Fibonacci Sequence — Patterns in Nature

Fibonacci appears everywhere in nature. The recursive rule is simple, the consequences profound. Indirect aim: sequences, recursion, mathematical aesthetics, preparation for calculus.

• Framework: Montessori
• Unit: Sensorial
• Learning area: Algebraic Sensorial
• Level: Ages 9-11

Objectives

• Generate the Fibonacci sequence: 1,1,2,3,5,8,13,21...
• Understand the recursive rule f(n) = f(n-1) + f(n-2)
• Find Fibonacci in nature (pine cones, sunflowers)
• Connect to the Golden Ratio

Materials

• Fibonacci sequence chart
• Sunflower, pine cone specimens
• Graph paper for spiral
• Calculator for ratio computation

Instructions

1. Start: 1,1. 2. Add: 1+1=2. 3. Next: 1+2=3, 2+3=5, 3+5=8, ... 4. Continue to 10+ terms. 5. Count spirals in a sunflower or pine cone — usually Fibonacci numbers. 6. Compute f(n+1)/f(n) — approaches golden ratio 1.618. 7. Draw the Fibonacci spiral. 8. File discoveries.

Educator tip

Show the Parthenon, Mona Lisa, nautilus — the golden ratio lives everywhere. This is math as aesthetics.

Assessment

Observe sequence generation, ratio computation, and nature-spotting.

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