New LEsson 1 - Mathematics in our World.pptx

Mathematics in Our World Lesson 1 Learning Objectives:  Identify patterns in nature and irregularities 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, re...

Mathematics in Our World Lesson 1 Learning Objectives:  Identify patterns in nature and irregularities 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.  Discuss the role of mathematics in some disciplines ; and  express appreciation for mathematics as human endeavor. KEY CONCEPTS  PATTERNS IN NATURE AND THE REGULARITIES IN THE WORLD Patterns and counting are correlative. Counting happens when there is a pattern. When there is counting, there is logic. Consequently, pattern in nature goes with logic or logical set-up. There are reasons behind a certain pattern. That’s why , oftentimes, some people develop an understanding of patterns, relationships, and functions and use them to represent and explain real-world phenomena.  Most people say that mathematics is the science behind patterns. Mathematics exists everywhere as patterns do in nature. Not only do patterns take many forms within the range of school mathematics, they are also a unifying mechanism. Number patterns – such as 2, 4, 6, 8, … are familiar to us since , they are among the patterns first learned in our younger years. As we advance, we experience number patterns again through the huge concept of functions in mathematics inside and outside school. But patterns are much broader and common anywhere anytime. Basic patterns:  Patterns can be sequential, spatial, temporal, and even linguistic.  Most basic patterns are as follows: a. dates in the calendar b. seven days in a week c. twelve months a year. d. the regular holidays – they are celebrated in the same sequence every year. - all theses phenomena create repetition of names and or events called regularity. What is regularity? And What is pattern? A regularity (Collins, 2018) is the fact that the same thing always happen in the same circumstances. While a pattern is a discernible regularity in the world or in a man-made design. As such, the elements of a pattern repeat in a predictable manner. What is Patterns in nature? Patterns in nature(Wikipedia) are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural and Geometric Patterns A. Natural Patterns 1. Symmetries 5. waves 9. stripes 2. trees 6. foams 3. spirals 7. tessellations 4. meanders 8. cracks B. Geometric Patterns – is a kind of pattern formed of geometric shapes and typically repeated. 1. wallpaper design c. Algebra Patterns 1. repeating pattern 2. growing pattern Some Examples of Patterns in Nature 1. Symmetry(Wikipedia) – means agreement in dimensions, due proportion and arrangement. In everyday language, it refers to a sense of harmonious and beautiful proportion and balance. In mathematics, “symmetry” means that an object is invariant to any of various transformations including reflection. Some Examples of Patterns in Nature 2. Spiral – is curve which emanates from a point, moving farther away as it revolves around the point. Some Examples of Patterns in Nature 3.Meander – is one of a series of regular sinuous curves, bends, loops, turns, or windings in the channel of a river, stream, or other watercourse. It is produced by a stream or river swinging from side to side as it flows across its floodplain or shifts, its channel within a valley. Some Examples of Patterns in NAture 4. Wave – is a disturbance that transfers energy through matter or space, with little or no associated mass transport. Waves consist of oscillations or vibrations of a physical medium or a field, around relatively fixed locations. Surface awves in water show water ripples. Some Examples of Patterns in Nature 5. Foam – is a substance formed by trapping pockets of gas in a liquid or solid. A bath sponge and the head on a glass of beer are examples of foams. In most foams, the volume of gas is large, with thin films of liquid or solid separating the regions of gas. Soap foams are also known as suds. Some Examples of Patterns in Nature 6. Tessellation of a flat surface – is the tiling of a plane using one or more geometric shapes called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions and a variety of geometries. Some Examples of Patterns in Nature 7. Fracture or Crack – is the separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular to the surface of displacement, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially to the surface of displacement, it is called a shear crack,slip band, or dislocation. Some Examples of Patterns in Nature 8. Stripes – are made by a series of bands or strips, often of the same width and color along the length. Some Examples of Patterns in Nature 9. Fractal – is a never – ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Fractal patterns are extremely familiar, since nature is full of fractals. Some examples of Patterns in Nature 10. Affine Transformation – these are the process of rotation, reflection and scaling. Many plant forms utilize these processes to generate their structure IMPORTANCE OF MATHEMATICS IN LIFE According to Katie Kin (2015), Math is a subject that makes students either jump for joy or rip their hair out. However, math is inescapable as you become an adult in the real world. From Calculating complicated algorithms to counting down the days till the next Game of Thrones episode, math is versatile and important, no matter how hard it is to admit. Reasons why learning math is important to you and the world.  1. Restaurant Tipping 6. Doing Exercises  2. Netflix film viewing 7. Handling Money  3. Calculating Bills 8. Making Countdowns  4. Computing Test Scores 9. Baking and Cooking  5. Tracking Career 10. 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. For some people, and not only professional mathematicians, the essence of mathematics lies in its beauty and the intellectual challenge. 1. Patterns and Relationships Mathematics is the science of patterns and relationship. As a theoretical discipline, mathematics explores the possible relationships among abstractions without concern for whether those abstractions have counterparts in the real world. The abstractions can be anything from strings of numbers to geometric figures to sets of equations. 2. Mathematics, Science and Technology Mathematics is abstract. Its function goes along well with Science and Technology. Because of its abstractness, mathematics is universal in a sense that other fields of human thought are not. It finds useful applications in business, industry, music, historical scholarship, politics, sports, medicine, agriculture, engineering, and the social and natural sciences. 3. Mathematical Inquiry Normally, people are confronted with problems. In order to live at peace, these problems must be solved. Using mathematics to express ideas or to solve problems involves at least three phases: 1. representing some aspects of things abstractly, 2. manipulating the abstractions by rules of logic to find new relationships between them, and 3. seeing whether the new relationships say something useful about the original things. 4. Abstractions and Symbolic representation Mathematical thinking often begins with the process of abstraction – that is, noticing a similarity between two or more objects or events. Abstraction are made not only from concrete objects or processes; they can also be made from other abstractions, such as kinds of numbers. 5. Manipulating Mathematical Sentences After abstractions have been made and symbolic representations of them have been selected, those symbols can be combined and recombined in various ways according to precisely defined rules. Typically, strings of symbols are combined into statements that express ideas or propositions. 6. Application Mathematical processes can lead to a kind of model of a thing, from which insights can be gained about the thing itself. Any mathematical relationships arrived at by manipulating abstract statements may or may not convey something truthful about the thing being modeled. Sometimes common sense is enough to enable one to decide whether the results of the mathematics are appropriate. The Role of Mathematics in some disciplines 1. Mathematics in Physical Sciences – mathematics gives a final shape to the rules of physics and mathematical calculations occur at every step in physics. 2. Mathematics in Chemistry – Math is extremely important in physical chemistry especially in advanced topics such as quantum or statistical mechanics. Other fields of chemistry also use a significant amount of math. 3. Mathematics in Biological Sciences – Biomathematics is a rich field with open, challenging and fascination problems in the areas of mathematical genetics, mathematical ecology, mathematical neuron- physiology, development of computer software for special biological and medical problems, mathematical theory of epidemics, use of mathematical programming and reliability theory in bioscience and mathematical problems in biomechanics, bioengineering and bioelectronics. The Role of Mathematics in Some Disciplines 4. Mathematics in Engineering and Technology – the use of mathematics in engineering is very well known. It is considered to be the foundation of engineering. Engineering deals with surveying, levelling, designing, estimating, construction, etc. Mathematics has played an important role in the development of mechanical, civil, aeronautical, and chemical engineering through its contributions to mechanics of rigid bodies, hydro- dynamics, aero-dynamics, heat transfer, lubrications, turbulence, elasticity and other. The Role of Mathematics in Some Disciplines 5. Mathematics and Agriculture Agriculture as a science depends extensively on mathematics. It needs a direct application of mathematics, such as measurement of land or area, average investment and expenditures, average return or income, production per unit or area, cost of labor, time and work , seed rate etc. Progress of the farm can be judged by drawing graphs of different items of production. Appreciating Mathematics as a Human Endeavor 1. Accountants 11. Meteorologist 2. Agriculture 12. Military Personnel 3. Architects 13. Nurses 4. Biologists 14. Politicians 5. Chemists 15. Salespeople 6. Computer Programmers 16. Technicians 7. Engineers 17. Tradesmen 8. Lawyers 9. Managers 10. Medical Doctors  With these, mathematics can be a great aid in all activities in the world and deserves huge appreciation and therefore everyone realizes the following: 1. Mathematics helps organize patterns and regularities. 2. Mathematics helps predict the behavior of nature and phenomena in the world. 3. Mathematics helps control nature and occurrences in the world for our own ends. 4. Mathematics has numerous applications in the world making indispensable.  Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty. - Archimedes