This is the second of the activities designed to help you celebrate Phi Day on November 23rd, so named for the date's relationship to the Fibonacci sequence: 1, 1, 2, 3, ...
This second activity builds on the first [Phi Day (1)--Golden Rectangles], but this activity works well as a stand-alone, and does NOT require that activity to be completed first.
In this activity the students first get a historical lesson on who Fibonacci was, and then read the problem that he posed that has led to the namesake sequence.
Students then explore recursive functions that lead them to the recursive definition of the Fibonacci sequence.
Students then explore exactly HOW the Fibonacci sequence leads to the Golden Ration, phi.
Finally, students are given an explicit (non-recursive formula) to calculate the terms of the Fibonacci sequence and are asked to practice with it. A calculator would be an excellent resource for this portion of the activity.