I’ve never been a huge fan of the polynomials unit that I teach in Algebra 2. It’s some pretty abstract stuff at times — factors, zeros, degree, end behavior, and crazy graphs. I took a bit of time over the summer and Christmas break to redo it, and while there’s still room for improvement, it’s SO MUCH BETTER now. Blogging so I can remember how things turned went.
Outline: (class notes I use with students here)
- Day 1: Lecture/notes on synthetic division, factoring higher degree polynomials, finding zeros. Debating moving this to between days 5 and 6.
- Day 2: Intro to end behavior (Desmos Activity) – handout to fill in as we go along. If students struggled to notice the difference in end behavior was due to even/odd degree, making a table on the board with the degrees of the polynomials in the purple/orange group helped.
- Day 3: Follow up to end behavior – lecture notes on notation, Kahoot!
- Day 4: Polygraph Polynomial Graphs for about 20 minutes, paused and discussed increasing/decreasing, turning points, roots, and concavity. Followed-up with notes on those same concepts after playing.
- Day 5: Connecting graphs to equations (Desmos Activity). Students wrote equations to match given roots, and looked at how the factored form of a polynomial relates to its graph. Discussed multiplicity and fundamental theorem of algebra.
- Day 6: Lecture notes on sketching graphs of polynomials — focused only on general shape and intercepts.
- Day 7: Solving polynomial equations by graphing (Desmos Activity).
I think incorporating all of the Desmos Activities I made (or borrowed) has helped us make much better connections between polynomial graphs and equations. Yay!
1ntegration by Parts 