me!- I've tried them all!  

 😩My students dreaded factoring, too!  Since students didn't really understand what factoring IS, they had a level of discomfort & a lack of confidence when factoring quadratic expressions.

 😩 I felt like I didn't have enough time or enough resources to build student understanding of factoring.

I shared at the resolution of my previous post that I had reflected on my teaching & decided 2 things:

1)  I needed to schedule the time that my students needed to really understand factoring.

2) I needed to find a better way to structure the quadratic expressions I introduced to my students as they built their understanding of factoring.

So how can what I learned help YOU "Defeat the Dread" along with me?  Let's talk about it!

👉⌚Take the time! ⌚

First things first:  You just need to sacrifice time in your schedule for students to be able to really process & practice factoring quadratic expressions.   Factoring is one of those skills that students will see again, and AgAiN, and AGAIN!  

Consider a student who is learning factoring quadratic expressions while enrolled in an Algebra 1 course.  This student will likely use their factoring quadratic expression skills again...

• ...in GEOMETRY!  Students may integrate their factoring skills when solving rectangular area problems.
• ...in ALGEBRA 2!  Students deepen their understanding of quadratic equations in Algebra 2, so factoring quadratic expressions is a must!  Algebra 2 also integrates factoring quadratic expressions while delving into many additional topics such as polynomial functions and equations, logarithmic equations, & rational expressions and equations.
• ...in PRECALCULUS!  Students deepen their understanding of polynomial, rational, & logarithmic functions again in Precalculus!  Students also begin work with conic sections & trigonometric identities that again employ student understanding of factoring.
• ...in CALCULUS & BEYOND!  Factoring quadratic expressions will CONTINUE to be integrated into student learning.

Help students avoid constant struggle & give them the time they need to master factoring quadratic expressions!  

Remember: we're ditching the shortcuts & gimmicks for factoring and instead teaching students to factor an expression using their understanding of distribution.  They will need to experiment with factor placement, write down and erase, and identify patterns.  Take the time!

👉🔓 Break from the norm!  🔓

In every resource that I've been provided as a teacher, factoring quadratic expressions has always been chunked in this way:  

1. Factoring expressions where a = 1 
2. Factoring expressions where a ≠ 1.

I found that chunking instruction in this way just didn't work for my students!  

Here's why:

Expressions with a=1 posed a diverse range of factoring challenges for students due to inconsistent difficulty levels.  While the first expression might have a single factor set, the subsequent one could have up to five.  This lack of consistency made it challenging for students to develop their factoring skills.

Additionally, in the transition to factoring expressions where a ≠ 1, students often neglected the a value since they had already been trained in examples that disregarded the a.

I began to brainstorm a solution to the issues I was seeing in my classroom:

💭 Could I adjust how I introduced factoring quadratic expressions to students so that they could experience a consistent level of difficulty as they built their understanding of factoring?

💭 Could I challenge students to factor quadratic expressions where a ≠ 1 from the beginning of my instruction so that they were consistently putting consideration into this value while factoring?

I took the chance & tried something new:

On my final blog post of this series, I'll offer some advice about how I teach students to reason logically as they factor quadratic expressions & the tools that I create for their use while building their skills!

In the mean time, you can purchase my Factoring Quadratic Expressions BUNDLE on my TPT Store (Wise Weyh's) to take a look at the relevant resources I offer on this topic!  

Click the thumbnail to the left to view these available resources!

Thanks for reading!
- Jamie