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I. MATHEMATICS IN OUR WORLD Core Idea: Mathematics is a useful way to think about nature and the world. Learning Objectives:  Identify patterns in nature  Articulate the importance of mathematics in one’s life  Argue about the nature of mathematics, what is it, how...

I. MATHEMATICS IN OUR WORLD Core Idea: Mathematics is a useful way to think about nature and the world. Learning Objectives:  Identify patterns in nature  Articulate the importance of mathematics in one’s life  Argue about the nature of mathematics, what is it, how it is expressed, represented, and used.  Express appreciation for mathematics as a human endeavor What is mathematics? Where is mathematics? What is mathematics for? What is mathematics all about? What role does mathematics play in our world?  Human mind and culture – develop a formal system of thoughts for recognizing, classifying, and exploiting patterns  Great secret: NATURE’S PATTERNS - rules that govern natural processes  Johannes Kepler – The Six-Cornered Snowflake  Nature’s Patterns Patterns - regular, repeated, or recurring forms or designs  In nature  Numerical patterns – Fibonacci sequence, flowers  Geometric patterns - snowflakes  Wave patterns - sand dunes, stripes, spots  Patterns of movement – flight of birds, motion of heavenly bodies  Chaos – clouds, rivers networks, mountains, trees  Fibonacci Sequence - Golden Rectangle Geometric Patterns What role does mathematics play in our world?  Mathematics is a useful and systematic way to think about and understand nature. Examples Storm is a functions of temperature and pressure Plant growth is a function of nutrients and sunlight Success is a function of good character, positive mind set and discipline What is mathematics all about?  Patterns  Numbers  Operations and Functions  Processes  Data structure  Proof – presents a story about mathematics that works. What do we want mathematics to tell us about nature?  How do things happen.  Why things happen. What is mathematics for?  Mathematics helps organize patterns and regularities in the world  Helps us to solve puzzles. It is a systematically way of digging out the rules and structures that lie behind some observed pattern or regularity  Rules and structures are then used to explain what’s going on.  What is mathematics for?  Helps organize the underlying patterns and regularities  Helps predict behavior of nature and phenomena  Helps control nature and occurrences for our own ends  Make practical use of what we have learned about our world END