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 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.
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.
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
Grade: 10th, 11th, and 12th
Age: 16 - 18
Skill Level: Geometry & Pre-Calculus
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.
Based off the design of the district's Pre-Calculus curriculum.
Explain the four different conic sections
Get with assigned partners
Create an account on tinkercad.com
Create the four conic sections
- Complete the worksheet
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
Students need to know what circles, parabolas, hyperbolas, and ellipses look like. Students will use Tinkercad to complete the activity.
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.
What are the four conic sections?
How are each of the four sections cut?
How did you use tinkercad.com to create the four conic sections?
- What did you learn from this activity?