The first part of an investigation into how to represent numbers using geometric transformations that ultimately leads us to discover numbers not on the number line.
Introduces the idea of a twizzle to represent number and asks how one can use this representation to add and subtract geometrically.
How can you use twizzles to multiply and divide?
Track the roots of quadratic equations as you move the corresponding graphs and discover the transitions from real to complex roots.
Make a conjecture about the curved track taken by the complex roots of a quadratic equation and use complex conjugates to prove your conjecture.