List of 8th Grade Math Concepts

List of 8th Grade Math Concepts At the eighth grade level, there are certain math concepts that your students should  attain by the end of the school year. A lot of the math concepts from eighth grade are similar to seventh grade. At the middle school level, it is usual for students to have a comprehensive review of all math skills.  Mastery of the concepts from the previous grade levels  is  expected.   Numbers No real new numbers concepts are introduced, but students should be comfortable calculating factors, multiples, integer amounts, and square roots for numbers. At the end of eighth grade, a student should be able to apply these number concepts in problem-solving. Measurements Your students should be able to use measurement terms appropriately and should be able to measure a variety of items at home and at school. Students should be able to solve more complex problems with measurement estimations and problems using a variety of formulas. At this point, your students should be able to estimate and calculate areas for trapezoids, parallelograms, triangles, prisms, and circles using the correct formulas. Similarly, students should be able to estimate and calculate volumes for prisms  and should be able to sketch prisms based on volumes given. Geometry Students should be able to hypothesize, sketch, identify, sort, classify, construct, measure, and apply a variety of geometric shapes and figures and problems. Given dimensions, your students should be able to sketch and construct a variety of shapes. You students should be able to create and solve a variety of geometric problems. And, students should be able to analyze and identify shapes that have been rotated, reflected, translated, and describe those that are congruent. In addition, your students should be able to determine if shapes or figures will tile a plane (tessellate), and should be able to analyze tiling patterns. Algebra and Patterning In eighth grade, students will analyze and justify the explanations for patterns and their rules at a more complex level. Your students should be able to write algebraic equations and write statements to understand simple formulas. Students should be able to evaluate a variety of simple linear algebraic expressions at a beginning level by using one variable. Your students should confidently solve and simplify algebraic equations with four operations. And, they should feel comfortable substituting natural numbers for variables when solving algebraic equations. Probability Probability measures the likelihood that an event will occur. It used it in everyday decision making in science, medicine,  business, economics, sports,  and engineering. Your students should be able to design surveys, collect and organize more complex data, and identify and explain patterns and trends in data. Students should be able to construct a variety of graphs and label them appropriately and state the difference between selecting one graph over another. Students should be able to describe collected data in terms of mean, median,  and  the mode and be able to analyze any bias. The goal is for students to make more accurate predictions and understand the importance of statistics on decision making and in real-life scenarios. Students should be able to make inferences, predictions,  and evaluations based on interpretations of data collection results. Likewise, your students should be able to apply the rules of probability to games of chance and sports. Other Grade Levels Pre-K Kdg. Gr. 1 Gr. 2 Gr. 3 Gr. 4 Gr. 5 Gr. 6 Gr. 7 Gr. 8 Gr. 9 Gr. 10 Gr.11 Gr. 12

Biography of Sociologist Charles Horton Cooley

Biography of Sociologist Charles Horton Cooley Charles Horton Cooley was born August 17, 1864,  in Ann Arbor, Michigan. He graduated from the University of Michigan in 1887 and returned one year later to study political economics and sociology. Cooley began teaching economics and sociology at the University of Michigan in 1892 and went on to receive his Ph.D. in 1894. He married Elsie Jones in 1890 with whom he had three children. The doctor preferred an empirical, observational approach to his research. While he appreciated the use of statistics, he preferred case studies, often using his own children as the subjects on his observation.  He died of cancer on May 7, 1929. Career and Later Life Cooleys first major work, The Theory of Transportation, was in economic theory. This book was notable for its conclusion that towns and cities tend to be located at the confluence of transportation routes. Cooley soon shifted to broader analyses of the interplay of individual and social processes. In Human Nature and the Social Order, he foreshadowed George Herbert Meads discussion of the symbolic ground of the self by detailing the way in which social responses affect the emergence of normal social participation. Cooley greatly extended this conception of the looking-glass self in his next book, Social Organization: A Study of the Larger Mind, in which he sketched a comprehensive approach to society and its major processes. In Cooley’s theory of the â€Å"looking glass self,† he states that our self-concepts and identities are a reflection of how other people perceive us. Whether our beliefs about how others perceive us are true or not, it is those beliefs that truly shape our ideas about ourselves. Our internalization of the reactions of others towards us is more important than reality. Further, this self-idea has three principal elements: our imagination of how others see our appearance; our imagination of the other’s judgment of our appearance; and some sort of self-feeling, such as pride or mortification, determined by our imagination of the other’s judgment of us. Other Major Publications Life and the Student (1927)Social Process (1918)Sociological Theory and Social Research (1930) References Major Theorist of Symbolic Interactionism: Charles Horton Cooley. (2011). http://sobek.colorado.edu/SOC/SI/si-cooley-bio.htm Johnson, A. (1995). The Blackwell Dictionary of Sociology. Malden, Massachusetts: Blackwell Publishers.

Personal statement Example | Topics and Well Written Essays - 1000 words - 8

Personal Statement Example It was this act of witnessing people around me falling into financial troubles leading to depravation of their happiness that I knew I should head towards a direction that would bring smiles back on their faces and improve the entire trade by ensuring fair and realistic mechanisms are in place. I followed my dream and landed in Durham University where I am currently in my third year of study, pursuing a BSc course in Accounting and Finance, and the experience has been eye opening. I have already learned to adapt to new situations since the setting was very different from my familiar Chinese background and I have learned to appreciate and value the differences in all cultures. The current situation is very promising and I can envision my self achieving what my young ambitious self was aiming to achieve since I have aligned all available choices to finance-preferred, both academically and practically. Experience is undoubtedly the best teacher that is why I ensure that each and every holiday since the summer of 2012 I have found my way back home to partake in my internships at my father’s financial company located in Shenzhen, Mainland China. I have worked in both the trading and investment advisory departments where I have always had the privilege to meet senior executives of the leading and most competitive institutions in China. This interaction has broadened my mind in terms of ideologies as we share our thoughts and views increasing my knowledge and logical thinking capabilities to avoid trouble before it brews and to seek financial facts in each situation. Generally, I have attained valuable field experiences such as valid trading techniques including how to perceive the variation of specific markets or stocks. I have so far grasped the full knowledge of trading large amounts of property without affecting share prices

Teaching Profession Essay Example | Topics and Well Written Essays - 1250 words

Teaching Profession - Essay Example Teachers are expected to nurture attributes, skills and capacities in the young people that will enable them succeed and prosper in the knowledge society. The profession is bloated with many responsibilities stemming from imparting knowledge to students to modifying their personalities. Thus, the profession requires effective socialization, providing the necessary foundations for a responsible citizen, and providing emotional support. The first impression of teaching is formed in the student life when a teacher conducts their role responsibly. This creates a notion that teaching is a noble profession that caters for the academic, emotional or spiritual needs of the learners. Effective and efficient childhood interaction between teachers and young learners creates a positive image of teaching as an industrious job. Students do not come into contact with the practical details and challenges associated with teaching; thus, the worth of teaching in a classroom context should not be weigh ed upon professional hassles and practical work. The current first time teachers fail to realize that professional knowledge is no longer viewed as a constituent of explicit and fixed knowledge base. Sharpe (2004) posits that knowledge exists in use, and any advancements or modification is caused by experience. Therefore, when teachers use their knowledge, the mode of its delivery changes the impact of its use among students. Discussion The reality between the impression of teaching and reality can be explained by the nature of having unfavorable returns or when the experience conforms to the initial impression. The transformation from student life to teacher status may lead into a different feeling that may make a first time teacher uncomfortable. This can be viewed as a negative stroke considering the earlier positive impression and willingness to indulge in the profession. Most students view the teaching profession as an uncomplicated and easy knowledge delivery task full of exci tement and fun. However, this notion is blown away once they become teachers and encounter the responsibilities required of them such as effectiveness, high-end communication skills, hard work, creativity and determination. Dalmau and Gudjonsdottir (2002) affirm this when they state the roles and obligations associated with teaching. They include acting as pedagogues and experts in teaching, reflective and critical problem solvers, knowledge creators and theory builders as well as acting as research and change agents. Those who are not prepared for such commitments get disappointed once they get involved in the profession. Superiority and aggression was normally viewed as the effective measures necessary to instill discipline in students. This notion made most aspiring and first time teachers view this as a privilege associated with the profession. However, the current education systems do not support dictatorial authority but prefer popularly-based authority. The school atmosphere is characterized by negotiation and persuasion rather than confrontation. Most school rules are made by the community as a whole; hence, they are student friendly with the teacher’s input being reduced to that of nurturing and persuading. This requires commitment and dedication of a decided mind. Proponents of democratic school system argue that a school which follows fairly the democratically enacted laws is the one in which community discipline prevails and supports the development of the concept of law and order (Sharpe, 2004). Most learners may regard teaching with a high esteem. Such notion makes them expect recognition and uplifting of their status in the community once they adopt the

The Pythagorean Theorem Essay Example for Free

The Pythagorean Theorem Essay In the world of mathematics, the Pythagorean Theorem is one of the most popular theorems and is widely applied in many problems and applications because of its basic and simple concept. It is a relation in Euclidean geometry relating the three sides of a right triangle. The theorem is named after the Greek mathematician and philosopher, Pythagoras, who lived in the 6th century B.  C.   It is one of the earliest theorems known since the ancient civilizations. The Pythagorean Theorem states that: â€Å"In any right angle triangle, the area of the square   of   the side opposite the right angle i. e. whose side is the hypotenuse   is equal to the sum of the areas of the squares of the two sides that meet at a right angle i.e. whose sides are the two legs.† In other words, â€Å"The square on the hypotenuse is equal to the sum of the squares on the other two sides.† Consider a right triangle ∆ABC with right angle at A. BAC = 90 degrees Then, the square drawn on BC opposite the right angle is equal to the two squares together on BA and AC. Thus,   the sides of a right triangle are related by the squares drawn on them. The Pythagorean Theorem is a statement about triangles containing a right angle. It states that: The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides.          Illustratation by numbers Let the sides of the right angle triangle be 3, 4, and 5.    Then the square drawn on the side opposite the right angle is 25, which is equal to the squares on the sides that make the right angle:   9 + 16. The side opposite the right angle is called the hypotenuse.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Thus the theorem can be expressed as the equation: 32 + 42  Ã‚   = 52. This proves the earlier statement which is â€Å"The square on the hypotenuse is equal to the sum of the squares on the other two sides.†    Proofs    This is a theorem that may have more known proofs than any other. Consider a right triangle with sides a, b, and c as hypotenuse.                         Let a, b, and c arrange four of those triangles to form a square whose side is a  +  b as shown above in Fig.  1. Now, the area of that square is equal to the sum of the four triangles, plus the interior square whose side is c. Two of those triangles taken together, however, are equal to a rectangle whose sides are a, b.   The area of such a rectangle is a times b:   ab.   Therefore the four triangles together are equal to two such rectangles.   Their area is 2ab. As for the square whose side is c, its area is simply c ².   Therefore, the area of the entire square is c ² + 2ab   .   .   .   .   .   .  (1) At the same time, an equal square with side a + b (Fig. 2) is made up of a square whose side is a, a square whose side is b, and two rectangles whose sides are a, b.   Therefore the area of that square is a ² + b ² + 2ab But this is equal to the square formed by the triangles, line  (1): a ² + b ² + 2ab = c ² + 2ab. Therefore, on subtracting the two rectangles 2ab from each square, we are left with a ² + b ² = c ². This is the Pythagorean Theorem Works Cited Bell, John L. The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development. USA: Kluwer, 1999. Dunham, W. Euclids Proof of the Pythagorean Theorem. Journey through Genius: The Great Theorems of Mathematics. New York: Wiley, 1990. Maor, Eli. The Pythagorean Theorem: A 4,000-Year History. Princeton. New Jersey: Princeton University Press, 2007. Morris, Stephanie J. â€Å"The Pythagorean Theorem.† 2008. The University of Georgia Department of Mathematics Education.   1 May 2008 http://jwilson.coe.uga.edu/emt669/Student.Folders/Morris.Stephanie/EMT.669/Essay.1/Pythagorean.html. Spector, Lawrence. â€Å"The Pythagorean Thoerem.† The Math Page. 2008. 30 April 2008 http:// www.themathpage.com/aTrig/pythagorean-theorem.htm. Weisstein, Eric W. â€Å"Pythagorean Theorem.† MathWorld. 1 May 2008. Wolfram Web Resource. 3 May 2008 http://mathworld.wolfram.com/Pythagorean Theorem.html.

How Our Universe Was Created :: essays papers

How Our Universe Was Created Creation Stories, myths that explain the origin of the universe, or cosmos. The origin of the cosmos forms one of the principal themes of mythology throughout the world. (Rev. Bruce Vawter). Cosmogony has attempted to explain everything from the Greek deities Uranus (sky god) and Gaea (earth goddess), to say the creation of humankind, after which the mythic cosmos comes to resemble the world of human experience. In mythic history, the earliest era of the world is usually the closest to perfection-a Golden Age or Garden of Eden. There are thirty-five religions that I have heard of and countless others that have not been documented. I have always wondered why we Latinos, African, Asians, Italians, Indians, and the rest of the cultures on this earth practice different religions and ideas. The answer is billions of years ago, in a galaxy far away, an intergalactic council was formed. The council members consisted of dozens of what we call Gods. Each was a ruler of a planet. And on each of these planets there were people who worshiped their Creator (God). The climate of each world was different from the other. Each planet could only sustain life for its people. The inhabitant’s needed a particular climate so that they could survive. Even there agriculture was dependant on the climate as well. One day the supreme deity who created each of the Gods, decided to allow each of the member’s to unite it’s people with the other. They wondered how they would be this since all of the planets differed in climate and no one could survive on the others planet. So it was decided that they would all create what today is know as the Milky Way. With careful planning the RNA/DNA was joined to create a human that would be able to withstand various climates and be able to eventually procreate. Fifteen billion years ago, give or take five billion years, the entirety of our universe was compressed into the confines of an atomic nucleus. Known as a singularity, this is the moment before creation when space and time did not exist. According to the prevailing cosmological models that explain our universe, an ineffable explosion, trillions

A Decision of Uncertainty Paper Essay

Just recently, this past spring my cell phone contract recently expired after a continuous extension of over lapping contracts for over ten years. I have decided to finally upgrade my cell phone. The saturated cellular device industry can meet various consumer needs just depending on how sophisticated of a device is needed. The new and advanced iPhone 5 is a huge investment for a cellular phone. The retail price for iPhone 5 ranges from an additional $199 with a two year contract and $500 compared to the contract price AT&T offers. If a consumer signs a two-year contract plan to purchase the phone at a reduced price and incentive. See more: Ethnic groups and racism essay Due to financial restrictions and the holidays, I decided to purchase the phone and my contract price for the phone during the 2012 Christmas holidays. â€Å"Through my research and compliance with my constraints, the most opportune time to† (UOP, 2010, Week Three Supplement) upgrade my phone is reasonable during the holidays. Most cell phone companies such as AT&T and Sprint offer huge savings when multiple agreements are made. An iPhone investment could be costly because the standard warranty does not cover accidental damage. The accidental damage insurance, for an additional 48% one-time fee off the contract price, provides consumers with a peace of mind by providing two year coverage for hardware repair, drops, fumbles, slips, and water damage. Purchasing a high costly device means comes with the decisions on whether to purchase the contract price iPhone and not worry about accidental insurance; thus risk purchasing a replacement phone at retail cost or purchase the contract price iPhone and pay an extra 48% insurance fee, which adds to my spending and reallocate my budget for this phone. To decrease my decision of uncertainty; I have complied research on the new iPhone 5. My researched data set was from Business Wire and it provided a survey of 10,000 iPhones including their warranty claims. More important, my researched specified the hardware and accidental warranty claims. The claims all occurred within two years of purchase. Considering a voice plan and data plan would cost at least $1440 over the term of the contract. Another viable option is setting up an agreement with Cricket, which is better known as a pay as you go company. Cricket does offer an unlimited plan that could cost a consumer more than $5,500 over a two year agreement. Based on research from T3 the Gadget Website, the iPhone 5 is 20% daintier than the iPhone 4s, 16% less bulky than the Samsung Galaxy S3 and 14% lighter that the HTC One X. The iPhone 5 reviews have shown that it has a bigger screen, 4G capability and a better front facing cameras. However, the review also shows that the battery life is still not great, there are no iP5-specifice iOS 6 features and the old maps design is highly preferred. Now, it’s time to review the ten best features of the new Apple iPhone. * iPhone 5 will have a 4-inch screen * The new iPhone will be available in only black and white * iPhone 5 comes with Apples new â€Å"A6† processor, which runs twice as fast as the previous generation. * The phone has more than 200 new features in iOS 6 * You can update your Facebook status using SIRI * 8 MP camera, 3264Ãâ€"2448 resolution, five lens element lens, f2.4 aperture, 25% smaller * 8hrs LTE browsing, 10hrs Wi-Fi browsing, 40 hours music, 10hrs video, 225hrs standby * 802.11n 2.4Gz & 5GHz up tp 150Mbps, 802.11 a/b/g/n * The phone will have Now: DC-HSPDA, HDPA+ and LTE * Apples Retina Display 326 pixels per inch (ppi) The iPhone 5 is now available and many consumers will enjoy the new device but it has also started the clock on the next new iPhone. In a year from now, Apple will release a new and improved model of the iPhone. It may possibly be the iPhone 5s or the newly enhanced iPhone 6. My uncertainty still remains to upgrade gracefully to the iPhone 5 or sit tight and wait for the new and improved iPhone. References Future Publishing Limited. (n.d.). Retrieved November 14, 2012, from T3 The Gadget WEBSITE: www.t3.com ZEE NEWS LIMITED. (n.d.). ZEEBIZ.COM. Retrieved NOVEMBER 14, 2012, from WWW.ZEENEWS.INDIA.COM