Visualizing Numbers Real and Imaginary

In the video below I try to give some of the "patter" I use when I introduce the idea of "i" for the first time. I think that there is a great benefit in doing it this way because it helps strengthen their understanding of what real numbers do as well. It also emphasizes that numbers often get paired with operations. I actually could make that clearer. Anyway, feel free to steal this introduction to use in your own classes.

Visualizing Complex Numbers

In my continued quest to spread an understanding of complex numbers I put together this little dance sequence with my Summer School Algebra 2 students. I used the function f(x)=(x-1)^2+1 determine the dance sequence. This function has two complex roots (1+i) and (1-i). I had students stand at 1+i, i, -1+i, 1, -1, 1-i, -i, and -1-i, then we went through the three steps of the function. These were "minus 1", "squared", and "plus 1". The most important visual here is to get a sense of what squaring does to the complex plane. This includes some expansion of the numbers with distance greater than 1 and a wrapping of plane on top of itself. Watch the video and let me know what you think?

How is a function like a recipe?

I was talking about function notation with my students, and trying hard to differentiate between f, f(x), and f(x)=x+3. The metaphor that I tried was recipe. Does anyone else have a good metaphor that helps to distinguish these concepts?

Sneetches = Inverse Functions

Teaching summer school today. I had a student not understand what f(f^(-1)(x))=x was trying to say. I was searching for a process that would help her understand doing and undoing. And then it hit me. Sylvester McMonkey McBean.

Conic Movie

I have been reading the book Conics by Kevin Kendig. This movie was made with Grapher on my Mac, and displays the viewpoint of taking conics and projecting them down on the sphere.