CHAPTER I

This chapter presents; introduction, background of the study, review related

literature, objectives of the game, significance of the game and measuring the

effectiveness of the game.

Introduction

Trigonometry is one of the most difficult branches of mathematics. Although

it is one of a kind among the terror subject yet it is very challenging and brings

encouragement to some math students’ hate this so much, while others enjoy having

this subject. There are some students who love trigonometry as other deviate to do

this. This branch of mathematics is very challenging and interesting that some needs

time, understanding and comprehension in learning it.

Background of the Study

The Trig-Damath is a board game designed for all. The name Trig-Damath

is derived from the word Trigonometry, “Dama” and Mathematics which were

integrated to produce a new game essential for learning. The focus of the game will

be on the three basic trigonometric function formulas namely; sine, cosine and

tangent wherein players will manipulate as they take the chips of their opponent.

This game can be played by two players.

The Trig-Damath is a unique board game making the players more

familiarize and appreciate not only of the game but also the field of trigonometry. It

1

also encompasses the mind of the certain individual in sharpening its intellectual

capabilities and mental alertness.

The said board game was really multi-purpose due to its advantages that can

infuse to the players. It is educational because players could learn more the proper

way of solving basic trigonometric function problem and more exploration with

regards on it. It is also designed for recreational, where players have fun, enjoy and

relieve stress as they learn without being tensed. Moreover, it practice the players’

socialization, especially those who were loners and do not know how to mingle with

others. As a game, it has a great value in emphasizing the importance of being

sportsmanship and competitiveness as players.

Review Related Literature

Trigonometry deals with the study of angles, triangles, and trigonometric

functions. Taken from the Greek words trigonon (triangle) and metria(measure),

the word literally means triangle measurement and the term came into use in the

17th century—the period when trigonometry, as an analytic science, started; but its

real origins lie in the ancient Egyptian pyramids and Babylonian astronomy that

date back to about 3000 BCE. It is the Greek astronomer and mathematician

Hipparchus of Nicaea in Bithynia (190 BCE - 120 BCE) that is often considered as the

founder of the science of trigonometry.

Regarding the six trigonometric functions: Aryabhata (476 CE - 550 CE)

2

discovered the sine and cosine; Muhammad ibn Musa al-Khwarizimi (780 CE -

850 CE) discovered the tangent; Abu al-Wafa’ Buzjani (940 CE - 988 CE)

discovered the secant, cotangent, and cosecant. Albert Girard (1595-1632), a

French mathematician, was the first to use the abbreviations sin, cos, and tan in a

treatise. 

Our modern word "sine" is derived from the Latin word sinus, which means

"bay", "bosom" or "fold", translating Arabic jayb. Fibonacci's sinus rectus

arcus proved influential in establishing the term sinus.These roughly translate to

"first small parts" and "second small parts".

A Greek mathematician, Euclid, who lived around 300 BC was an important

figure in geometry and trigonometry. He is most renowned for Euclid's Elements, a

very careful study in proving more complex geometric properties from simpler

principles. Although there is some doubt about the originality of the concepts

contained within Elements, there is no doubt that his works have been hugely

influential in how we think about proofs and geometry today; Indeed, it has been

said that the Elements have "exercised an influence upon the human mind greater

than that of any other work except the Bible. In the second century BC a Greek

mathematician, Hipparchus, is thought to have been the first person to produce a

table for solving a triangle's lengths and angles.

Early study of triangles can be traced to the 2nd millennium BC, in Egyptian

mathematics (Rhind Mathematical Papyrus) and Babylonian mathematics.

Systematic study of trigonometric functions began in Hellenistic mathematics,

3

reaching India as part of Hellenistic astronomy. In Indian astronomy, the study of

trigonometric functions flowered in the Gupta period, especially due

to Aryabhata (6th century). During the middle Ages, the study of trigonometry

continued in Islamic mathematics, when it was adopted as a separate subject in the

Latin West beginning in the Renaissance with Regiomontanus. The development of

modern trigonometry shifted during the western Age of Enlightenment, beginning

with 17th-century mathematics (Isaac Newton and James Stirling) and reaching its

modern form with Leonhard Euler (1748).

Objectives of the Game

This project is designed to:

1. Create a positive impression towards trigonometry and appreciate its

contribution in other field of mathematics

2. Motivate students to exert more effort in learning the subject and design their

own mathematical game

3. Enhance one’s ability in solving mathematical problem specifically in

trigonometric functions

4. Have fun while learning without spending money.

4

Significance of the Game

The proponents were optimistic that this project would be significance to the

following persons:

PLAYERS- This project will help players to develop mental alertness and to boost

their self-confidence in solving mathematical problems.

STUDENTS- This will develop the analytical and logical thinking skills of the

students within a given period of time. It will also serves as the venue of meaningful

recreation for students without spending money.

TEACHERS- This will help teachers motivate students to learn and appreciate

mathematics in a very unique and enjoyable way.

Testing the effectiveness of the game

To prove the effectiveness of the game and to see if it has met the objectives,

the proponents decided to have the game tested by 30 students who were randomly

selected from Camarines Norte State College, College of Education. The number of

students was determined through the Slovin’s formula as follows:

n= N

1+N e2

N = total population of students in College of Education

e = margin of error

n = sample

5

The proponents had investigated and found out that the population of the

students in College of Education is 1621 and have chosen 18% as the margin of

error.

Then, to determine the sample, the proponents used the formula:

¿ 1621

1+621(0.18)2

¿ 16211+1621(0.0324)

¿ 16211+52.5204

¿ 162153.5204

n = 30.34

Thirty students were randomly chosen randomly to test the effectiveness of

the game. After determining the number of students which is requires in testing the

game, the proponents of the showcase also considered the formulated criteria (see

appendix) to test the effectiveness of the game. An evaluation sheet was given to the

students who played the game so that they can evaluate and show their insights for

its improvement.

6

CHAPTER II

METHODOLOGY

This chapter presents; materials and tools used, procedure in constructing

the showcase, the rules of the game and how to use the showcase.

MATERIALS AND TOOLS USED

A. Materials

a. Materials in constructing the playing board.

1 pc Ready-made playing board

Small size(1/4 liter) Black paint (latex)

60 CC Silver paint

1 pc. Paint brush

1 bottle (350 ml.) Thinner

2 pcs. Glass 9” x 18”

8 pcs. Printed Photo paper

1 pc. Permanent marker

1 pc. Electrical tape

b. materials in making the chips.

12 pcs. Red Poker chips

12 pcs. Blue poker chips

1 pc. Printed Photo paper

1 small pc. Tape

c. materials in making score board:

1 pc. White board 12”x24”

7

Black paint

Thinner

Paint brush

Electrical tape

Printed photo paper

Tape

B. Procedure in constructing showcase.

a.) Playing Board

1. Prepare all the materials needed

2. Make sure that the ready-made board is in good condition

3. Paint the sides of whole board evenly with black paint except to its edges.

4. After painting, let it dry under the sun for three hours.

5. When the board dried, paint the edges with silver paint and dry it for one

hour.

6. Paste the printed tiles on the board. Make sure that they are properly

attached.

7. Paste the 9” x 18” glass to side or face of the board thoroughly and avoid

moving it until it is totally fixed.

8. Put the scoreboard model and formula inside the board and paste it well.

b.) Chips

1. Prepare the materials needed.

8

2. Cut the printed materials or the data to paste in the chips according to the

poker chips size which will suit at the center of the circle.

3. Paste the customized data with double-sided tape.

4. Paste well the labeled data at the center.

.

5. Cover the data with transparent tape.

c.) Scoreboard and Solving Board

1. Cut the 12”x24” white board into three equal parts.

2. After getting the equal parts, cut a piece of 12”x8” white board into two

equal parts to produce 2 pieces of 6”x8”.

3. Cover the edges of each board with electrical tape.

4. Draw a table inside the 2 pieces of 12”x8” boards and label it with the

printed materials.

9

60°30°120°90°

10 cm 16 cm14 cm12 cm

240° 270° 300°330°

5. Paste the printed text “solving board” on the 2 pieces of 6”x8” and attached

the printed formula at the back of it.

C. How to Use the Showcase.

a. Content of the showcase

Playing board

24 chips( red and blue ) (16 extra chips)

Score board

Solving board

Formula

Eraser

White board marker

b. Setting Up

1. Get the playing board and set up the chips on the violet tiles of the

board according to this manner.

10

c. Movements

1. Like in “DAMA” (checkers), the movements of the chips should be

diagonally forward.

Difficulty: Average

Time required: maximum of 1 hour

d. Rules:

11

sinƟ tan

Ɵ

cos

Ɵ

sinƟ

C b a c

sinƟtan

Ɵ

cos

ƟsinƟ

c b a c

c a b c

sinƟ tan

ƟsinƟ

c a b C

sinƟ cos

Ɵ

tan

ƟsinƟ

1. Trig-Damath shall be played by two players. Each player begins the

game with 12 colored chips. (Typically, one set of chips is blue and the

other is red.)

2. The board consists of 64 squares, alternating between 32 violet and

32 pink squares with printed data such as sine, cosine, tangent, a ,b

and c. It is positioned so that each player has a pink square on the

right side corner closest to him or her.

3. Each player places his or her chips on the 12 violet squares closest to

him or her.

4. Blue moves first, then alternate moves.

5. Moves are allowed only on the violet squares, so chips shall always

move diagonally. Flip the chips as needed (cm for the sides or a, b and

c and degrees for tangent, sine and cosine). Single chips are always

limited to forward moves (toward the opponent).

6. A chip making a non-capturing move (not involving a jump) may

move only to one square.

7. A chip making a capturing move (a jump) leaps over one of the

opponent's chip, landing in a straight diagonal line on the other side.

Only one chip may be captured in a single jump; however, multiple

jumps are allowed on a single turn.

8. Each player shall make a careful move and it will be base to

trigonometric formula to avoid having a negative score. A player shall

12

solve a problem within the limited time only before making a move or

taking a chips.

9. When a chip is captured, player would get the corresponding value of

the chips and will write it on the score board according to the place

where it has been captured. The said chip/s shall be removed from

the board.

10. If a player captured a chip, he should make a jump. In case that a

player has more than one chip to capture, he/she is free to choose

whatever he/she prefers.

11. When a chip reaches the furthest row from the player who controls

that chip, it is crowned and be recognized as a powerful chip.

12. Powerful chips are limited to moving diagonally, but may move both

forward and backward. (Remember that single pieces, i.e. non-kings,

are always limited to forward moves.)

13. Kings may combine jumps in several directions -- forward and

backward -- on the same turn. Single pieces may shift direction

diagonally during a multiple capture turn, but must always jump

forward (toward the opponent).

14. If the opponent cannot make a move or lost all his/her chips then the

game is over.

e. Scoring:

13

1. At the end of the game, the scores on the score board shall be

computed by applying the desired trigonometric formulae to find the

unknown part.

2. After finding the unknown values, every value on each column shall

be added to get to the partial score.

3. After finding the partial score, use the required formula “cos Ɵ +

tan + sin Ɵ Ɵ” to arrive at the total angle and “a + b + c” for the total

side or the perimeter.

4. Get the sum of the total side and total angle to arrive at the total

score.

5. Deduct the value of the sides of the remaining chips to the opponent

for the final score.

6. Player with the highest score obtain shall be declared as the winner.

14

CHAPTER III

Result and Discussion

This chapter presents; findings and analysis of the results.

Findings

The 30 students who were selected randomly were asked to try the Trig-

DaMath. After playing they were given the evaluation form so that they could

express their opinions and comments about the game. The form and the formulae

used to find the mean can be found on appendix. The summary of the results of their

evaluation after playing the game is as follows.

Criteria Mean

Over-all appearance 4.63

Excitement factor/unpredictability 4.47

Portability (if it is ideal to be played anywhere) 4.57

Uniqueness of the game 4.3

Effectiveness of the game as learning tool I mathematics. 4.77

Rating:

5- Excellent 4- Very satisfactory 3-Satisfactory

15

2-Fair 1-Poor

Analysis of the Result

Based on the data we gathered, the students appreciated the game and found

it presentable, exciting and portable. It is a good feedback from them because it

means that the game holds the interests of the player due to its quite

unpredictability. There is also no doubt that the game is truly appealing and can be

played anywhere. Moreover, the game is truly effective as a learning tool in

mathematics. However, the game cannot be said excellent in terms of uniqueness

due to the same concept of the checker/dama.

Considering the 5 criteria, below is the average rating of the Game Trig-

DaMath;

x=4.63+4,47+4.57+4.3+4.775

x=22.675

x = 4.534

As shown by the total rating, the ovser-all effectiveness of the game is very

satisfactory.

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CHAPTER IV

CONCLUSIONS AND RECOMMENDATIONS

This chapter presents conclusion and recommendation

Conclusion

Trig-DaMath is an educational game which motivates the students to learn. It

is a kind of mathematical game which is convenient to use.

Upon playing the game, the players realized that little by little they becoming

a better one in terms of solving mathematical problem.

Through players’ development and response to the game, Trig-DaMath

serves as tool for recreation without spending money. One way of appreciating

mathematics, holding the attention and interest of the players all throughout the

game, enhances the skills and ability of each individual in solving and the most

important is, it attained the main objective which is to serve as a tool in effective

learning process of a player. Trig-DaMath has the capacity to entertain the player

aside from educating and teaching them. The over-all appearance of the showcase

greatly satisfied the students’ interests.

Recommendation

17

In view of the feedback given by the respondents who played the game, the

following recommendations were made:

1. Light materials should be used since the board was heavy to carry.

2. Lock with keys should be used since the lock of the board was not

secured.

18

Appendix A

The Showcase’s Layout

sinƟ

tanƟ

cosƟ

sinƟ

c b a c

sinƟ

tanƟ

cosƟ

sinƟ

c b a c

c a b c

sinƟ

tanƟ

sinƟ

c a b C

sinƟ

cosƟ

tanƟ

sinƟ

19

Appendix B

The proponents while constructing the showcase

20

21

Appendix C

CamarinesNorte State College

Dr. Jose R. Abaño Campus

College of Education

Daet, CamarinesNorte

Name:_______________________________________________ Course/Year/Block:_____________

22

Trig-DaMathCriteria on the Effectiveness of the Game

Direction:Rate the game according to your perception given the following criteria by checking the numbers in the given table below. Please give your opinion honestly for the improvement of the game.

The following numbers correspond to your choices:

1. Poor 2. Fair 3.Satisfactory

4. Very Satisfactory 5. Excellent

Perception 1 2 3 4 5a. Over-all Appearance

b. Excitement Factor/Unpredictability

c. Portability (if it is ideal to be played anywhere)

d. Uniqueness of the Game

e. Effectiveness of the Game as a Learning Tool in Mathematics

__________________________________ Signature over Printed Name

Appendix D

Summary of the Responses of the 30 Respondents

Criteria

Mean

5 4 3 2 1

Over-all Appearance 20 9 1 0 0 4.63

Excitement Factor/Unpredictability 15 14 1 0 0 4.47

23

Portability (if it is ideal to be played anywhere) 19 9 2 0 0 4.57

Uniqueness of the Game 13 13 4 0 0 4.3

Effectiveness of the Game as a Learning Tool in Mathematics

23 7 0 0 0 4.77

24

Appendix E

Computation for the Mean

Over-all Appearance

X=3 (1 )+4 (9 )+5 (20)

30 = 13930

=4.63

Excitement Factor/Unpredictability

X=3 (1 )+4 (14 )+5(15)

30= 13430

= 4.47

Portability (if it is ideal to be played anywhere)

X=3 (2 )+4 (9 )+5(19)

30= 13730

=4.57

Uniqueness of the Game

X=3 (4 )+4 (13 )+5 (13)

30= 12930

= 4.3

Effectiveness of the Game as a Learning Tool in Mathematics

X=3 (0 )+4 (7 )+6(23)

30 =14330

=4.77

25

Appendix F

The Commercial and Actual Cost of the Game

Quantity Unit ArticleCommercial

CostActual Cost

1 pc. Playing Board P185. 00 P 185.001 pc. Double-sided tape 8.00 8.00

2 pcs.Tape (Large & Small

Size) 21.00 21.00

7 pcs. Photo Paper 35.00 35.001 ¼ ml Black Paint 55.00 55.001 60 cc Silver Paint 28.00 28.001 350 ml bottle Thinner 26.00 26.001 pc. Paint Brush 10.00 10.001 packs Poker Chips 90.00 90.002 pcs. Marker 48.00 48.003 pcs. Small box 20.00 20.002 pcs. Eraser 24.00 24.002 9”x18” Glass 100.00 100.002 pc. Electrical Tape 15.00 15.001 Print 70.00 70.001 12”x24” White Board 115.00 Used materials

Total Amount P 850.00 P 735.00

26

Appendix G

Curriculum Vitae

CORUNO, MA. JOCHAS S.

EXPERIENCE

As a 22 years old student, I had a lot experience I encountered. One of this is to

become a maid because of financial problem. I worked as a part timer and full timer

maid. In my age there was a time that I lose my confidence to study harder because

of this circumstance. I worked very hard to sustain my everyday salary. To continue

my study I do my best to search a job to suit my schedule. Last year I joined in Math

Quiz bee to be held in Abaño Campus in this activity we won as 2nd RUNNER UP. 2

27

years ago I joined the National Statistic Quiz to be held in Provincial Capitol as a

participant I learned a lot of things. I am a guarantee scholar of BNAA because I’ll

passed the entrance exam and because of my dedication to my course.

SEMINARS/ TRAINING

Seminar and Workshop k-12 Curriculum (2014)

Leadership Training(2014)

AFFILATION/ POSITION HELD

P.I.O of Solidarity Of Integrated Governance Of Mathematicians Association

(SIGMA) (2013-2014)

Scholar Guarantee member

EDUCATIONAL ATTAINMENT

Camarines Norte State College – Bachelor of Secondary Education major in

Mathematics (presents)

Eugenia M. Quintela Memorial High School –

Honor student/ Academic Awardee

CAT Assistant Corp.

SSG Secretary

Banocboc Elementary School

Honor student

INSPIRATION

28

Mrs. Rosemarie R. Gamelo is one of my inspirations why I am

choosing Mathematics as my major because she inspired me to do

something possible and to have a confidence to say that “every

problem has a solution”.

GUPONG, JINKY BELLO

Experiences:

As one of the proponents if the Trig-DaMath game

Seminars and Training:

I had attended the leadership training last year and K-12 curriculum seminar and

workshop just this year held at Camarines Norte State College, Abaño Campus College of

Education.

Affiliation and Position held

I am a scholar guarantee member of Local Government Unit of Mercedes,

Camarines Norte and a member of Solidarity Integrated Governance of Mathematician

Association of College of Education of Camarines Norte State College.

Educational Attainment:

29

Camarines Norte State College- Bachelor of Secondary Education major in

Mathematics (present)

Godofredo Reyes Sr. National High School graduate

An honor student

Elementary Graduate

An honor student

Inspiration:

Mrs. Jessilyn Eje my math teacher, one of my inspirations why I am now

taking Mathematics as my major. She inspired me during my high school days

and I really admire her for her excellent and mastery in her major, mathematics.

PELAOSA, LARINO JR. SALAZAR

30

EXPERIENCE:

As a 20 years old student, I had a lot of experience encountered. I work as a dish washer at the eatery, house cleaner and now currently working as a part-time Mathematics tutor. I also became part of making a compilation of formula in Mathematics last semester. On 2012, as a requirement in Filipino II subject, I with my group mates made a research. I also participated in Mathematics Quiz Bee hosted by Mr. Bryan I. Torres last year. In addition, I was one of the Science Quizzer during my 3rd year and 4th year high school. We also won 2nd runner-up in 2009 UP KAADHIKA Megalobrania.

SEMINARS/TRAININGS:

Leadership Training at the Church of Jesus Christ of Latter - day Saints (2014- present).

Bookkeeping NC II Training (2011) First Aid Training (2009)

Affiliation and Position Held:

Solidarity of Integrated Governance of Mathematician Association (SIGMA) - Member (2013- present).

LGU- Mercedes- Iskolar ng Bayan Guarantee (2011-present). Ward Mission Leader & Young Men Secretary at the Church of Jesus Christ of

Latter - day Saints (2014- present). Supreme Student Government Officer- Auditor (2010-2011) YES-O- Member (2010-2011) Red Cross Officer- P.R.O. (2009-2010)

Educational Background:

College: Camarines Norte State College (2011-present)

31

Bachelor of Secondary Education Major in Mathematics (3rd Year) Bachelor of Science in Accountancy (2011-2012)

Secondary: San Roque National High School (2007-2011) Graduated as 2nd Honorable Mention. Honor student from 1st year to 3rd year high school.

Elementary: Mercedes Central Elementary School (2001-2007) Honor student from Grade 1 to Grade 6.

Inspiration:

Ms. Myra R. Taay

32

References

http://boardgames.about.com/cs/checkersdraughts/ht/play_checkers.htm

http://en.wikipedia.org/wiki/History_of_trigonometry

http://en.wikipedia.org/wiki/Game

33