Intro to Graphing Polynomials

Yes, it’s been way too long since I’ve blogged about activities going on in my classroom.  That’s what happens when I have 4 preps… sorry!

This week in Algebra 2 we started our polynomial unit, and I was out of the building Monday, Tuesday, and Wednesday.  So I started the students with polynomial operations since I felt it was a skill they could do without me.  I created videos each day for them to watch and take notes and then used Delta Math to practice.  They learned how to name and classify polynomials as well as add/subtract and multiply.  I used a lot of Sarah Carter‘s stuff on polynomials.

Today we started on graphing polynomials. Of course we started with DESMOS Polygraph:  Polynomials.  The students don’t have all the language yet, but they were able to discuss intercepts, opening up/down and then they got into the bumps and humps which produced quite a bit of laughter…

Moving on with about 30 minutes left of class.

I had them glue in this graph organizer that I created based on something I’d seen somewhere else.  It looks like this and can be found here:

polynomial end behavior

I knew I wanted the students to investigate how this works, so that I wasn’t just giving them notes.  But it took me a while to figure out a way that would be effective and manageable.  Here’s what I came up with…

I created 7 functions for each of the 4 different possibilities.  Here’s a link to the Google Doc with the different functions.  I divided the students up into 4 groups simply by numbering off.  And then gave the following instructions:

polynomial function jigsaw instructions

When I gave the instructions for finding similarities of the graphs, I did encourage them to look at the arrows.  We talked about if the graph went off the page in DESMOS, add an arrow to their graph on paper

I was constantly walking around asking probing questions like what do all the leading terms have in common?  The students were able to see the commonalities in the leading coefficients (positive or negative).  But the leading terms were a little more challenging.  The only questions I asked were:  “what do 2 and 4 have in common?”  “What do 3 and 5 have in common?”.  At least 2 in every group were able to identify even/odd.

When looking at the graphs, I encouraged them to look from left to right.  The prompting questions I used were:  “where are the arrows on the left?” “where are the arrows on the right?”… there were a lot of “ohhhh, they all point down” or “they all point up”.

Once each group was confident in their own commonalities, they did a gallery walk to see how the other graphs were different from theirs.  They got 1-minute at each poster to notice and discuss similarities and differences.

Then they went back to their own desks and we looked at the graph organizer.  All classes were able to identify each of these graphs.  I had them point to the station that fit the description.  They were dead on every time.  This is what we filled out in our graphic organizer:


On Monday I will have some kind of entry activity where they identify “arrow” behavior.  I haven’t talked about what end behavior is… just the arrows.

This went way better than expected with the exception of 1 class which is always much harder to manage.  They didn’t get to do the gallery walk.  Instead I had each group tell me the characteristics of their graphs.  It was not nearly as effective as the classes that did the gallery walk.  The gallery walk embedded the behavior into their brains.  That was the key AFTER they had become confident in their own graphs.

Here are the pictures of the posters from my last class:


This was a great activity for a Friday.  It got them up and moving around.  They were collaborating and for the most part everyone did a good job.  I was able to walk around and talk to all the groups and nudge those students who weren’t actively working… it was very accessible to all students.

I’m excited to see where this goes and how they make connections to the specifics of the graphs once we get there.


Author: Megan Heine

I am a HS math teacher - teaching Algebra 2, Geometry, Financial Literacy, and Prob & Stats. I am loud, passionate, intense, and fanatical about students, math, INB's, Apple, Google, and softball. I read a book a week, get up at 4am, and change my hair every year.

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