## Reflection: Flexibility Complex Addition - Section 2: Individual Time: Complex Addition

Today, I found that 10 minutes wasn't quite enough time.  Since my students found the addition easy (even though they were still making mistakes), they began to lose interest.  In their eyes, the requirement to plot the solutions in the complex number plane was beginning to smack of "busy work".  So, I decided to make it clear that I was expecting them to see something, to identify some sort of pattern or rule.

They didn't know what I was looking for, and they weren't seeing any sort of pattern, so I made the instructions more explicit by telling them to draw lines connecting each of the addends to zero and to their sum.  Just so there was no confusion, I sketched an example on the board.  In just a minute or two, students all over the classroom were recognizing the parallelograms, but they were thrown off a bit because many of them also had trapezoids of some sort due to mistakes in their addition.

Time for another explicit direction: If you are looking at something other than a parallelogram, you'd better go back and double-check your arithmetic.  Usually I don't like to tell the class what pattern they're supposed to be finding, but in this case it seemed necessary.

Flexibility: Taking Your Time

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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