Polynomial End Behavior and Multiple Roots Video
You just NEVER know where a math lesson is going to go once you bring in the “teenager” element. After a few very random events in class I decided to make a video to help explain end behavior and multiple roots to my students. Music included!
I was teaching multiple roots with the help of the fun terms “bounce” (double root) and “wiggle” (triple root) coined by Rachel. (Thank you again Rachel for sharing your files). So as I was talking about “bounce” and “wiggle” in class I MAY have said (sang?), “Wiggle, wiggle, wiggle” once…or twice. I have a tendency to sing random song clip-its throughout class, so it just may have happened. Towards the end of the lesson one of my students, Michael, raised his hand to share how he was thinking of it with the class to help everyone. He then started taking about Bounce It with Juicy J and Wiggle with Jason Derulo. EVERYONE in the room was like, “Oh yeah! I get it now.” Well, everyone but me that is. You know you are old when you cannot even understand what the teen people are saying. At least I DID know the Wiggle song, but all of the J names completely threw me.
After class I shared all of the dance fun with my teaching partner Chris. He talked about how he hi-lights what the roots look like at the graph when explaining multiplicities. He said he even draws a little frame around the root so the picture inside the frame looks like a line, a parabola, or a cubic function. I don’t think I’ve thought of roots visually this way, but when I shared it with my students they were like, “Duh, Mrs. Reulbach”. How do I always miss obvious things?
We also did the “End Behavior” dance to High School Musical (my sophomores are obsessed with High School Musical – it’s adorable). I threw in a lightening round of Simon Says End Behavior at the end but quickly had to cease all manic dancing when I noticed I was being observed from the door by several other teachers and one of our deans. Luckily I don’t embarrass easily! During all of the madness one of my students found an adorable picture of little ghosts doing math graph dances. I had seen this with stick figures before, but never ghosts! Adorable. Thanks Kallie!
Thanks to Fawn, my students actually cared about making the maximum sized box out of their 8.5″x10″ piece of graph paper. If you don’t do this, you should! It was very easy and great fun! You will need to go and read Fawn’s popcorn post because she has all of the great lesson details.
I went minimalist and only showed them a box I had made, and the squares I had cut out to make my box. I gave them a ruler, scissors, tape and ONE piece of graph paper. I told them they only got ONE piece of paper. They worked well and carefully. Most students chose to fold the sides in instead of cutting just in case they messed up. Love them.
I recently bought an Orville Redenbacher air popper so I brought that in to make the popcorn. Seriously, this is the best $22.49 I’ve spent in a long time even before I used it for a math lesson! I even brought in butter. One of the students took a picture of the air popper so she could buy one. It was pretty cool with all of the popping going on right in the back of the room. It smelled heavenly!
Once they made their box they measured it and entered the measurements and resulting volume on a Google Form. Then I filled up their box with popcorn! We ate while looking at the Google Form results and then I challenged them to find a general equation for an size cut. Several students came up with it pretty quickly and then I had them graph it in Desmos to show them how their maximum volume was also on the graph.
I really don’t know how people taught before the internet. Luckily, I don’t have to! I found some beautiful “end behavior” cards on the amazing Amy Gruen’s blog, “Square Root of Negative One Teach Math“. I doubled the set, adding the number of roots (real and imaginary), as well as direction and wanted to share them back out.
I passed them out to review end behavior and roots, but I wish I would have had these as a discovery lesson to introduce the concepts.
The amazing Amy is some sort of card sort savant. I also saw a Desmos card sort that I can’t wait to explore.
Polynomial Roots and End Behavior Cards (these are just the word cards, the graph cards that go with them can be found on Amy’s blog.) Thanks Amy!