For many years as a Mathematics Education, Consultant/Adviser I encouraged teachers to look beyond the calculations that many maths' programs seem to focus on.
"Mathematics is the language in which God has written the universe."
In fact Galileo suggested;
As I look around me I don't tend to see numbers everywhere(unless put there by people!). What I see are flowers and trees and natural things.
So why is it in maths class we tend to start with the "abstract numbers" rather than the real thing as Galileo would suggest?
In 1987 I had the opportunity to visit California investigating maths approaches. I was fortunate to visit a class in Santa Barbara where for the start of the lesson all the groups of students were given a pineapple! I did not notice any WALTs or AOs, but I heard the teacher ask the students to explore the pineapple and to see what sort of patterns they saw. The students were then engaged in debate and investigation for the rest of the lesson.
Of course we could use Pine Cones and do the same but we cant eat them at the end of the lesson
I have just re watched a TED Talk called : The Magic of Fibonacci Numbers admittedly it goes on into the number patterns that Leonardo of Pisa (Fibonacci) found many years ago but depending on out age group will depend on how far you take the abstract numbers.
A couple of years back I was asked to present at the PMA Maths Seminar Day and I started the session with Water Lillies, Bananas, and pine cones on the desks for the teachers to explore.
I am sure for some teachers they had never started with the "Real Thing"
Why not give it a go-dont start with the Fibonacci Numbers - 1 1 2 3 5 8... but start with various natural objects that the students should be able to come up with similar numbers
(the number or clockwise and anticlockwise spirals on a Pine Cone,
How many seed heads in one of the spirals?
How many petals on a Tulip? Daffodil?
How many parts to a Banana?
Enjoy watching the students' curiosity and interest in maths soar.
Do an Internet Search for more ideas and Approaches for the Fibonacci Numbers
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