This year I’ve committed to posting each unit of both my Algebra 1 and Algebra 2 INBs.
My district is moving to a standards based curriculum, and has identified priority standards for every course. These are the standards we are required to address and assess our students over, so they pretty much form our units.
You can find my Algebra 1 (year long class) INB posts here:
And my Algebra 2 INB posts here:
I am starting Algebra 1 again from the beginning as a semester class, so you can find my revised posts for that here:
Our fifth standard for Algebra 2 is F.IF.7c:
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
Ignore the proficiency log side of the index file – I decided about two days into this unit that I HATED the way I had set this up and wanted a new one, which I am now using successfully, so you’ll see more about that in my next posts! Also ignore the fact that skill 3 has been pasted in in the picture above – I realized we needed that skill to say something totally different from what it originally read after we had already put them in our notebooks. The change is in the uploaded files, though 🙂
Skill 1: I can name a polynomial based on its degree and number of terms
I got the naming polynomials chart from Sarah Carter here and I really like it. It’s to the point and does its job! I had a total mind blank moment when I was filling my copy out, as you can see in the picture, because I forgot about degree 0. I did not have this mind blank during class, thankfully! We also use a Frayer model as she does in that post to talk about the definition of a polynomial.
I throw in adding and subtracting polynomials here because it is actually an Algebra 1 standard, but I find that my Algebra 2 students need a refresher on combining like terms and putting polynomials into standard form before we start working with graphs and other manipulations of polynomials in our next few units. This also let us get some practice naming the resulting polynomials!
Skill 2: I can graph a polynomial function with technology and identify its key features
On the outside of this you see definitions of what each of these key features is – where do we look for them? My students already know where to find the intercepts, but the extrema and end behavior are new ideas to them. When you open up the flaps, you see instructions on how to find each one using a TI – 83 plus graphing calculator, which is what we have a class set of. I need to find some better way to phrase the instructions on how to place the “left bound” and “right bound” when finding the x-intercepts and the extrema. I have some ideas from working with my students when we were practicing, but this is a tricky thing to communicate without individually showing each student!
Then I put two practice polynomials in the center, one with the graph given so they could make sure it looked okay before finding the key features, and one with just the equation. These two examples took us an entire 47 minute class period to discuss and get through together, so I’m glad I only put 2!
Skill 3: I can match a polynomial function to its graph and identify its increasing/decreasing intervals
I decided to separate increasing and decreasing intervals from the other key features because the other four that students have to be able to find (extrema, x-intercepts, y-intercept, and end behavior) all essentially involve looking in one single place on a graph. The increasing and decreasing are intervals, so they’re a bit different. I’m really glad I separated these this year because my students understood all of the key features a lot better than last year’s Algebra 2, when I tried to do all of those at the same time.
The inside of this needs to be edited to align more with our assessments. The main skill needed in our assessments is to be able to identify the minimum degree of the polynomial by visually inspecting the graph. I will change this page next year to just include that skill, because any other matching can be done by just graphing the equation in a calculator and matching the image that results.
I threw in two more examples that asked to find all possible key features, which gave us some good practice as a class manipulating the calculators and how to list each feature.
Skill 4: I can write a polynomial function based on its graph
My students LOVED doing this. I was so surprised, but they kept asking me if we could do more practice with this skill because they just wanted more of this! That made it really fun to teach. I like the structure I used for these notes as well, I think it was really clear to students.
After we did these for practice, they played Match My Polynomial on Desmos, which they loved and was good practice with immediate feedback!
Skill 5: I can write a polynomial function based on a list of its key features
This essentially is a preview of a skill we will go deeper into about two standards from now. It leads somewhat naturally from the previous skill and our sequence guide suggests that we include it here, but it is also included in that other standard in the future. I think that I plan to just let it be in that other standard the next time I teach this and conclude this unit after skill 4, since this unit is so focused on the graphs of polynomials and this skill doesn’t particularly fit there.
You can find the files I created for this unit here, in Publisher and PDF versions. Any files that were not my own are linked within this post 🙂