## Reflection: Joy Area Models for Multiplying Polynomials and Factoring Quadratic Expressions - Section 2: Mini-Lesson: SLT 6.1 and Area Models

If I look back to carefully consider the year's worth of lessons I've posted here, I see that I've spent a lot of time reviewing, reteaching, and expanding upon ideas to which students have already been exposed, before entering high school.  We've spent plenty of time working with linear equations and linear functions in different forms.  Students might learn a different way to look at a concept, but it remains something they've seen before.  We've looked at abstraction and we've worked to cultivate a growth mindset and a strong classroom culture.  Students have certainly become better problem solvers.  In Unit 4, students saw exponential functions for the first time, but mostly in the context of what distinguishes those from linear functions.

It's been rare for students to learn something brand new in this class.

Until now.

A few days ago, I informally asked my classes if they've ever studied quadratic functions, and only one student (a transfer from another district) told me she had.  So today, when we got to multiplying binomials and factoring trinomials, we could feel the excitement!  Building on those foundations of strong classroom culture and problem solving, students were stoked about the new-ness of today's work.  In one class, as he looked at my example on the board, a boy blurted out, "This is that high school s---!"  This is a kid who has come an incredibly long way this year, so I let the language slide.  And even more importantly, the class agreed with him!

It's exciting to get to this point in the year, where all the hard work of August through March pays off.  Now I know my students, and they trust me.  Everyone is willing to try.  And finally, I can spend the last few months of the year teaching in a "more traditional" high school style - both in terms of content and lesson delivery - and everyone is ready to roll.  No, it's even better than that: students are excited to see what's coming each day, and as they get to work, their recognition that they're crossing into a new frontier builds the energy even further, to the point where several times each day, I'll hear a student shout, "I FEEL SMART!" as they practice their work.

All of which makes me want to shout, "MISSION ACCOMPLISHED!"

I FEEL SMART! (Or, This is some of that High School %@#&!)
Joy: I FEEL SMART! (Or, This is some of that High School %@#&!)

# Area Models for Multiplying Polynomials and Factoring Quadratic Expressions

Lesson 3 of 21

## Big Idea: This fast-paced lesson introduces multiplication of binomials and factoring of quadratic expressions for the first time, which sets students up to explore both in depth over the next few days.

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43 minutes

### James Dunseith

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