One fun way to start this lesson (which we all know is one of the toughest concepts for our students to grasp) is to start with a story.
Factoring is about understanding and then calculating where a mathematical statement comes from. It is nothing more than that. I know, sounds boring.... Bear with me! It gets better 🙂
The reason our students understand distributing and multiplying so much more than factoring and dividing is because passing things out, making something happen in the future, and making things bigger are all things that all people understand and accept.
Factoring and Dividing are not readily acceptable. Why? Because taking things away, things that happened in the past, and undoing are all things that most people struggle with.
What is Factoring?
Factoring is essentially figuring out where the current state of the Quadratic Equation came from. Essentially, what are it's Roots (This is where the story comes in, more later)? Rather than right off the rip teaching your students how to factor quadratic equations and do the mathematical calculations you really have to get them to grasp the fact that all they are really trying to do when factoring is figure out where the Equations came from. What factors made it?
Start class by asking some of the students how many of them know their roots (Family Roots). Ask a few of them where their families came from. Ask them about what makes up their families. How many brothers and sisters do they have. What does the make up of their immediate family look like?
Then get them to realize their roots are what made them what they are!
Now for the Transition into the Lesson
Put a Quadratic Equation on the board and say these simple words.
"Today we are going to find the Roots of this Quadratic Equation. Like all of you and your families, it is made up of roots that were multiplied and distributed together to form it."
Now you have them and their full attention. You can directly show them how these quadratic equations came from factors and roots that they have already multiplied and distributed together to form them.