Constructions of Conic Sections

thingiverse

By: Michelle Lorentzen, Ariana Wanderlingh, Kevin Valenza This project introduces students to conic sections, which include circles, parabolas, hyperbolas, and ellipses. This is done by demonstrating how they are formed when a plane intersects a single or double cone. How I Designed This Project For the circle, we began with a cone and the letter "I" before spreading it out to resemble a plane. We achieved this same effect for the ellipse by angling the plane. To create a parabola, we started with the cone and positioned a plane that passed through its base. For the hyperbola, we duplicated the cone, rotated it 180 degrees, and moved it upwards before cutting it with a plane. Custom Section Overview & Background By completing this project, students will gain an understanding of how conic sections are formed when a plane intersects a single or double cone. They will learn about their formation: hyperbola is created from two cones, while circles, parabolas, and ellipses result from a single cone. Objectives Students will learn: 1. How to cut a cone with a plane 2. What forms after cutting a cone with a plane 3. The differences between the four conic sections Audience Grade: 10th, 11th, and 12th Age: 16 - 18 Skill Level: Geometry & Pre-Calculus Subjects Math and Physics Students will derive equations for ellipses and hyperbolas given their foci. This knowledge from geometry will lead into conic sections. Once they see these formulas, students can understand where they come from – the conic sections. Later in pre-calculus and physics classes, students will learn the formulas for all conic sections. Standards CCSS.MATH.CONTENT.HSG.GPE.A3 This project is based on the district's Pre-Calculus curriculum design. Lesson/Activity Steps: 1. Explain the four different conic sections. 2. Assign partners to work together. 3. Create an account on tinkercad.com. 4. Create the four conic sections using Tinkercad. 5. Complete the provided worksheet. Duration Time breakdown: 10 minutes: Explaining what conic sections are 20 minutes: Students create the conic sections with a partner on Tinkercad 10 minutes: Class discussion to share ideas and insights Preparation Students need to be familiar with the shapes of circles, parabolas, hyperbolas, and ellipses. They will use Tinkercad to complete this activity. References If students are unfamiliar with conic sections, they can refer to the link below for further understanding: https://www.khanacademy.org/math/precalculus/conics-precalc After research, create the worksheet. Rubric & Assessment Students must save the link to their created conic sections and send it to us. They will complete a handout based on this activity. Grading will be done on effort rather than correctness, using a scale of 1-4. Handouts Name: __________ Date: ___________ Period: _________ Conic Sections What are the four conic sections? a. b. c. d. How are each of the four sections cut? a. b. c. d. How did you use Tinkercad.com to create the four conic sections? What did you learn from this activity?