Human Conics: Circles and Ellipses

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SWBAT define circles and ellipses as a locus of points and apply locus definitions to draw conic sections.

Big Idea

Students collaborate with partners to become a human conic section and draw circles and ellipses using sidewalk chalk.

Warm-up: Define Circles and Ellipses

10 minutes

Overview: This lesson is adapted from the Human Conics lessons from the NCTM Illuminations website. I will be doing half of the lesson today with my students and the other half at a later time.

Preparation: For this first part of the lesson, students will need access to a compass. Later in the lesson, students will need sidewalk chalk and a rope (one piece, 10-12 feet long per group of 3 students). Human Conics, Supplies Needed.

Narrative:  As students enter class today they should begin working on questions 1-2 of the Human Circle Student Worksheet. (I am going to copy this back to back with the Human Ellipse worksheet which is located in next section of lesson).  After about 5 minutes bring the class back together. Discuss how the parts of the compass relate to the parts of the circle. Emphasize the importance of not changing the width of the compass (the radius of the circle) by squeezing too tightly when using the compass. Also, emphasize that the definition of a circle describes the points on the circle, not the area inside.

Next, present the definition of an ellipse using Teacher Resource - Ellipse Definition. I am not planning on giving students a copy of the definition. I will project this resource under the document camera. I am going to use different colors on the paper to highlight the pieces of the definition. I will take this paper with us when we go outside in case any teams want to reference it while we are outside.

Human Conics

35 minutes

Students will now venture outside (in Arizona we generally don't have to check the weather). Teams of three students will complete the tasks posed on the Human Circle and Ellipse handout. Each group will need to apply the definition of both conic sections (circle and ellipse) in order to draw these accurately with sidewalk chalk. I will be checking in with teams and to ensure their drawings are accurate. Students should start with the circle and then work on the ellipse.

I think this activity is going to be challenging for students to figure out how to work as a team to draw the conic sections. I am guessing there are going to be a lot of great student conversations going on.

I hope to see a lot of activity with respect to Mathematical Practice 3: Construct viable arguments and critique the reasoning of others.

Closure: Class Huddle

5 minutes

With about 5 minutes remaining in the class period, I am going to call students over to a huddle outside. I just want to collect student work now and also ask some closure questions of the class.

Here are the questions I will pose to students:

  1. How many people minimally does it take to draw a circle? An ellipse?
  2. What would happen if the rope was longer? Shorter?
  3. Are you able to draw these conics continuously (without picking up the chalk)?