Monomials and Polynomials and Factoring - BTC Style

 This is the topic I've been waiting for!  Why?  Well, it feels like multiplying, dividing, and factoring of polynomials lends itself really well to thin-slicing and now I have a much better handle on how to moderate thin-slicing lessons.  I am definitely not even close to being what I would say is "good" at it, but I'm getting better.

This is the first of many posts for this unit.  I anticipate a lot of reflection on my part!!

So, the first post is about preparation.  Though I heard this during a workshop at last year's BTC conference, I really learned it through experience.  You can prepare, but it will likely be all thrown out at some point.  So, don't over prepare.  Peter says that, regarding consolidation, experience is better than anticipation.  In other words, don't assume anything but be ready to respond to what the students demonstrate in the classroom.

So, in preparation of not preparing :) I decided to start by setting up a progression for the unit.  Here is what I came up with:

Multiplying Monomials

Multiplying a Monomial by a Polynomial

Dividing a Polynomial by a Monomial

Finding the GCF of Whole Numbers

Finding the GCF of Monomials

Factoring out a GCF from a Polynomial

Multiplying Polynomials

Factoring Quadratic Trinomials (only a=1 is required for Algebra 1, but I may be able to present trinomials with a prime leading coefficient)

Factoring a Difference of Squares

I feel like this progression makes sense and I can easily connect each topic to the next.

The next step was to create thin-slicing questions for each of these topics.  To thin-slice, each subsequent question should be similar in difficulty to the previous question, or add a new element.  I admit that I start with Chat GPT here.  I ask the program to create a set of 10 problems for a given topic that progresses with those parameters.  Once the set is created, I may modify it or just print it out and modify on my own.  It's important to remember that Chat GPT is not a mind reader and that reviewing the material is necessary!  That said, I have found it to be a great starting point.

Of course, I have modified my plan quite a bit before the first day.  Sometimes, we can overthink and just need to jump in!