Graphing Polynomials Using Vases 📈🏺

Polynomials is one of the hardest sections to teach, over the past four years I have acquired different handouts, activities, lessons, and tasks for Algebra 2 students and almost no material for the section on polynomials. Adding, subtracting, multiplying, and dividing polynomials always seemed like an algebraic process and not so much visual or hands on.

Now I have one activity!!! Graphing polynomials was always tricky, but teaching quadratics before made it seem like a piece of cake for them. One of my favorites is graphing polynomials using vases, yes vases.

So to preface this I with I spent a week searching all the Goodwills in the Omaha metro area for different vases and this is basically what I found when you take all of the repeats out.

I did replace the big one in the middle and the one on the far right, well you can tell why.

The way I set this up is I provided each group a vis-a-vis marker, ruler, set of measuring cups, and a vase. Students were given the following directions:

1. they needed to mark off every inch on the outside of the glass 

2. make a table for how many mL in every inch.

3. Put the table into Desmos

4. Find the line of best fit on Desmos (I gave them the different equations)

5. Look at the R squared value to find which one is best.

6. Present your vase to the class the following day.

I had students present from their iPads, but having them create a poster would have been better so they could compare and contrast the vase with the graph to identify key attributes.

What is even better the day before the students presented they practiced with a Desmos activity. At the end of the activity students had to create their own vase and graph.

Below are some photos of my students working on their vase.

How I Teach Direct Variation

I use to teach direct variation by having students take notes, but the past few years I have been using Jon Orr's Water Bottle Flip.

[New Post] Flippity Flip, Bottle Flip! Volume, rates, equations. https://t.co/FQ2QyFJ8Rf #mtbos #bottleflipping pic.twitter.com/tyMtBtyCX8

— Jon Orr (@MrOrr_geek) October 7, 2016

There is an excellent Desmos activity that goes along with it. This year I copied and edited my first Desmos activity which was this one.

https://teacher.desmos.com/activitybuilder/custom/57f788035db373e705868c8b

I added two slides:

I wanted to emphasize direct variation and ask them deep meanings of graphs. One of the questions I asked was looking at the graph on the bottom, what inferences can you draw?

On September 8, there was the NATM (Nebraska Association of Teachers of Mathematics) Conference. During Lenny VerMass presentation, Smoke and you Croak or Huffing and Puffing to Understand Slope, he had a very interesting task. 

Students had to measure how much air filled their lungs. So we exhaled into a balloon and measured (3) breaths and the circumference of the balloon. Then on a big sheet of paper we had to plot all of our data points for the following graphs and interesting things happened. Try it with your students.

Children's Books for Algebra 2 Part 2

Children's books are a great way to get students interested in your content. Picking the right book is more difficult for the topic area. Here are three more children's books perfect for Algebra 2 class.

We are Growing by Laurie Keller

This book shows grass growing, yes literally. A theme the book has is that being unique is okay and that everyone is different.

A great math topic for using this book would be introducing unit rates or graphing linear functions. You could have some real grass growing in different stages per day and ask them if grass growing is linear or not? It would be a good exploratory lesson on linear functions.

You can further go into graphing and think about what non-linear grass would look like? How long would it take to cut the grass?

Giraffes Can't Dance by Giles Andreae

The giraffe believes he can't dance, but with words of encouragement he learns that he can dance in his own way.

In the book there are a bunch of different animals dancing. It would be a perfect time to look into transformations, you can look at it in a variety of different ways from linear transformations to parabolic transformations.

It will be good for students to look for similarities and differences. With the book you can even include more social learning skills learning about kindness and encouraging others.



Dragons Love Tacos by Adam Rubin

Dragons love tacos. They love chicken tacos, beef tacos, great big tacos, and teeny tiny tacos. So if you want to lure a bunch of dragons to your party, you should definitely serve tacos. Buckets and buckets of tacos. Unfortunately, where there are tacos, there is also salsa. And if a dragon accidentally eats spicy salsa . . . oh, boy. You're in red-hot trouble.


In the classroom this book would be a great introduction to probability. You could talk about what goes in a taco. What ingredients it would take, alternatives, how many different types of tacos are there?

Polynomial Video Games Using Floors

As we were progressing through our polynomial unit in Algebra 2 I thought looking back that the focus was on factoring polynomials and not too much on graphing polynomials. I wanted them graphing polynomials and learning about polynomials without traditionally learning about polynomials.

First, I had students go the graphing calculator on desmos.com had them enter the expression

I had them enter sliders and each one around. 

Students had to determine what a, b, c, and d did.

Then they had to find three graphs that interested them and make a video game floor based on those three graphs.  Students had to create 3 levels of a video game based on the three polynomials they graphed. By the end of the weekend they needed a playable working video game and will be peer assessed based on their video game.

Here are some of the students working on their levels.

    

Video Game Success: Making Video Games with Math

Start with Pixel Press Floors

Pixel Press Floors allows you to create your own video game.  In our algebra and algebra 2 units we talk about lines and graphing lines for a solid part of our curriculum.  I wanted students to collaborate and have an ending project that brought a final bang to our unit.

This app allows you to draw on screen (in paper mode) and draw out the different levels of the game. There are a ton of lesson plans and tried and true ideas here: http://www.projectpixelpress.com/education

The Rules for the Project

• Student's need to create at least one level where they have an undefined, positive, negative, and zero slope.  They also need to have at least one other slope that is different from the rest (e.g. y=-3x instead of y=-x.)
• Student's level needs to be playable, you need to be able to get from beginning to end as a player of the game.
• The student's need to take a screen shot of their different levels to show their different slopes and use Desmos to graph each of the different slopes.

Here is an example level:

Students final examples should look something like this:

I want students to have a different final project.  Students will peer assess with others in the room.  Student's will need three other people to play their level and look over their paper they will have to write.  They will have a rubric to fill out about the playability of the game and the features of the game.

Drones and the Coordinate Plane

The school year is wrapping up and with just three days left I realized I hadn't used the drones I received for Christmas this year.  In Algebra we are looking forward to their next year, so I rearranged the desks and made a giant coordinate plane on the floor of the classroom.

There was some great build-up since it took me a couple days in advance to lay it all out.  Students from all my classes were wondering what we would do.

I had a bell-ringer about graphing coordinate points.  Then I pulled the drones out and since our students had to turn in their iPads the day before I used my iPhone and iPad as the two driving devices. (It also turned out that is why I have very few pictures.)

Here is the game that I laid out for each team.  

It was a learning curve since I didn't tell them how to fly, but students got the hang of it and it moved pretty quickly.  Here is a picture of one student's drone landing and another's trying to find the spot.

Next year I will have students graph the coordinates who are not flying the drone on a separate sheet of paper and help give directions on which way to fly the drone.  It was a great end of the year activity, will definitely use this in the classroom next year.

#12: Podcasts

I have been an avid listener of podcasts for the past two years.  My morning commute to and from work now tops a hour both directions and the radio just wasn't cutting it.  I had heard things about a new-"ish" podcast called Serial, which is amazing, but that got me hooked.  Now instead of listening to music, I listen to things I care about on Podcasts.

The best thing about podcasts from an educators perspective is that if you are 1-1 with iPads you can download them at school and have your students listen to them at home.  In my class I had students go to Podcasts and download an episode of the Math-Dude on Graphing Parabolas, they took notes as they went along and completed a worksheet after.

There are lots of great podcasts for any classroom including history, art, and science.

Completely Optional Knowledge Podcast is a great, short podcast for interesting science questions.

Presidential provides short biographies and interesting insights on the history of presidents leading up to the election.

Stuff You Should Know is a general podcast that informs on a wide range of subjects.  There are lots of great podcasts around and new ones become available everyday.

Next year I will try to incorporate this lesson, with the walking classroom.