Students will explore a variety of middle level content as they examine Fibonacci connections to divisibility and to the golden ratio. They will discover interesting Fibonacci properties and use basic algebraic properties and symbols to prove conjectures about those properties.
Before the Activity
Open the file Fibonacci_Fun.tns on your handheld and work with a small group to complete pages 1.1 through 1.4. Use these answers as a reference while completing the rest of the activities.
During the Activity
Complete the remaining activities as presented in Fibonacci_Fun.tns.
After the Activity
Facilitate a whole class discussion in which students share their method of proving the conjecture in Problem 3. Be sure that a number of different proofs are shared and that you end with a discussion of the advantages and disadvantages of the various types of proof. Allow time for students to revise their own proof if needed.