Breaking Up the Second Number: An Addition Strategy | Math

# Breaking Up the Second Number: An Addition Strategy

Breaking up the second number is a mental math strategy for addition. Some students may find this method more efficient than left-to-right addition. This strategy involves breaking up the second number in an equation into more manageable parts. Like many other mental math strategies, this strategy encourages students to think flexibly and to manipulate numbers in different ways. This is the big goal of mental math! Includes two FREE printable worksheets.

MATHEMATIC HISTORY

Mathematics is among 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 spell it out it in a couple of sentences. What I have to express now will soon be words that emphasize its various aspects, as opposed to describe mathematics. In one aspect, mathematics is an art form like painting and music. A large proportion of mathematicians perform it as an art. Out of this perspective, the truth that a work done, a developed theory works in one of the ways or another apart from mathematics doesn’t concern them much. What matters to them is the depth of the task 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 goal of science is the universe; If it is to comprehend, rule and direct everything in the universe, we must manage to browse 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 is definitely an intellectual game like chess.

Some mathematicians also notice it as a game. Mathematics is just a tool for the 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 believe those that deal with mathematics tend to be more than we understand and perceive it from mathematics compared to blind touched net understands and perceives the elephant. The phrase mathematics, for initially, BC. It 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 phrase meaning is “what must be learned”, that is, information. In the years before these dates, as opposed to the word mathematics, words that mean geometry, equal to it in geometry or old languages ​​were used.

It is not possible to express anything definite about where and how mathematics started. When we take documents which are not predicated on archaeological findings that want interpretation, but open enough to require interpretation, We are able to say so it started between 3000 and 2000 in Egypt and Mesopotamia. In accordance with Heredotus (485-415 BC), mathematics started in Egypt. You may already know, 97% of the Egyptian lands aren’t suitable for agriculture; It’s the 3% portion that offers life to Egypt and forms the Nile delta. Therefore, these lands are extremely valuable. However, at the end of the floods brought on by the Nile river annually, the boundaries of the landowners’lands become obscure. Considering that the landowners also pay taxes in proportion to the land they own, after each and every flood, the “geometricists” of the state, that are accountable for these works, should arrive at take the mandatory measurements and give the landowners just as much land as they had in the last year. Herodotus says that geometry has begun to emerge consequently of these measurements and calculations. An additional opinion concerning the birth of mathematics is the main one put forward by Aristotle (384-322 BC). Based on Aristotle, mathematics came to be in Egypt. Nonetheless it was born out of the boredom of clergymen and priests, not the requirement for measurement-calculation caused by Nile floods. At that time, the only intellectual class of countries such as for instance Egypt was the priest class. Since the livelihood of the class is provided by the general public or the state, they’ve much time and energy to share with intellectual pursuits. To keep them busy, they invented geometry and arithmetic, the mathematics of the period, just like others invented games like chess, bridge, and go&hellip ;.Both of these views might be true; priests wanted to simplify the task of the geometric, or they found out 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 manner generated the birth of geometry.

We will divide the written history of mathematics into five periods. The very first period is likely 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 will 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 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 are surviving in, dating back once again to early 1900s, called the age of modern mathematics, could be the fifth period. I will try to provide details about the development of mathematics for the reason that period, contributing mathematicians, the place of mathematics in social life and the essential 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 will find two major causes for this. The foremost is that the ancient Egyptians wrote the writing on papyrus; The next reason is the 3 big fires of the Alexandria libraries, the last of the fires happened throughout the conquest of Egypt by 641 Muslims, the written documents disappeared. Papyrus could be the leaves of a reddish, reed type plant growing in the Nile delta, normally 15-25 meters long and 30-50 inches wide. These leaves were used to create text in place of paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are derived 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 linked to mathematics appear to own been hidden under exceptional circumstances. The main sourced elements of our understanding of Egyptian mathematics are these two papyri. The initial of those papyrus is 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 really 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, after a few exercises given to instruct operations with fractional numbers, 87 questions are made making use of their solutions. These are the type of questions people can encounter in lifestyle, such as for instance sharing account, interest calculation, or finding the area of ​​some geometric shapes. That is more or less our 8th grade mathematics. The next papyrus, referred to as the Moscow papyrus and now in the Moscow museum, is also BC. It is a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the sort of questions in the Ahmes papyrus, except for the two. When it comes to other two questions, one may be the calculation of the volume and area of ​​the surface of the sphere part cut by a plane. One other is the question of finding the volume of a pyramid cut by a plane. Both questions were solved correctly. Both of these questions are accepted while the pinnacle of Egyptian mathematics. The Egyptians realized that the area 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 at this level for 2000 years and has not made any significant progress.

B.C. 600s are the years once the Persians began to dominate the middle east. B.C. By the 550s, Persians are the sole 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, annually later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 may be the date that has been accepted as the start of Greek civilization. This date is the beginning 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 considered to be the father of Greek mathematics. Tales Milet (Aydın) was also born. It is known he went along to Egypt, stayed there for a time and learned geometry in Egypt. Whilst in Egypt, it’s described in books where he calculates the height of the fantastic pyramid by measuring the size of the shadow of the fantastic pyramid, multiplying this number by the ratio of its length to along the existing shadow. After returning to Tales Milet, he taught them geometry by forming a group around him to instruct what he learned. It is assumed that abstract proof centered on reasoning, that will be not based on mathematics – experimental verification, entered into Tales. Additionally, Tales is the one who is known as the initial 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 while, visited Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken 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 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 are connected to one another with oath. The second group consists of students attending school. Pythagoras school is founded on number cult. According to them, everything could 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 example 1,2,3,…; and kes, ¾,… will be the fractional numbers that indicate the ratio of the part to the whole. The emergence of irrational numbers with the theorem called the Pythagorean theorem (the square of the right sides of the right triangle equals the square of the hypotenuse) put the Pythagorean school in a heavy crisis. The discovery of irrational numbers is the initial major crisis of mathematics. Many of the members of the Pythagorean school were massacred with a raid led with a big cyber named Cylon. Pythagoras saved his life, but after a few years he died. Pythagoras’thoughts, the Pythagorean school lived for several years under this or that name. As could be understood from this information, Egyptian and Mesopotamian mathematics are the foundation of Greek mathematics.