Constructions of Conic Sections

thingiverse

By: Michelle Lorentzen, Ariana Wanderlingh, Kevin Valenza This project is an introduction to conic sections. The four conic sections are: circles, parabolas, hyperbolas, and ellipses. This is to show how they are formed by cutting either a single or double cone with a plane. How I Designed This How we designed this For the circle, we started with the cone and the letter "I" and spread it out to look like a plane. For the ellipse, we did the exact same thing, but angled the plane to create an ellipse. For the parabola, start with the cone and a plane where the plane passes through the base of the cone. For the hyperbola, we started with a cone then duplicate the same cone and rotate it 180 degrees and move it up. Then take a plane and cut the double cone to create the hyperbola. Custom Section Overview & Background By completing this project, students will learn how the four different conic sections are formed by cutting either a cone or a double cone with a plane. They will learn how they are formed: hyperbola is a double cone where circles, parabolas, and ellipses are single cones. Objectives Students will learn: How to cut a cone with a plane What is formed after cutting a cone with a plane What the difference between the four conic sections are Audience Grade: 10th, 11th, and 12th Age: 16 - 18 Skill Level: Geometry & Pre-Calculus Subjects Math and Physics Students derived the equations of ellipses and hyperbolas given the foci. That from Geometry will lead into conic sections. From seeing these formulas, they will now be able to see where they come from, which is the conic sections. Later on in Pre-Calculus and Physics, the students will be learning the formulas for all of the conic sections. Standards CCSS.MATH.CONTENT.HSG.GPE.A3 Based off the design of the district's Pre-Calculus curriculum. Lesson/Activity Steps: Explain the four different conic sections Get with assigned partners Create an account on tinkercad.com Create the four conic sections Complete the worksheet Duration 10 minutes - Explaining what conic sections are 20 minutes - Let the students create the conic sections with a partner on Tinkercad 10 minutes - Class Discussion to get ideas on how they created their conic sections Preparation Students need to know what circles, parabolas, hyperbolas, and ellipses look like. Students will use Tinkercad to complete the activity. References If students are unfamiliar with the conic sections, refer to the link below to further understand each section. https://www.khanacademy.org/math/precalculus/conics-precalc Post research - Create the worksheet Rubric & Assessment The students will have to save the link to their conic sections and send us the link. The students will complete a handout based on the activity they just completed. We will grade it on a scale of 1 - 4, not based off of correctness, but on effort. 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?