Pre-Trip Activity: Generalized Fibonacci Sequences
Objective: To understand Fibonacci sequence and how it is expressed in nature.
Materials: pictures of flower petals, cauliflower florets, pinecones, and seed heads
Things to Do:
1.
Write this sequence 1 1 2 3 5 8 on the board. Ask the students to find the pattern. (Add the previous two numbers to get the next number in the sequence).
Have students calculate 12 more terms of the sequence. Tell students that this sequence has intrigued mathematicians for centuries and it has appeared in different patterns in nature.
2.
Watch this video:
Maths in the Nature:
3.
Divide students into groups. Distribute illustrations and ask them to answer these questions: (The numbers vary, but they are all Fibonacci numbers.)
a. Flower petals: Count the number of petals on these flowers. Are they Fibonacci numbers? (Lilies and irises have 3 petals, buttercups have 5 petals and asters have 21 petals; all are Fibonacci numbers.)
b. Seed heads: Each circle represents a seed head. Do the circles form spirals? Start from the center; find a spiral going towards the left. How many seed heads can you count?
c. Cauliflower florets: Locate the center of the cauliflower. Count the number of florets that make up a spiral. Are they Fibonacci numbers?
d. Pinecones: Look carefully; do the seed cases make spiral shapes? Find as many spirals as possible. How many seed cases make up each spiral? Are they Fibonacci numbers?
Things to Discuss:
1.
Ask which shape emerges the most often from the clusters of seeds (the spirals). Discuss if there are advantages to this shape. (Seeds may form spirals because this is an efficient way of packing the most number of seeds into an area).
2.
Ask where else they see the spiral shape in nature (nautilus shell). Are those spirals also formed from Fibonacci numbers? Are these shapes pleasing? To conclude, discuss other pleasing patterns in nature, such as leaves, branches, etc. Do they have mathematical basis?
Extensions:
Further explore Fibonacci numbers in nature. Challenge students to find other patterns of numbers in crystals and rocks, in the distance of planets from the sun and so on.
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