Polynomial Operations Tips
Becky Rahm
Luverne Public School Math teacher (8th & 12th grade)
MCTM Region 2 Director
I recently attended the Regional NCTM conference in Minneapolis where I sat in on a lot of great sessions. One of the sessions I sat in on was titled Using Area Models To Teach Multiplying, Factoring And Polynomial Division. I have used area models when demonstrating distributive property to my eighth grade students and I had just gotten done doing polynomial division in my college algebra class so I thought this session would be great for me. And boy was I right.
The presenter was Lisa Fisher-Comfort from AFSA High School in Vadnais Heights, MN. She talked about how she uses the area model with algebra tiles to demonstrate the distributive property, multiplying polynomials, factoring, completing the square and dividing polynomials. Here are a few of the great ideas she shared from the session:
*If you do not have algebra tiles in your district, print some x², x and 1 tiles on paper and cut them out with one side being blank and the other side having a pattern to represent negative terms. Lisa had baggies for our tables that had algebra tiles for us to manipulate as we worked through problems. Check out her handout here.
*Lisa shared a website (http://technology.cpm.org/general/tiles/) that allowed us to use algebra tiles electronically to project for students to see for demonstration or even have students use in a 1-1 setting. I have tried to make algebra tiles using SMART notebook before and this website looks more user friendly than what I had developed.
*Students can sometimes make conceptual mistakes like 2x – x = 2 or 2x + x = 2x². Lisa demonstrated that using algebra tiles helps students put a physical representation to those problems and hopefully make less mistakes.
*Using area models for multiplying polynomials helps link a student’s thinking into his/her previous work with multiplying 2 to 3 digit numbers using area models. Area model also leads well into working backwards and doing polynomial division.
The only question that I had after the session – why didn’t I attend this session one week earlier, before we had discussed polynomial division in class?