## Reflection: High Expectations Complex Addition - Section 3: Discussion: Complex Addition

In the narrative, I said that "I expect students to offer a variety of justifications."  In fact, today they didn't offer any at first.  When I tried the pair-share, I saw quite a few students just turn to their partner and say, "I have no idea."  Ouch!  Now what?

Now, I know that my students have the knowledge they need in order to explain this pattern.  I also know that they're perfectly capable of putting the pieces together to formulate a good argument.  However, they may need to be reminded of what they know and how to think about it.

"Ok," I said, "it seems like these points form a parallelogram each time.  Do you know of any way to prove that it's a parallelogram?  Do you recall some of the properties of parallelograms?"

To this, students responded that we could prove the lines are parallel, prove the opposite sides are equal, or prove the opposite angles are equal.

"Good," I responded, "how can we prove lines are parallel? [Look at the slope.]  Do we have a way of proving lines are equal? [The Pythagorean theorem.]  How about proving the angles are equal? [Hmm...]"

"Ok, then, it's time to get back to work trying to justify or prove this pattern.  I'd suggest you consider the slopes of these line segments.  Good luck!"

With this, I gave the class more time to discuss the problem and work collaboratively to justify the pattern.  Within a few minutes, two or three students thought they had it figured out, so I began sending other students to them for help.

What if they don't?
High Expectations: What if they don't?

Unit 2: The Complex Number System
Lesson 5 of 16

## Big Idea: The lowly parallelogram helps students make sense of addition and subtraction of complex numbers.

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Subject(s):
Math, complex conjugates, Algebra, Algebra 2, master teacher project, complex numbers, Imaginary Numbers
45 minutes

### Jacob Nazeck

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