MMW-CHAPTER-1-final.pptx major Elementary Education

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1. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) MATHEMATICS in the MODERN WORLD INTRODUCTION: INSTRUCTOR: RHEA C. GATON

2. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) MIDTERM: SECTION 1. NATURE OF MATHEMATICS CHAPTER 1. MATHEMATICS IN OUR WORLD Patterns in Nature and the Regularities in the World Some Examples of Patterns in Nature Fibonacci Sequence Importance of Mathematics Nature of Mathematics COURSE OUTLINE CHAPTER 2. THE LANGUAGE OF MATHEMATICS The Language, Symbols, Syntax and Rules of Mathematics Mathematical Language (Expression/Sentence) Operations on Mathematical Expressions CHAPTER 3. PROBLEM SOLVING AND REASONING Inductive And Deductive Reasoning Intuition, Proof And Certainty Polya’s 4-Steps In Problem Solving Other Problem Solving Strategies Mathematical Recreation

3. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) FINAL SECTION 2. MATHEMATICS AS A TOOL CHAPTER 1. DATA MANAGEMENT Descriptive Statistics Measures of Central Tendency Normal Distribution Hypothesis Testing Regression and correlation Chi-Square CHAPTER 2. LOGIC Logic Statements and Quantifiers Truth Tables, Equivalent Statements and Tautologies Conditional, Biconditional, Related Statements Symbolic Arguments Arguments and Euler Diagrams

4. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) CRITERIA FOR GRADING Midterm Grade B. Tentative Final Grade Quizzes/assignments - - 20% Quizzes/Assignments - - - - - -20% Attendance - - - - - - - - -10% Attendance - - - - - - - - - - - - 10% Class Participation - - - - 20% Class Participation - - - - - - - 20% Output Presentation - - - 20% Output Presentation - - - - - - 20% Midterm Exam - - - - - - - 30% Final Exam - - - - - - - - - - - - 30% T o t a l 100% T o t a l 100% C. Final Grade = (MTG + 2TFG)/3

5. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 1. Satisfactory attendance 2. Active participation in class 3. Submit assignments and exercises 4. Satisfactory results of quizzes 5. Pass midterm and final examinations OTHER REQUIREMENTS

6. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) CRITERIA Points   21-25 16-20 11-15 0-10     LEVEL OF ENGAGEMENT IN CLASS Student proactively contributes to class by offering ideas and/or asks questions more than once per class and/or works consistently on group activity the entire time. Student proactively contributes to class by offering ideas and/or asks questions once per class and/or works on group activity for most of the allotted time. Student rarely contributes to class by offering ideas and asking questions and/or works on group activity only some of the allotted time.   Student never contributes to class by offering ideas and asking questions and/or has trouble staying on task during group activity time.       LISTENING SKILLS Student listens when other talks both in group and in class; incorporates or builds off the ideas of others. Student listens when others talk, both in groups and in class. Student does not listens occasionally when others talk, both in groups and in class. Student rarely listens when others talk, both in groups and in class; sometimes interrupts when others speak     BEHAVIOR Student almost never displays disruptive behaviour during class. Student rarely displays disruptive behaviour during class. Student occasionally displays disruptive behaviour during class. Student almost always displays disruptive behaviour during class.     PREPARATION Student is almost always prepared for class with assignments and required class materials. Student is usually prepared for class with assignments and required class materials. Student is rarely prepared for class with assignments and required class materials Student is almost never prepared for class with assignments and required class materials.   T O T A L   CLASS PARTICIPATION RUBRIC

7. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) CLASSROOM POLICIES DO’S: Students must follow the university policies. Students must follow classroom policies, rules and regulations Students must listen to the professor while presenting and explaining the topics. Students are allowed to give group sharing of idea to their classmates in group activities. Students are required to submit excuse letter sign by the parent and class adviser. Students are required to maintain the cleanliness and orderliness in the classroom. Students are required to put- off the lights, ceiling fans and air-condition unit after the class. Students must show respect to his/her classmates and professors.

8. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) DON’T’S Students are not allowed to disturbed his/her classmates while listening to the class session. Students are not allowed to make any unnecessary behavior and attitude inside the classroom. Students are not allowed to forge the signature of the professor. Students are not allowed to cheat during the examination. Students are not allowed to make any form of bullying inside the classroom or even inside the school campus.

9. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) NATURE OF MATHEMATICS Chapter 1: MATHEMATICS IN OUR WORLD Patterns in Nature and the Regularities in the World

10. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) WHAT IS MATHEMATICS? Mathematics is the study of numbers, shapes, and patterns. Mathematics, the science of structure, order, and relation that has evolved from counting, measuring, and describing the shapes of objects. Mathematics helps us make sense of these patterns and occurrences WHERE IS MATHEMATICS? Many patterns and occurrences exist in nature, in our world, in our lives. Mathematics is everywhere. It is in the objects we create, in the works of art we admire. Although we may not notice it, mathematics is also present in the nature that surrounds us, in its landscapes and species of plants and animals, including the human species. WHAT ROLE DOES MATHEMATICS PLAY IN OUR WORLD? Mathematics is a tool to quantify, organize, and control our world, predict phenomena, and make life easier.

11. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) Patterns and counting are correlative. Counting happens when there is 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. Patterns In Nature And The Regularities In The World

12. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) The most basic pattern is the sequence of the dates in the calendar such as 1 to 30 being used month after month; the seven (7) days in a week i.e. the twelve (12) months i.e. and the regular holidays in a year ie . These are celebrated in the same sequence every year. All these phenomena create a repetition of names or events called regularity.

13. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) In this world, a regularity (Collins, 2018), is the fact that the same thing always happens 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. Patterns in nature ( wikipedia ) are visible regularities of form found in the natural world. Regularity in the world states the fact that the same thing always happens in the same circumstances.

14. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) According to Ian Stewart (1995) , we live in a universe of patterns. Every night the stars move in circles across the sky. The seasons cycle at yearly intervals. By using mathematics to organize and systematize our ideas about patterns, we have discovered a great secret: nature’s patterns are not just there to be admired, they are vital clues to the rules that govern natural processes.

15. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) SOME EXAMPLES OF PATTERNS IN NATURE 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.

16. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) A SPIRAL is a curve which emanates from a point, moving farther away as it revolves around the point. Cutaway of a nautilus shell shows the chambers arranged in an approximately logarithmic spiral.

17. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) A MEANDER is one of a series of regular sinuous curves, bends, loops, turns, 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.

18. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) A 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 waves in water show water ripples.

19. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 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.

20. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) A 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.

21. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) A 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.

22. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) STRIPES are made by a series of bands or strips, often of the same width and color along the length.

23. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) A 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. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc.

24. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) AFFINE TRANSFORMATIONS These are the processes of rotation, reflection and scaling. Many plant forms utilize these processes to generate their structure. What is happening in Cauliflower head is perhaps not so obvious but in the case of a fern the rotating pattern is very evident. Each branch appears to be a smaller version of the main plant and so on, at smaller scales

25. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) FIBONACCI SEQUENCE Another one in this world that involves pattern is the Fibonacci number (Grist, 2011) These numbers are nature’s numbering system. They appear everywhere in nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple.

26. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) FIBONACCI SEQUENCE In Mathematics, ( wikipedia ), the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones: 1,1,2,3,5,8,13,21,34,55,89, 144,

27. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) The sequence F of Fibonacci numbers is defined by the recurrence relation:   With seed values:   The first 6 Fibonacci numbers for   1 1 2 3 5 8 1 1 2 3 5 8

28. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) LEONARDO FIBONACCI came up with the sequence when calculating the ideal expansion pairs of rabbits over the course of one year. GEORGE DVORSKY (2013) highlighted that the famous Fibonacci sequence has captivated mathematicians, artists, designers, and scientists for centuries. Also known as the Golden Ratio, its ubiquity and astounding functionality in nature suggests its importance as a fundamental characteristic of the universe. phi = 1.61803

29. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) SEED HEADS The head of a flower is also subject, to Fibonaccian processes. Typically, seeds are produced at the center, and then migrate towards the outside to fill all the space. Sunflowers provide a great example of these spiraling patterns. HERE ARE SOME EXAMPLES:

30. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 2 . PINE CONES Similarly, the seed pods on a pinecone are arranged in a spiral pattern. Each cone consists of a pair of spirals, each one spiraling upwards in opposing directions. The number of steps will almost always match a pair of consecutive Fibonacci numbers.

31. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 3. TREE BRANCHES The Fibonacci sequence can also be seen in the way tree branches form or split. A main trunk will grow until it produces a branch, which creates two growth points. Then, one of the new stems branches into two, while the other one lies dormant. This pattern of branching is repeated for each of the new stems.

32. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 4. SHELLS The unique properties of the Golden Rectangle provide another example. This shape, a rectangle in which the ratio of the sides a/b is equal to the golden mean (phi), can result in a nesting process that can be repeated into infinity and which takes on the form of a spiral. It's called the logarithmic spiral, and it abounds in nature.

33. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 5. SPIRAL GALAXIES AND HURRICANE Not surprisingly, spiral galaxies a l so follow the familiar Fibonacci pattern. The Milky Way has several spiral arms, each of them a logarithmic spiral of about 12 degrees. As an interesting aside, spiral galaxies appear to defy Newtonian physics.

34. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) Importance of Mathematics in Life According to Katie Kim (2015), Math is a subject that makes students either sump for joy or rip their hair out. However, math is inescapable as you become an adult in the real world. Before you decide to doze off in math class, consider this list of reasons why learning math is important to you and the world.

35. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) RESTAURANT TIPPING CALCULATING BILLS NETFLIX FILM VIEWING COMPUTING TEST SCORES TRACKING CAREER Importance of Mathematics in Life DOING EXERCISE HANDLING MONEY MAKING COUNTDOWNS BAKING AND COOKING SURFING INTERNET

36. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) NATURE OF MATHEMATICS It is important to further discuss the nature of mathematics, what it is, how it is expressed, represented and used . 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 its intellectual challenge.

37. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) PATTERNS AND RELATIONSHIPS Mathematics is the science of patterns and relationships. 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 or ideas can be anything from strings of numbers to geometric figures to sets of equations. MATHEMATICS, SCIENCE AND TECHNOLOGY Mathematics is abstract. Its function goes along well with Science and Technology. It finds useful applications in business, industry, music, historical scholarship, politics, sports, medicine, agriculture, engineering, and the social and natural sciences.

38. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) MATHEMATICAL INQUIRY Normally, people are confronted with problems. In order to live at peace, these problems must be solved. M athematics is used to express ideas or to solve problems.

39. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 4. ABSTRACTION AND SYMBOLIC REPRESENTATION Mathematical thinking often begins with the process of abstraction-that is, noticing a similarity between two or more objects or events. Aspects that they have in common, whether concrete or hypothetical, can be represented by symbols such as numbers, letters, other marks, diagrams, geometrical constructions, or even words.

40. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 5. MANIPULATING MATHEMATICAL STATEMENTS 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. For example, the symbol A for the area of any square may be used with the symbol s for the length of the square's side to form the proposition A = s This equation specifies how the area is related to the side-and also implies that it depends on nothing else.

41. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 6. APPLICATION Mathematical processes can lead to a kind of model of a thing, from which insights can be gained about the thing itself. For example, if 2 cups of water are added to 3 cups of water and the abstract mathematical operation 2+3 = 5 is used to calculate the total, the correct answer is 5 cups of water. However, if 2 cups of sugar are added to 3 cups of hot tea and the same operation is used, 5 is an incorrect answer, for such an addition actually results in only slightly more than 4 cups of very sweet tea. Sometimes common sense is enough to enable one to decide whether the results of the mathematics are appropriate.

42. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) THE ROLE OF MATHEMATICS IN SOME DISCIPLINES Mathematics is offered in any college course. It is found in every curriculum because its theories and applications are needed in any workplace. That's why students can't stay away from attending math classes. There has to be mathematics in the real world. This subject always brings life to any person or professional. Every second of the day needs mathematical knowledge and skills to perform academic activities and office routines. If ordinary people have to use math, then much more for students to know and master it so they will succeed in class in the school. As posted by Angel Rathnabai (2014), Mathematics is not only number work or computation, but is more about forming generalization, seeing relationships, and developing logical thinking and reasoning.

43. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) HERE ARE SOME MAIN DISCIPLINES IN WHICH THE ROLE OF MATHEMATICS IS WIDELY ACCEPTED: MATHEMATICS IN PHYSICAL SCIENCES In Physics, every rule and principle take the mathematical form ultimately. Mathematics gives a final shape to the rules of physics. The units of measurement are employed to substances in physics a frequently as in mathematics. The Chare's law of expansion of gases is base upon mathematical calculations. The concept is involved in Fluid Dynamics, Computational Fluid Dynamics, Physical Oceanography. MATHEMATICS IN CHEMISTRY Math is extremely important in physical chemistry especially in advanced topics such as quantum or statistical mechanics.

44. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 3. MATHEMATICS IN BIOLOGICAL SCIENCES 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 biosciences and mathematical problems in biomechanics, bioengineering and bioelectronics. 4. MATHEMATICS IN ENGINEERING AND TECHNOLOGY It is considered to be the foundation of engineering. Engineering deals with surveying, levelling, designing, estimating, construction etc., By the application of geometric principles to design and constructions, the durability of things constructed can be increased. With its help, results can often be verified in engineering. 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 expenditure, average return or income, production per unit area, cost of labor, time and work, seed rate etc.

45. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 6. MATHEMATICS AND ECONOMICS social sciences are also beginning to draw heavily upon mathematics. Mathematical language and methods are used frequently in describing economic phenomena. The whole economic situation is regarded as a game between consumers, distributors, and producers, each group trying to optimize its profits. 7. MATHEMATICS AND PSYCHOLOGY The great educationist Herbart said, "It is not only possible, but necessary that mathematics be applied to psychology". Now, experimental psychology has become highly mathematical due to its concern with such factors as intelligence quotient, standard deviation, mean, median, mode, correlation coefficients and probable errors. Statistical analysis is the only reliable method of attacking social and psychological phenomena. 8. MATHEMATICS AND ACTUARIAL SCIENCE, INSURANCE AND FINANCE For example, if an organization embarks on a large project, an actuary may analyze the project, assess the financial risks involved, model the future financial outcomes and advise the organization on the decisions to be made. Much of their work is on pensions, ensuring funds stay solvent long into the future, when current workers have retired. They also work in insurance, setting premiums to match liabilities, areas of finance, from banking and trading on the stock market, to producing economic forecasts and making government policy.

46. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 9. MATHEMATICS AND ARCHAEOLOGY Archaeologists use a variety of mathematical and statistical techniques to present the data from archaeological surveys and try to distinguish patterns in their results that shed light on past human behavior. Statistical measures are used during excavation to monitor which pits are most successful and decide on further excavation. 10. MATHEMATICS AND LOGIC Pascal says, "Logic has borrowed the rules of geometry; the method of avoiding error is sought by everyone. The symbols and methods used in the investigation of the foundation of mathematics can be transferred to the study of logic. They help in the development and formulation of logical laws.

47. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 11. MATHEMATICS IN MUSIC Leibnitz, the great mathematician said, "Music is a hidden exercise in arithmetic of a mind unconscious of dealing with numbers". Pythogoras said "Where harmony is, there are numbers". 12. MATHEMATICS IN ARTS "Mathematics and art are just two different languages that can be used to express the same ideas." It is considered that the universe is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures.

48. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 13. MATHEMATICS IN PHILOSOPHY Mathematics occupies a central place between natural philosophy and mental philosophy. It was in their search of distinction between fact and fiction that Plato and other thinkers came under the influence of mathematics. 14. MATHEMATICS IN SOCIAL NETWORKS Graph theory, text analysis, multidimensional scaling and cluster analysis and a variety of special models are some mathematical techniques used in analyzing data on a variety of social networks.

49. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 15. MATHEMATICS IN POLITICAL SCIENCE In Mathematical Political Science, we analyze past election results to see changes in voting patterns and the influence of various factors on voting behavior, on switching of votes among political parties and mathematical models for conflict resolution. 16. MATHEMATICS IN LINGUISTICS The concepts of structure and transformation are as important for linguistic as they are for mathematics. 17. MATHEMATICS IN MANAGEMENT Mathematics in management is a great challenge to imaginative minds. It is not meant for the routine thinkers. Different mathematical models are being used to discuss management problems of hospitals, public health, pollution, educational planning and administration and similar other problems of social decisions.

50. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 18. MATHEMATICS IN COMPUTERS An important area of applications of mathematics is in the development of formal mathematical theories related to the development of computer science. Now most applications of mathematics to science and technology today are via computers. The foundation of computer science is based only on mathematics. 19. MATHEMATICS IN GEOGRAPHY Geography is nothing but a scientific and mathematical description of our earth in its universe. The dimension and magnitude of earth, its situation and position in the universe the formation of days and nights, lunar and solar eclipses, latitude and longitude, maximum and minimum rainfall, etc.

51. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) APPRECIATING MATHEMATICS AS A HUMAN ENDEAVOR In order to appreciate mathematics much better, every person should have the thorough understanding of the discipline as a human endeavor. Mathematics brings impact to the life a learner, worker, or an ordinary man in society. The influences of mathematics affect anyone for a lifetime. Mathematics works in the life of all professionals. 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:

52. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ACCOUNTANTS assist businesses by working on their taxes and planning for upcoming years. They work with tax codes and forms, use formulas for calculating interest, and spend a considerable amount of energy organizing paperwork. AGRICULTURISTS determine the proper amounts of fertilizers, pesticides, and water to produce bountiful amounts of foods. ARCHITECTS design buildings for structural integrity and beauty. They must know how to calculate loads for finding acceptable materials in design which involve calculus. BIOLOGISTS study nature to act in concert with it since we are very closely tied to nature. They use proportions to count animals as well as use statistics/probability. CHEMISTS find ways to use chemicals to assist people in purifying water, dealing with waste management, researching superconductors, analyzing crime scenes, making food products and in working with biologists to study the human body.

53. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) COMPUTER PROGRAMMERS create complicated sets of instructions called programs/software to help us use computers to solve problems. ENGINEERS (Chemical, Civil, Electrical, Industrial, Material) build products/structures/systems like automobiles, buildings, computers, machines, and planes, to name just a few examples. GEOLOGISTS use mathematical models to find oil and study earthquakes. LAWYERS argue cases using complicated lines of reason. That skill is nurtured by high level math courses. They also spend a lot of time researching cases, which means learning relevant codes, laws and ordinances. MANAGERS maintain schedules, regulate worker performance, and analyze productivity. MEDICAL DOCTORS They research illnesses, carefully administer the proper amounts of medicine, read charts/tables, and organize their workload and manage the duties nurses and technicians.

54. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) METEOROLOGISTS forecast the weather for agriculturists, pilots, vacationers, and those who are marine-dependent. MILITARY PERSONNEL carry out a variety of tasks ranging from aircraft maintenance to following detailed procedures. Tacticians utilize a branch of mathematics called linear programming NURSES carry out the detailed instructions doctors given them. They adjust intravenous drip rates, take vitals, dispense medicine, and even assist in operations. POLITICIANS help solve the social problems of our time by making complicated decisions within the confines of the law, public opinion. SALESPEOPLE typically work on commission and operate under a buy low, sell high profit model. TECHNICIANS repair and maintain the technical gadgets we depend on like computers, televisions, DVDs, cars, refrigerators. They always read measuring devices, referring to manuals, and diagnosing system problema . TRADESMEN (carpenters, electricians, mechanics, and plumbers) estimate job costs and use technical math skills specific to their field. They deal with slopes, areas, volumes, distances and must have an excellent foundation in math.

55. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) HOW CAN MATH BE SO UNIVERSAL? According to Annenberg Learner (2017) First, human beings didn't invent math concepts; we discovered them. Math can help us to shop wisely, buy the right insurance, remodel a home within a budget, understand population growth, or even bet on the horse with the best chance of winning the race. When you put money in a savings account, the bank pays you interest according to what you deposit. In effect, the bank is paying you for the privilege of "borrowing your money. The same is true for the interest you pay on a loan you take from the bank or the money you "borrow" from a credit card. With population growth, new members of the population eventually produce other new members of the population. Population increases exponentially as time passes.

56. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) What does math have to do with home decorating? Most home decorators need to work within a budget. But in order to figure out what you'll spend, you first have to know what you need. Understanding some basic geometry can help you stick to your budget. Not all people are chefs, but we are all eaters. Most of us need to learn how to follow a recipe at some point. To create dishes with good flavor, consistency, and texture, the various ingredients must have a kind of relationship to one another. For instance, to make cookies that both look and taste like cookies, you need to make sure you use the right amount of each ingredient. Mathematics is the only language shared by all human beings regardless of culture, religion, or gender, country you are in. Adding up the cost of a basket full of groceries involves the same math process regardless of whether the total is expressed in dollars rubles, or yen. With this universal language, all of us, no matter what our unit of exchange, are likely to arrive at math results the same way“ Being fast in mental arithmetic can save your money when you go to the market. Mathematics is all around us.

57. ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )