Science Encyclopedia Mathematics

Science Encyclopedia Mathematics — page 3 — MATHEMATICS Timeline of Mathematics 70,000 to 300 BC South Africa ochre rocks adorned with scratched geometric patterns 70,000 BC 35,000 BC to 20,000 BC Africa and France earliest known prehistoric attempts 20,000 BC 3400 BC 3100 BC 2800 BC 2700 BC 2600 BC 1000 BC 400 BC 300 BC 300 BC 300 BC to quantify time Nile Valley the Ishango Bone is possibly the earliest reference to prime numbers and Egyptian multiplication Mesopotamia the Sumerians invent the first numeral system and a system of weights and measures Egypt earliest known decimal system allows indefinite counting by way of introducing new symbols Indus Valley Civilization on the Indian subcontinent earliest use of decimal ratios in a uniform system of ancient weights and measures Egypt precision surveying Indus Valley Civilization objects streets pavements houses and multi-storied buildings are constructed at perfect right angles Egypt use of common fraction by Egyptians India mathematicians write a mathematical text which classifies all numbers into three sets enumerable innumerable and infinite Egypt Euclid proves the infinitude of prime numbers and presents the Euclidean algorithm Mesopotamia the Babylonians invent the earliest calculator the abacus India mathematician Pingala writes the Chhandah Shastra which contains the first Indian use of zero as a digit indicated by a dot and also presents a description of a binary numeral system along with the first use of Fibonacci numbers and Pascal’s triangle W H A T I S M A T H E M A T I C S 5

Science Encyclopedia Mathematics — page 4 — MATHEMATICS Timeline of Mathematics 260 BC to AD1100s Mexico the Olmecs people were using a true zero a shell glyph several centuries before Ptolemy Greece Eratosthenes uses his sieve algorithm to quickly isolate prime numbers Greece Hipparchus develops the bases of trigonometry India Indian numerals the first positional notation base-10 numeral system begins developing in India Greece Diophantus uses symbols for unknown numbers in terms of the syncopated algebra India the earliest known use of zero as a decimal digit is introduced by Indian mathematicians India Shridhara gives the rule for finding the volume of a sphere and also the formula for solving quadratic equations Europe Al-Khawarizmi is considered father of modern algebra since he was the first to bring Indian mathematics to Europe Iran Ali Ahmad Nasawi divides hours into 60 minutes and minutes into 60 seconds India Indian numerals were modified by Arab mathe maticians to form the modern Hindu-Arabic numeral system used universally in the modern world Europe the Hindu-Arabic numeral system reaches Europe through the Arabs 250 BC 240 BC 140 BC 50 BC AD 250 AD 300 AD 700s AD 750 AD 1030 AD 1100s AD 1100s Like any science mathematics must show us things we didn’t know Proofs and theorems are the basis for math A proof is a mathematical argument that convinces others to believe it is true A theorem is a mathematical statement supported by one or more proofs Mathematicians can prove that theorems are true There are many proofs and theorems in math Mathematics uses reasoning and logic to solve problems In math you solve a problem by thinking Other sciences rely on experiments to solve a problem S C I T A M E H T A M S I T A H W 6

Science Encyclopedia Mathematics — page 5 — MATHEMATICS Common Core and STEM Give Meaning to Mathematics When the math wars began in the 1990s on one side were those who argued for a new focus on concepts and reasoning rather than drilling students on their times-tables On the other were the traditionalists who said the progressive approach allowed students to become unmoored from the building blocks of the subject leaving them unprepared for more advanced mathematics The writers of the Common Core math standards have sought a middle ground By the early 2000s every state had developed and adopted its own learning standards that outlined what students in grades 3-8 and high school should be able to do Every state also had its own definition of proficiency which is the level at which a student is determined to be sufficiently educated at each grade level and upon graduation This lack of standardization was one reason why states decided to develop the Common Core State Standards in 2009 The creation of the math standards was in large part an editing process So the Common Core math standards tackle fewer topics and also move students more slowly through arithmetic subtraction multiplication and the other operations that build up to more complex math particularly algebra Applying mathematics during engineering design challenges can help children develop critical thinking problem solving and communication skills Understanding involves making connections Challenging students with important mathematics prepares them to solve problems in class and at home NCTM’s Principles and Standards for School Mathematics 2000 outlines five Process Standards that are essential for developing deep understanding of mathematics 1 Problem Solving 2 Reasoning and Proof 3 Communication 4 Connections 5 Representation Integrated engineering units of study allow for the application of mathematics skills in real-world contexts removing barriers and enhancing the development of NCTM’s five Process Standards and the Common Core’s eight Standards for Mathematical Practice The purpose for learning is evident with a coherent integrated curriculum freeing students to reason about complex problems analyze multiple solutions and communicate ideas and results They develop habits of mind along with the necessary mathematics skills M A T H E M A T I C S W H A T I S 7

Science Encyclopedia Mathematics — page 6 — A hairstylist uses math to measure the chemicals to color hair Businesses use mathematics when dealing with money Stores add up our bills using math Math is also the basic tool used by scientists and engineers They use it to describe the universe and everything within it Math isn’t just for school Math is everywhere and we use it every day Number Systems Humans have used numbers for a very long time Throughout the history of man every culture used some form of mathematics The numbers that we use today have been around for thousands of years The Base Ten System Today we use a base ten number system The digits used in base ten are 0 1 2 3 4 5 6 7 8 9 Using those 10 digits we can make any number in the system The base ten system was probably created because we have ten fingers to count on There are other bases as well Some bases use more than ten numbers Some use fewer What numbers can you make with these digits S C I T A M E H T A M S I T A H W 8 MATHEMATICS Digits Whole Numbers 5 7 57 75 1 3 9 139 193 319 391 913 931 In the base two system only two The Base Two System Binary Numbers digits are used They are 0 and 1 Most computers use the binary system Binary numbers are base two because all numbers can be made using zero or one Let’s look at how the base ten numbers look in binary Can you figure out the pattern The Base In Base Two There Would Be Ten Digits 0 1 2 3 4 5 6 7 8 9 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001

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