My Struggles With Completing the Square

This year I have been struggling with this quadratics unit. I feel as if there are no cohesive elements tying one concept from one to the other. The outline from this unit has been as follows:

11/6	3-1	1	Graphing Quadratic Functions
11/7	3-1	1	Graphing Quadratic Functions
11/8	3-2	1	Solving Quadratic Equations by Graphing
11/9	3-4	1	Solving Quadratic Equations by Factoring
11/12		1	Review
11/13		1	Quiz
11/14	3-3	1	Complex Numbers
11/15		1	Complex Numbers
11/16		1	Complex Numbers
11/19	3-5	1	Solving Quadratic Equations by Completing the Square
11/20		1	Solving Quadratic Equations by Completing the Square
11/26	3-6	1	The Quadratic Formula and the Discriminant
11/27	3-6	1	The Quadratic Formula and the Discriminant

With 35 minute periods I have been trying to include different strategies, but overall I want them to know that by completing the square we are finding vertex form of a standard form of a parabola. 

I had students use a visual model of completing the square with algebra tiles from Bob Lochel's site: https://mathcoachblog.com/2017/06/05/area-models-and-completing-the-square/

They came away from this with the idea that they are actually trying to fill out a square. The next day I borrowed Julie Morgan's ideas and used this tweet.

New blog post: The week that was (no. 12) https://t.co/KwGqjpdOym with shout outs to @ChrisMcGrane84 and @mpcopland #mtbos #mathschat #iteachmath

— Julie Morgan (@fractionfanatic) November 17, 2018

I felt like it tied it more directly to properties of a parabola, but I feel like I need a better way to assess what they really know about parabolas.

I think I am going to use Nat Banting's post about writing everything they know about a specific parabola and print out each one for groups or partners to discuss.

Today I showed this image and asked my class to “tell me everything you know about this graph and/or the function that generated this graph.”

They were very annoyed when I said I couldn’t zoom out.

“I just can’t deal with full Banting this early” #MTBoS pic.twitter.com/nTwgeTlh2W

— Nat Banting (@NatBanting) November 22, 2018

I need to find a better way to teach this where I am developing conceptual and procedural understanding evenly. If you have any thoughts let me know.

My Favorite: Marshmallow Catapult

When graphing parabolas I had lots of students ask when are we going to use this. One way I wanted to answer the question was by getting their hands dirty and make things. As of lately I have been big into the maker push, where students learn best by building and making things.

Next year I will teach and introduce the catapult at the same time, but this year I used it as more of an activity in between graphing parabolas and solving parabolas. 

To start we watched this video to get their interested sparked: 

Students received 10 popsicle sticks, one spoon, and 7 rubber bands. Their challenge was to create a catapult that will launch a marshmallow more times than any other group. Once students have created their catapult they will test and launch a marshmallow.

Students will take a burst photo and combine these photos on an app called SplitPic. On SplitPic you can have multiple photos overlapped onto one image. Students will put this in Desmos and find the equation of the parabola.

Students will use this picture in a Seesaw activity.  They had to describe the graph of the parabola and what it meant, how using the graph would help them, and do you need to change anything?

Here were some example blog posts:





The next day I gave students 10 minutes to practice, then we put their catapults to the challenge of getting as many shots into a paper bag as possible.  Here were some of the photos of our competition.

Parabola Gallery Walk

I am currently take a grad class called Sparking Student Curiosity at Doane College. This week we had to make a gallery walk that sparked student curiosity. I created a gallery walk that introduced students to parabolas.

Here are the images:

Activity:

Students will be put into groups of three (or you could come up with more images and have smaller groups) and as a group they will take notes from all of the students.  Each student will have a paper, but all students input will be put into each one. They can only record what others in their groups say. On the handout each student will have three columns to fill out:

• Descriptions of what students see in each image.
• What math do you see?
• What is commonalities between the photos?

Students will have 2-3 minutes at teach station (or photo).

Then when all the students have cycled through their groups they will have a short reflection of what they think we are going to study next. Then as a group we will talk about parabolas and introduce them.

#15: Conic Section Cartoons

One of my favorite parts of the end of the year is the conic section test I give.  I give students a blank comic section of Calvin and Hobbes and they color and have to describe one of the conic sections. (Circle, Parabola, Ellipse, or Hyperbola)  They use vocabulary and teach the subject to another in 8 frames. I also gave the students a chance to make their own comic strip and got an excellent response this year.

I wanted to give students a chance to show what they know in an unique way.

I also gave students a rubric and directions.

Students had to create a comic strip that explains the thought process involved in one of the following: Parabola, Circle, Ellipse, or Hyperbola.  The comic strip should explain the characteristics of the conic section, and it should show an understanding of the process.

Here is what the rubric looked like.  I gave students two days in class to work on it and it was due by the end of the second day.

#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.

Conic Section Surgery

I had students fill out a worksheet with their guided learning experience.  They cut the Play Doh in different ways to find circle, parabola, ellipse.  

Here is the link to the worksheet: https://goo.gl/1Ih64F

Materials:

Play Doh

Plastic Knives

Latex Gloves

Face masks

I made homemade PlayDoh which some of them didn't turn out as well as they could have.  The gloves made it more of an experience.  Next year I will see if I can get something to make it feel more authentic.