I decided it was time to steal from another post (Part 2: Factor by Grouping) because really, I should have started with Factoring Prep before delving into Greatest Common Factor. There’s a reason and a process for everything I do in the classroom. Being that factoring is probably the MOST COMPLEX topic we’ll broach all year, the prep work we do deserves its own post.
The Prep Work for Factoring:
(1) Multiplication Boxes!
Use boxes to structure any type of polynomial multiplication. You can later use these boxes as a potential factoring method. Even if you choose to go with a “factor by grouping” approach, these boxes help students to check their factoring work quickly and easily. You can find a much longer post on Multiplication Boxes here.
(2) Factor Lists!
Leading up to the unit on factoring (maybe even during the addition, subtraction, multiplication, and division of polynomials unit), I have students practice writing down all factors of given numbers. This takes away some of their reliance on the calculator later on.
It’s a great white-board activity when you have 5 minutes of free time. We don’t focus on negative numbers times negative numbers to get positive results, but eventually discuss them when we get to trinomial factoring.
(3) Diamond Math!
I’m not sure where I got this Diamond Math Resource (FREE! And posted on Teachers Pay Teachers), but I love how it builds intuition with factoring. It asks students to determine the patterns in each diamond, and then eventually builds to the students doing the most difficult part. (If it’s yours and you happen to find my blog, please message me! I’ll gladly recognize you for your work and post the link to your file on TPT, etc.)
These diamonds are a FABULOUS way for students to organize their thinking around “what 2 numbers *multiply* to give you ____ and *add* to give you____?” The top of the diamond is the multiply number and the bottom is the add number. In conjunction with factor lists, these diamonds are dynamite. After all, diamonds *ARE* a girl’s best friend, no?!
I begin leading students through these exercises for 5-10 minutes a day for a week or two before we begin trinomial factoring. Until students get really comfortable with the structure, I actually write a small multiply dot in the top part of the x and a small addition sign in the bottom part of the x.
Look up https://www.worksheetworks.com/math/diamond-problems.html for additional practice pages. The early worksheets on this website even help to build understanding of how the diamond numbers are related, and you can regenerate infinitely many options for however many practice sessions you need.