Reflection: Discourse and Questioning Another Solution - Section 3: Wrap it Up

 

I sometimes just walk around and listen rather than collecting student work.  In this lesson, I heard a student explaining to his partner:

Student 1: "Imaginary roots happen when an equation factors out to give answers that don't make sense, like when we got imaginary ohms for one problem." 

Student 2: (His partner) "What about answers that aren't imaginary but still don't make sense like getting a negative profit?" 

Student 1: "Some answers are like that, but most imaginary answers are not for real problems, while sometimes you can have just a negative answer, like when you owe money or when something happened back in time." 

Student 2:  "OK, so just because it doesn't work doesn't mean it's imaginary, but then how do we explain imaginary if Mrs. Rampy calls on us?" 

Student 1: "We just say that it's any answer with an i in it!"

This dialogue is valuable to me because I can see that my students actually have some understanding that not all solutions to a problem are viable, but it also shows me that some are still not solid in what an imaginary number might mean in a real-world situation, so I need to continue to build that connection.

  Student Discussion
  Discourse and Questioning: Student Discussion
Loading resource...
 

Another Solution

Unit 4: Complex Numbers
Lesson 4 of 8

Objective: SWBAT solve quadratic equations with real coefficients and complex solutions from real-world problems.

Big Idea: Imaginary answers to real-world problems! How is that possible? Let your students explore that question for themselves.

  Print Lesson
11 teachers like this lesson
Subject(s):
Math, Algebra, Quadratic Equations, complex numbers, Algebra II, master teacher project, algebraic methods, 11th Grade
  55 minutes
4192576317 b960e47d26 q
 
1
2
3
Similar Lessons
 
Complex Solutions to Quadratic Equations
Algebra II » The Complex Number System
Big Idea: Students investigate the geometry of the complex solutions to a quadratic equation in a dynamic setting.
  Favorites(3)
  Resources(13)
Fort Collins, CO
Environment: Suburban
Jacob Nazeck
 
Roots of Polynomial Functions - Day 2 of 2
12th Grade Math » Polynomial and Rational Functions
Big Idea: Find complex roots and learn about the history of imaginary numbers.
  Favorites(1)
  Resources(12)
Troy, MI
Environment: Suburban
Tim  Marley
 
Rabbit Run -- Day 2 of 2
Algebra I » Quadratics!
Big Idea: Students look for and express regularity in repeated reasoning (MP8) as they generalize a formula.
  Favorites(2)
  Resources(16)
Boston, MA
Environment: Urban
Amanda Hathaway
 
Something went wrong. See details for more info
Nothing to upload
details
close