This lesson on graphing conic sections rocked on multiple levels. For the students, it involved concrete mastery of standards, conceptual understanding of several topics, higher order thinking skills, student autonomy and intellectual need. For the teacher, Mr. Cornelius of Great Oak High School, it was a weeks worth of experimenting with new software and pedagogy. The genesis of the lesson was a combination of an email and a diagram. I had sent to my Math Department a link to the free online graphing calculator Desmos.com; a mutual colleague, Michael White, shared the idea of having students use their knowledge of equations to graph a smiley face. Mr. Cornelius merged these ideas into a new 5-day lesson in the computer lab. That week produced a multitude of pleasant surprises.
Michael started with a whole-class demonstration of Demos at the end of the period on a Friday. He posed the Smiley Face graph (shown above) as the minimal requirement for passing the assignment. The strength of this lesson is two-fold: 1) There are a variety of equations involved (circle, ellipse, parabola, absolute value, as well as linear), and 2) repeated restriction of the domain and range.
Michael invited students to create their own designs for a higher grade. He expected only a few takers, but in the end only a few decided to produce the Smiley Face, and this is where the richness of the lesson was truly found. During the week-long lab session, I observed one of the days and took a few pictures of some works-in-progress.
As you can see, the students independently chose to include inequalities in order to produce the shading. Here was my favorite use of shading.
What really impressed me about the lesson was the examples of students who asked to learn something new in order to produce something they chose to create. In the example below, a student wanted a curly (wavy) tail for her pig. Mr. Cornelius taught her how to graph sine and cosine waves. Granted, this was a superficial lesson, but to see someone wanting to learn a skill from next years course was a treat.
The rigor that the students imposed upon themselves, again as demanded by their creative idea, was remarkable. Look at the detail of the door handle on this house.
My favorite moment was this one with Michael and a handful of students. It is not as sexy as the pictures that the students were producing, but it was far more significant. Three students all had a similar question, so Mr. Cornelius conducted a mini-lesson on the board while the rest of the class worked away on their graphs. The topic on the board was not part of Michaels lesson plan. It was sheer improvisation. For me, this interaction was the treasured gem of the lesson experience: A teachable moment generated by an intellectual need.
This was the first run of Michaels lesson and in a conversation that we had while he was grading the assignments he conceded that he needed a scoring rubric. We also discussed how this idea could be woven throughout both Algebra 1 and 2 courses. The idea of Graphing Designs could span linear, exponential, quadratic and conic equations. I smell a lesson plan brewing!
(P.S. For those of you that get hooked on Desmos, I suggest you also check out the Daily Desmos Challenge)
Not only did students make great pictures, they did some pretty awesome math in the intersection part. And they told me that they really understood translating and conics so much better! Here are some pictures of their work.
What was even cooler is that some learned about trig curves and polar curves and how to rotate conics, even though they did not learn that in class.
And my other students, who saw the projects on display, were so impressed with their work! They wanted to know how the graphs were made, etc.
Above are parts of projects--I didn't take every picture because it would have been a lot.
Below is one full project, with the graphs made on Desmos colored in, the equations, and the points of intersection shown on Desmos and done algebraically.
And here is a close-up of one student's intersection work.
*Note: if you see any of these projects already online, please let me know, as we have a strict honor code on plagiarism. In addition, my students worked super hard on their projects and have gotten very upset when they see their projects copied online after I showcase their work on this blog. Let's keep sharing ideas and encouraging students to come up with their own :)
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Last year, my Algebra 2 kiddos simply created art through conic sections. This was a part of what we call a Design Challenge and I didn't want it to be too intense. For Algebra 2 this year, I've decided to assign the project at the beginning of the unit as well as add onto it!
I found the idea of having the kids take real life pictures of conics through nature/architecture/every day items and tracing the sections. Easy enough, right? Well, that's part 1 because it can be done rather quickly plus the kids can technically use the pictures they take around the school as our intro. activity (tomorrow). I found this ideafrom, I believe, a graduate student! Part 2 is the art projectthat I did last year but they have to choose one of these real life objects from part 1 to make an art piece representing. Part 3 is where the application skills come into play. I found several real world problems from several sources and compiled them into Part 3.
In total, the project becomes 75 points and it's a project that can be worked on throughout the unit! I know the kids will groan as it's more work than last year's project but hey, I have to change something each time I teach it, right?
Algebra 2 Unit 5 Real World Project.docxSours: http://secondarymissrudolph.blogspot.com//10/real-world-conics-project.html
April edit: interested in how I present this activity, and many others, to teachers? Check out my talk at the AMTNJ Tech Conference: Desmos Talk
Here on the blog, the conic sections project we use at my HS in Algebra 2 is one of the most popular posts, generating lots of hits and e-mails to me asking for more information. I am just now grading conic sections projects for this year, and want to share some new additions to the project, and a rubric you can use. The projects are all over my living room now, just waiting to be graded.
For the newbies to this project the concept is simple: use equations you have used, specifically conic sections, to draw something. The Desmos calculator is perfect for this task, and students turn in their graph-based picture, then a completed, colored picture.
So, whats new this year?
FOLDERS AND LINKS
In the past, students printed their equations and submitted them. This year, students instead shared a link to their Desmos product using Edmodo. Also, using folders has improved student organization, making it easier to locate and edit crucial equations.
In my conics unit, students learn to solve both linear-conic and conic-conic systems. This year, I asked students to choose two systems from their drawing and verify the intersection points. This served as a personal review of the chapter, and students had an investment in linking the algebra they had learned to their picture.
Last year, I participated in a Desmos webinar where I explained the evolution of the conics project. For the webinar, one of our sophomore students recorded a screencast where she explained an aspect of her picture. Having a student comment and reflect on their work was so powerful that I made it a requirement for all students this year. Many students chose ScreenCastOMatic to record, and the reflections were excellent. Edmodo was used to share links, though some students had tech issues which I will work to head off earlier the next time I give this project. Below is a screencast from Nick, who was kind enough to allow me to share his work with you:
I have received many e-mails from folks asking for guidelines and a rubric for this project, and am happy to share with you a more detailed document. Feel free to use any part of it, and let me know how it works in your classroom!
Download the project description and rubric
My first blog post on the conics project
More conics news
The Desmos YouTube Channel Classroom Conics Project:
Picture project ideas conic
The guy's eyes stopped expressing universal boredom and was completely chained to her legs. He looked so attentively that a wave of warm pleasure began to rise up the girl's body from. The very legs.AlgebraII Conic Project Example
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