What patterns can we find in nature? Plants, flowers and fruits have all kinds of patterns, from petal numbers that are in the Fibonacci sequence, to symmetry, fractals and tessellation.

2. Who IS Fibonacci?
Fibonacci was an Italian mathematician. He was
really named Leonardo de Pisa but his nickname
was Fibonacci.
About 800 years ago, in 1202, he wrote himself a
Maths problem all about rabbits that went like this:
"A certain man put a pair of rabbits in a place
surrounded by a wall. How many pairs of rabbits can
be produced from that pair in a year if it is supposed
that every month each pair breed a new pair from
which the second month on becomes productive?"
(Liber abbaci, pp. 283-284)

3. Fibonacci’s
Rabbits!
Like all good mathematicians he stayed
working on this problem for months and
eventually came up with a solution:

4. A load of…
 Fibonacci’s
rabbit theory turned out not
to be true BUT the sequence he created
IS incredibly useful…
 The sequence goes:
Can you work
1, 1, 2, 3, 5, 8, 13, 21, 34 ….
out which
numbers come
next?

5. Continue the sequence…

Fibonacci’s sequence is made by adding the two
previous numbers together to create the next, starting
with zero and one:

0+1=1
1+1=2
1+2=3
2+3=5
3+5=8
…keep going in your notebooks!

6.  The
sequence Fibonacci created
may not have solved his rabbit
reproduction problem
 BUT other mathematicians looked
at his numbers and started seeing
them all over the place.

7. Find Fibonacci!

11. Other patterns in nature…
 Nature
may be full of Fibonacci but
not EVERY plant or flower has a
Fibonacci number.
 There
are plenty of other interesting
patterns to look out for.
 Can
you think of any patterns?

12. 1. Symmetry…
SYMMETRY
– You can find symmetry
in leaves, flowers, insects and
animals.
Can
you think of any examples?

16. 2. Spirals…
Can you
count the
spirals??

17. A
Fibonacci
number?

20. Check this out!
 Look
at what your teacher has brought in
and talk about any pattern you see.

21. 3. Fractals…
 Some
plants have fractal patterns. A
fractal is a never-ending pattern that
repeats itself at different scales.
A
fractal continually reproduces copies of
itself in various sizes and/or directions.
 Fractals
are extremely complex,
sometimes infinitely complex.

24. Watch this fractal zoooom!
 Watch
from 3:05 for one minute:
 http://www.youtube.com/watch?v=IIOQcJZlJE
 Watch
the same minute again and write
your own definition of a fractal.

25. A never-ending pattern

27. Tessellation…
Sometimes in nature we find tessellation.
A tessellation is a repeating pattern of polygons
that covers a flat surface with no gaps or
overlaps.


Think about when you tile a floor. No gaps
and no overlapping tiles! There are regular
tessellations (all the same shape tiles) and
irregular (a mix of shapes).

Can you think of any examples in nature?

30. Where is
THIS
tessellation
from?!

31. Pattern hunters!
 With
all these patterns to search for, fifth
graders will be pattern hunters on Friday!
 With
your clipboards, pencils and lots of
curiosity, you will be searching for and
sketching patterns.
Good luck! 