GEMMW01X_1 Mathematics in Our World PDF

Mathematics in the Modern World MATHEMATICS IN OUR WORLD Patterns and Numbers in Nature and the World The Fibonacci Sequence Applications of Mathematics Learning Outcomes: At the end of this lesson, learners should be able to: 1. Identify patterns in nature and regularities in the w...

Mathematics in the Modern World MATHEMATICS IN OUR WORLD Patterns and Numbers in Nature and the World The Fibonacci Sequence Applications of Mathematics Learning Outcomes: At the end of this lesson, learners should be able to: 1. Identify patterns in nature and regularities in the world. 2. Articulate the importance of mathematics in one's life. 3. Argue about the nature of mathematics, what it is, how it is expressed, represented, and used. 4. Express appreciation for mathematics as a human endeavor. What is mathematics and what is it about? Where can we see mathematics? How is mathematics done? Why is mathematics important to know? What is mathematics? ► the study of the relationships among numbers, quantities, and shapes ► enhance our critical thinking skills, reasoning, spatial thinking and creativity ► helps organize patterns and regularities in the world What is mathematics about? ► Numbers, symbols, notations Operations, equations, and functions Processes ► Proof  Where can we see mathematics? We see hints or clues of Math in : ► Patterns in Nature Fish Scales Honey Beehive Snowflake We see hints or clues of Math in : ► Our daily routine We see hints or clues of Math in : ► Our World Petronas Tower Leaf Chapel Pyramid We see hints or clues of Math in : ► People and Communities We see hints or clues of Math in : ► Events “When scientists seek to understand the patterns of our world, they often turnto a powerful tool.” How is mathematics done? ► with curiosity ► with a love for seeking patterns and generalities ► with a desire to know the truth ► with trial and error ► without fear of facing more questions and problems to solve ► with willingness to keep working Let’s think about this! Have you ever stopped to look around and notice all the amazing shapes and patterns we see in the world around us? Let’s think about this! Let’s think about this! Let’s think about this! 1. What number comes next in 1, 3, 5, 7, …? 2. What number comes next in 1, 4, 9, 16, 25, …? Patterns and Numbers in Nature and the World Patterns regular, repeated, or recurring forms or designs studying patterns help us in identifying relationships and finding logical connections to form generalizations and make predictions Patterns and Numbers in Nature and the World Symmetry a proportionate and balanced similarity that is found in two halves of an object, that is, one-half is the mirror image of the other half Patterns and Numbers in Nature and the World Patterns and Numbers in Nature and the World Spiral a shape of a continuous, curving line that forms circles around a center point Patterns and Numbers in Nature and the World Meander one of a series of regular sinuous curves, bends, loops, turns, or windings in the channel of a river, stream or other watercourse Patterns and Numbers in Nature and the World Waves a disturbance that transfers energy through matter or space Patterns and Numbers in Nature and the World Foam a substance formed by trapping pockets of gas in a liqu or solid Patterns and Numbers in Nature and the World Tessellation the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps Patterns and Numbers in Nature and the World Fracture or crack the separation of an object or material into two or more pieces under the action of stress Patterns and Numbers in Nature and the World Fractals a never-ending pattern Infinitely complex patterns that are self-similar across different scales created by repeating a single process over and over in an ongoing feedback loop Patterns and Numbers in Nature and the World Stripes made by a series of bands or strips, often of the same width and color along the length SEQUENCE an ordered list of numbers, called terms, that may have repeated values the arrangement is set by a definite rule 1, 10, 100, 1000, … 2, 5, 9, 14, 20, … The Fibonacci Sequence Leonardo Pisano Bigollo Øan Italian mathematician who discovered the sequence Øthe nickname was “Fibonacci” which roughly means “Son of Bonacci” ØNovember 23 – “Fibonacci Day” The Fibonacci Sequence The Fibonacci Sequence The Fibonacci Sequence The Fibonacci Sequence The sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, … Each number in the sequence is the sum of the two numbers which precede it. We define Fib(n) be the nth term Fib(1)=1, Fib(2)=1, Fib(3)=2, Fib(4)=3, … The Fibonacci Sequence Binet’s Formula Golden Ratio  Fibonacci Sequence and the Golden Ratio A remarkable property of the sequence is that the ratio between two numbers in the sequence eventually approaches the “Golden Ratio” as a limit Patterns and Regularities in the World as Organized by Mathematics Motion of a pendulum Patterns and Regularities in the World as Organized by Mathematics Reflection in a plane mirror Importance of Mathematics in Life According to Katie Kim (2015), Math is a subject that makes students jump for joy or rip their hair out. However, Math is inescapable as you become an adult in the real world. a. Restaurant Tipping f. Doing Exercise b. Netflix Film Viewing g. Handling Money c. Calculating Bills h. Making Countdowns d. Computing Test Scores i. Baking and Cooking e. Tracking Career j. Surfing Internet Nature of Mathematics According to the American Association for the Advancement of Science (1990), Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its intrinsic interest. a. Patterns and Relationships b. Mathematics, Science and Technology c. Mathematical Inquiry d. Abstraction and Symbolic Representation e. Manipulating Mathematical Statements f. Application Role of Mathematics in Some Disciplines As posted by Angel Rathnabai (2014), Mathematics is not only number word or computation, but is more about forming generalization, seeing relationships, and developing logical thinking and reasoning. 1. Physical Science 7. Economics 2. Chemistry 8. Psychology 3. Biological Science 9. Archeology 4. Engineering and Technology 10. Logic 5. Agriculture 6. Actuarial Science, Insurance and Finance Role of Mathematics in Some Disciplines As posted by Angel Rathnabai (2014), Mathematics is not only number word or computation, but is more about forming generalization, seeing relationships, and developing logical thinking and reasoning. 11. Music 16. Linguistics 12. Arts 17. Management 13. Philosophy 18. Computers 14. Social Networks 19. Geography 15. Political Science Appreciating Mathematics as a Human Endeavor Mathematics is appreciated as human endeavor because all professionals and ordinary people apply its theories and concepts in the office, laboratory and marketplace. According to Mark Karadimos (2018), the following professions use Mathematics in their scope and field of work. Appreciating Mathematics as a Human Endeavor üAccountants ü Agriculturists üArchitects üBiologists üChemists ü Computer Programmers ü Engineers Appreciating Mathematics as a Human Endeavor üLawyers ü Managers ü Medical Doctors ü Meteorologists ü Military Personnel ü Nurses ü Politicians Appreciating Mathematics as a Human Endeavor üSalespeople ü Technicians ü Tradesmen Mathematics is the only language shared by all human beings regardless of culture, religion, or gender.