Investigatory project: Trig-DaMath

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It contains Chapter 1-4 and Appendices

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  • 1. 1CHAPTER IThis chapter presents; introduction, background of the study, review relatedliterature, objectives of the game, significance of the game and measuring theeffectiveness of the game.IntroductionTrigonometry is one of the most difficult branches of mathematics. Althoughit is one of a kind among the terror subject yet it is very challenging and bringsencouragement to some math students hate this so much, while others enjoy havingthis subject. There are some students who love trigonometry as other deviate to dothis. This branch of mathematics is very challenging and interesting that some needstime, understanding and comprehension in learning it.Background of the StudyThe Trig-Damath is a board game designed for all. The name Trig-Damathis derived from the word Trigonometry, Dama and Mathematics which wereintegrated to produce a new game essential for learning. The focus of the game willbe on the three basic trigonometric function formulas namely; sine, cosine andtangent 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 morefamiliarize and appreciate not only of the game but also the field of trigonometry. It

2. also encompasses the mind of the certain individual in sharpening its intellectual2capabilities and mental alertness.The said board game was really multi-purpose due to its advantages that caninfuse to the players. It is educational because players could learn more the properway of solving basic trigonometric function problem and more exploration withregards on it. It is also designed for recreational, where players have fun, enjoy andrelieve stress as they learn without being tensed. Moreover, it practice the playerssocialization, especially those who were loners and do not know how to mingle withothers. As a game, it has a great value in emphasizing the importance of beingsportsmanship and competitiveness as players.Review Related LiteratureTrigonometry deals with the study of angles, triangles, and trigonometricfunctions. Taken from the Greek words trigonon (triangle) and metria(measure),the word literally means triangle measurement and the term came into use in the17th centurythe period when trigonometry, as an analytic science, started; but itsreal origins lie in the ancient Egyptian pyramids and Babylonian astronomy thatdate back to about 3000 BCE. It is the Greek astronomer and mathematicianHipparchus of Nicaea in Bithynia (190 BCE - 120 BCE) that is often considered as thefounder of the science of trigonometry.Regarding the six trigonometric functions: Aryabhata (476 CE - 550 CE) 3. 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), aFrench mathematician, was the first to use the abbreviations sin, cos, and tan in a3treatise.Our modern word "sine" is derived from the Latin word sinus, which means"bay", "bosom" or "fold", translating Arabic jayb. Fibonacci's sinus rectusarcus 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 importantfigure in geometry and trigonometry. He is most renowned for Euclid's Elements, avery careful study in proving more complex geometric properties from simplerprinciples. Although there is some doubt about the originality of the conceptscontained within Elements, there is no doubt that his works have been hugelyinfluential in how we think about proofs and geometry today; Indeed, it has beensaid that the Elements have "exercised an influence upon the human mind greaterthan that of any other work except the Bible. In the second century BC a Greekmathematician, Hipparchus, is thought to have been the first person to produce atable for solving a triangle's lengths and angles.Early study of triangles can be traced to the 2nd millennium BC, in Egyptianmathematics (Rhind Mathematical Papyrus) and Babylonian mathematics.Systematic study of trigonometric functions began in Hellenistic mathematics, 4. reaching India as part of Hellenistic astronomy. In Indian astronomy, the study oftrigonometric functions flowered in the Gupta period, especially dueto Aryabhata (6th century). During the middle Ages, the study of trigonometrycontinued in Islamic mathematics, when it was adopted as a separate subject in theLatin West beginning in the Renaissance with Regiomontanus. The development ofmodern trigonometry shifted during the western Age of Enlightenment, beginningwith 17th-century mathematics (Isaac Newton and James Stirling) and reaching its4modern form with Leonhard Euler (1748).Objectives of the GameThis project is designed to:1. Create a positive impression towards trigonometry and appreciate itscontribution in other field of mathematics2. Motivate students to exert more effort in learning the subject and design theirown mathematical game3. Enhance ones ability in solving mathematical problem specifically intrigonometric functions4. Have fun while learning without spending money. 5. 5Significance of the GameThe proponents were optimistic that this project would be significance to thefollowing persons:PLAYERS- This project will help players to develop mental alertness and to boosttheir self-confidence in solving mathematical problems.STUDENTS- This will develop the analytical and logical thinking skills of thestudents within a given period of time. It will also serves as the venue of meaningfulrecreation for students without spending money.TEACHERS- This will help teachers motivate students to learn and appreciatemathematics in a very unique and enjoyable way.Testing the effectiveness of the gameTo 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 randomlyselected from Camarines Norte State College, College of Education. The number ofstudents was determined through the Slovins formula as follows: =1 + 2N = total population of students in College of Educatione = margin of errorn = sample 6. 6The proponents had investigated and found out that the population of thestudents in College of Education is 1621 and have chosen 18% as the margin oferror.Then, to determine the sample, the proponents used the formula:=16211 + 621(0.18)2=16211 + 1621 (0.0324)=16211+52.5204=162153.5204n = 30.34Thirty students were randomly chosen randomly to test the effectiveness ofthe game. After determining the number of students which is requires in testing thegame, the proponents of the showcase also considered the formulated criteria (seeappendix) to test the effectiveness of the game. An evaluation sheet was given to thestudents who played the game so that they can evaluate and show their insights forits improvement. 7. 7CHAPTER IIMETHODOLOGYThis chapter presents; materials and tools used, procedure in constructingthe showcase, the rules of the game and how to use the showcase.MATERIALS AND TOOLS USEDA. Materialsa. 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 tapeb. materials in making the chips. 12 pcs. Red Poker chips 12 pcs. Blue poker chips 1 pc. Printed Photo paper 1 small pc. Tapec. materials in making score board: 1 pc. White board 12x24 8. 8 Black paint Thinner Paint brush Electrical tape Printed photo paper TapeB. Procedure in constructing showcase.a.) Playing Board1. Prepare all the materials needed2. Make sure that the ready-made board is in good condition3. 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 onehour.6. Paste the printed tiles on the board. Make sure that they are properlyattached.7. Paste the 9 x 18 glass to side or face of the board thoroughly and avoidmoving it until it is totally fixed.8. Put the scoreboard model and formula inside the board and paste it well.b.) Chips1. Prepare the materials needed. 9. 2. Cut the printed materials or the data to paste in the chips according to the9poker 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 Board1. Cut the 12x24 white board into three equal parts.2. After getting the equal parts, cut a piece of 12x8 white board into twoequal parts to produce 2 pieces of 6x8.3. Cover the edges of each board with electrical tape.4. Draw a table inside the 2 pieces of 12x8 boards and label it with theprinted materials. 10. 5. Paste the printed text solving board on the 2 pieces of 6x8 and attached1030 60 9012010 cm 12 cm 14 cm 16 cm240270300330the 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 markerb. Setting Up1. Get the playing board and set up the chips on the violet tiles of theboard according to this manner. 11. 11c. Movements1. Like in DAMA (checkers), the movements of the chips should bediagonally forward.sin tan cos sinC b a csin tan cos sinc b a cc a b ctan sinc a b Csin cos tan sinDifficulty: AverageTime required: maximum of 1 hoursind. Rules:1. Trig-Damath shall be played by two players. Each player begins thegame with 12 colored chips. (Typically, one set of chips is blue and theother is red.)2. The board consists of 64 squares, alternating between 32 violet and32 pink squares with