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Imaginary Numbers Lesson Plan

Instructor: Sharon Linde

Sharon has a Masters of Science in Mathematics

Teach your students about imaginary numbers with this lesson plan. Students will watch an engaging video explaining the basics of imaginary numbers such as where they come from and how to solve with them. Discussion questions, activities and a quiz will help make concepts memorable.

Learning Objectives

After this lesson, students will be able to:

  • define imaginary numbers
  • explain how to solve with imaginary numbers

Length

1 - 1.5 hours

Materials

  • Index cards
  • Copies of the lesson quiz, one for each student

Key Vocabulary

  • Imaginary number
  • Complex number

Curriculum Standards

  • CCSS.Math.Content.HSN.CN.B.4

(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

Instructions

  • Start the lesson by asking students to share everything they know about the quadratic formula. You can either have them write down their existing knowledge, discuss it as a whole group, or divide students into partners.
  • After three or four minutes, have students share answers. Write the formula on the board or poster paper and review, making sure students are up-to-date on this concept.
  • Now start the lesson video What is an Imaginary Number?.
  • Pause at 2:28. Define 'imaginary number,' then ask:
    • Why is the answer -16 a problem for the equation b^2 - 4ac?
    • How do imaginary numbers help us find answers to questions?
    • What types of questions do imaginary numbers help us to solve?
  • Resume the lesson and pause again at 4:48. Ask:
    • What is the square root of -25?
    • What is the square root of -4?
    • What is a discriminant?
    • What does it say about your solution if you have a positive discriminant? A negative one?
    • What is a complex number?
    • What do you call it when you combine a real number and a number with an imaginary number?
  • Restart the lesson and pause at 7:43 and have students, independently, with partners, or in teams do the following:
    • Simplify i to the second, third, fourth and fifth power.
    • Identify the pattern.
  • Discuss student answers, then play the remainder of the lesson video.

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