# Equivalent Fraction: Hands-On Task Cards with Pattern Blocks

Do you need fraction activities for your third graders, fourth graders, or fifth graders? These free fraction task cards will challenge and extend thinking while building deep understanding of number relationships. Perfect for differentiation and math workshop! They also provide many possibilities for creativity, individual answers, and math writing. #fractions

MATHEMATIC HISTORY

Mathematics is one of many oldest sciences in human history. In ancient times, Mathematics was defined while the science of numbers and shapes. Mathematics, like other branches of science, has evolved with time; it is no further possible to explain it in a couple of sentences. What I have to say now will soon be words that emphasize its various aspects, as opposed to describe mathematics. In taking care of, mathematics is a skill like painting and music. The great majority of mathematicians perform it as an art. From this standpoint, the fact a work done, a developed theory works in one way or another besides mathematics doesn’t concern them much. What matters to them is the depth of the task done, the novelty of the strategy used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is really a language. If the objective of science is the universe; If it’s to know, rule and direct everything in the universe, we must have the ability to read 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. To be able 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 notice it as a game. Mathematics is just a tool for its user. After entering it, we understand and perceive what mathematics is inside our knowledge and in the direction of our interest. Mathematics has become far beyond the dimensions any human can rule. Therefore, I do not think that people who handle mathematics are more than we understand and perceive it from mathematics compared to the blind touched net understands and perceives the elephant. The phrase mathematics, for the first time, BC. It had been utilized by the members of the Pythagorean school in the 550s. His entry in to the written literature, with Plato BC. It was in the 380s. The phrase meaning is “what needs to be learned”, that’s, information. In the years before these dates, instead of the word mathematics, words that mean geometry, comparable to it in geometry or old languages were used.

It is difficult to say anything definite about where and how mathematics started. When we take documents that aren’t predicated on archaeological findings that require interpretation, but open enough to require interpretation, We can say so 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 suitable for agriculture; It is the 3% portion that provides life to Egypt and forms the Nile delta. Therefore, these lands are incredibly valuable. However, by the end of the floods brought on by the Nile river annually, the boundaries of the landowners’lands become obscure. Because the landowners also pay taxes in proportion to the land they own, after each flood, the “geometricists” of their state, who’re responsible for these works, should arrive at take the necessary measurements and supply the landowners as much land as they’d in the earlier year. Herodotus says that geometry has begun to emerge consequently of these measurements and calculations. A second opinion in regards to the birth of mathematics is the one put forward by Aristotle (384-322 BC). Based on Aristotle, mathematics came to be in Egypt. But it came to be from the boredom of clergymen and priests, not the need for measurement-calculation caused by Nile floods. In those days, the only intellectual class of countries such as for example Egypt was the priest class. Considering that the livelihood of the class is supplied by the general public or the state, they have much time and energy 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 wished to simplify the job of the geometric, or they found out how to calculate the regions of some geometric shapes such as triangular and trapezoidal to check on that the distribution was fair, and this way led to the birth of geometry.

We shall divide the written history of mathematics into five periods. The first period will be Egypt and Mesopotamia; this period BC In 2000s BC. It’ll cover an amount of 1500-2000 years between 500s. The 2nd period, BC. 500-M.S. It will cover a period of 1000 years, called the Greek Mathematics period, between 500 years. The 3rd term, M.S. It’ll cover a 1200-year period from the 500’s until the start of calculus and will mainly cover European mathematics in the Hind, Islam and Renaissance era. The fourth semester will cover the classical mathematics era, referred to as the golden age of mathematics, dating from 1700-1900. The time we’re living in, dating back again to early 1900s, called the age of modern mathematics, will be the fifth period. I will attempt to offer information regarding the development of mathematics because period, contributing mathematicians, the place of mathematics in social life and the basic top features of mathematics because period.

We will start the very 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 first is that the ancient Egyptians wrote the writing on papyrus; The next reason may be the 3 big fires of the Alexandria libraries, the past of the fires happened throughout 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 word papyrus. The average lifespan of a papyrus is 300 years; 300 years later, it is flaky as a result of moisture, heat and similar reasons. Currently, two papyrus linked to mathematics appear to possess been hidden under exceptional circumstances. The key sourced elements of our familiarity with Egyptian mathematics are both of these papyri. The first 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 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 guide written to instruct math. In the introduction part, after having a few exercises given to show operations with fractional numbers, 87 questions receive with their solutions. They’re the type of questions people can encounter in lifestyle, such as for instance sharing account, interest calculation, or finding the region of some geometric shapes. That is pretty much our 8th grade mathematics. The next papyrus, known as the Moscow papyrus and now in the Moscow museum, can also be BC. It is really a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the sort of questions in the Ahmes papyrus, aside from the two. When it comes to other two questions, one may be the calculation of the volume and section of the surface of the sphere part cut with a plane. The other is the question of finding the amount of a pyramid cut by way of a plane. Both questions were solved correctly. Those two questions are accepted because the pinnacle of Egyptian mathematics. The Egyptians seen that the region of the circle was proportional to its diameter and found how many pi to be 4x (8/9) squared, ie 256/81 = 3.16. It’s understood that Egyptian mathematics has remained only at that level for 2000 years and has not made any significant progress.

B.C. 600s would be the years when the Persians started initially to dominate the center east. B.C. By the 550s, Persians are the only real rulers of the whole 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, a year later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 is the date that has been accepted as the beginning of Greek civilization. This date is the beginning of an extremely bright period in science, art and literature. Greek mathematics actually started earlier than this period. Two people, Tales (624-547 BC) and Pythagoras (569-475 BC), are regarded as being the daddy of Greek mathematics. Tales Milet (Aydın) was also born. It is famous that he went along to Egypt, stayed there for a while and learned geometry in Egypt. Whilst in Egypt, it’s described in books where he calculates the height of the truly amazing pyramid by measuring along the shadow of the fantastic pyramid, multiplying this number by the ratio of its length to the length of the present shadow. After returning to Tales Milet, he taught them geometry by forming friends around him to teach what he learned. It’s assumed that abstract proof centered on reasoning, that will be not centered on mathematics – experimental verification, entered into Tales. Furthermore, Tales is the person who is recognized as the very first philosopher in human history. He came to be on the island of Pythagoras Samos (Samos), another father of Greek mathematics. Pythagoras stayed with Tales for some time, went along to Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken up to Babylon by capturing the Persians during the occupation of Egypt by the Persians. it is known. During his 5 years in Babylon, he learned mathematics, music and religious information, and after time for Samos, he created a school and tried to show the people he gathered around. For political reasons, BC. He left 518 Samos, settled in southern Italy, in the town of Crotone, where he created a semi-mystical-semi-scientific, cult-like school. The senior individuals of this school called “mathematics” live together and they’re connected together with oath. The next group contains students attending school. Pythagoras school is dependant on number cult. According to them, everything may be reduced to numbers; It posseses an unusually perfect harmony among numbers, and harmony is a reflection of the divine harmony. Known numbers for that day are integers indicating the plurality such as for example 1,2,3,…; and kes, ¾,… are 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. Many of the members of the Pythagorean school were massacred by way of a raid led with 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 may be understood from these records, Egyptian and Mesopotamian mathematics are the cornerstone of Greek mathematics.

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