Mastery Made Fun

Now look at how factoring is taught and tell me it doesn't play a role. We take a skill made of two basic math operations—multiplication and addition and we avoid putting them together during middle school. Then, we debut that skill—for the very first time—with brand-new notation and wording, in Algebra I, possibly the most high-stakes course a student takes. But that’s not all. We attach all that to a standardized test, a grade, and in some cases, a graduation, and then throw in quadratics and everything else that builds on it. Everything all at once and hey, you have to pass this to graduate, kiddo. If you wanted to design a program to create math anxiety in students, here you go.

So why don’t we give these students better scaffolding for this topic? Many good teachers touch on this before they introduce factoring, but we need to do more.

We need to teach pre-factoring. And we need to start teaching it in middle school. But first, it needs a definition:

Pre-factoring is the intentional development of fluency in factoring's foundational concept: the product–sum relationship between a pair of integers. Built without the use of variables and entirely on arithmetic and integer operations students already know, pre-factoring solidifies the number sense students need to master factoring in Algebra 1.

— Dr. Angela Ruark, 2026

Pre-factoring is simple, but impactful. It can be taught effectively without mentioning variables or complex algebraic expressions. All it takes is a simple framework for wording questions more like puzzles. In fact, students can be taught pre-factoring before they are introduced to integers. Let me explain.

When you ask a student who knows their addition and multiplication facts to tell you two numbers that multiply to give 15 and add to give 8, that is teaching pre-factoring. When you ask a student to label the sides of a rectangle that has an area of 24 and a perimeter of 20, you are teaching pre-factoring.

As students progress and learn integers, you can slightly alter the phrasing: What two integers multiply to give 35, but combine to give −12? The students who spend significant time interacting with these types of problems will find the leap to factoring in Algebra 1 quite a small step.

I would love to help you integrate pre-factoring into your current teaching plan. I believe it will not only support you in helping your students build the number sense they need to succeed in factoring and beyond, but will also help prevent and reduce the anxiety that can creep in as factoring progresses and becomes more challenging.

 And I'm not just naming the problem — I'm building the fix. I've spent months turning pre-factoring into classroom-ready tools: a free sampler you can try with your students this week, Math Showdown, a game that turns product–sum puzzles into friendly competition, and Pre-Factoring in a Day, a complete course for teaching it from the ground up, and Factoring in a Day, a complete course to learn factoring for Algebra I. The first pieces launch soon. If you'd like to know the moment they do, click below.