☆ Learn to understand and apply the Distributive Property | Common Core Algebra | Math

# ☆ Learn to understand and apply the Distributive Property | Common Core Algebra

Check out our newest animated math lesson, which explores the concepts and procedures associated with the distributive property. This lesson is aligned with the common core learning standards for algebra and is an excellent resource for flipped classroom math teachers and visual learners! Please subscribe to our YouTube channel to access all of our video lessons 🙂

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 longer possible to explain it in several sentences. What I have to say now will be words that emphasize its various aspects, rather than describe mathematics. In taking care of, mathematics is an art like painting and music. The great majority of mathematicians perform it as an art. Out of this point of view, the truth that a work done, a developed theory works in one of the ways or another apart from mathematics does not concern them much. What matters for them is the depth of the job done, the novelty of the techniques used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is a language. If the purpose of science is the universe; If it is to comprehend, rule and direct everything in the universe, we must be able 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. In order to understand and interpret them, we must 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 only 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 is currently far beyond the dimensions any human can rule. Therefore, I do not believe those that handle mathematics tend to be more than we understand and perceive it from mathematics than the blind touched net understands and perceives the elephant. The term mathematics, for the first time, BC. It had been used by the members of the Pythagorean school in the 550s. His entry into the written literature, with Plato BC. It was in the 380s. The word meaning is “what must be learned”, that is, information. In the years before these dates, instead of the word mathematics, words which means that geometry, comparable to it in geometry or old languages ​​were used.

It is not possible to state anything definite about where and how mathematics started. If we take documents that are not based on archaeological findings that require interpretation, but open enough to require interpretation, We could say so it started between 3000 and 2000 in Egypt and Mesopotamia. Based on Heredotus (485-415 BC), mathematics started in Egypt. Everbody knows, 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 end of the floods due to the Nile river every year, the boundaries of the landowners’lands become obscure. Since the landowners also pay taxes in proportion to the land they own, after each and every flood, the “geometricists” of the state, that are in charge of these works, should arrived at take the mandatory measurements and provide the landowners the maximum amount of land as they’d in the earlier year. Herodotus says that geometry has begun to emerge as a result of these measurements and calculations. A second opinion about the birth of mathematics is the one put forward by Aristotle (384-322 BC). According to Aristotle, mathematics was created in Egypt. But it came to be from the boredom of clergymen and priests, not the necessity for measurement-calculation caused by Nile floods. During those times, the sole intellectual class of countries such as for example Egypt was the priest class. Since the livelihood with this class is given by the public or the state, they’ve much time for you to give to intellectual pursuits. To help keep them busy, they invented geometry and arithmetic, the mathematics of that time, just like others invented games like chess, bridge, and go&hellip ;.Both of these views might be true; priests wished to simplify the job of the geometric, or they discovered how to calculate the areas of some geometric shapes such as triangular and trapezoidal to check that the distribution was fair, and in this manner resulted in the birth of geometry.

We shall divide the written history of mathematics into five periods. The first period is going to be Egypt and Mesopotamia; this period BC In 2000s BC. It’ll cover a period of 1500-2000 years between 500s. The next period, BC. 500-M.S. It’ll cover a period of 1000 years, referred to as the Greek Mathematics period, between 500 years. The next 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, referred to as the golden age of mathematics, dating from 1700-1900. The time scale we’re living in, dating back to the first 1900s, called the age of modern mathematics, will be the fifth period. I will try to offer information about the development of mathematics because period, contributing mathematicians, the area of mathematics in social life and the basic features of mathematics for the reason that 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 will find two significant reasons for this. The very first is that the ancient Egyptians wrote the writing on papyrus; The second reason could be the 3 big fires of the Alexandria libraries, the last of these 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 as opposed to paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are produced from the term papyrus. The typical lifespan of a papyrus is 300 years; 300 years later, it is flaky because of moisture, heat and similar reasons. Currently, two papyrus related to mathematics appear to have been hidden under exceptional circumstances. The key sources of our familiarity with Egyptian mathematics are those two papyri. The very first of the papyrus is really a 6-meter long and 35-cm wide papyrus called the Ahmes (or Rhind) papyrus. This papyrus, BC. You’re a puree written in 2000s, BC. It is a copy published 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 teach math. In the introduction part, following a few exercises given to instruct operations with fractional numbers, 87 questions get making use of their solutions. These are the kind of questions people can encounter in everyday life, such as for example sharing account, interest calculation, or finding the location of ​​some geometric shapes. This is pretty much our 8th grade mathematics. The next papyrus, referred to as the Moscow papyrus and now in the Moscow museum, is also BC. It is just a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the type of questions in the Ahmes papyrus, aside from the two. As for the other two questions, one of them could be the calculation of the volume and part of ​​the surface of the sphere part cut by way of a plane. One other is the question of finding the volume of a pyramid cut by way of a plane. Both questions were solved correctly. These two questions are accepted because the pinnacle of Egyptian mathematics. The Egyptians realized 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 is understood that Egyptian mathematics has remained only at that level for 2000 years and has not made any significant progress.

B.C. 600s are the years once the Persians started 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, per year later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 may be the date which was accepted as the start of Greek civilization. This date is the start of a really bright period in science, art and literature. Greek mathematics actually started earlier than this period. Two different 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 famous he visited 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 great pyramid by measuring along the shadow of the great pyramid, multiplying this number by the ratio of its length to along the present shadow. After time for Tales Milet, he taught them geometry by forming an organization around him to teach what he learned. It’s assumed that abstract proof predicated on reasoning, which can be not centered on mathematics – experimental verification, entered into Tales. Furthermore, Tales is the one who is recognized as the 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 a 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 throughout 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 college and tried to show the folks 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 people of this school called “mathematics” live together and they are connected together with oath. The second group consists of students attending school. Pythagoras school is based on number cult. According for them, everything may be reduced to numbers; It comes with 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 deep crisis. The discovery of irrational numbers is the first major crisis of mathematics. Most of the members of the Pythagorean school were massacred by way of a raid led by way of a big cyber named Cylon. Pythagoras saved his life, but after a couple of years he died. Pythagoras’thoughts, the Pythagorean school lived for several years under this or that name. As can be understood from these records, Egyptian and Mesopotamian mathematics are the cornerstone of Greek mathematics.