day-3-Patterns-and-Numbers-in-Nature-and-the-World-and-Fibonacci-Sequence (1).pptx

Math

1. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT

2. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT PATTERNS AND NUMBERS IN NATURE AND THE WORLD

3. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Objectives: Identify patterns in nature and regulatory in the world. Classify the objects according to symmetry. Articulate the importance of mathematics in one’s life. Explain Fibonacci numbers and their origin. Illustrate how the Fibonacci sequence is expressed in nature.

4. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Have you ever thought of the ff. questions? What does mathematics have to do with nature? What is mathematics about and what it is for? What is a mathematical pattern?

5. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT What does mathematics have to do with nature? - The natural world is full of beauty and amazing shapes and patterns. In his book, Nature by Numbers, Ian Stewart mentioned that we live in a universe of patterns. If you observe our nature diligently, you can prove that our nature bounds in mystical colors and intricate shapes and patterns that can be described mathematically.

6. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT

7. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT What is mathematics about and what it is for? Mathematics makes our life orderly and systematic, and it prevents chaos. It helps us to see patterns needed to generalize a broader solution to a problem. It can be used to express, solve, and interpret the puzzles observed in nature. It expounds the power of reasoning, creativity, abstract or spatial thinking, critical thinking, problem solving ability, and even effective communication skills.

8. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT What is a mathematical pattern?

9. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT PATTERN

10. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Pattern Is a structure, form, or design that regular, consistent, or recurring. Can be found in nature, human-made designs, or in abstract ideas. Occur in different contexts and various forms. They are repetitive and duplicative, their underlying structure regularities can be modeled mathematically.

11. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Different Kinds of Patterns

12. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Pattern of Visuals These patterns are often unpredictable, never quite repeatable, and often contain fractals. Can be seen from the seeds and pinecones to the branches and leaves.

13. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Pattern of Flow Are usually found in water, stone and even in the growth of trees. There is also a flow of pattern present in meandering rivers with the repetition of undulating lines.

14. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Pattern of Movement In the human walk, the feet strike the ground in a regular rhythm: the left-right-left rhythm. When a horse, a four-legged creature walks, there is more of complex but equally rhythmic pattern.

15. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Pattern of Rhythm Rhythm is conceivably the most basic pattern in nature. Our hearts and lungs follow a regular repeated patterns of sounds or movement whose timing is adapted to our body’s needs.

16. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Pattern of Texture It exists as a literal surface that we can feel, see, and imagine. Texture can be bristly and rough, but it can also be smooth, cold, and hard.

17. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Geometric Patterns Is a kind of pattern which consists of a series of shapes that are typically repeated. These are regularities in the natural world that are repeated in a predictable manner.

18. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Determine what comes next in the given patterns. A, C, D, G, I, _____, _____, _____ 15, 10, 14, 10, 13, 10, _____, _____, ______ 3, 6, 12, 24, 48, 96, ____, ____, _____

19. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT PATTERNS FOUND IN NATURE

20. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT SYMMETRY Is an exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis.

21. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT a. BILATERAL SYMMETRY A symmetry in which the left and right sides of the organism can be divided into approximately mirror image of each other alone the midline. Animals have mainly bilateral or vertical symmetry, even leaves of plants and some flowers such as orchids.

22. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Examples:

23. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT b. RADIAL OR RATIONAL SYMMETRY describes living and non-living forms; these forms can be equally divided into three or more sections that, when rotated through a center of rotation by more than 0° and less than 360°, exactly match each other in orientation and shape.

24. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT

25. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Order of Rotation is the number of times a figure can be rotated within 360° such that it looks the same as the original figure. Formula:  

26. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Example: The patterns on a snowflake repeat six times, indicating there is a six-fold symmetry. Find its angle of rotation.  

27. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Example: A compass rose is a symbol used on maps to indicate direction. It has rotational symmetry of order 8. Find its angle of rotation.  

28. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Example: A regular pentagon has rotational symmetry of order 5 . Find its angle of rotation.  

29. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT c. WALLPAPER SYMMETRY also known as a plane crystallographic group, is a pattern with translation symmetry in two directions. is a plane figure which has more than one direction of translation symmetry.

30. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Examples:

31. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT FRACTALS These are never-ending patterns that are self-similar across different scales. The image just reappears repeatedly no matter how many times the object is magnified.

32. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT SPIRALS These are curved patterns made by series of circular shapes revolving around a central point.

33. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT SPOTS AND STRIPES Patterns are also exhibited in the external appearances of animals.

34. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT FLOWER PETALS Flowers are easily considered as things of beauty. Their vibrant colors and fragrant odors make them very appealing as gifts or decorations.

35. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT NUMBER PATTERNS AND SEQUENCES

36. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT FIBONACCI SEQUENCE

37. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Fibonacci Sequence are a series of number that often occur in nature. This number sequence was developed in the Middle Ages, and it was named after Leonardo Pisano Bigollo , a famous Italian mathematician who also happened to discover Fibonacci. Fibonacci is a short term for the Latin Filius Bonacci, which means “the son of Bonacci”.

38. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Fibonacci Sequence

39. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Binet’s Formula:  

40. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Example: Find the using Binet’s Formula.  

41. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Fibonacci Sequence and the Golden Ratio The golden ratio is an irrational number that results when the ratio of two numbers is the same as the ratio of their sum to the larger of the two numbers.

42. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Fibonacci Sequence in Nature The Fibonacci appears in the smallest, to the largest objects in nature. It is a way for information to flow in a very efficient manner. Some examples are Romanesque Broccoli, Aloe Plant, Spiraled Chili Pepper, Sunflower, Rock Daisy, Pinecone, Chameleon Tail, American Giant Millipede, Monarch Caterpillar, and many more.

43. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT SEATWORK #2

44. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Aside from the objects that exhibit patterns in nature, give another example (only one (1)) by illustrating it through a drawing. Put it on a short bond paper. It can be in a portrait or landscape orientation. Write a brief explanation (3-5 sentences) about the pattern being presented in your illustration. Your work will be graded as follows: Pattern used in the artwork – 10 points Creativity – 10 points Originality – 5 points Explanation of artwork – 5 points

45. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT Quiz 1

46. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT I t is conceivably the most basic pattern in nature. A. Regularity B. Symmetry C. Movement D. Rhythm

47. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT 2. It contains both radial and bilateral symmetry. A. Honeycomb B. Sunflower C. Human body D. Butterfly

48. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT 3. What type of sequence deals with common ratio? A. Arithmetic B. Fibonacci C. Geometric D. Harmonic

49. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT 4. This kind of pattern is unpredictable and it often contain fractals. A. Geometric B. Forms C. Movement D. Visual

50. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT 5. It is the value of the golden ratio. A. 1.861 B. 1.168 C. 1.186 D. 1.618

51. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT 6. Who introduced the Fibonacci Sequence? A. Leonardo di Carpio B. Leonardo Da Vinci C. Leonardo Pisano D. Leonardo Gaisano

52. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT 7. Which is a repeated design and mathematically speaking, is series or sequence that repeats? A. pattern B. sequence C. tessalation D. numbers

53. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT 8. What is one way to decide if two numbers follow a Fibonacci sequence? A. If their sum is the same as their difference B. If their ratio is approximately the golden ratio C. If each number is prime D. If their product is approximately the golden ratio

54. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT 9. Which among the following are correct with respect to the nature of mathematics? Mathematics has its own language. There is always one solution to any mathematical problem. Mathematical concepts are abstract. I and II I and III II and III I, II, III

55. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT 10. Modern understanding of visible patterns correlates mathematically with simple translation of patterns. True False

56. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT 11. In the formula of Angle Rotation A= n, n stands for? 12-13. Give at least two types of patterns 14. It is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design. 15. They are called as the “heart of mathematics”.  

57. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT 16-20. How is mathematics used in our day-to-day life and how can you imagine your life without mathematics?

58. ISABELA COLLEGE OF ARTS & TECHNOLOGY, INC. Tagaran , Cauayan City, Isabela Telefax: [phone] Email: [email protected] COURSE DESCRIPTIVE TITLE: Mathematics in the Modern World INSTRUCTOR: EDA MAY C. SIMON LPT