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
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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.

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11 teachers like this lesson
Math, Algebra, Quadratic Equations, complex numbers, Algebra II, master teacher project, algebraic methods, 11th Grade
  55 minutes
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