This is the third 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 third activity builds on the first two [Phi Day (1)--Golden Rectangles and Phi Day (2)--The Fibonacci Sequence], but this activity works well as a stand-alone, and does NOT require that activity to be completed first.
Like the previous activities, this begins with some basic facts about the number phi.
Students then explore, using images of a pine cone and a sunflower, how the spirals of the scales and the seeds relate to the Fibonacci sequence.
Students then make a Fibonacci spiral by repeatedly making Golden Rectangles. [It may help for them to have seen the earlier activity, but directions provided should allow students to create the rectangles without having done Phi Day (1).] Students then look at Fibonacci spirals that occur in nature.
Finally, the students explore how the Fibonacci sequence can be found in Pascal's Triangle. As a closing activity, the students learn to calculate the individual elements of Pascal's Triangle by using the formula for combinations.