Republic of the Philippines
CAMARINES NORTE STATE COLLEGE
F. Pimentel Avenue, Brgy. 2, Daet, Camarines Norte – 4600, Philippines
INSTITUTE OF COMPUTER STUDIES
GEC 3 – Mathematics in the Modern World
Page 1 of 8
Republic of the Philippines
CAMARINES NORTE STATE COLLEGE
F. Pimentel Avenue, Brgy. 2, Daet, Camarines Norte – 4600, Philippines
INSTITUTE OF COMPUTER STUDIES
GEC 3 – MATHEMATICS IN THE MODERN WORLD
DOROTHY S. SURETA
Assistant Professor
Contact Details
Contact Number: 09167422338/09184922805
E-mail Address: Momsureta28@gmail.com
Web Address: [Type your web address or social media link]
Consultation Schedule
Every Friday 2 -5 pm
OUTLINE OF LEARNING TOPICS
TIME ALLOCATION
A. The Nature of Mathematics
A.1 Mathematics in the Modern World
-Patterns and Numbers in Nature and the World
-The Fibonacci Sequence
Week 2 [Prelim]
INTENDED LEARNING OUTCOMES (ILOs)
At the end of the topic, students should be able to
• Identify patterns in nature and regularities in the world.
• Articulate the importance of mathematics in one’s life.
• Argue about the nature of mathematics, what it is, how it is expressed, represented and used.
• Express appreciation for mathematics as a human endeavor.
INSTRUCTIONS TO THE LEARNERS
This learning material serves as a reflection among one of the flexible learning strategies that complement
the outcomes-based education approach. This material contains the essential discussions for the specified
topic together with a learning activity in order to achieve the indicated intended learning outcomes.
In addition, students will undergo pre-test and post-test short-examination. The pre-test questionnaires will
be given at the start of each rating period (Prelims, Midterms, Finals) while the post-test questionnaires will
be given at the end of each rating period. The results of the assessment will serve as one of the key indicators
that determine the effectiveness of this learning material. Thus, exemplifying honesty and rectitude in this
particular undertaking are highly appreciated and commendable.
Always keep connected and updated with announcements and relevant information concerning this course.
Lastly, do not hesitate to ask for assistance and raise your concerns to your instructor / professor.
GEC 3 – Mathematics in the Modern World
Page 2 of 8
Republic of the Philippines
CAMARINES NORTE STATE COLLEGE
F. Pimentel Avenue, Brgy. 2, Daet, Camarines Norte – 4600, Philippines
INSTITUTE OF COMPUTER STUDIES
A. The Nature of Mathematics
Introduction
Mathematics is more than numbers (constants) and variables (e.g. a, b, or x & y). It does not end in
finding the value of a variable nor finding the solution set to a particular mathematical expression. It is more
than graphing on a Cartesian plane and constructing a 3-dimensional figure. During your Research Subject,
mathematics plays a big role in collecting, organizing and presenting your data. However, its application goes
beyond than that of an academic requirement. In this learning material, you will find out how mathematics is
reflected in our nature.
A.1 Mathematics in the Modern World
A.1.1. Patterns and Numbers in Nature and the World
A pattern may have a list of numbers in which a constant is added to get the succeeding terms. For
other sequences, the terms are increasing because the number to be added is increasing in a predictable
way. There are also number patterns whose terms are decreasing, because the number to be added is
decreasing in an expected way.
Let us refer to Table 1 for the different set of examples.
To generate the next term,
the number to be added is
repeating
growing / increasing
shrinking / decreasing
Table 1. Patterns and Numbers
Example 1
10, 20, 30, 40, 50, 60, …
14, 15, 17, 20, 24, 29, …
118, 98, 73, 43, 8, -32, …
Example 2
9, 18, 27, 36, 45, 54, …
4, 5, 7, 10, 14, 19, 25, …
200, 190, 170, 140, …
Learning Activity No. 1 – Abstraction (Critical Thinking)
Write the next three terms of the following sequences. Once you are done, present your output to your
instructor/professor or classmates. Then share how did you able to conceptualize and arrive on those
answers.
1) 8, 16, 24, 32, …
Answers: ________, ________, ________
2) 1, 2, 4, 7, 11, …
Answers: ________, ________, ________
3) 100, 78, 54, 28, 0, ...
Answers: ________, ________, ________
4) 30, 35, 45, 60, 80, …
Answers: ________, ________, ________
5) 151, 149, 145, 137, 121, …
Answers: ________, ________, ________
6) 36, 43.5, 51, 58.5, 66, …
Answers: ________, ________, ________
7) 500, 450, 350, 200, …
Answers: ________, ________, ________
1
2
11 23 37 53
,
,
,
,…
2
2
2
2
Answers: ________, ________, ________
5
6
13 21 29 37
,
, ,
,…
6
6
6
6
Answers: ________, ________, ________
8) ,
9) ,
10) √3, 3 + √3, 6 + √3, …
GEC 3 – Mathematics in the Modern World
Answers: ________, ________, ________
Page 3 of 8
Republic of the Philippines
CAMARINES NORTE STATE COLLEGE
F. Pimentel Avenue, Brgy. 2, Daet, Camarines Norte – 4600, Philippines
INSTITUTE OF COMPUTER STUDIES
Learning Activity No. 2 – Application (Creativity)
Create a sequence satisfying the following conditions as stated below. Once you are done, share your
output to your classmate/s, then observe both of your answers. Prove each answers that they both satisfy
the given condition.
1) The fifth term is 40.
2) The tenth term is 300.
3) The first term is ½.
4) The third term is 0.
A.1.2. The Fibonacci Sequence
The Fibonacci sequence is one of the most famous formulas in mathematics. Each number in the
sequence is the sum of the two numbers that precede it.
So, the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.
The man behind this sequence is Leonardo Pisano Bogollo,
whose nickname was “Fibonacci” which roughly means “Son of
Bonacci”. He lived between 1170 and 1250 in Italy.
Study the pattern of the Fibonacci sequence below.
Term
0
1
1
2
3
5
8
13
21
…
Term
Number (n)
0
1
2
3
4
5
6
7
8
…
What is the 9th term?
Answer: __________
How did you solve the 9th term?
Answer: __________________________________________________________________________
GEC 3 – Mathematics in the Modern World
Page 4 of 8
Republic of the Philippines
CAMARINES NORTE STATE COLLEGE
F. Pimentel Avenue, Brgy. 2, Daet, Camarines Norte – 4600, Philippines
INSTITUTE OF COMPUTER STUDIES
What is the pattern of the Fibonacci Sequence?
Answer: __________________________________________________________________________
If you have noticed, adding the two consecutive terms will result to another term of the Fibonacci
sequence, Hence, it could be expressed as:
Fn = Fn-1 + Fn-2
Where:
Fn = Fibonacci number
Fn-1 = previous term
Fn-2 = the term before Fn-1
Apply this concept to be able to find the 10th to 15th term of the Fibonacci Sequence.
10th term: ____________
13th term: ____________
11th term: ____________
14th term: ____________
12th term: ____________
15th term: ____________
Since you’re already familiar with the numbers that constitutes the Fibonacci Sequence, prepare for
a learning activity where you’ll be able to see that Fibonacci numbers exist in nature.
Learning Activity No. 3 – Activity (Self-Exploration)
Look for three (3) certain flowers that are nearly available within your vicinity. Identify the flower and the
number of its petals. Put the data of your findings in the table as provided below and answer the
succeeding questions.
Details
Flower 1
Flower 2
Flower 3
Name
Number of Petals
What did you find out? Do they follow the numbers stipulated in the Fibonacci Sequence?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
What can you say about on the results of this activity?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
GEC 3 – Mathematics in the Modern World
Page 5 of 8
Republic of the Philippines
CAMARINES NORTE STATE COLLEGE
F. Pimentel Avenue, Brgy. 2, Daet, Camarines Norte – 4600, Philippines
INSTITUTE OF COMPUTER STUDIES
Have you considered if you’re being asked what is the 80 th term of the Fibonacci Sequence? It may
take you an hour or more to find it. However, one may calculate the Fibonacci number using the Golden
Ratio. It is usually denoted using the Greek letter “phi” 𝜑 or ∅.
The Golden Ratio is a special number, which is approximately equal to 1.618034 and may be used
to find the nth term of a Fibonacci Sequence using the Binet’s formula.
𝑛
(
𝐹𝑛 =
1 + √5
1 − √5
) −(
)
2
2
2
√5
Use this formula to find the following terms of the Fibonacci Sequence.
a. 15th term: _______________
b. 20th term: _______________
c. 25th term: _______________
Learning Activity No. 4 – Abstraction (Critical Thinking)
Use the Binet’s Formula to find the following terms of the Fibonacci Sequence.
1) 40th term
Answer: _____________
2) 47th term
Answer: _____________
th
Answer: _____________
3) 59 term
Aside from the famous painting Mona Lisa, Leonardo da Vinci was also known for his Vitruvian Man.
It was one of the most important works of the Italian Renaissance. According to Vitruvius (1492), the 15th
century drawing was also known as “the proportions of the human body”.
GEC 3 – Mathematics in the Modern World
Page 6 of 8
Republic of the Philippines
CAMARINES NORTE STATE COLLEGE
F. Pimentel Avenue, Brgy. 2, Daet, Camarines Norte – 4600, Philippines
INSTITUTE OF COMPUTER STUDIES
Learning Activity No. 5 – Activity (Collaboration)
Form a group with four (4) members and discover how golden ratio is evident on human body. But you
must also provide yourself a certain measuring instrument (i.e. meter stick, ruler, tape measure,
measuring tape). Then, measure the following parameters as indicated below in the data sheet. You are
free to choose whichever unit of measurement is convenient to your group.
My Data Sheet
Parameters
Measurement
Distance from your knees to the ground
A = __________________
Distance from your belly button to the ground
B = __________________
Distance from the top of your head to your belly button
C = __________________
Distance from your wrist to your elbows
D = __________________
Length of your hand
E = __________________
Refer to the figure below:
F = __________________
G = __________________
H = __________________
Get the ratio of the following and express your answer in three decimal places.
1) B ÷ C = __________________
2) B ÷ A = __________________
3) D ÷ E = __________________
4) G ÷ F = __________________
5) H ÷ G = __________________
GEC 3 – Mathematics in the Modern World
Page 7 of 8
Republic of the Philippines
CAMARINES NORTE STATE COLLEGE
F. Pimentel Avenue, Brgy. 2, Daet, Camarines Norte – 4600, Philippines
INSTITUTE OF COMPUTER STUDIES
What can you say about the ratios from numbers 1 to 5?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
Collect the data from the members of your group and fill in the table for group’s data.
Group’s Data
No.
Members
B÷C
B÷A
D÷E
G÷F
H÷G
1
2
3
4
Abstraction (Critical Thinking)
Write your conclusion on how evident is golden ratio on the human body.
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
References:
Manlulu, E.A. and Hipolito, L.M.M. (2019) A Course Module for Mathematics in the Modern World.
https://www.mathsisfun.com/numbers/fibonacci-sequence.html
https://www.livescience.com/37470-fibonacci-sequence.html
GEC 3 – Mathematics in the Modern World
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