Conic Sections Lesson Plan

Instructor: Tammy Galloway

Tammy teaches business courses at the post-secondary and secondary level and has a master's of business administration in finance.

This lesson explores conic sections and the different types. Students will complete a reading assignment, answer discussion questions, complete an activity and take a quiz. The class activity can also be used as an online individual project.

Learning Objectives

After this lesson, students will be able to:

  • Define conic sections
  • Describe various types of conic sections
  • List and explain the formulas for each conic section

Length

60 minutes

Curriculum Standards

  • CCSS.Math.Content.HSG.GPE.A.1

Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

  • CCSS.Math.Content.HSG.GPE.A.2

Derive the equation of a parabola given a focus and directrix.

  • CCSS.Math.Content.HSG.GPE.A.3

(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

Materials

Instructions

  • Begin this lesson by asking students to draw and identify their favorite geometric shapes.
  • Now explain that a few of those shapes are known as conic sections, and this lesson will explore them in further detail.
  • Distribute a copy of the Practice with the Conic Sections lesson, select a student to read the first section, 'What are Conic Sections?', then ask students to define a conic section and provide a few examples.
  • Now choose another student to read 'Circles' then ask these questions:
    • What is the formal definition of a circle?
    • Write the formula associated with a circle.
  • Afterwards, select another student to read 'Ellipses' and ask the following:
    • Describe an ellipse.
    • Does an ellipse have a radius? Explain.
    • Why do ellipses have a formula for an x direction and y direction?
    • Write each formula for an ellipse.
  • Reconvene the class, choose another student to read 'Parabolas' and pose the following:
    • How are parabolas formed?
    • Explain parabolas from a mathematical perspective as outlined in the lesson.
    • Describe the two possible forms of a parabola equation.
  • Now, select another student to read the remainder of the lesson, then ask these questions:
    • Describe a hyperbola.
    • A hyperbola is similar to which type of conic section previously mentioned?
    • How would you decipher between the ellipse and hyperbola formulas?
  • Now, distribute a copy of the lesson quiz. Allow students to complete in pairs, individually or in groups.

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