# Math Workshop in Action

Math Workshop- this teacher explains exactly how she conducts her guided math lessons in her third grade classroom. (extremely informative post that includes a FREEBIE!)

MATHEMATIC HISTORY

Mathematics is one of the oldest sciences in human history. In ancient times, Mathematics was defined since the science of numbers and shapes. Mathematics, like other branches of science, has evolved with time; it’s no more possible to describe it in a couple of sentences. What I have to state now will undoubtedly be words that emphasize its various aspects, as opposed to describe mathematics. In one aspect, mathematics is a skill like painting and music. The great majority of mathematicians perform it as an art. Using this perspective, the fact that a work done, a developed theory works in one of the ways or another besides mathematics doesn’t concern them much. What matters to them may be the depth of the work done, the novelty of the methods used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is really a language. If the goal of science could be the universe; If it’s to comprehend, rule and direct everything in the universe, we must have the ability to see the book of nature. The book of nature is written in the language of mathematics, with the highly cited words of Galile; its letters are shapes of geometry. In order to understand and interpret them, we have to know the language of mathematics. In another aspect, mathematics can be an intellectual game like chess.

Some mathematicians also see it as a game. Mathematics is merely a tool for its user. After entering it, we understand and perceive what mathematics is within our knowledge and in the direction of our interest. Mathematics is now far beyond the dimensions any human can rule. Therefore, I do not genuinely believe that people who handle mathematics are far more than we understand and perceive it from mathematics compared to the blind touched net understands and perceives the elephant. The word mathematics, for the very first time, BC. It absolutely was utilized by the members of the Pythagorean school in the 550s. His entry to the written literature, with Plato BC. It was in the 380s. The term meaning is “what needs to be learned”, that is, information. In the years before these dates, as opposed to the word mathematics, words which means that geometry, equal to it in geometry or old languages were used.

It’s not possible to say anything definite about where and how mathematics started. When we take documents that aren’t predicated on archaeological findings that want interpretation, but open enough to require interpretation, We could say that it started between 3000 and 2000 in Egypt and Mesopotamia. According to Heredotus (485-415 BC), mathematics were only available in Egypt. As you know, 97% of the Egyptian lands aren’t ideal for agriculture; It is the 3% portion that gives life to Egypt and forms the Nile delta. Therefore, these lands are incredibly valuable. However, at the conclusion of the floods caused by the Nile river each year, the boundaries of the landowners’lands become obscure. Since the landowners also pay taxes in proportion to the land they own, after every flood, the “geometricists” of their state, that are accountable for these works, should come to take the required measurements and provide the landowners as much land as they’d in the earlier year. Herodotus says that geometry has begun to emerge consequently of the measurements and calculations. A second opinion in regards to the birth of mathematics is the main one put forward by Aristotle (384-322 BC). In accordance with Aristotle, mathematics was created in Egypt. However it was born out from the boredom of clergymen and priests, not the necessity for measurement-calculation caused by Nile floods. During those times, the only real intellectual class of countries such as for instance Egypt was the priest class. Considering that the livelihood of this class is supplied by people or their state, they have much time for you to give intellectual pursuits. To keep them busy, they invented geometry and arithmetic, the mathematics of the period, in the same way others invented games like chess, bridge, and go&hellip ;.Both these views might be true; priests desired to simplify the job of the geometric, or they discovered just how to calculate the regions of some geometric shapes such as for example triangular and trapezoidal to check on that the distribution was fair, and in this way resulted in the birth of geometry.

We will divide the written history of mathematics into five periods. The first period is likely to be Egypt and Mesopotamia; this period BC In 2000s BC. It will cover an amount of 1500-2000 years between 500s. The next period, BC. 500-M.S. It will cover an amount of 1000 years, known as the Greek Mathematics period, between 500 years. The third term, M.S. It’ll cover a 1200-year period from the 500’s until the beginning of calculus and will mainly cover European mathematics in the Hind, Islam and Renaissance era. The fourth semester will cover the classical mathematics era, known as the golden age of mathematics, dating from 1700-1900. The time scale we are surviving in, dating back once again to early 1900s, called age modern mathematics, could be the fifth period. I will endeavour to give details about the development of mathematics in that period, contributing mathematicians, the spot of mathematics in social life and the essential top features of mathematics because period.

We will start the first semester with Egyptian mathematics. Written documents about ancient Egyptian mathematics and generally Egyptian history – I don’t mean the remains of archaeological works – are almost nonexistent. You can find two major causes for this. The foremost is that the ancient Egyptians wrote the writing on papyrus; The 2nd reason may be the 3 big fires of the Alexandria libraries, the past of those fires happened during the conquest of Egypt by 641 Muslims, the written documents disappeared. Papyrus is the leaves of a reddish, reed type plant growing in the Nile delta, typically 15-25 meters long and 30-50 inches wide. These leaves were used to publish text in place of paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages such as “Paper”, “papier” are based on the term papyrus. The average lifespan of a papyrus is 300 years; 300 years later, it’s flaky as a result of moisture, heat and similar reasons. To date, two papyrus related to mathematics appear to own been hidden under exceptional circumstances. The main sources of our understanding of Egyptian mathematics are these two papyri. The initial of the papyrus is a 6-meter long and 35-cm wide papyrus referred to as the Ahmes (or Rhind) papyrus. This papyrus, BC. You’re a puree written in 2000s, BC. It is just a copy written by a “mathematician” named Ahmes in the 1650s. This papyrus was bought by the Irish antiquarian H. Rhind in the 1850s, now in the British museum. This papyrus is a book written to show math. In the introduction part, following a few exercises given to teach operations with fractional numbers, 87 questions get making use of their solutions. These are the sort of questions people can encounter in daily life, such as sharing account, interest calculation, or finding the location of some geometric shapes. That is just about our 8th grade mathematics. The 2nd papyrus, called the Moscow papyrus and now in the Moscow museum, can be BC. It is really a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the kind of questions in the Ahmes papyrus, aside from the two. As for the other two questions, one of them is the calculation of the quantity and section of the surface of the sphere part cut by a plane. Another is the question of finding the quantity of a pyramid cut with a plane. Both questions were solved correctly. These two questions are accepted whilst the pinnacle of Egyptian mathematics. The Egyptians seen that the region of the circle was proportional to its diameter and found the amount of pi to be 4x (8/9) squared, ie 256/81 = 3.16. It is understood that Egyptian mathematics has remained as of this level for 2000 years and has not made any significant progress.

B.C. 600s are the years once the Persians started to dominate the middle east. B.C. By the 550s, Persians are the only real rulers of the entire middle east, including Anatolia and Egypt. The Persians organize three trips to Greece between 500-480 BC; They captured Athens in 480, but burned it, per year later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 is the date which was accepted as the start of Greek civilization. This date is the start of a very bright period in science, art and literature. Greek mathematics actually started sooner than this period. Two people, Tales (624-547 BC) and Pythagoras (569-475 BC), are regarded as the father of Greek mathematics. Tales Milet (Aydın) was also born. It is known he went along to Egypt, stayed there for some time and learned geometry in Egypt. During Egypt, it is described in books where he calculates the height of the truly amazing pyramid by measuring the length of the shadow of the great pyramid, multiplying this number by the ratio of its length to the size of the current shadow. After returning to Tales Milet, he taught them geometry by forming friends around him to teach what he learned. It is assumed that abstract proof based on reasoning, which can be not centered on mathematics – experimental verification, entered into Tales. Furthermore, Tales is the one who is recognized as the very first philosopher in human history. He was born on the island of Pythagoras Samos (Samos), another father of Greek mathematics. Pythagoras stayed with Tales for some time, went to Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken fully to Babylon by capturing the Persians through the occupation of Egypt by the Persians. it’s known. During his 5 years in Babylon, he learned mathematics, music and religious information, and after time for Samos, he created a college and tried to teach the people he gathered around. For political reasons, BC. He left 518 Samos, settled in southern Italy, in the city of Crotone, where he created a semi-mystical-semi-scientific, cult-like school. The senior people of this school called “mathematics” live together and they’re connected to one another with oath. The 2nd group contains students attending school. Pythagoras school is founded on number cult. According for them, everything may be reduced to numbers; It has an unusually perfect harmony among numbers, and harmony is really a reflection of the divine harmony. Known numbers for that day are integers indicating the plurality such as for instance 1,2,3,…; and kes, ¾,… would be the fractional numbers that indicate the ratio of the part to the whole. The emergence of irrational numbers with the theorem referred to as the Pythagorean theorem (the square of the best sides of the right triangle equals the square of the hypotenuse) put the Pythagorean school in a strong crisis. The discovery of irrational numbers is the initial major crisis of mathematics. Lots of the members of the Pythagorean school were massacred by a raid led by way of a big cyber named Cylon. Pythagoras saved his life, but after many years he died. Pythagoras’thoughts, the Pythagorean school lived for several years under this or that name. As could be understood from these details, Egyptian and Mesopotamian mathematics are the basis of Greek mathematics.

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