4. 1. Identify patterns using Fibonacci sequence
2. Recognize patterns in nature cause by the Fibonacci
process.
5. FIBONACCI SEQUENCE
The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers
before it. Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth. Written as a
rule, the expression is
0, 1, 1, 2, 3, 5, 8, 13, 21, 34
5th
Examaple: the 5th
number in the series is 3. 0, 1, 1, 2, 3
= 2 + 1 = 3
Named after Fibonacci, also known as Leonardo of Pisa or Leonardo Pisano,
Fibonacci numbers were first introduced in his Liber Abbaci (Book of
Calculation) in 1202. The son of a Pisan merchant, Fibonacci traveled widely
and traded extensively. Mathematics was incredibly important to those in
the trading industry, and his passion for numbers was cultivated in his youth.
x x x
th
5 3 3 1 3 2
6. TYPES OF SEQUENCE
In dealing of the sequence of the set of
numbers classify them accordingly:
Geometric, Arithmetic, Harmonic and
Fibonacci. To know them, please refer to
the video taken from TikTok
7. FIBONACCI SEQUENCE
• THE HABBIT RABBIT
Chapter 1: Mthematics in our World
One of the book’s exercises which is written like this “A man put a pair of rabbits in a place surrounded on all
sides by a wall. How many pairs of rabbits are produced from that pair in a year, if it supposed that every month
each pair produces a new pair, which from the second month onwards becomes productive?” This is best
understood in this diagram:
8. FIBONACCI SEQUENCE
Chapter 1: Mthematics in our World
GROWTH OF RABBIT COLONY
MONTHS ADULT PAIRS YOUNG PAIRS TOTAL
1 1 1 2
2 2 1 3
3 3 2 5
4 5 3 8
5 8 5 13
6 13 8 21
7 21 13 34
8 34 21 55
9 55 34 89
10 89 55 144
11 144 89 233
12 233 144 377
The sequence encountered in the rabbit problem 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, …. is
called the Fibonaccisequence and its terms the Fibonacci numbers
.
9. GOLDEN RECTANGLE
• Leonardo of Pisa also known as Fibonacci discovered a sequence of numbers that
created an interesting numbers that created an interesting pattern the sequence 1,
1, 2, 3, 5, 8, 13, 21, 34… each number is obtained by adding the last two numbers of
the sequence forms what is known as goldenrectangle a perfect rectangle.
Chapter 1: Mthematics in our World
11. Chapter 1: Mthematics in our World
FIBONACCI SEQUENCE IN NATURE
The sunflower seed conveys the Fibonacci sequence. The pattern of two spirals goes in
opposing directions (clockwise and counter-clockwise ).
The number of clockwise spirals and counter clockwise spirals are consecutive Fibonacci
numbers and usually contains 34 and 55 seeds.
12. FIBONACCI SEQUENCE IN NATURE
Chapter 1: Mthematics in our World
The Fibonacci sequence can also be seen in the way tree branches form or split. A main trunk will grow
until it produces a branch, which creates two growth points. Then, one of the new stems branches into two,
while the other one lies dormant. This pattern of branching is repeated for each of the new stems. A good
example is the sneezewort. Root systems and even algae exhibit this pattern
16. Solution
1 0
1
1
4 2
2 1 3
3 2 5
5 3 8
8 5 13
1
2
3
5
6
7
8
. F
F
F
F
F
F
F
F
2. 2584
3.
F
F
F
F F F
F
F
F
22
23
24
24 23 22
23
23
23
10 946
28 657
28 657 10 946
28 657 10 946
17 711
,
?
,
, ,
, ,
,
1 0
2 1
3 1
4 2
5 3
6 5
7 8
8 13
9 21
10 34
11 55
12 89
13 144
14 233
15 377
16 610
17 987
18 1597
19 2584
17. GENERALIZATION
Based from the lesson, without opening a slide or your notes,
give the definitions in your own words the following
1.Fibonacci numbers
2.Fibonacci Sequence
18. ASSESSMENT
Students will answer the task indicated on this
module. Task includes fill-in the blanks, Identification
and completion of table with data
19. Students will be given time to feedback on
the lesson. A short discussion will follow
and concerns will be noted to address
accordingly.
20. Performance Task
Read or watch the video clip of “The
Great Mystery of Mathematics.
Make your own Reflection. (Be creative in
presenting your output)
21. ASSIGNMENT
Do the advance reading of our next lesson
intended for week 4; mathematics as a
language and symbols
