Conic Art Project With Equations. CONIC SECTIONS: ics, they become aware that the conics involve parabolas, circles, ellipses, and hyperbolas, and they learn to manipulate the equations that pertain to those figures. Students gain greater un- derstanding of the relationships between conics and their equations when they create art-based projects.

Entered the equations so as to shade, restrict domain and/or range, etc. Online – perhaps a famous work of art, statue, etc., and try to simulate it using Desmos (include the picture somewhere on or below the construction paper). Conics Section Project. Project – Art with Conics Conic sections are used in a wide variety of fields and are present in the world around you. You are going to use conic sections to create a work of art. This will require you to identify the presence of curves in familiar images and connect them to mathematical forms. The picture below is a very simple example. Some of the Project Requirements Create a drawing/design on graph paper (cartoon character, sports object or mascot, design or a scene—BE CREATIVE!!). It should include (at least) the following 11 graphs (or pieces of graphs in your creation: a. 2 horizontal or vertical ellipses (or 1 of each) c. 1 horizontal parabola.

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 week’s 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 year’s course was a treat.

Conic Art Project With Equations Crossword

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 Michael’s 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 Michael’s 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)

I'll let one of my students tell you the story of this project:

It all started on a Monday morning around 9:05 a.m when the class decided to go for a walk in and around the school. That’s when I felt I was surrounded by conics, but not just ellipse there were also parabolas and hyperbola. I felt a bit overwhelmed because I had never seen so many conics on a single walk in my whole life. I was down stairs in the field house when I saw the perfect conic. I cried at the first sight because it was so beautiful. There the conic was on the side of a vending machine; it was a Pepsi symbol was a circle. Once this breath-taking picture was captured I immediately sent it to [student email]. Next I open this amazing program called Geogebra. I pasted the picture and made it transparent so I could see the graph in order to plot point on the circle. Next after I plotted my points I figured out the key information to making the equation for the circle. I founded the center was (0,0), and the radius was perfect two which worked out perfectly for me. Once I had the center and the radius of the circle I was ready to form an equation for this conic. I Enter the equation (X^2/4)+(Y^2/4)=1 and turns out I was right on the money, which made me feel like I actually understood something for once.

Conic Art Project With Equations Pdf

AP Exams interrupted class for two days so I knew I needed something that would be beneficial for the students in class, but that the students in exams could do on their own. A quick search led me to this awesome project. Monday we spent some time wandering the school taking pictures. Some days it's annoying that everyone in class has their phone out, but that day I appreciated just how easy it was to say 'okay class, photo scavenger hunt!' and they all had cameras at the ready. The gym was the best place because the basketball court is covered with conic sections. Students couldn't find any hyperbolas, so they grabbed some ropes and tried to make one. An unintended bonus of this project was the discussions that came up about curvature. Telling the difference between a parabola and a semi-circle was a challenge and many students held the misconception that they could make a parabola fit a semi-circle. Students were also upset if their circular object came out elliptical because of the angle they took the photograph. All great concepts to work out.

Conic Art Project With Equations Answer

On Monday I gave everyone handouts and the week before students made dichotomous keys which told them how to write equations, but at the beginning of class on Friday everyone started with just their computers. They whined and complained. They demanded help with tiny things. They could not believe I would make them use decimals rather than round to the nearest whole number. They basically threw teenage temper tantrums. I was more helpful than normal since there were only seven students but I finally realized what I was doing, sat down and refused to help anyone until they had the relevant papers on their desk. One by one, students learned to work in GeoGebra and realized the task was just like what we were doing the previous class. Soon, everyone was focused and quiet. One student requested music and we turned on the bachata pandora station. They helped each other and most had finished the project by the end of class, after admitting it was a fun assignment. The next class went much smoother thanks to my realization that being less helpful was the key to everyone’s sanity.
Other things to note:

• Drop It To Me is awesome (assuming kids read that far on the paper, I had a few email their projects and a couple tried to print them).
• Grading these is the best thing ever since very, very few students submitted something that didn't line up perfectly. Technology is great for the instant feedback aspect.
• I didn't need to do any math (usually a downside to having everyone solve a different problem) since I told them to take a screenshot of the GeoGebra file - I could see the image, points and equation all on the coordinate grid.
• I wish GeoGebra didn't expand the equations. It was annoying for kids who wanted to check if they typed something right and it didn't tell me how they set up their equations.
• Kids are not all fluent in technology, when I told them to take a screenshot of the GeoGebra file one student took a picture of her screen, with a camera. Not what I meant, but it worked and it made me smile.
• Seriously, grading was so easy. Open DropItToMe folder, check some boxes, maybe write a note, done.