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Tidal currents occur in conjunction with the rise and fall of the tide. The vertical motion of the tides near the shore causes the water to move horizontally, creating currents. When a tidal current moves toward the land and away from the sea, it “floods.” When it moves toward the sea away from the land, it “ebbs.” These tidal currents that ebb and flood in opposite directions are called “rectilinear” or “reversing” currents. Rectilinear tidal currents, which typically are found in coastal rivers and estuaries, experience a “slack water” period of no velocity as they move from the ebbing to flooding stage, and vice versa. After a brief slack period, which can range from seconds to several minutes and generally coincides with high or low tide, the current switches direction and increases in velocity. Tidal currents are the only type of current affected by the interactions of the Earth, sun, and moon. The moon’s force is much greater than that of the sun because it is 389 times closer to the Earth than the sun is. Tidal currents, just like tides, are affected by the different phases of the moon. When the moon is at full or new phases, tidal current velocities are strong and are called “spring currents.” When the moon is at first or third quarter phases, tidal current velocities are weak and are called “neap currents.”

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European immigrants are credited for “civilizing” the United States, but prior to their arrival America had long been inhabited by tribes of indigenous people. In the fifteenth century, when Christopher Columbus landed in what he presumed was the Indies, he began calling these inhabitants “Indians,” a label that would last centuries until the modern term “Native Americans” came into use. Prior to white settlement, Indian tribes stretched from coast to coast across North America. Spanish explorers introduced horses to the Plains Indians during the sixteenth and seventeenth centuries, which allowed the Indians to cover ground more rapidly and made them nomadic, able to follow their main source of food, clothing, and shelter—the buffalo—along its migratory path. Indians were divided into tribes, or small societies. A chief served as the religious, moral, and political leader of each tribe. Tribes were divided into “bands,” with each band containing around 500 members, including men, women, and children. A governing council for each band, along with the tribal chief, served as the authority for members of the tribe. Only the males from the tribe were entrusted with governance responsibilities, and the men also provided food, shelter, and safety, while the women assumed domestic roles. Tribal lines were typically strong. Men and women rarely married outside their tribe, and it was unusual for two tribes to work in cooperation. Young male tribe members were warriors who competed with warriors from other tribes for superiority, often in bloody battles. This lack of Indian unity contributed to the losses they suffered at the hands of the white society. When European settlers began to inhabit the Atlantic Coast, Indians native to that region spread westward—often encroaching on other tribes. Still, the vast expanse of the western plains would have been adequate for a relatively peaceful existence for the Indians, but the white society followed them west. By the early nineteenth century, the United States government had claimed most of North America as its own, either as states or territories. Initially, Indians were “allowed” to remain on this land, although the federal government made attempts to regulate their habitation. The U.S. government was not sure how to classify Indians who occupied U.S. territory, so tribes were considered to be both independent nations and wards of the state. This dual—albeit contradictory—perspective, required that treaties negotiated with Indian tribes be ratified by the U.S. Senate. However, the ratification requirement did not ensure fair enforcement. White settlers recognized that the Indians inhabited land that could be beneficial to agriculture, settlement, and other endeavors. In an effort to obtain these native lands, tribes were often victimized, sometimes by the very people that the Senate had put in charge of protecting them. The desire to attain tribal lands often led people in power to ignore treaties and look the other way as Indians were unlawfully and unfairly removed from their locations. In 1851, the United States government began to introduce a Concentration Policy. This strategy would provide white settlers with the most productive lands and relocate Indians to areas north and south of white settlements. Over the next decade, Indians were evicted from their land to make way for a white society. However, the settlers were not satisfied with the Concentration Policy, and they sought to restrict Indians to even smaller areas through relocation. For example, the Sioux tribe, which had previously spread across the northern United States, was relocated to an area in Dakota Territory known as the Black Hills. Present-day Oklahoma became known as “Indian Territory” as additional tribes were relocated to reservations there. The federal government relocated hundreds of thousands of Indians under the guise of protecting them, when in truth the government’s primary goal was attaining the Indians’ lands. The federal government established the Bureau of Indian Affairs (BIA) in 1836 to be in charge of the relocated Indians. Illustrating the government’s sentiment toward Indians, this bureau was initially placed under the Department of War, and one of its primary responsibilities was to prevent Indian military action against whites. However, by the mid-nineteenth century, the BIA had shifted its focus to overseeing Indian concentration and relocation. It aimed to provide reasonable protection to the Indians—however, their lands were still fair game. Corruption by BIA leaders and agents further resulted in the destruction of the Indian lifestyle. Many agents were paid to look the other way as white men took land and game that rightfully belonged to the Indians. This flawed federal aid program furthered the Indians’ resentment toward white society and created an atmosphere of conflict. Warfare was constant between whites and Indians in the late nineteenth century, as Native Americans fought to protect their land and their heritage from white encroachment. Although they had the benefit of state-of-the-art weapons (repeating rifles obtained from fur traders), they were up against formidable U.S. forces. As the dust settled from the Civil War, soldiers from both sides of that conflict were ready to step into another fray. The battle to acquire U.S. territories from Indians was predominantly fought by Civil War veterans, including a significant number of black men who were assigned to a fighting group called the Buffalo Regiment. Under the guidance of Generals William T. Sherman, P.T. Sheridan, and George Custer, these “Buffalo Soldiers” advanced confidently and repeatedly against Indian tribes. Although some battles against Indians were brutal on both sides, other conflicts were nothing but displays of dominance by U.S. troops. One such battle was the Sand Creek Massacre, which occurred in Colorado in 1864. At that time, Cheyenne and Arapaho tribes inhabited the Sand Creek region after being forcibly relocated there due to the gold rush in 1861. Miners overtook their area and pushed the tribes into a desolate locale. The approximately 400 Indians living in this area believed they had been granted immunity and protective custody by the United States government when Colonel J.M. Chivington’s troops arrived. Chivington ordered his troops to slaughter the Indian men, women, and children to flaunt their dominance over the natives. The gold rush also led to another legendary conflict. The Sioux tribe, led by Chief Sitting Bull, had been relocated to the Black Hills of the Dakota Territory and had been living there in peace when miners determined the Black Hills to be another gold rush target in 1875. General Custer was called to lead troops to move the Sioux away from the area the miners sought to excavate. Undaunted, the Sioux pushed back in a clash that would become known as the Sioux War and would span from 1876 to 1877. The warfare came to a head on June 25, 1877 at Little Bighorn in the Montana Territory. General Custer, seeking to overtake the ore-rich land for the miners, came across a settlement of over 7,000 Indians from the Sioux, Cheyenne, and Arapaho tribes. Even though he realized the U.S. forces were largely outnumbered, Custer believed that the element of surprise would work to his advantage. Dividing his troops into three groups of approximately 200 men each, he directed the groups to encircle the camp and launch an attack. However, before the attack could commence, Custer and his group found themselves surrounded by an Indian sneak attack led by famed war Chief Crazy Horse. The well-armed Indians attacked Custer and his men without mercy. In a two-hour battle, Crazy Horse’s 2,500 warriors massacred Custer and his 264 men. Winning the Sioux War did not ensure their safety, so Chief Sitting Bull led his Sioux to Canada, where they established themselves as peaceful and law-abiding residents. While the Sioux were struggling in the northern plains, the Nez Perce tribe, led by Chief Joseph, was fighting a similar battle in the Pacific Northwest. This tribe was centralized in Oregon and Idaho after ceding large amounts of land to the United States in the name of peace. However, the United States made continued attempts to concentrate the Nez Perce into smaller and smaller areas. In 1877, the U.S. told the Nez Perce that they would be removed either by agreement or force from the Wallowa Valley. The tribe resisted this encroachment with several battles that reduced both U.S. and Nez Perce forces. Chief Joseph had a reputation for being a humane and noble leader, and he did not wish for the bloodshed to continue. He decided to seek Chief Sitting Bull’s advice, but needed to travel to Canada to do so. He mobilized his troops and began the 75-day, 1,500 mile trip to Sitting Bull’s locale, only to be overcome by U.S. forces 30 miles from the Canadian border. After first promising to return the tribe to their ancestral lands in Idaho, the U.S. government redirected the Nez Perce’s trek south, placing them in an Indian camp in Kansas. The camp was infected with malaria and over one-third of the Nez Perce died while in Kansas. Eventually, the remaining members of the Nez Perce tribe were relocated to Oklahoma. They would later be allowed to return to the northwest but were never allowed to return to the Wallowa Valley. These moves took their toll on the Nez Perce tribe, and by the time they were allowed to return to the northwest, they numbered only a fraction of the once-strong tribe. The Apache was another tribe damaged by warfare. Although several Apache accepted the relocation effort and became relatively successful farmers and cattle ranchers in Oklahoma, many others firmly resisted relocation efforts. Led by Geronimo and Cochise, Apache warriors established a base in the Rocky Mountains, where they fought a nine-year guerilla war against U.S. troops. The U.S. eventually pushed the Apache further into the southwest and Mexico and captured Geronimo. Cochise surrendered and allowed his tribe to be relocated and concentrated. There was one final event in the series of Indian Wars. An Indian named Wovoka, who also went by the English name Jack Wilson, dreamt that a supreme being would rescue the Indians from the opposing U.S. forces. Wovoka’s dream indicated that Indians could hasten the rescue by performing a “Ghost Dance” on the eve of each New Moon. Indian tribes, especially the Sioux, placed their faith in the Ghost Dance and performed it with unprecedented fervor. White settlers, although not believing Wovoka’s prophecy, feared the atmosphere the Ghost Dance created and asked the federal government to make the religious ceremony illegal. Although the government never fulfilled that request, they watched Ghost Dance ceremonies with a cautious eye. When a particularly passionate Ghost Dance raised concerns in 1890, authorities stepped in to control the furor by arresting the Chief. During the arrest, the Chief was killed, which only served to inflame the already resentful Indians. The atmosphere was tense. The tension spilled over into conflict on the night of December 29, 1890. An accidental gunfire at Wounded Knee, South Dakota, caused both sides to mistakenly believe that warfare had begun. The result was a bloodbath, with over 200 Indians—men, women, and children—and a significant number of U.S. soldiers killed. The Indians harbored resentment for the massacre, but for the most part they sought an end to the Indian Wars and allowed themselves to be integrated into American society. The cruelty inflicted on the natives during the Indian Wars was chronicled by Helen Hunt Jackson in her book “A Century of Dishonor,” which was published in 1881 and distributed by Jackson to every member of Congress. Jackson had become incensed at the harsh treatment of Indians during a lecture by Chief Sitting Bear of the Ponca tribe in 1879. Her mission to improve Indian conditions furthered the effort to assimilate Indians onto reservations “for their own good.” By 1890, all Indian tribes were consolidated onto government-structured reservations. The government accepted the responsibility of establishing these reservations because they believed the cost of caring for the Indians would be less than the cost of fighting them. Once the reservations were established, the government played a miniscule role in their day-to-day management and provided little support. The cost of the Indian Wars was great. In addition to the financial cost of sustaining troops and the loss of human life, the Indian Wars wreaked havoc on the country’s natural resources, particularly the buffalo. The government encouraged the slaughter of buffalo to eliminate the Indians’ food and housing resources to make them easier to fight. Buffalo had numbered over 50 million across the United States prior to the Indian Wars. That number was reduced to around 15 million by 1868, and less than 1,000 by 1885. Amidst the many detriments of the Indian Wars, there was one positive result. The conflicts and the relocation of Indians benefited the newly established railroads by providing a steady steam of travelers. Troops rode the rails to and from battles, and Indians were loaded onto railway cars and shipped to reservations. The Indian Wars helped solidify the railroad as a necessary transportation source. The effects of the Indian Wars on the Indians themselves were significant. The many skirmishes greatly reduced the number of Indians living within U.S. borders, and the wars also had a deep emotional impact on those Indians who survived. Many Indians felt dehumanized by the experience of being relocated to reservations, since the moves had not been by choice. Although Indians living on reservations tended to socialize only with other Indians, they were forced to interact with non-Indian teachers, merchants, and Bureau of Indian Affairs (BIA) agents. This contact was not always beneficial to the Indians. Physical interaction with white society—sometimes consensual, sometimes not—introduced diseases into the native population. It also introduced vices, including the over-consumption of alcohol. Thus far, attempts to contain the natives had only resulted in transference of the most negative characteristics of white society. However, attempts to “civilize” the Indians continued. Recognizing that Native Americans were easier to deal with individually rather than by tribe, Massachusetts Senator Henry M. Dawes sponsored an act which provided Indians with land and U.S. citizenship. The Dawes Severalty Act of 1887, also known as the Allotment Act, gave the president authority to divide tribal lands and award 160 acres to each family head and lesser amounts to other tribe members. In addition, the government would hold the property in trust for 25 years, and at the end of that time the Indians would be granted ownership of the land and United States’ citizenship. Although this act was beneficial for individual Indians, it was irreparably harmful to tribes. Essentially, it removed all tribal ownership of land. Two-thirds of the Indian lands were lost forever to the United States government. It also ended legal entity status for tribes. With the destruction of the tribal structure, it furthered the assimilation of Indians into white culture at the cost of devastating Indian culture. Indian children were sent to army-style boarding schools, where acts and discussions of Indian culture were prohibited.Although Indian culture was rapidly decaying, the end of the Indian Wars and the government-protected reservations allowed the Indian population to increase. In 1887, approximately 243,000 Indians lived within U.S. borders. Today, that number is over two million. However, modern leaders continue to fight the loss of Indian lands and the diminishing culture caused by the Indian Wars.

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Share this page: Having a good understanding of basic facts is critical to help make learning more difficult math problems easier for the student. Students that are quick and confident with their basic facts will learn difficult processes like long division more quickly because they won't get distracted with counting on their fingers or in their heads to figure out 'basic facts' at each step of the process. The worksheets below are to help your student become confident with basic facts: 1. Addition Basic Facts: Questions up to 12 + 12 2. Subtraction Basic Facts: Questions up to 20 - 10 3. Multiplication Basic Facts: Questions up to 9 x 9 4. Division Basic Facts: Questions up to 81 ÷ 9 5. Mixed Basic Facts: Addition, Subtraction, Multiplication and Division

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This eight-week course focuses on the fundamental unit of essays and reports: the paragraph. Students will learn the parts of the paragraph (topic, supporting, and concluding sentences) and the types of paragraphs (narrative, descriptive, expository, and persuasive). Unit 1 – The Beginning – What Makes a Paragraph? Students will understand what makes up a paragraph and will write their own topic sentences. Unit 2 – The Middle – Supporting Sentences in Your Paragraph Students will continue to write topic sentences and will create supporting sentences for those topic sentences. Unit 3 – The End – Concluding Sentences Students will be writing concluding sentences that reflect the topic and provide a sense of closure for the reader. Unit 4 – The Narrative Paragraph Students will write a personal narrative paragraph. Unit 5 – The Descriptive Paragraph Students will write a descriptive paragraph using all of their senses to include exciting verbs, colorful adjectives, and vivid adverbs. Unit 6 – The Expository Paragraph Students will write an expository paragraph in the third person perspective (he, she, it, they, their), including the topic sentence, supporting detail sentences, and a closing sentence. Unit 7 – The Persuasive Paragraph Students will be able to write persuasively using solid persuasive strategies. Unit 8 – It’s a Party! Students will write a specific kind of paragraph of their choosing and share it with classmates. Register Now to get started right away View our course overview

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Elements of Language: 7th Grade - Using Verbs Correctly (Ch. 18) ||5.0 (1 WK096) ||Jan 11, 2009| [FROM THE TEXT] The four principal parts of a verb are the “base form,” the “present participle,” the “past,” and the “past participle.” A “regular verb” forms its past and past participle by adding “–d” or “–ed” to the base form. An “irregular verb” forms its past and past participle in some other way than by adding “–d” or “–ed” to the base form. The “tense” of a verb indicates the time of the action or the state of being that is expressed by the verb. The six tenses are “present,” “past,” “future,” “present perfect,” “past perfect,” and “future perfect.” Each of the six tenses also has a form called the “progressive form.” The progressive form expresses continuing action or state of being. The verb “be” is the most irregular of all the irregular verbs in English. Do not change needlessly from one tense to another. To write about events that take place at about the same time, use verbs in the same tense. To write about events that occur at different times, use verbs in different tenses. [ABOUT THE COURSE] This online version of “Elements of Language” features your textbook and a variety of interactive activities. The First course is aimed at Seventh Graders. The Elements of Language Online Edition offers activities from these workbooks: * Communications * Sentences and Paragraphs * Grammar, Usage, and Mechanics Language Skills Practice * Chapter Tests in Standardized Test Formats. It provides practical teaching strategies, differentiated instruction, and engaging presentation tools that offer more ways to reach more students than ever before.

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In this Concept, you will learn how to combine probabilities with the Additive Rule and the Multiplicative Rule. Through the examples in this lesson, it will become clear when to use which rule. You will also be presented with information about mutually exclusive events and independent events. For an explanation of how to find probabilities using the Multiplicative and Additive Rules with combination notation (1.0) , see bullcleo1, Determining Probability (9:42). For an explanation of how to find the probability of 'and' statements and independent events (1.0) , see patrickJMT, Calculating Probability - "And" Statements, Independent Events (8:04). When the probabilities of certain events are known, we can use these probabilities to calculate the probabilities of their respective unions and intersections. We use two rules, the Additive Rule and the Multiplicative Rule, to find these probabilities. The examples that follow will illustrate how we can do this. Suppose we have a loaded (unfair) die, and we toss it several times and record the outcomes. We will define the following events: Let us suppose that we have and . We want to find . It is probably best to draw a Venn diagram to illustrate this situation. As you can see, the probability of events or occurring is the union of the individual probabilities of each event. Therefore, adding the probabilities together, we get the following: We have also previously determined the probabilities below: If we add the probabilities and , we get: Note that is included twice. We need to be sure not to double-count this probability. Also note that 2 is in the intersection of and . It is where the two sets overlap. This leads us to the following: This is the Additive Rule of Probability , which is demonstrated below: What we have shown is that the probability of the union of two events, and , can be obtained by adding the individual probabilities, and and subtracting the probability of their intersection (or overlap), . The Venn diagram above illustrates this union. Additive Rule of Probability The probability of the union of two events can be obtained by adding the individual probabilities and subtracting the probability of their intersection: . We can rephrase the definition as follows: The probability that either event or event occurs is equal to the probability that event occurs plus the probability that event occurs minus the probability that both occur. Consider the experiment of randomly selecting a card from a deck of 52 playing cards. What is the probability that the card selected is either a spade or a face card? Our event is defined as follows: There are 13 spades and 12 face cards, and of the 12 face cards, 3 are spades. Therefore, the number of cards that are either a spade or a face card or both is That is, event occurs when 1 of 22 cards is selected, the 22 cards being the 13 spade cards and the 9 face cards that are not spade. To find , we use the Additive Rule of Probability. First, define two events as follows: Note that Remember, with event , 1 of 13 cards that are spades can be selected, and with event , 1 of 12 face cards can be selected. Event occurs when 1 of the 3 face card spades is selected. These cards are the king, jack, and queen of spades. Using the Additive Rule of Probability formula: Recall that we are subtracting 0.058 because we do not want to double-count the cards that are at the same time spades and face cards. If you know that 84.2% of the people arrested in the mid 1990’s were males, 18.3% of those arrested were under the age of 18, and 14.1% were males under the age of 18, what is the probability that a person selected at random from all those arrested is either male or under the age of 18? First, define the events: Also, keep in mind that the following probabilities have been given to us: Therefore, the probability of the person selected being male or under 18 is and is calculated as follows: This means that 88.4% of the people arrested in the mid 1990’s were either male or under 18. Mutually Exclusive Events If is empty , or, in other words, if there is not overlap between the two sets, we say that and are mutually exclusive . The figure below is a Venn diagram of mutually exclusive events. For example, set might represent all the outcomes of drawing a card, and set might represent all the outcomes of tossing three coins. These two sets have no elements in common. If the events and are mutually exclusive, then the probability of the union of and is the sum of the probabilities of and : . Note that since the two events are mutually exclusive, there is no double-counting. If two coins are tossed, what is the probability of observing at least one head? First, define the events as follows: Now the probability of observing at least one head can be calculated as shown: Multiplicative Rule of Probability Recall from the previous section that conditional probability is used to compute the probability of an event, given that another event has already occurred: This can be rewritten as and is known as the Multiplicative Rule of Probability . The Multiplicative Rule of Probability says that the probability that both and occur equals the probability that occurs times the conditional probability that occurs, given that has occurred. In a certain city in the USA some time ago, 30.7% of all employed female workers were white-collar workers. If 10.3% of all workers employed at the city government were female, what is the probability that a randomly selected employed worker would have been a female white-collar worker? We first define the following events: We are trying to find the probability of randomly selecting a female worker who is also a white-collar worker. This can be expressed as . According to the given data, we have: Now, using the Multiplicative Rule of Probability, we get: Thus, 3.16% of all employed workers were white-collar female workers. Suppose a coin was tossed twice, and the observed face was recorded on each toss. The following events are defined: Does knowing that event has occurred affect the probability of the occurrence of ? The sample space of this experiment is , and each of these simple events has a probability of 0.25. So far we know the following information: Now, what is the conditional probability? It is as follows: What does this tell us? It tells us that and also that . This means knowing that the first toss resulted in heads does not affect the probability of the second toss being heads. In other words, . When this occurs, we say that events and are independent events . If event is independent of event , then the occurrence of event does not affect the probability of the occurrence of event . Therefore, we can write . Recall that . Therefore, if and are independent, the following must be true: That is, if two events are independent, . The table below gives the number of physicists (in thousands) in the US cross-classified by specialty and base of practice . (Remark: The numbers are absolutely hypothetical and do not reflect the actual numbers in the three bases.) Suppose a physicist is selected at random. Is the event that the physicist selected is based in academia independent of the event that the physicist selected is a nuclear physicist? In other words, is event independent of event ? Figure: A table showing the number of physicists in each specialty (thousands). These data are hypothetical. We need to calculate and . If these two probabilities are equal, then the two events and are indeed independent. From the table, we find the following: Thus, , and so events and are not independent. Caution! If two outcomes of one event are mutually exclusive (they have no overlap), they are not independent. If you know that outcomes and do not overlap, then knowing that has occurred gives you information about (specifically that has not occurred, since there is no overlap between the two events). Therefore, . The Additive Rule of Probability states that the union of two events can be found by adding the probabilities of each event and subtracting the intersection of the two events, or . If contains no simple events, then and are mutually exclusive . Mathematically, this means . The Multiplicative Rule of Probability states . If event is independent of event , then the occurrence of event does not affect the probability of the occurrence of event . Mathematically, this means . Another formulation of independence is that if the two events and are independent, then . A college class has 42 students of which 17 are male and 25 are female. Suppose the teacher selects two students at random from the class. Assume that the first student who is selected is not returned to the class population. What is the probability that the first student selected is female and the second is male? Here we can define two events: In this problem, we have a conditional probability situation. We want to determine the probability that the first student selected is female and the second student selected is male. To do so, we apply the Multiplicative Rule: Before we use this formula, we need to calculate the probability of randomly selecting a female student from the population. This can be done as follows: Now, given that the first student selected is not returned back to the population, the remaining number of students is 41, of which 24 are female and 17 are male. Thus, the conditional probability that a male student is selected, given that the first student selected was a female, can be calculated as shown below: Substituting these values into our equation, we get: We conclude that there is a probability of 24.7% that the first student selected is female and the second student selected is male. For 1-4, you toss a coin and roll a die. Find each of the following probabilities: - P(a head and a 4) - P(a head and an odd number) - P(a tail and a number larger than 1) - P(a tail and a number less than 3) Two fair dice are tossed, and the following events are identified: - Are events and independent? Why or why not? - Are events and mutually exclusive? Why or why not? - The probability that a certain brand of television fails when first used is 0.1. If it does not fail immediately, the probability that it will work properly for 1 year is 0.99. What is the probability that a new television of the same brand will last 1 year? A coin is tossed 3 times. Determine the probability of getting the following results: - head, head, head - Head, tail, head - Given that a couple decides to have 4 children, none of them adopted. What is the probability their children will be born in the order boy, girl, boy, girl? Two archers, John and Mary, shoot at a target at the same time. John hits the bulls-eye 70% of the time and Mary hits the bulls-eye 90% of the time. Find the probability that - They both hit the bulls-eye - They both miss the bulls-eye - John hits the bulls-eye but Mary misses - Mary hits the bulls-eye but John misses A box contains 8 red and 4 blue balls. Two balls are randomly selected from the box without replacement. Determine each of the following probabilities: - Both are red - The first is blue and the second is red - A blue and a red are obtained - A hat contains tickets with numbers 1, 2, 3, ……20 printed on them. If three tickets are drawn from the hat without replacement, determine the probability that none of them are primes. Suppose you have a spinner with 4 sections: Black, black, yellow and red. You spin the spinner twice; - What is the probability that black appears on both spins? - What is the probability that red appears on both spins? - What is the probability that different colors appear on both spins? - What is the probability that black appears on either spin? - Bag A contains 4 red and 3 blue tickets. Bag B contains 3 red and 1 blue ticket. A bag is randomly selected by tossing a coin and one ticket is removed from it. Using a tree diagram, determine the probability that the ticket chosen is blue. Matthew and Chris go out for dinner. They roll a die and if the number of dots comes up even Matthew will pay and if the number of dots comes up odd Chris will pay. They roll the die twice, once for the decision about who pays for dinner and the second roll for the decision about who leaves the tip. A possible outcome lists who pays for dinner and then who leaves the tip. For example a possible outcome could be Chris, Chris. - List all the possible simple events in this sample space. - Are these events equally likely? - What is the probability that Matthew will have to pay for lunch and leave the tip? When a fair die is tossed each of the six sides is equally like to land face up. Suppose you toss two die, one red and the other blue. Explain if the following pairs of events are disjoint. - A = red die is 4 and B = blue die is 3 - A = red die and blue die sum to 5 and B = blue die is 1 - A = red die and blue die sum to 5 and B = red die is 5 Amy is taking a statistics class and a biology class. Suppose her probabilities of getting A’s are: P(grade of A in statistics) = .65 P( grade of A in biology) = .70 P(grade of A in statistics and a grade of A in biology) = .50 - Are the events “a grade of A in statistics” and a grade of A in biology independent? Explain. - Find the probability that Amy will get at least one A between her statistics and biology classes. Intersection of events Multiplicative Rule of Probability Union of events

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Take the first steps toward geometry learning. Hover over each Learning Benefit below for a detailed explanation. Memory and Memorization Gross Motor Skills What you need: - pictures of different shapes What to do: - Prepare this activity by drawing shapes on a piece of paper — a triangle, circle, square, rectangle, oval, and diamond. - Look at the shape drawings with your child. - Play follow the leader! Walk in the outline of a shape and let your child follow you. Narrate what you're doing: When you turn a corner to make a square, for example, you might say "Sharp turn coming up!" - Can your child match the shape she walked with the drawing of the shape? - For an additional challenge, draw a shape with your finger on your child's back. Can she guess the shape? - develops large-motor skills - encourages shape recognition

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Federalism is a political system with multiple levels of government, each of which has some degree of autonomy from the others. The United States has a federalist system that encompasses the national government, states, and localities. The United States adopted federalism in part to prevent abuses of power and to preserve individual liberty. Federalism serves those goals by helping individuals to “vote with their feet,” thereby fostering interjurisdictional competition. Such benefits are most likely to be found in federal systems where subnational governments have an incentive to compete for residents and businesses because they must raise most of their revenue from their own taxpayers, as opposed to receiving subsidies from the central government. In many ethnically divided societies, federalism can also enhance liberty by reducing ethnic conflict and oppression. However, federalism can also endanger liberty or property by empowering subnational governments to exploit owners of immobile assets, most notably land. Federalism can also permit local majorities to oppress local minorities. Contrary to James Madison’s expectations, federalism in the current era is unlikely to constrain the national government since states have incentives to support the expansion and centralization of power in Washington. Whether federalism enhances liberty depends on circumstances and institutional design.

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Project Java Webmaster: Glenn A. Richard Mineral Physics Institute SUNY Stony Brook What is Bragg's Law and Why is it Important? Bragg's Law refers to the simple equation: nλ = 2d sinΘ derived by the English physicists Sir W.H. Bragg and his son Sir W.L. Bragg in 1913 to explain why the cleavage faces of crystals appear to reflect X-ray beams at certain angles of incidence (Θ, λ). The variable d is the distance between atomic layers in a crystal, and the variable lambda is the wavelength of the incident X-ray beam (see applet); n is an integer. This observation is an example of X-ray wave interference (Roentgenstrahlinterferenzen), commonly known as X-ray diffraction (XRD), and was direct evidence for the periodic atomic structure of crystals postulated for several centuries. The Braggs were awarded the Nobel Prize in physics in 1915 for their work in determining crystal structures beginning with NaCl, ZnS and diamond. Although Bragg's law was used to explain the interference pattern of X-rays scattered by crystals, diffraction has been developed to study the structure of all states of matter with any beam, e.g., ions, electrons, neutrons, and protons, with a wavelength similar to the distance between the atomic or molecular structures of interest. How to Use this Applet The applet shows two rays incident on two atomic layers of a crystal, e.g., atoms, ions, and molecules, separated by the distance d. The layers look like rows because the layers are projected onto two dimensions and your view is parallel to the layers. The applet begins with the scattered rays in phase and interferring constructively. Bragg's Law is satisfied and diffraction is occurring. The meter indicates how well the phases of the two rays match. The small light on the meter is green when Bragg's equation is satisfied and red when it is not satisfied. The meter can be observed while the three variables in Bragg's are changed by clicking on the scroll-bar arrows and by typing the values in the boxes. The d and Θ variables can be changed by dragging on the arrows provided on the crystal layers and scattered Deriving Bragg's Law Bragg's Law can easily be derived by considering the conditions necessary to make the phases of the beams coincide when the incident angle equals and reflecting angle. The rays of the incident beam are always in phase and parallel up to the point at which the top beam strikes the top layer at atom z (Fig. 1). The second beam continues to the next layer where it is scattered by atom B. The second beam must travel the extra distance AB + BC if the two beams are to continue traveling adjacent and parallel. This extra distance must be an integral (n) multiple of the wavelength (λ) for the phases of the two beams to be the same: nλ = AB +BC (2). Fig. 1 Deriving Bragg's Law using the reflection geometry and applying trigonometry. The lower beam must travel the extra distance (AB + BC) to continue traveling parallel and adjacent to the top beam. Recognizing d as the hypotenuse of the right triangle Abz, we can use trigonometry to relate d and q to the distance (AB + BC). The distance AB is opposite Θ so, AB = d sinΘ(3). Because AB = BC eq. (2) becomes, nλ = 2AB (4) Substituting eq. (3) in eq. (4) we have, = 2 d sinΘ, and Bragg's Law has been derived. The location of the surface does not change the derivation of Bragg's Law. Experimental Diffraction Patterns The following figures show experimental x-ray diffraction patterns of cubic SiC using synchrotron radiation. Players in the Discovery of X-ray Diffraction Friedrich and Knipping first observed Roentgenstrahlinterferenzen in 1912 after a hint from their research advisor, Max von Laue, at the University of Munich. Bragg's Law greatly simplified von Laue's description of X-ray interference. The Braggs used crystals in the reflection geometry to analyze the intensity and wavelengths of X-rays (spectra) generated by different materials. Their apparatus for characterizing X-ray spectra was the Laue knew that X-rays had wavelengths on the order of 1 Å. After learning that Paul Ewald's optical theories had approximated the distance between atoms in a crystal by the same length, Laue postulated that X-rays would diffract, by analogy to the diffraction of light from small periodic scratches drawn on a solid surface (an optical diffraction grating). In 1918 Ewald constructed a theory, in a form similar to his optical theory, quantitatively explaining the fundamental physical interactions associated with XRD. Elements of Ewald's eloquent theory continue to be useful for many applications in Do We Have Diamonds? If we use X-rays with a wavelength (l) of 1.54Å, and we have diamonds in the material we are testing, we will find peaks on our X-ray pattern at q values that correspond to each of the d-spacings that characterize diamond. These d-spacings are 1.075Å, 1.261Å, and 2.06Å. To discover where to expect peaks if diamond is present, you can set l to 1.54Å in the applet, and set distance to one of the d-spacings. Then start with q at 6 degrees, and vary it until you find a Bragg's condition. Do the same with each of the remaining d-spacings. Remember that in the applet, you are varying q, while on the X-ray pattern printout, the angles are given as 2q. Consequently, when the applet indicates a Bragg's condition at a particular angle, you must multiply that angle by 2 to locate the angle on the X-ray pattern printout where you would expect a peak. Last modified January 29, 2010 [More Applets: Project Java Home]

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English Bill of Rights (1689) The English Bill of Rights is an English precursor of the Constitution, along with the Magna Carta and the Petition of Right. The English Bill of Rights limited the power of the English sovereign, and was written as an act of Parliament. As part of what is called the “Glorious Revolution,” the King and Queen William and Mary of Orange accepted the English Bill of Rights as a condition of their rule. The Bill of Rights asserted that Englishmen had certain inalienable civil and political rights, although religious liberty was limited for non-Protestants: Catholics were banned from the throne, and Kings and Queens had to swear oaths to maintain Protestantism as the official religion of England. Unless Parliament consented, monarchs could not establish their own courts or act as judges themselves; prevent Protestants from bearing arms, create a standing army; impose fines or punishments without trial; or impose cruel and unusual punishments or excessive bail. Free speech in Parliament was also protected. These protections are roots of those in the Constitution and the First, Second, Fourth, Fifth, Sixth, and Eighth Amendments.

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Display various triangular shapes and ask, "How do you know that these shapes are triangular?" The following properties of triangles should emerge from this discussion: three sides, three corners and angles, straight rather than curved sides. Distribute pattern blocks to each group of two to four students. Have students explore ways to make triangles with the patterning blocks. Alternatively, you can use the Patch Tool for pattern blocks. This is an applet version of physical pattern blocks. Patch Tool Have students share solutions with each other. As a class share any common findings and anything unique that students may have discovered. Distribute and follow directions in the How Do You Build Triangles? Activity Sheet. Have students work in pairs to give or write directions for building one of the triangles, then see if another pair of students can build it by following the directions. Some possible solutions for the activity sheet include: Have students compare their drawings with those of several classmates. What do they notice? Questions for Students 1. How many different triangles can be built with two, three, and then four shapes? What happens if all twelve shapes are used to build one "huge" triangle? [Note: One more small triangle is needed because the pattern for the triangular area is one, four, nine, sixteen, and twenty-five small triangles.] 2. What is the largest triangle that can be built with twelve shapes? [You may wish to challenge students' responses to this question by asking them how they know they have discovered the largest triangle.] 3. How many different symmetrical designs can be created for the largest triangle? [It may be helpful to record the various symmetrical designs on chart paper as students discover them.]

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Did you know that you can use an inequality to describe a real-world situation? Take a look at this dilemma. You’re going to a party! You’re supposed to bring sodas and chips but you only have $20 to spend. Sodas cost $1.50 per bottle and chips cost $2.50 per bag. How many of each can you buy? This situation can be modeled with a linear inequality. Here, you will learn how to solve this inequality by graphing. Listing solutions to single variable inequalities is useful but, because there are infinitely many solutions, it is impossible to show the entire solution set with a list. For that reason, we use number lines. So when , we show it like this. With the less than , greater than , and not equal to symbols, we use an open circle because, although the solution set is infinitely close to the endpoint, the endpoint itself is not actually a solution. With the less than or equal to and greater than or equal to symbols, the endpoint is a solution so we use a closed circle. Just as we graphed linear equations, we can also graph linear inequalities. We will graph the linear inequalities using slope-intercept form. As the circle on a number line marks the end of the solution set of a single variable inequality, so the line on the coordinate plane will mark the boundary of the solution set of a linear inequality. The solution set will be on one side of the line or the other. We will take a test point to figure out which side makes the inequality true and then shade that half of the coordinate plane to indicate the solution set. With the less than , greater than , and not equal to symbols, we will use a dotted line instead of an open circle because, although the solution set is infinitely close to the line, the points on the line itself are not actually solutions. With the less than or equal to and greater than or equal to symbols, the points on the line are solutions so we use a solid line. Take a look at this situation. Graph the solution set of the inequality . Graph using . Use a dotted line because the symbol is . Now, the solution set is on one side of the line or the other. In order to determine which side, we will just try a point that is not on the line itself. Try, for example, (1, 1). Does the point make the inequality true? No! The solution set must be on the other side of the line. As you can see in the graph, we shaded the opposite side. We can graph any inequality in this way. First, graph the equation of the line. Then check if it is a solid or dashed line. Then shade above or below the line based on the inequality symbol. Write these steps down in your notebook. Answer each question about graphing inequalities. True or false. If the inequality is less than, then a graph will show that the area below a dotted line is shaded. True or false. If the inequality is greater than or equal to, then a graph will show that the area above a dotted line is shaded. Solution: False. The line will be a solid line. True or false. With a system of linear inequalities, the area that is shaded must be shared by both inequalities. Now let's go back to the dilemma from the beginning of the Concept. This situation can be modeled with a linear inequality. Let equal the number of sodas you buy and the number of chips that you buy. The inequality is because the cost of the sodas plus the cost of the chips must not be more than $20. Graph the inequality and shade the correct region. Find 5 combinations of sodas and chips that you could buy by looking at the ordered pairs within the solution on the graph. You can buy any combination that is one of the ordered pairs in the shaded region. Possible answers are (11, 1) (9, 2) (7, 3) (6, 4) etc. - A situation where quantities are not necessarily equal. Here is one for you to try on your own. Write the inequality represented by this graph. First, notice that the area shaded is greater than the line. Also, it is a solid line, so we know that the solution to the inequality is above the line and includes the values on the line. The slope of the line is . The y-intercept is . This is our answer. Directions: Write an inequality for each graph. Directions: Graph the following inequalities on the coordinate plane. Directions: Answer each question true or false. - You can't shade less than a vertical line. - A dotted line can only be used in an inequality with greater than. - A dotted line is used when the inequality sign does not include an equals. - You can shade less than or greater than a horizontal line. - You can graph a linear inequality in two variables.

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ten trillion and counting Students will explore: - Important economic terms related to government budgeting and borrowing - The process used for developing a government budget - Trade-offs that must be made when developing a budget - How government pays its debt - What can happen if the percentage of debt to GDP is too high - Ten Trillion and Counting DVD or Internet access to watch the video online - Student handouts: Glossary and Be a Budget Hero (Note: This activity requires access to the Internet. If classroom access is not available, assign this as homework prior to teaching the lesson. Students can complete it by using computers at home, in your school's media center or the public library.) Time Needed: The lesson should take about 45 minutes. Watching the video clip and the discussion questions take about an hour. Add another hour if you use the entire film. An optional extension activity, You Make the U.S. Budget, requires research that will take students a class period to research and a class period to present and debate. - As a class, read and review the glossary of economic terms provided. - Distribute the Be A Budget Hero handout to students. Review the following background information with students concerning government budgets and borrowing: - Spending is part of fiscal policy. If you spend more than you have in your budget, it creates what is called a budget deficit. Total debt or surplus is the addition of the budget deficit or surplus from preceding years plus interest owed to anyone that is financing that debt. - A trade-off involves giving up something in order to gain something else in return as well as understanding the upside and downside to the choices that were made. You can ask the students, "Can you tell me an example of a trade-off decision you have had to make recently?" Also ask, "What trade-offs do you think the U.S. has to make when it comes to spending priorities?" - In order to understand whether the overall debt is too big for a government, total debt is often compared to the gross domestic product (GDP), which is the total value of all the goods and services produced in a country. The following link ranks countries according to their debt-to-GDP percentages. Note that the U.S. percentage is 60.8, putting it at number 23 out of the 126 countries listed. Countries with high debt percentages include Japan, Italy, Norway, France and Canada. - Governments generate revenues to cover budgetary obligations through taxation. If tax income does not generate enough money to cover spending, governments need to borrow. This borrowing takes place in the forms of bonds. - Deficit spending can help minimize or end a recession. However, if a government has too much debt and needs to borrow too much, or people or countries stop lending the money, problems could include: - The need to pay more interest - Inability to pay for important programs - Lower growth rates - Future tax increases - As a class, if time permits, watch the entire video of Ten Trillion and Counting. If time does not permit, watch segment 5, "The Greatest Threat Is Health Care," which begins at 40:00 and runs for 7 minutes. - Use the discussion questions to guide the students through what they watched in the video. - Have students enter the following Web site that contains the Budget Hero Game. - Prior to having students play the game, review the instructions on the handout and have students click the link and complete the briefing. - Discuss and debate each of the questions on the handout. Seek multiple opinions about each of the questions and prompt students to share why they prioritized their budget decisions differently from their classmates. Optional Extension Activity: - Divide the class into six groups. - Distribute the handout You Make the U.S. Budget and review the directions with students. Each group should complete the budget assignment and also research one of the six categories and prepare a presentation. You may wish to assign each group a category, or let them choose, making sure that each category is allocated. - When their research is completed, each group should share its findings with the whole class. Discuss with the class what would be an acceptable budget for everyone. The Congressional Budget Office Web site includes charts, graphs, projections, historical data, Webcasts and blogs on key issues surrounding the U.S. government budget. Method of Assessment: Completion of homework assignments

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The absolute value of a number is a measure of the size of that number. The absolute value of x is written | x | . - If x is a positive number, then | x | = x. - If x is a negative number, then | x | = x. - If x = 0 then | x | = 0. Absolute value has several useful properties. One is the multiplicative property. If x and y are two numbers, then . Another is the triangle inequality, which is the fact that . For example, if x = 3 and y = − 5, then | x + y | = | 3 + ( − 5) | = | 3 − 5 | = | − 2 | = 2, while | x | + | y | = | − 5 | + | 3 | = 5 + 3 = 8. In this case, the triangle inequality is the fact that 2 is not more than 8. Complex numbers also have an absolute value. If z = x + iy is a complex number with real part x and imaginary part y, then . If we represent z as a point in the complex plane with coordinates (x,y), then | z | is the distance from this point to the origin. The absolute value of complex numbers also has the multiplicative property and satisfies the triangle inequality.

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Let's describe a sunspot's movement geometrically, as Galileo did: Look at the figure, where the circle represents a view of the Sun from above and "you" represents you, an observer on Earth. The points A, B, and C are points taken at equal distances on the surface of the Sun, and thus represent positions of a sunspot at equal intervals of time. The apparent motion from A to B, as seen by you, is measured by the angle A-you-B. Compare it to the angle B-you-C, which is obviously much larger. Since the time and distance are the same for A-you-B and B-you-C, the spot appears to move much more slowly as it rounds the edge of the Sun than when it passes across the middle of the disk. On the other hand, if the spot were a planet revolving around the Sun, as shown by the black circle, the angles A-you-B and B-you-C differ by only a very small amount. This page is http://solar-center.stanford.edu/sunspots/galileo1.html Last revised by DKS on May 19, 1997

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The Unit Circle The unit circle is a circle whose center is the origin and whose radius is 1. It is defined by equation x2 + y2 = The most useful and interesting property of the unit circle is that the coordinates of a given point on the circle can be found using only the measure of the angle. Any radius of the unit circle is the hypotenuse of a right triangle that has a (horizontal) leg of length cos and a (vertical) leg of length sin . The angle is defined as the radius measured in standard position. These relationships are easy to see using the trigonometric functions: As you can see, because the radius of the unit circle is 1, the trigonometric functions sine and cosine are simplified: . This means that another way to write the coordinates of a point (x on the unit circle is (cos is the measure of the angle in standard position whose terminal side contains the point. Here’s an example of a typical Math IC question that tests are the coordinates of the point P pictured below? is the endpoint of a radius of the unit circle that forms a 30º angle with the negative x This means that an angle of 210º in standard position would terminate in the same position. So, the coordinates of the point are (cos 210º, sin 210º) = (–/2 Both coordinates must be negative, since the point is in the third The unit circle also provides a lot of information about the range of trigonometric functions and the values of the functions at certain angles. For example, because the unit circle has a radius of one and its points are all of the form (cos ), we know that: Tangent ranges from –∞ to ∞, but it is undefined at every angle whose cosine is 0. Can you guess why? Look at the formula . If cos = 0, then division by 0 occurs, and so the quotient, tan , is undefined. The Unit Circle and Important Angles Using the unit circle makes it easy to find the values of trigonometric functions at quadrantal angles. For example, a 90º rotation from the positive x-axis puts you on the positive y-axis, which intersects the unit circle at the point (0, 1). From this, you know that (cos 90º, sin 90º) = (0, 1). Here is a graph of the values of all three trigonometric functions at each quadrantal angle: There are a few other common angles besides the quadrantal angles whose trigonometric function values you should already know. Listed below are the values of sine, cosine, and tangent taken at 30º, 45º, and 60º. You might recognize some of these values from the section on special triangles.

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- Adding basic facts - Subtracting basic facts - Naming cubes, spheres, and cylinders Introducing the Activity Draw the picture of the two weight scales shown in Weight Problem 1 on the board. Label the scales A and B, as shown. Weight Problem 1 Tell the students that these are scales and that they show the weights of the blocks that have been placed on them. Ask the following - (Point to scale B.) What is on scale B? [A sphere] How much does it weigh? [Six pounds] - (Point to scale A.) What is on scale A? [A cube and a sphere] How much do the objects weigh all together? [Nine pounds] - Figure out the weight of the cube. How did you do it? [The sphere is 6 pounds, so the cube weighs 9 - 6, or three, pounds.] Next, draw the two scales for weight problem 2 on the chalkboard or on poster board. Weight Problem 2 As in problem 1, the weight of one block is given in this problem. But unlike in problem 1, to find the weight of a cube, two operations must be performed. First the total weight of the cubes must be determined. Then the weight of each cube must be found. Ask the - What block is on scale A? [A sphere] - How much does the sphere weigh? [Four pounds] How do you know? [The scale shows four pounds.] - (Point to scale B.) What is on scale B? [One sphere and two cubes] - How much do the blocks weigh all together? [Fourteen pounds] - (Point to the sphere on scale B.) How much does this sphere weigh? [Four pounds] - How can you figure out how much each cube weighs? [The sphere is four pounds. So the two cubes are 14 - 4, or ten, pounds. So each cube weighs five pounds.] Point out to the students that the blocks of the same shape have the same weight. So since the sphere on scale A weighs four pounds, the sphere on scale B must also weigh four pounds. In like manner, the cubes weigh the same number of pounds. Present weight problem 3 to the students. Unlike in the first two weight problems, in this problem the weight of one of the blocks is not given directly. The students have to decide which scale to consider first. The scale with two identical blocks is the best place to begin because, through guess and check or the recall of the addition of doubles, the students can find the weight of one sphere. Weight Problem 3 Ask the following questions: - Which blocks are on scale A? [A sphere and a cube.] How much do they weigh all together? [Eleven pounds] - Do you know how much the sphere weighs? [No, we can't tell.] - Do you know how much the cube weighs? [No, we can't tell.] - Which blocks are on scale B? [Two spheres] - How much do they weigh all together? [Twelve pounds] - Do you know how much each sphere weighs? [Yes, each weighs six pounds.] - How did you figure it out? [6 + 6 = 12, so half of 12 is 6.] - Can you figure out the weight of the cube? [Yes] - How will you do that? [The sphere weighs 6 pounds, so the cube is 11 - 6, or five, pounds.] Distribute copies of the Block Pounds Activity Sheet for students to complete individually or in pairs. Encourage the students to record the weights on the blocks as they are determined. Once the students have completed the problems, have them talk about how they solved them. Note that the problems on "Block Pounds" are ordered by difficulty. Problem A gives the weight of one of the blocks directly. Problem B requires a knowledge of a doubles addition fact to find the weight of one block before the weight of the other can be computed. Problems C and D show three scales with three different types of blocks. In problem C, the weight of the sphere is given directly and the students have to replace the sphere on each of the other two scales with its weight to find the weights of the cylinder and cube. In problem D, no weight of a block is given directly.

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view a plan This is a very elegant volume lesson, complete with worksheets Title – Volume By – Stacey Karpowicz-Boring Primary Subject – Math Secondary Subjects – Math Grade Level – 8 - TEKS: 111.24 — Measurement 8.8 (B) - TAKS Objective VIII: Measurement - A. Students will able to identify and use the following vocabulary words: Volume, prisms, cylinders, pyramids, and cones. - B. Students will be able to find the volume of prisms, cylinders, pyramid, and cones. - C. Students will be able to determine which volume formulas to use with the correct shape. - D. Students will be able to solve problems using the volume formulas. - Think of different objects that we see and/or use in every day life that has volume. What are these objects? Can you describe the shape that makes up the three dimensional object? - The teacher will first ask the students “What is the definition of a prism?” followed by “What is the definition of a cylinder, pyramid, and cone?” After the class discusses these definitions the teacher will ask “What is Volume?” - The teacher will then explain by using a three dimensional diagram (on the board or overhead) what each side of the figure is and the shapes that make up the figure, so that the students will be able to understand the make up of the formula when it is presented. - Then teacher will introduce the formulas. | Cube : V = a 3 Prism : V = Bh Cylinder : V = Bh = [Pi] r 2 h Pyramid : V= 1/3(Bh) = 1/3(1/2bh)(h) Cone : V = 1/3 (Bh) = 1/3 [Pi] r 2 h Note 1: B represents the area of the Base of a solid figure. Note 2: [Pi] represents the symbol for Pi - The teacher will also demonstrate each formula and ask if there are any questions. Checking for Understanding: - The teacher will but problems on the board for each formula and instructs the students to work the problems. As the students are working the problems, the teacher will walk around the classroom and answer questions and help students on an individual bases. - The teacher will also ask questions openly about volume and if time allows the teacher will have students come to the problem and work the problems to demonstrate their understanding of volume. - The students the will work in their groups to complete the “Volume” worksheet. - While the students are working on the worksheet, I will move around the classroom and answer any questions. During this time, I will also ask the class general questions about surface area to ensure that every on understands. - The students will be given a worksheet called “Cones, Pyramids, and Spheres”. The students are required to show all work for credit. - The students will be asked to describe what was covered today in class. I will also ask the students how they fell about solving volume problems. - The students will be given a Performance Assessment problem. This is worksheet “Volume Performance Assessment”. The student will be required to justify their answer to this problem. - The teacher will have students complete the web activities - ) for the volume of a cube, - ) for the volume of a Rectangular Prism, - ) for the volume of a Triangular Prism, - ) for the volume of a Cylinder, - ) for the volume of a Cone, and - ) for the volume of a Pyramid. - Teacher should evaluate which activity the student should participate in to aid the learner in further their understanding in volume. - The students will be asked to write a problem over volume that relates to a real life situation. - Chalk board/overhead - Worksheets (“Cones, Pyramids, and Spheres”, “Volume”, “Volume Performance - Computer with internet access - Web sites Mrs. Sandly asked her students to create a cylinder to hold chocolate candies for a statistics problem using a standard piece of paper. (8.5 inches by 11 inches). Some of the students made cylinders that were 11 inches tall, and others created cylinders that were 8.5 inches tall. The students in Mrs. Sandly’s class began having a discussion regarding the amount of chocolate candies that each person could store. Oliver said that each cylinder would hold the same amount of chocolate candies, because all of them used the same size paper, but others disagreed. Who is correct? Justify your answer. E-Mail Stacey Karpowicz-Boring !

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Tsunami Lesson Plans The Tsunami Lesson Plans provide teachers and students, especially in remote coastal areas, with an opportunity to investigate how tsunami happen and how to stay safe if a tsunami occurs. These lessons challenge students to learn more about tsunami by asking them to: An Assessment Guide for teachers is also included within these lesson plans. Key Learning Areas The Key Learning Areas (KLAs) for these lesson plans include: - Study of Society and Environment The objectives of these lesson plans are for students to: - develop an understanding of the causes of a tsunami - understand how tsunami occur - develop an understanding of the impact of tsunami on people and the environment - develop an understanding of how best to be prepared for a tsunami event Please note: These lessons can be modified to incorporate other KLAs and to meet the needs of the students and specific content taught. Get the facts The Lesson Plans have been developed paying particular attention to: - What is a tsunami? - Where do tsunami occur? - Tsunami warnings - Be Prepared - Report a tsunami - Build your own resource guide To find out more, visit the six lesson plans download below. Students are also encouraged to visit the Tsunami – Learn page, Tsunami – In My Backyard page, Tsunami – Ready and Able page and Tsunami – Get the Facts page. Take time to investigate! Using the information from the case studies on Tsunami – Get the Facts page, students can complete the questions found in the following activities: The following activities are designed for students in the early years of primary school: Teachers can assess with questioning, through group discussion and direct observation of how students are able to complete the Take time to investigate! activities. Questacon Tsunami Show The Attorney-General's Department worked closely with Questacon (the National Science and Technology Centre) to develop a Tsunami Awareness Show for school aged children, teachers and the general public. Over a period of 13 months, a total of 412 Tsunami Awareness Shows were performed at Questacon to a collective audience of 19,460 people. The thirty minute show and nine associated "Frequently Asked Questions" have been recorded on DVD and includes an option to use closed captioning in English. Watch a short trailer for the Show (YouTube). Watch one of the Frequently Asked Questions about tsunami. To order a free DVD of the Show, please email firstname.lastname@example.org. This presentation by Questacon provides an overview for the topic. It includes the following Meaning of tsunami Distinguishing between normal waves and tsunami waves Explaining shoaling and drawback Causes of tsunami Frequency and distribution of earthquakes Frequency and risk in Australia Official warning systems Natural warning signs The Attorney-General's Department and Questacon have developed a Tsunami "Choose-Your-Own-Adventure" style game. This game was developed to teach school-aged children important safety messages about tsunami. This game is also housed within the Awesome Earth Exhibit at Questacon in Canberra. To order the game on CD, please contact email@example.com. Additional tsunami resources

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A relative clause is a way to add essential information to a sentence. Imagine that you are at a social gathering with some friends and some other co-workers. You see your friend Charles talking to a girl that is unknown to you and you want to know who she is. You could say to your friend “A girl is talking to Charles. Do you know the girl?” But it sounds quite formal and abrupt. A better way to ask this question, would be to start with the most relevant piece of information, “Do you know the girl?” But that doesn’t give us quite enough information; there are probably a lot of girls in the room. So how do we distinguish this particular girl? The girl is talking to Charles, but instead of repeating the words ‘the girl’, we use a relative pronoun, in this case you use who (the relative pronoun used for people). So the final sentence is: “Do you know the girl who is talking to Charles?” Have a look at these chart related to the use of relative pronouns: How do we distinguish between subject pronouns or object pronouns? You cannot distinguish between object and subject pronouns simply by form, as that, which and who can be used in both cases. Instead you must look at what is next to the relative pronoun to discover what form it is in: A subject pronoun is always followed by a verb: eg. Have you seen the cat that was sleeping on the neighbour’s porch? An object pronoun is followed by a noun or a pronoun. In defining relative clauses, the object pronoun can be dropped from the sentence, which is then called a contact clause: eg. The cat (that) Ann saw asleep on the neighbour’s porch. 1. Relative Adverbs: A relative adverb is sometimes used instead of a relative pronoun + preposition to make the sentence clearer. Have a look at this example: This is the day on which I left for France / This is the day when I left for France. 2. Defining relative clauses Defining relative clauses give information to be clear that both you and the person you are talking with know exactly who or what it is you are talking about. They give essential information (Note that that can replace who or which). Imagine there are now two girls talking to Charles, but you don’t know one of them and you want to ask your friend if he does, how do we differentiate between them? Perhaps you could look at what they are wearing. The unknown girl has a red dress on, so we would say :“ Do you know the girl that is wearing the red dress?”. If further clarification is needed: “The one wearing the red dress who is talking to Charles”. Now you and your friend are absolutely clear who it is you are talking about. The girl is defined through the extra attributed given to her, without these, it would be unclear which girl we were talking about. Defining relative clauses do not give extra information, so they are not put into commas. Defining relative clauses are often used in definitions, as in: A miner is someone who works in a mine. Object pronouns (who, which or that) in defining relative pronouns can usually be dropped from the sentence without a change in meaning. For example: The girl (who/whom) I met last night was very pretty. 3. Non-defining relative clauses In a non-defining relative clause, extra information is given about a subject, but it is not necessary to make the subject of the sentence clear. They give non-essential information. They are put into commas (or pauses in spoken English). If there is only Charles and one girl in the room talking, then it is not necessary to add in extra information about her. We would simply say: “Do you know the girl, who is talking to Charles?” In non-defining relative clauses, who/whom cannot be replaced with that: Jill, who/whom I went out with last week, is a fully trained nurse. Object pronouns cannot be removed from non-defining relative clauses: The girl, who/whom I met last night, is very pretty. Defining relative clauses: - have no commas; - can replace who, or which with that; - can omit who, which or that when they are the object of the clause. Non-defining relative clauses: - use commas (or pauses in spoken English); - do not use that; - cannot omit relative pronouns. Are these sentences containing defining or non-defining relative clauses? 1. The girl, that I met last week, works at a shopping centre. 2. Can you spot the lion which is lying on the rock? 3. An Etymologist is a person who is a specialist in the history of words. 4. My cousin, who you met last week, will be visiting me this weekend. Choose the best relative pronoun or relative adverb for these sentences. Sometimes more than one is possible. 1. I have a daughter who/where/that makes her own clothes. 2. I met an old man that/which/where had known my grandmother. 3. My favourite shirt, which/that/where I brought in Edinburgh, was ruined. 4. I have a cat who/that/whose likes to hide in boxes. 5. This is the office whose/in which/where I had my first real job. 6. Whose/Where/Which is that bag lying there on the table? 7. On my last holiday, when/that/where we went to Greece, I learnt how to make the perfect Greek salad. 8. On the Sundays of my childhood, in which/when/that the afternoons were long and golden, we always went swimming. 9. An accountant is often a person which/that/who loves counting money. 10. An old friend, whom/who/that I saw at a recent garden party, has a grandson. Make sentences in either the defining or non-defining relative clause using the words given. 1. Who/my sister (non defining) 2. That/assistant director (defining) 3. Whom/a man (non defining) 4. Where/the park (defining) 5. Why/umbrella (non defining) 7. When/last week (non defining) 8. Whose/gloves (defining) 9. Which/horse (non defining) 10. At Which/time (defining) Pick out whether the sentences contain subject pronouns or object pronouns. 1. I was talking to the old lady who lives across the street yesterday. 2. I was talking to that old lady living across the street yesterday. 3. I saw Harriet who was a friend from school. 4. I saw Harriet who I knew from school. 1. E-mailing. Business English. Correo electrónico en inglés Escribir e-mails o correos en inglés , inglés para los negocios con correo... [21/01/10] 2. Preposiciones. Gramática en inglés Cuando hablamos en inglés y nos referimos a lugares o para describir dónde hay... [23/09/11] 3. Gramática en inglés. El presente perfecto En estos cursos de inglés practicaremos el presente perfecto. Cuanto más... 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Designing Classroom Experiments Elements of a Design a successful lab/experimentOne of the keys to successful classroom experiments is making sure that the experience matches up to the course content that students are trying to master. If this requirement is not met then at best the experiment might be fun, at worst the experiment may be confusing, and in any case the experiment will not help to achieve course goals. The best classroom experiments share a number of other features: - They focus on topics students have difficulty mastering - Otherwise the experiment may not have a clear advantage over other teaching methods - The instructor has selected measurable learning objectives related to the experiment - They focus on one concept or a group of highly related concepts - They motivate discussion or material from future classes and possibly further experiments - Students should have a possibility of being surprised by the outcome, either because it confounds their expectations or because the experiment takes the student to an unfamiliar environment Please Keep this in Mind... Never design an experiment to MAKE something happen. Design an experiment where students can make decisions and watch what happens. Here is why: - Standard economics theories often fail. That is one of the reasons why experimental research in economics has become such a useful research methodology. But often failures of theories are more interesting and can create even better learning opportunities for students. For example, if you let students play a Prisoner's Dilemma game it is unlikely that everyone will choose the equilibrium strategy. This produces interesting opportunities to discuss - Assumptions of models and what happens when assumptions are unmet - Strategic differences between one shot and repeated games - Modifications of the game that make it more or less likely that one will observe equilibrium behavior - In order to MAKE something happen you are going to have to constrain students so much it won't feel REAL to them and they won't get the experience we are going for when we right experiments. Then won't get it and that defeats the whole purpose. Other Practical Tips! It is a good strategy to write an experiment with another instructor or two. In workshops on classroom experiments a team can typically design a complete draft of an experiment from idea through instructions and teaching notes in about a day. Test your new experiment with a small group of students (maybe buy them pizza or make it an extracurricular club activity) before you take an experiment to a whole class. It can be hard to tell what points in the instructions will be unclear and if students make unintended decisions because they don't understand the game then the experiment will be disappointing. Steps in Designing an Experiment - Identify a topic that you want to illustrate and some learning objectives you hope that students will achieve. - Design an environment where students can make decisions related to the selected topic. It is often not necessary to start from scratch on this point - often the very best classroom experiments are modifications of published research experiments. This means all you need to do is make it practical to conduct the experiment in class! - Think about some variations on your decision making environment that you can implement during class. You might want to try one or two variations and leave the others for students to discover. For example, if students play a prisoner's dilemma game repeatedly with different partners you might let the class discover the idea that playing repeatedly with the same partner would yield different results. - Think about how you will collect student decisions and how and when you will communicate others' decisions back to them. Class size will be an important factor in determining whether students will make decisions in small groups as well as the form of communication. Some ideas: - If there are only two possible decisions and there is no strategic advantage in seeing what others do before you make your decision it is often easiest to have students raise their hands. - Asking students to fill out decision forms which you can collect helps keep student actions private. In some environments students will take different actions if they will become public. - If calculations involving decisions are involved think about using a pre-formatted Excel spreadsheet in class. - Sometimes it is helpful to prepare a blank table or graph that you can fill in after decisions are collected. - Make sure that you record the data to preserve it for later discussion and analysis.

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Sequences and series are really just patterns of numbers, and numerical patterns are everywhere. Patterns are found in the growth of trees, the enrollment in an online group, the movement of a bird, the layout of atoms in a crystal, and a million other places. Understanding how numerical patterns work is a fundamental step toward predicting future events. Imagine using numbers to predict the best way to throw a baseball, or pick the best pitcher out of a collection of free agents. Number series appear in the way people choose to buy products, or donate money. In this chapter, you will explore the topics above and will learn to both use formulas designed to help you create series, and create formulas from series in order to predict later members of sequences. This chapter covers the application and creation of arithmetic and geometric formulas. Students are introduced to Sigma (sum) notation and are taught to calculate the sum of a partial or infinite series. Later in the chapter, students will learn about induction and inductive proofs. The chapter wraps up with combinations/permutations and factorials and an introduction to the binomial theorem and binomial expansion.

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· Today we are going to focus on comparing fractions. When we compare numbers there are many things we can focus on to compare them but today we are going to speak specifically about their size. · Discuss where we’ve been – understanding numbers and where this will take us – to comparing fractions to estimating with fractions · There are many different ways to compare numbers according to their size. Over the next couple of months as we work with fractions in lots of different contexts we will learn about and develop many ways to compare fractions. · Today we are going to work on comparing numbers by using benchmarks. The reason we are going to do this is it helps us to reason with fractions mentally and make sense of the size of fractions. As we continue to learn about · TPS – Where have you heard the word benchmark before? What does that word mean to you? · In math a benchmark number is a number that serves a reference point. It helps us to estimate the size of other numbers very quickly. · The benchmarks we are going to use today are 0, 1/2 and 1 – Show a number line to students and have them decide where the number ½ would go – possible TPS. · Ask students – we are really familiar with the number ½ is there another way to say that number? · Write down students generated list – ask if there are more or if we found all of the equivalents to ½ · Discuss what is common about all equivalents to half · Offer an equivalent to half where the denominator is an odd number – or ask to guide them through – I noticed that all the equivalents to have that we were able to come up with have even denominators. Can anyone think of an equivalent to half that has an odd denominator? · Tell students I’m going to model an example using the knowledge I have gained over the course of the week. We will be thinking through two guiding questions: o Is the fraction between 0 and 1/2 or ½ and 1? o Is the fraction closer to 0, ½ or 1? o USE EXAMPLE 2/5 – focus on the strategy of using equivalent fractions but allow others when students are working – Model how to make the decision if 2/5 is closer to zero or one half o The first question I want to ask myself is what two benchmarks is this number between – 0 and ½ or ½ and 1? o Well I see that the denominator in 2/5 is five and I know that half of five is 2.5 so I know that 2.5/5 is the same as half. o Now when I look at my numerator, I see that 2 is smaller than 2.5 so I know that 2/5 must be between 0 and ½ o Next I want to ask myself Which benchmark is my number closest to? o I know that two fifths is closer to 2.5 fifths than it is to zero fifths, so I 2/5 is closest to the ½ benchmark. o Last I can check to see if my reasoning makes sense by using my fraction pieces to prove my answer. o Use the pieces – draw a number line if needed. · Review with students – what questions did I ask myself, what process did I go through to compare my fraction to the benchmarks. · Reveal steps to students · In pairs students are going to be given two fractions. Students will ask each other the guiding questions to guide each other through comparing to the benchmark and deciding which benchmark it is closest to. PROVIDE DIALOGUE for students- STUDENT A will ask the questions to the partner – STUDENT B will answer for the first set. Then the students will switch · Student A fraction – 2/10 · Student B fraction – 5/6 · Review students’ results and allow them to explain why they thought their numbers were larger than one, less than one, etc. · Tell students that they will probably start to notice some patterns when they are comparing fractions to benchmarks and they should note them or remember them for when we come back to discuss · Discuss the assignment – tell students what I expect to SEE when I come around and what I expect to HEAR when I come around · Remind students of “S” and “E” · Give students a worksheet with fractions and a table to decide which interval it is between and which benchmark the fraction is closest to. · Walk around and ask guiding questions to students. · Tally what students are talking about · Together put everything into the chart – discuss how decisions were made. How did we know which fractions went into each bucket – what was our thinking? · How would using benchmarks help us to compare two fractions that are not ½? · Exit Ticket.

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This investigation of Rosa Parks and the Montgomery bus boycott focuses on the stories we tell about the past. Rosa Parks is one of the best known figures in American history and students most likely enter your class knowing a particular story about Rosa and the Montgomery bus boycott. That story emphasizes the bravery of a “tired” seamstress and casts her refusal to give up her bus seat as an unprecedented act of defiance. Similarly, the subsequent Montgomery boycott of a segregated bus system is portrayed as spontaneous. To challenge this simplified and inaccurate story, the warm-up activity focuses on a concrete question that students often answer with confidence--where did Rosa Parks sit? The answer is not immediately clear given the two documents. By carefully reviewing the evidence, students discover that the affidavit, given its signatories, is the more reliable source. The main inquiry further complicates and challenges students’ narratives about Rosa Parks. They read primary sources that document the leadership and extensive planning behind the boycott and the ugliness of the opposition--all of these directly challenge the familiar story or narrative. Use this module to teach students that historical narrative is grounded in evidence, and that the tremendous mobilization of the Montgomery Bus Boycott was more than a one-woman show. On this teacher page, you will find lessons, worksheets, alternative source versions, samples of student work, and an annotated webography to help you teach this unit.

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Metallic atoms hold some of their electrons relatively loosely, and as a result, they tend to lose electrons and form cations. In contrast, nonmetallic atoms attract electrons more strongly than metallic atoms, and so nonmetals tend to gain electrons and form anions. Thus, when a metallic element and a nonmetallic element combine, the nonmetallic atoms often pull one or more electrons far enough away from the metallic atoms to form ions. The positive cations and the negative anions then attract each other to form ionic bonds. The atoms of the noble gases found in nature are uncombined with other atoms. The fact that the noble gas atoms do not gain, lose, or share their electrons suggests there must be something especially stable about having 2 (helium, He), 10 (neon, Ne), 18 (argon, Ar), 36 (krypton, Kr), 54 (xenon, Xe), or 86 (radon, Rn) electrons. This stability is reflected in the fact that some metallic atoms form cations in order to get the same number of electrons as the nearest noble gas. The metallic elements in groups other than 1, 2, or 3 also lose electrons to form cations, but they do so in less easily predicted ways. It will be useful to memorize some of the charges for these metals. Ask your instructor which ones you will be expected to know. To answer the questions in this text, you will need to know that iron atoms form both Fe2+ and Fe3+, copper atoms form Cu+ and Cu2+, zinc atoms form Zn2+, cadmium atoms form Cd2+, and silver atoms form Ag+. The image below summarizes the charges of the ions that you should know at this stage. The names of monatomic cations always start with the name of the metal, sometimes followed by a Roman numeral to indicate the charge of the ion. For example, Cu+ is copper(I), and Cu2+ is copper(II). The Roman numeral in each name represents the charge on the ion and allows us to distinguish between more than one possible charge. Notice that there is no space between the end of the name of the metal and the parentheses with the Roman numeral. If the atoms of an element always have the same charge, the Roman numeral is unnecessary (and considered to be incorrect). For example, all cations formed from sodium atoms have a +1 charge, so Na+ is named sodium ion, without the Roman numeral for the charge. The following elements have only one possible charge, so it would be incorrect to put a Roman numeral after their name. The alkali metals in group 1 are always +1 when they form cations. The alkaline earth metals in group 2 are always +2 when they form cations. Aluminum and the elements in group 3 are always +3 when they form cations. Zinc and cadmium always form +2 cations. Although silver can form both +1 and +2 cations, the +2 is so rare that we usually name Ag+ as silver ion, not silver(I) ion. Ag2+ is named silver(II) ion. We will assume that all of the metallic elements other than those mentioned above can have more than one charge, so their cation names will include a Roman numeral. For example, Mn2+ is named manganese(II). We know to put the Roman numeral in the name because manganese is not on our list of metals with only one charge. There is only one common polyatomic ion. Its formula is NH4+, and its name is ammonium.

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In This Issue: The term geothermal is used to refer the heat that comes from the Earth's interior. This heat often rises to the Earth's surface through volcanoes. Hot lava (molten rock) flows out of volcanoes and is a pretty awesome sight. But besides volcanoes, lava, and ash, Earth's internal heat makes its way to the surface in other unique ways. What Causes Geothermal Areas? In places such as Yellowstone National Park, New Zealand, and Iceland, the land is covered in spewing geysers, colorful hot springs, and bubbling mud pots. Even in winter, these areas are very steamy. These parts of the Earth are known as geothermal areas and form when an abundant source of water meets an intense source of heat. Since the Earth is covered in about 70% water, it's the heat source that is crucial. Beneath the Earth's crust is a layer of magma (hot liquid rock). Geothermal areas exist where this magma is closer to the surface of the Earth than in other areas, causing these regions to have significantly higher surface temperatures. For instance, the average thickness of the Earth's crust is about 12 to 50 miles thick, but in Yellowstone National Park, the magma chamber (magma housed by a layer of rock) is only 3 miles below the surface. Volcanoes are one of the main ways that magma gets pushed up so close to the surface. For this reason, geothermal areas often exist close to where volcanoes exist, though sometimes there is no apparent evidence of a volcano nearby. In these cases, it may be an isolated hotspot in the crust of the Earth where a new volcano may someday appear, or it is the remnants of an extinct volcano. Features of Geothermal Areas Hot springs, geysers, fumaroles, and mud pots are all geothermal features. They arise when cold groundwater seeps down and is heated by the rocks touching the underlying magma chamber. The hot water then rises to the surface in the form of a geothermal feature. Hot springs occur when this heated water forms a pool on the surface of the Earth. Since that's all it takes to form a hot spring, it the most common geothermal feature and can be found in places all over the Earth. Hot springs vary in temperature and can be calm, effervescent, or boiling depending on how hot the magma chamber below it is. When the hot water travels up, it dissolves material from the surrounding bedrock and brings this material up to the surface with it. For this reason, hot springs tend to be full of minerals, and people have used these hot pools for medicinal purposes for centuries. However, not all hot springs are safe to bathe in. Some are way too hot and/or way too acidic and can severely injure anyone stepping foot in them. A geyser is a type of hot spring that periodically erupts, shooting columns of water and steam into the air. Like hot springs, geysers need an abundant supply of water and an intense heat source to exist. However, one more key ingredient is needed to keep them from being just a hot spring - the right plumbing. Unlike hot springs where the heated water has a simple path to travel upwards to reach the surface, geysers have a complex network of underground tunnels and reservoirs that trap the water and delay its arrival to the surface. While the water is trapped in the ground - sometimes as low as 10,000 feet - it gets heated far above the normal boiling point. However, due to the immense pressure that far down in the ground, the water cannot boil. The super heated water rises to the surface. As it rises, the pressure becomes less and less, and the water starts to boil and steam starts to escape. This release of steam allows some of the water to overflow out of the geyser's mouth. This alleviates the pressure on the water below, causing a chain reaction. As the water at the top of the plumbing system starts to boil, it expands and is shot out of the geyser. This removes the pressure on the water below it, which suddenly boils and expands, causing the lower water to also be ejected out of the mouth of the geyser. This keeps happening to all the water within the chambers until there is no longer enough water left to continue the eruption. Groundwater then starts seeping back into this underground network, starting the cycle all over again. Fumaroles are basically steam vents that allow water vapor and gases to escape the surface of the Earth. They can be found at the base of volcanoes or in geothermal fields, both on land and on the floor of the ocean. They are hotter than hot springs and geysers because any groundwater that enters a fumarole is instantly turned into steam - no liquid water is present in fumaroles. For this reason, they are sometimes called "dry geysers." One more unique feature found in these areas are mud pots. Mud pots are basically very acidic hot springs that dissolve the nearby rock. This rock turns into fine particles of clay and silica that becomes suspended in the water. Due to their sometimes close proximity to volcanoes, volcanic ash often gets mixed in the sediment in a mud pot. The hot water and steam rises from below, forming bubbles that burst when they reach the top. The bursting bubbles fling water and sediment to the edges and the ejected sediment builds a mound around the mud pot, making the opening look like a crater. A delicate balance of water and sediment is needed in order to keep a mud pot a mud pot. Too much water, and it becomes a hot spring. Too little water, and it becomes dry, cracked earth. Most mud pots go through cycles of overly wet to overly dry to just the right amount of water, depending on the season and the water table of the area. Many of these geothermal features are very colorful. These colors are due to the substances found in the water, and the color is a very good indicator of what these substances are. If a spring has a red color to it, most likely it is caused by a large amount of iron. If it is yellow, it is probably due to the presence of sulfur (though the smell of rotten eggs pretty much guarantees it is sulfur). Pinks and whites are often caused by the presence of calcium. Amazingly, not all of the colors are caused by minerals. Due to the extreme heat and high acidity of many hot springs, for a long time it was believed that life forms could not exist in them. Then it was discovered that microorganisms known as thermophiles (literally "heat loving") can live and actually thrive in this very hot water. If the water is blue or green in color, that gives a very good indication that microorganisms, such as algae, protozoa, and bacteria, make their home here. Try this experiment to get an idea of where the hot water for hot springs comes from. When the red jar was placed on top of the blue jar, the distinction between red water and blue water stayed fairly clear. But when the blue jar was placed on top of the red jar, there was a very rapid mixing of colors. Why is this? Well, simply put, cold water is "heavier" than hot water. When the hot water is heated, the water molecules start moving around pretty fast and move apart from each other. The water molecules in the cold water, on the other hand, are packed closer together. So, in two equal size jars, more cold water molecules can fit in their jar than hot water molecules can fit in their jar. In scientific terms, the cold water is more dense than the hot water. So when hot water is placed beneath cold water, it will rise up while the cold water sinks down. This causes the mixing of the water you saw earlier. However, when the hot water is placed on top of the cold water, nothing moves because the hot water is already where it wants to be - at the top. The water in hot springs generally originates as cold rain water or snow melt. This cold water sinks into the ground until it reaches a layer of rock that is being heated by a chamber of magma. The hot rock heats the water, and the hot water rises back up to the surface of the Earth in the form of hot springs. This cycle of cold water sinking and hot water rising is known as convection. (The same is true of air - hot air rises while cold air sinks.) Ever wonder why some fumaroles produce large amounts of steam, while others produce very little? Try out this experiment to find out one of the reasons! This experiment requires adult help and supervision. In this experiment, you were demonstrating how fumaroles work. A fumarole is a vent (hole) that lets out steam from within the Earth. The holes in the tin pan are simulating how steam escapes the Earth. When there is just one hole or fumarole, steam only has one exit, causing it to exit quickly and forcefully. Sometimes, the amount of steam coming out of one fumarole becomes too much for it, and the steam will follow cracks in the Earth to a new place to vent out of the surface. This formation of a new fumarole causes the pressure of the steam to ease up a bit, and the escaping steam comes out less quickly and less forcefully from both fumaroles. The more fumaroles present, the less pressure the steam is under. Later on in the life of these fumaroles, the steam escaping may decrease due to not enough water and/or a decrease in the heat from the underground magma chamber, causing smaller steaming vents. Flashback in History: The Pink and White Terraces The beauty of geothermal areas often overshadows the ever present danger related with them. Seeing abundant wildlife and vegetation seeming to live harmoniously with bubbling hot springs and spewing geysers leads many to believe that these areas are unique but tame places. However, in many of these areas, there is a dormant giant that awakes with very little notice. One such place is on the North Island of New Zealand near a town called Rotorua. During the mid to late 1800's, this geothermal area was a popular tourist destination for many European travelers. Like Yellowstone National Park, the area is full of hot springs, geysers, mud pots, and fumaroles. But its main attraction was the famous Pink and White Terraces, known for their awesome beauty and use as warm mineral baths. They were formed by hot springs and geysers at the top of two hills. The hot water full of dissolved calcium bicarbonate would flow down the hills, leaving behind calcium carbonate precipitate that formed into limestone and travertine terraces, which were filled with water. The calcium carbonate and other minerals in the water colored the terraces so that they were named appropriately enough the White Terraces and the Pink Terraces. However, in the early morning hours of June 10, 1886, the volcano Mount Tarawera erupted and spewed hot mud, huge boulders, and thick ash over an estimated area of 5,800 square miles. The eruption lasted for about four hours and was so violent that it completely destroyed the Pink and White Terraces. Two Maori villages (natives of New Zealand) that thrived on the tourism created by the terraces were also completely wiped out, being buried in the huge mudslide created by the erupting mountain. All that remains of the Pink and White Terraces are black and white photos. What's in a name? The Great Geysir can be found in Iceland and is the namesake for the world's geysers. The Icelandic word "geysir" means "to gush" or "rush forth." Earthquakes can do that? On November 3, 2002, a magnitude 7.9 earthquake in Alaska sent underground vibrations that affected some of the geysers in Yellowstone National Park. That's about 1,900 miles away! For a few weeks after the quake, some geysers started to erupt more frequently while other geysers erupted less often. Imploded volcano! Most of Yellowstone National Park is located in a caldera - a large crater-looking feature formed by the collapse of a volcano. The collapse is triggered when a volcano spews out so much magma, it no longer has enough magma to support itself. See just how hot Yellowstone is! These infrared pictures show the temperatures of geysers, mud pots, hot springs, and other geothermal features found in the park. Here's a home video of one of the world's most famous geysers, Old Faithful, erupting. Watch this animation of a geyser erupting to get a better idea of how geysers work.

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Common Core Standards: ELA 3. Text Types and Purposes: Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences. When you get right down to it, a narrative is just a fancy word for a story. Narratives are everywhere—from the novels you read in class to the movies you watch on Saturday nights to the way your students respond to their parents’ nightly question of “What did you do in school today?” (That is, if they answer by saying anything other than “Nothing.”) Being able to tell a story that makes sense from beginning to end is an important skill, as anyone who has ever gotten stuck next to crazy Uncle Irwin at Thanksgiving dinner can tell you. To be college and career ready in their story telling, your students will need to be able to explain a series of events that either actually happened or that they made up. (This is the one time in school they can get away with “lying” because they call it fiction!) Narrative techniques are ways to make a story more interesting, and they are also the things that make a narrative different from other types of writing (like an essay or a poem or a status update). There are five types of techniques you might use in a narrative: 1. Dialogue. This is when people are talking, and it’s often the most interesting part of the story. The author might use dialogue to have two characters declare their undying love for each other despite the fact that he’s married to a madwoman he has locked in the attic and she can’t believe that anyone could ever love her because of the terrible abuse she suffered as a child. 2. Pacing. This means that the author doesn’t reveal everything all at once. It’s important to keep back the information about the madwoman in the attic until Jane and Mr. Rochester are standing at the altar, because that’s way more exciting than Jane learning about the first Mrs. Rochester because she found an unpaid bill for mental services rendered. 3. Description. This is the part of the book where the author gives information about the setting, characters, time period, etc. Descriptions help you visualize Mr. Rochester’s house and the terror of encountering crazy Mrs. Rochester in the middle of the night. 4. Reflection. This is when the narrator looks back over what has happened so far and thinks about what it all means. Once Jane knew that Mr. Rochester had not told her that he was married, she might think about everything else he had told her, and wonder if he was always full of it. 5. Multiple plot lines. No story is about just one thing (otherwise the poor characters would never get a break!). Just like your favorite soap opera jumps from one part of a story to another, good narratives provide different little stories within the big story. We don’t just read about Jane and Mr. Rochester’s love for each other, but also about Jane’s life as an abused child and about her finding long-lost family once her uncle dies. 1. Let’s read “The Princess and the Pea” by Hans Christian Anderson, and see how its narrative components can be broken down: Once upon a time there was a prince who wanted to marry a princess; but she would have to be a real princess. He traveled all over the world to find one, but nowhere could he get what he wanted. There were princesses enough, but it was difficult to find out whether they were real ones. There was always something about them that was not as it should be. So he came home again and was sad, for he would have liked very much to have a real princess. One evening a terrible storm came on; there was thunder and lightning, and the rain poured down in torrents. Suddenly a knocking was heard at the city gate, and the old king went to open it. It was a princess standing out there in front of the gate. But, good gracious! what a sight the rain and the wind had made her look. The water ran down from her hair and clothes; it ran down into the toes of her shoes and out again at the heels. And yet she said that she was a real princess. “Well, we’ll soon find that out,” thought the old queen. But she said nothing, went into the bed-room, took all the bedding off the bedstead, and laid a pea on the bottom; then she took twenty mattresses and laid them on the pea, and then twenty eider-down beds on top of the mattresses. On this the princess had to lie all night. In the morning she was asked how she had slept. “Oh, very badly!” said she. “I have scarcely closed my eyes all night. Heaven only knows what was in the bed, but I was lying on something hard, so that I am black and blue all over my body. It’s horrible!” Now they knew that she was a real princess because she had felt the pea right through the twenty mattresses and the twenty eider-down beds. Nobody but a real princess could be as sensitive as that. So the prince took her for his wife, for now he knew that he had a real princess; and the pea was put in the museum, where it may still be seen, if no one has stolen it. There, that is a true story. Here’s the breakdown: 1. This is description. Notice how vividly Andersen describes the princess’s rain-soaked clothes and shoes. 2. This is reflection. The queen has trouble believing that the princess is really what she says she is because she looks so bedraggled. So she thinks she will put her to a test. 3. This is pacing. We know that the queen is kind of a crazy hostess, since most people just change the sheets in the guest room, but we don’t yet know why she’s gathering all the mattresses in the castle, as well as a leftover piece of dinner. 4. This is dialogue. Someone is speaking! (You’d think a well-brought up princess would not complain about her accommodations, but clearly this is a royal family that cares less about manners and more about how easily bruised a princess is—which suggests she might be hemophiliac and not a great addition to the bloodline, anyway.) Mr. Andersen does not include multiple plotlines, but we would certainly like to know what a respectable princess is doing out alone at night in the middle of a terrible storm. There is definitely something more to her story! 2. Now, read “Snow White and the Seven Dwarfs” by the Brothers Grimm, and see if you can figure out how its narrative components work: Once upon a time in a great castle, a Prince’s daughter grew up happy and contented, in spite of a jealous stepmother. She was very pretty, with blue eyes and long black hair. Her skin was delicate and fair, and so she was called Snow White. Everyone was quite sure she would become very beautiful. Though her stepmother was a wicked woman, she too was very beautiful, and the magic mirror told her this every day, whenever she asked it. “Mirror, mirror on the wall, who is the loveliest lady in the land?” The reply was always: “You are, your Majesty,” until the dreadful day when she heard it say, “Snow White is the loveliest in the land.” The stepmother was furious and, wild with jealousy, began plotting to get rid of her rival. Calling one of her trusty servants, she bribed him with a rich reward to take Snow White into the forest, far away from the Castle. Then, unseen, he was to put her to death. The greedy servant, attracted to the reward, agreed to do this deed, and he led the innocent little girl away. However, when they came to the fatal spot, the man’s courage failed him and, leaving Snow White sitting beside a tree, he mumbled an excuse and ran off. Snow White was all alone in the forest. Night came, but the servant did not return. Snow White, alone in the dark forest, began to cry bitterly. She thought she could feel terrible eyes spying on her, and she heard strange sounds and rustlings that made her heart thump. At last, overcome by tiredness, she fell asleep curled under a tree. Snow White slept fitfully, wakening from time to time with a start and staring into the darkness round her. Several times, she thought she felt something, or somebody touch her as she slept. At last, dawn woke the forest to the song of the birds, and Snow White too, awoke. A whole world was stirring to life and the little girl was glad to see how silly her fears had been. However, the thick trees were like a wall round her, and as she tried to find out where she was, she came upon a path. She walked along it, hopefully. On she walked till she came to a clearing. There stood a strange cottage, with a tiny door, tiny windows and a tiny chimney pot. Everything about the cottage was much tinier than it ought to be. Snow White pushed the door open. “I wonder who lives here?” she said to herself, peeping round the kitchen. “What tiny plates! And spoons! There must be seven of them, the table’s laid for seven people.” Upstairs was a bedroom with seven neat little beds. Going back to the kitchen, Snow White had an idea. “I’ll make them something to eat. When they come home, they’ll be glad to find a meal ready.” Towards dusk, seven tiny men marched homewards singing. But when they opened the door, to their surprise they found a bowl of hot steaming soup on the table, and the whole house spick and span. Upstairs was Snow White, fast asleep on one of the beds. The chief dwarf prodded her gently. “Who are you?” he asked. Snow White told them her sad story, and tears sprang to the dwarfs’ eyes. Then one of them said, as he noisily blew his nose: “Stay here with us!” “Hooray! Hooray!” they cheered, dancing joyfully round the little girl. The dwarfs said to Snow White: “You can live here and tend to the house while we’re down the mine. Don’t worry about your stepmother leaving you in the forest. We love you and we’ll take care of you!” Snow White gratefully accepted their hospitality, and next morning the dwarfs set off for work. But they warned Snow White not to open the door to strangers. Meanwhile, the servant had returned to the castle, with the heart of a roe deer. He gave it to the cruel stepmother, telling her it belonged to Snow White, so that he could claim the reward. Highly pleased, the stepmother turned again to the magic mirror. But her hopes were dashed, for the mirror replied: “The loveliest in the land is still Snow White, who lives in the seven dwarfs’ cottage, down in the forest.” The stepmother was beside herself with rage. “She must die! She must die!” she screamed. Disguising herself as an old peasant woman, she put a poisoned apple with the others in her basket. Then, taking the quickest way into the forest, she crossed the swamp at the edge of the trees. She reached the bank unseen, just as Snow White stood waving goodbye to the seven dwarfs on their way to the mine. Snow White was in the kitchen when she heard the sound at the door. KNOCK! KNOCK! “Who’s there?” she called suspiciously, remembering the dwarfs’ advice. “I’m an old peasant woman selling apples,” came the reply. “I don’t need any apples, thank you,” she replied. “But they are beautiful apples and ever so juicy!” said the velvety voice from outside the door. “I’m not supposed to open the door to anyone,” said the little girl, who was reluctant to disobey her friends. “And quite right, too! Good girl! If you promised not to open up to strangers, then of course you can’t buy. You are a good girl indeed!” Then the old woman went on. “And as a reward for being good, I’m going to make you a gift of one of my apples!” Without a further thought, Snow White opened the door just a tiny crack, to take the apple. “There! Now isn’t that a nice apple?” Snow White bit into the fruit, and as she did, fell to the ground in a faint: the effect of the terrible poison left her lifeless instantaneously. Now chuckling evilly, the wicked stepmother hurried off. But as she ran back across the swamp, she tripped and fell into the quicksand. No one heard her cries for help, and she disappeared without a trace. Meanwhile, the dwarfs came out of the mine to find the sky had grown dark and stormy. Loud thunder echoed through the valleys and streaks of lightning ripped the sky. Worried about Snow White, they ran as quickly as they could down the mountain to the cottage. There they found Snow White, lying still and lifeless, the poisoned apple by her side. They did their best to bring her around, but it was no use. They wept and wept for a long time. Then they laid her on a bed of rose petals, carried her into the forest and put her in a crystal coffin. Each day they laid a flower there. Then one evening, they discovered a strange young man admiring Snow White’s lovely face through the glass. After listening to the story, the Prince (for he was a prince!) made a suggestion. “If you allow me to take her to the Castle, I’ll call in famous doctors to waken her from this peculiar sleep. She’s so lovely I’d love to kiss her!” He did, and as though by magic, the Prince’s kiss broke the spell. To everyone’s astonishment, Snow White opened her eyes. She had amazingly come back to life! Now in love, the Prince asked Snow White to marry him, and the dwarfs reluctantly had to say goodbye to Snow White. From that day on, Snow White lived happily in a great castle. But from time to time, she was drawn back to visit the little cottage down in the forest. 1. Identify some examples of description. 2. Identify an example of pacing. 3. Identify a secondary plot line. 4. Identify an example of reflection. 5. Identify an example of dialogue. 1. Possible answers include the description of Snow White’s beauty at the beginning, the description of the dwarfs’ cottage, or the description of the storm raging. 2. The author uses pacing by not telling the reader right away what the servant did after leaving Snow White. 3. The evil stepmother’s death in the swamp is a secondary plot line. 4. Snow White realizing that the forest was not dangerous is an example of reflection. 5. Possible answers include the stepmother’s conversations with the mirror, Snow White’s conversation with the dwarfs or the stepmother’s conversation with Snow White about the apple. Quiz QuestionsHere's an example of a quiz that could be used to test this standard. - Teaching A Tale of Two Cities: Serial Publishing - Teaching A Tale of Two Cities: Mix and Match Plot Arrangements - A Christmas Carol: Parable Party - Teaching A Good Man is Hard to Find: Take Two: A Good Ending Is Hard to Find - Teaching Romeo and Juliet: Shakespeare Goes Modern (Understanding the Bard's Influence) - Night: Virtual Field Trip - The Giver: Remember the Time - The Great Gatsby: Come a Little Closer - Teaching Lord of the Flies: Real-Life Lord of the Flies - The Book Thief: The Post-Memory Project - The Book Thief: Re-Imagining the Story

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suggested grade levels: 9-12 view Idaho achievement standards for this lesson 1. Students will review some basic hydrology. 2. Students will learn how valuable the Digital Atlas can be as a resource. 1. Students can work alone or have partners. Assign each student or pair of students a question from the FAQ hydrology section of the digital atlas. Teachers should pick the questions that they feel would be most useful for the class. Encourage your students to use the Hydrology Basic section of the Digital Atlas. 2. To get there: Click on Atlas Home, Hydrology, Basics then on FAQ. Look at the list of questions on the right side of the screen. Students can use the series of links from these questions to explore the answers in depth. 3. Give your students the opportunity to learn by having them click on their assigned question. Have the students answer their question using the information and diagrams that are presented. Assign each student or pair of students to present their question and answer to the class on the next day. These are links to access the handouts and printable materials. Hydrology: Hydrology Topics

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Students will make a three-dimensional candy model of their school using their sketches as a guide. Day 3: Candyland Elementary Models can be created to represent complex aspects of the real world. Scientists use models to study complex real world situations. (per pair of students) - 8.5 X 11 sheet of paper glued to a piece of cardboard - Student sketches of the school - Colored candies (6 colors, 18 oz candy/student pair) - Explain to the class that the they will be using their sketches to make a model of their school grounds using different colored candies. The candy is for the model, NOT for eating! Have the students try to imagine what a miniature version of their school would look like, and some of the key features that must be included, such as trees, buildings, etc. - Hand out the cardboard with grid sheets, and pencils. The 8.5 X 11 paper represents the school property. Have the students mark with pencil where on the paper they believe key features should go. An example on the chalkboard will aid with this. Did they remember play fields and lawns? Once they have a plan they can proceed to the next step. - Pass out the candies and glue, and have the students choose what type of feature each color should represent. Examples are: Lawn, cement, road, buildings, trees, etc. Be aware that there are only six colors. Each pair of students should design a color key before they start creating the model. (See student handout.) - Students use the candies and glue to create a 3-dimensional model of their schoolyard. - Ask the students how accurate they believe their models are, and what someone new to their school might learn from looking at such a model. - Candyland Model Handout (pdf, 15 KB)

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This diagram illustrates two ways to measure how fast the universe is expanding. In the past, distant supernovae, or exploded stars, have been used as "standard candles" to measure distances in the universe, and to determine that its expansion is actually speeding up. The supernovae glow with the same intrinsic brightness, so by measuring how bright they appear on the sky, astronomers can tell how far away they are. This is similar to a standard candle appearing fainter at greater distances (left-hand illustration). In a new survey from NASA's Galaxy Evolution Explorer and the Anglo-Australian Telescope atop Siding Spring Mountain in Australia, the distances to galaxies were measured using a "standard ruler" (right-hand illustration). This method is based on the preference for pairs of galaxies to be separated by a distance of 490 million light-years today. The separation appears to get smaller as the galaxies move farther away, just like a ruler of fixed length (right-hand illustration). The California Institute of Technology in Pasadena leads the Galaxy Evolution Explorer mission and is responsible for science operations and data analysis. NASA's Jet Propulsion Laboratory, also in Pasadena, manages the mission and built the science instrument. The mission was developed under NASA's Explorers Program managed by the Goddard Space Flight Center, Greenbelt, Md. Researchers sponsored by Yonsei University in South Korea and the Centre National d'Etudes Spatiales (CNES) in France collaborated on this mission.

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Reinforcement is the process by which natural selection increases reproductive isolation. Reinforcement can occur as follows: When two populations which have been kept apart, come back into contact, the reproductive isolation between them might be complete or incomplete. If it is complete, speciation has occurred. If it is incomplete, hybrids would be produced. If the hybrids had lower fitness than either parental form, selection would act to increase the reproductive isolation because each form would do better not to mate with the other and form the disadvantageous hybrids. Speciation might then be speeded up by favoring genes which caused individuals to avoid mating with hybrids. Reinforcement is a necessary requirement for both the parapatric and sympatric theories of speciation: it is the process by which a hybrid zone develops into a full species barrier. • Secondary reinforcement: Reinforcement is known as secondary reinforcement if the reproductive isolation has partly evolved allopatrically, and is then reinforced when the two populations come into secondary contact. Reinforcement could occur whenever two forms coexist, and the hybrids between them have lower fitness than crosses within each form. • Artificial selection experiments: Reinforcement can be simulated by artificial selection experiments. By continually selecting for assortative mating it has been possible to obtain significant changes in prezygotic isolation mechanisms. However, the theoretical conditions for speciation to take place by reinforcement are difficult and it is controversial whether the process takes place in nature. Does reinforcement exist in nature?

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We have previously shown in Lesson 4 that any charged object - positive or negative, conductor or insulator - creates an electric field that permeates the space surrounding it. In the case of conductors there are a variety of unusual characteristics about which we could elaborate. Recall from Lesson 1 that a conductor is material that allows electrons to move relatively freely from atom to atom. It was emphasized that when a conductor acquires an excess charge, the excess charge moves about and distributes itself about the conductor in such a manner as to reduce the total amount of repulsive forces within the conductor. We will explore this in more detail in this section of Lesson 4 as we introduce the idea of electrostatic equilibrium. Electrostatic equilibrium is the condition established by charged conductors in which the excess charge has optimally distanced itself so as to reduce the total amount of repulsive forces. Once a charged conductor has reached the state of electrostatic equilibrium, there is no further motion of charge about the surface. Electric Fields Inside of Charged Conductors Charged conductors that have reached electrostatic equilibrium share a variety of unusual characteristics. One characteristic of a conductor at electrostatic equilibrium is that the electric field anywhere beneath the surface of a charged conductor is zero. If an electric field did exist beneath the surface of a conductor (and inside of it), then the electric field would exert a force on all electrons that were present there. This net force would begin to accelerate and move these electrons. But objects at electrostatic equilibrium have no further motion of charge about the surface. So if this were to occur, then the original claim that the object was at electrostatic equilibrium would be a false claim. If the electrons within a conductor have assumed an equilibrium state, then the net force upon those electrons is zero. The electric field lines either begin or end upon a charge and in the case of a conductor, the charge exists solely upon its outer surface. The lines extend from this surface outward, not inward. This of course presumes that our conductor does not surround a region of space where there was another charge. To illustrate this characteristic, let's consider the space between and inside of two concentric, conducting cylinders of different radii as shown in the diagram at the right. The outer cylinder is charged positively. The inner cylinder is charged negatively. The electric field about the inner cylinder is directed towards the negatively charged cylinder. Since this cylinder does not surround a region of space where there is another charge, it can be concluded that the excess charge resides solely upon the outer surface of this inner cylinder. The electric field inside the inner cylinder would be zero. When drawing electric field lines, the lines would be drawn from the inner surface of the outer cylinder to the outer surface of the inner cylinder. For the excess charge on the outer cylinder, there is more to consider than merely the repulsive forces between charges on its surface. While the excess charge on the outer cylinder seeks to reduce repulsive forces between its excess charge, it must balance this with the tendency to be attracted to the negative charges on the inner cylinder. Since the outer cylinder surrounds a region that is charged, the characteristic of charge residing on the outer surface of the conductor does not apply. This concept of the electric field being zero inside of a closed conducting surface was first demonstrated by Michael Faraday, a 19th century physicist who promoted the field theory of electricity. Faraday constructed a room within a room, covering the inner room with a metal foil. He sat inside the inner room with an electroscope and charged the surfaces of the outer and inner room using an electrostatic generator. While sparks were seen flying between the walls of the two rooms, there was no detection of an electric field within the inner room. The excess charge on the walls of the inner room resided entirely upon the outer surface of the room. Today, this demonstration is often repeated in physics demonstration shows at museums and universities. The inner room with the conducting frame that protected Faraday from the static charge is now referred to as a Faraday's cage. The cage serves to shield whomever and whatever is on the inside from the influence of electric fields. Any closed, conducting surface can serve as a Faraday's cage, shielding whatever it surrounds from the potentially damaging effects of electric fields. This principle of shielding is commonly utilized today as we protect delicate electrical equipment by enclosing them in metal cases. Even delicate computer chips and other components are shipped inside of conducting plastic packaging that shields the chips from potentially damaging effects of electric fields. This is one more example of "Physics for Better Living." Electric Fields are Perpendicular to Charged Surfaces A second characteristic of conductors at electrostatic equilibrium is that the electric field upon the surface of the conductor is directed entirely perpendicular to the surface. There cannot be a component of electric field (or electric force) that is parallel to the surface. If the conducting object is spherical, then this means that the perpendicular electric field vectors are aligned with the center of the sphere. If the object is irregularly shaped, then the electric field vector at any location is perpendicular to a tangent line drawn to the surface at that location. Understanding why this characteristic is true demands an understanding of vectors, force and motion. The motion of electrons, like any physical object, is governed by Newton's laws. One outcome of Newton's laws was that unbalanced forces cause objects to accelerate in the direction of the unbalanced force and a balance of forces causes objects to remain at equilibrium. This truth provides the foundation for the rationale behind why electric fields must be directed perpendicular to the surface of conducting objects. If there were a component of electric field directed parallel to the surface, then the excess charge on the surface would be forced into accelerated motion by this component. If a charge is set into motion, then the object upon which it is on is not in a state of electrostatic equilibrium. Therefore, the electric field must be entirely perpendicular to the conducting surface for objects that are at electrostatic equilibrium. Certainly a conducting object that has recently acquired an excess charge has a component of electric field (and electric force) parallel to the surface; it is this component that acts upon the newly acquired excess charge to distribute the excess charge over the surface and establish electrostatic equilibrium. But once reached, there is no longer any parallel component of electric field and no longer any motion of excess charge. Electric Fields and Surface Curvature A third characteristic of conducting objects at electrostatic equilibrium is that the electric fields are strongest at locations along the surface where the object is most curved. The curvature of a surface can range from absolute flatness on one extreme to being curved to a blunt point on the other extreme. A flat location has no curvature and is characterized by relatively weak electric fields. On the other hand, a blunt point has a high degree of curvature and is characterized by relatively strong electric fields. A sphere is uniformly shaped with the same curvature at every location along its surface. As such, the electric field strength on the surface of a sphere is everywhere the same. To understand the rationale for this third characteristic, we will consider an irregularly shaped object that is negatively charged. Such an object has an excess of electrons. These electrons would distribute themselves in such a manner as to reduce the effect of their repulsive forces. Since electrostatic forces vary inversely with the square of the distance, these electrons would tend to position themselves so as to increase their distance from one another. On a regularly shaped sphere, the ultimate distance between every neighboring electron would be the same. But on an irregularly shaped object, excess electrons would tend to accumulate in greater density along locations of greatest curvature. Consider the diagram at the right. Electrons A and B are located along a flatter section of the surface. Like all well-behaved electrons, they repel each other. The repulsive forces are directed along a line connecting charge to charge, making the repulsive force primarily parallel to the surface. On the other hand, electrons C and D are located along a section of the surface with a sharper curvature. These excess electrons also repel each other with a force directed along a line connecting charge to charge. But now the force is directed at a sharper angle to the surface. The components of these forces parallel to the surface are considerably less. A majority of the repulsive force between electrons C and D is directed perpendicular to the surface. The parallel components of these repulsive forces are what cause excess electrons to move along the surface of the conductor. The electrons will move and distribute themselves until electrostatic equilibrium is reached. Once reached, the resultant of all parallel components on any given excess electron (and on all excess electrons) will add up to zero. All the parallel components of force on each of the electrons must be zero since the net force parallel to the surface of the conductor is always zero (the second characteristic discussed above). For the same separation distance, the parallel component of force is greatest in the case of electrons A and B. So to acquire this balance of parallel forces, electrons A and B must distance themselves further from each other than electrons C and D. Electrons C and D on the other hand can crowd closer together at their location since that the parallel component of repulsive forces is less. In the end, a relatively large quantity of charge accumulates on the locations of greatest curvature. This larger quantity of charge combined with the fact that their repulsive forces are primarily directed perpendicular to the surface results in a considerably stronger electric field at such locations of increased curvature. The fact that surfaces that are sharply curved to a blunt edge create strong electric fields is the underlying principle for the use of lightning rods. In the next section of Lesson 4, we will explore the phenomenon of lightning discharge and the use of lightning rods to prevent lightning strikes. Check Your Understanding Use your understanding to answer the following questions. When finished, click the button to view the answers. 1. Suppose that the sphere of a Van de Graaff generator gathers a charge. Then the motor is turned off and the sphere is allowed to reach electrostatic equilibrium. The charge ___. a. resides both on its surface and throughout its volume b. resides mostly inside the sphere and only emerges outside when touched c. resides only on the surface of the sphere 2. Describe the electric field strength at the six labeled locations of the irregularly shaped charged object at the right. Use the phrases "zero," "relatively weak," "moderate," and relatively strong" as your descriptions. 3. A diagram of an irregularly shaped charged conductor is shown at the right. Four locations along the surface are labeled - A, B, C, and D. Rank these locations in increasing order of the strength of their electric field, beginning with the smallest electric field. 4. Consider the diagram of the thumbtack shown at the right. Suppose that the thumbtack becomes positively charged. Draw the electric field lines surrounding the thumbtack. See electric field line diagram. 5. Diagram the electric field lines for the following configuration of two objects. Place arrows on your field lines. See electric field line diagram. 6. A favorite physics demonstration used with the Van de Graaff generator involves slowly approaching the dome holding a paper clip stretched towards the device. Why does the demonstrator not become toast when approaching the machine with the blunt edge of the paper clip protruding forward? 7. TRUE or FALSE: Lightning rods are placed on homes to protect them from lightning. They work because the electric field is weak around the lightning rods; thus, there is little flow of charge between the lightning rods/home and the charged clouds. Electric Field Line Diagram for Question #4: The above diagram was not created by a Field Plotting software program; it would certainly look better if it had been. Your answer may look different (especially when the details are compared) but it should share the following general characteristics with the diagram given here: The electric field lines should be directed from the positively charged thumbtack to the extremities of the page. Each field line MUST have an arrowhead on it to indicate such directions. All electric field lines should be perpendicular to the surface of the thumbtack at the locations where the lines and the thumbtack meet. There should be more lines concentrated at the pointed extremity of the thumbtack and the two sharply curved sections and fewer lines along the flatter sections of the thumbtack. Return to Question #4 Electric Field Line Diagram for Question #5: Once more, the above diagram was not created by a Field Plotting software program; it would likely look better if it had been. Your answer may look different (especially when the details are compared) but it should share the following general characteristics with the diagram given here: The field lines should be directed from + to - or from the edge of the page to the - or from + to the edge of the page. Each field line MUST have an arrowhead on it to indicate such directions. At the surface of either object, the field lines should be directed perpendicular to the surface. There should be more lines at the sharply curved and pointed surfaces of the objects and less lines at the flatter sections. Return to Question #5

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Copyright © University of Cambridge. All rights reserved. Why do this problem? is an appealing way for children to recognise, interpret, describe and extend number sequences. Developing their own patterns, as in the later part of the activity, provides an opportunity for them to justify their own thinking, and evaluate others' patterns. The children should be familiar with dominoes through free-play and domino games before attempting more formal tasks such as pattern building. It would be good to gather the group on the carpet using large floor dominoes for this activity, or alternatively use virtual dominoes on the interactive whiteboard which you can drag around the screen (you might find our Dominoes Environment useful). Begin with single patterns as in the first example in the problem, keeping one end of the dominoes constant (as in all sixes, all blanks, all ones etc.). You may want to deliberately get the sequence wrong to challenge pupils to correct your mistake. Encourage them to explain why it is wrong and also why their correction is right. Having two patterns running at the same time is quite a challenge for the very young, but you could pair them up and give a set of dominoes to each pair, asking them to find those which complete the sequence. Having a partner will enable them to talk about what they are doing, and will force them to justify their thinking to each other. Another way to challenge the children is to locate the missing elements within the sequence, rather than just at the end. This could form the basis of a plenary activity. Let's look at the top of the dominoes first. Can you say the numbers out loud? What comes next? Can you say the numbers at the bottom of the domino? What comes next? There are some slightly more challenging examples of domino patterns to complete in Domino Sequences and Domino Number Patterns . Encourage children to build and explain their own patterns. You may just be surprised by the complexity of their thinking! The examples given in the problem are clearly designed for quite young children who have basic counting skills, but more complex patterns can be devised to challenge more advanced children. For example, include addition or subtraction, odds and evens, patterns that build row-by-row, or grid patterns like this one: Many children will benefit from saying the numbers in the sequence out loud to reinforce the familiar counting patterns. Handouts for teachers are available here (Word document ), with the problem on one side and the notes on the other.

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Plants need warmth and sunlight to grow and reproduce. In the Arctic tundra, warmth and sunlight are in short supply, even in the summer. The ground is frequently covered with snow until June, and the Sun is always low in the sky. Only plants with shallow root systems grow in the Arctic tundra because the permafrost prevents plants from sending their roots down past the active layer of soil. The active layer of soil is free from ice for only 50 to 90 days. Arctic plants have a very short growing season. However, in spite of the severe conditions and the short growing season, there are approximately 1,700 kinds of plants that live in the Arctic tundra. Some of the plants that live in the Arctic tundra include mosses, lichens, low-growing shrubs, and grasses--but no trees. In fact, "tundra" is a Finnish words which means "treeless". close together and low to the ground are some of the adaptations that plants use to survive. This growing pattern helps the plant resist the effects of cold temperatures and reduce the damage caused by the impact of tiny particles of ice and snow that are driven by the dry winds. Photo © 2000-www.arttoday.com Plants also have adapted to the Arctic tundra by developing the ability to grow under a layer of snow, to carry out photosynthesis in extremely cold temperatures, and for flowering plants, to produce flowers quickly once summer begins. A small leaf structure is another physical adaptation that helps plants survive. Plants lose water through their leaf surface. By producing small leaves the plant is more able to retain the moisture it has stored.

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Chapter 1: Molecules in Motion Students will experience all five elements of inquiry as they ask questions about M&M’s in water, design and conduct experiments to answer these questions, and develop explanations based on their observations. - Mysterious M&Ms - Racing M&M Colors - Colors Collide or Combine? - Investigating the Line - M&M's in Different Temperatures - M&M's in Different Sugar Solutions Chapter 2: Physical Properties & Physical Change in Solids In this chapter, students compare the properties of four different household crystals to the properties of an unknown crystal. Chapter 3: Physical Properties & Physical Change in Liquids Even though different liquids may look similar, they act differently when placed on various surfaces. Students compare the way four known liquids and an unknown liquid bead up, spread out, or absorb into different surfaces. - Look-alike Liquids - Developing Tests to Distinguish Between Similar-Looking Liquids - Using Color to See How Liquids Combine - Using the Combining Test to Identify Unknown Liquids Chapter 4: Dissolving Solids, Liquids, and Gases In this chapter, students participate in activities that help them better understand the different factors that affect the solubility of solids, liquids, and gases. - Defining Dissolving - Dissolving a Substance in Different Liquids - Temperature Affects Dissolving - Dissolving Different Liquids in Water - Temperature Affects the Solubility of Gases - A Dissolving Challenge Chapter 5: Chemical Change In this chapter, students gain experience with the evidence of chemical change—production of a gas, change in temperature, color change, and formation of a precipitate. - Powder Particulars - Using Chemical Change to Identify an Unknown - Exploring Baking Powder - Change in Temperature—Endothermic Reaction - Production of a Gas—Controlling a Chemical Reaction - Change in Temperature—Exothermic Reaction - Color Changes with Acids and Bases - Neutralizing Acids and Bases - Comparing the Amount of Acid in Different Solutions - Formation of a Precipitate Chapter 6: States of Matter In the first activity from this chapter, students consider how heating and cooling affect molecular motion. The subsequent activities extend this idea to explore the relationship between temperature and the state changes of water. - Matter on the Move - Exploring Moisture on the Outside of a Cold Cup - Exploring Moisture on the Outside of a Cold Cup (for dry evironments) - From Gas to Liquid to Solid Chapter 7: Density In this chapter, students will explore the concept of density through the familiar experiences of sinking and floating. - Defining Density - Comparing the Density of an Object to the Density of Water - Comparing the Density of Different Liquids - Changing the density of a liquid—Adding salt - Changing the density of a liquid—Heating and cooling - Changing the density of an object—Adding material - Changing the density of an object—Changing shape

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Simplifying Multiplication Lessons Using methods from arithmetic, you can multiply two numbers like, 5 * 11 (Note * is used as the multiplication symbol.) When solving problems using algebra, it is often important to be able to multiply algebraic terms which have variables. Examine this problem: 5x * 11x2 Clearly the methods for multiplying numbers in arithmetic do not apply here. This lesson explains a method for doing this multiplication. Before actually walking through such multiplication problems, we will present a few concepts which are important to understand before learning the multiplication technique. The Commutative Property of Multiplication is a statement or observation about multiplication which indicates that the product of a multiplication problem is the same, regardless of the order the terms were multiplied in. For example, 2 * 10 = 20 Note that the product of 2 and 10 is 20 and that the product of 10 and 2 is 20, the products are the same. It turns out that this is true for real numbers in general. That is, the order in which two numbers are multiplied does not affect the result. This property can be extended to the case where we multiply more than 2 terms. For example, 4 * 6 * 5 = 120 The next important concept is understanding the various styles of writing multiplication in algebra. So far we have been using the * symbol in this lesson to denote multiplication. There are several other mothods of showing multiplication which are also acceptable. Consider the examples below. Each line shows one way of writing "x squared times two". You may recall using a "x" as the multiplication symbol in arithmetic. This is generally avoided in algebra because x is the most common variable used in expressions and equations. It would be extremely confusing if x were used for both a variable and a multiplication sign. In this lesson, we will continue to use * to represent multiplication because it is easily entered with the keyboard, and because this notation is consistent with our calculators and many handheld calculators. Finally, it is important to understand the implied exponent on some variables. When we consider a term like x3, we know that x has an exponent of three. But what about the term x? When a variable does not have a superscript which indicates its exponent, it has an implied exponent of 1. Thus, x has an exponent of 1 and we can say that x1 = x Now proceed to the next page to begin an example of algebraic multiplication.

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Click on the image to enlarge it. Click again to close. Download PDF (1070 KB) AO elaboration and other teaching resources This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. find fractions of regions within geometric shapes Number Framework Links Use this activity to help students consolidate and apply their knowledge of fractions (stages 7 and 8). In question 1 of this activity, students use the properties of geometrical shapes to work out what part of their areas are white. Dots and lines give additional structure to the shapes and allow for a variety of strategies. Students must explain how they arrived at their solutions. Strategies that involve multiplication of fractions belong at stage 8 on the Number Framework; strategies based on counting belong at a lower stage. It is important that you allow for the sharing of strategies so that students who rely on counting are exposed to other, more efficient strategies. Give your students an opportunity to do this when everyone has had a chance to solve question 1. Students need to know that any strategy that works is valid, while at the same time, they get a feel for what constitutes an efficient strategy. In this context, an efficient strategy is one that makes use of symmetry and multiplication to avoid unnecessarily counting. The extra lines on the question 1 diagrams are there to provide clues about what some of these more efficient strategies might be. In question 1a, students could simply count the number of smaller squares (16) that make up the large square. They could then look at the white part and see that it covers 1/2 of 4 squares, which is the same as 2 smaller squares, so 2/16 or 1/8 of the large square is white. Alternatively, they could recognise that the square has been divided in half and then in half again and again (as shown by the lines). This means that the area of the white square is 1/2 of 1/2 of 1/2 = 1/8 of the area of the large square. Other multiplicative strategies are possible. Question 1b can be completed in the same way as question 1a. If we count all the triangles, then the white triangle is of the large triangle. Alternatively, we can see that the large triangle has been divided into quarters and the middle quarter has been divided into quarters again, and one of those quarters is white: 1/4 of 1/4 = 1/16. Question 1c can be broken into 12 rhombuses or 24 triangles and the white pieces added or the red pieces added and subtracted from 1. A more efficient strategy would be to divide the hexagon into quarters or, as in the diagram below, sixths. The diagram shows how the sixth can be divided into 4 equal triangles, of which 3 are white. In other words, 3/4 of the sixth is white, but the same is also true of each of the other 5 sixths, making it true of the hexagon as a whole. The rectangle in question 1d has been divided into quarters, then each quarter has been divided in half and each half divided into quarters, one of which is white. This means that the area of the white triangle is 1/4 x 1/2 x 1/4 = 1/52 of the whole rectangle. In questions 2 and 3, the students divide the shapes into equal-sized pieces and the name the parts as fractions. Question 4a poses a challenge that could occupy students for some time. They are likely to think that they have run out of possibilities once they have found four or five different ways of dividing the triangle into quarters, yet the question says that there are at least 10. The trick is to stop thinking of symmetrical divisions and to realise that a dot doesn’t always have to be joined to its closest neighbour. The triangle in question 4b is a further case of division into quarters. There are various ways of showing that the areas of the four parts are equal; one is demonstrated step by step in the Answers. Answers to Activity 1. a. 1/8. Explanations will vary. (1/2 of 1/2 of 1/2) b. 1/16. Explanations will vary. (1/4 of 1/4) c. 3/4. Explanations will vary. ( 18/24, using triangle units) d. 1/32. Explanations will vary. (1/4 of 1/2 of 1/4 ) 2. Answers will vary. Here are four: 3. Answers will vary. Here are four: 4. a. Here are 10 distinct ways: b. Yes, the lines do divide the triangle into quarters. Here is one way of showing this:

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This lesson focuses on the Crito, in which Socrates argues against the idea that he should escape the penalty of death imposed on him by Athens, laying the groundwork for future debates over the rights of the individual and the rule of law. Students read the dialogue and analyze its arguments in class discussion, extending the dialogue by adding themselves to it. They then consider how Socrates might have responded to extenuating circumstances: for example, if his sentence had been imposed by a tyrant rather than in a trial, or if it had been influenced by prejudice. To conclude, students consider whether this Socratic argument still holds true today, finding examples in contemporary American society to demonstrate their point of view. Begin by introducing students to Socrates and Plato, using resources available through EDSITEment at the Episteme Links website. At the website's homepage, click "Philosophers," then select "Plato" for a link to the Clark College "Last Days of Socrates" Project, which includes background and a text of the Crito, as well as additional lesson plan ideas. For more extensive background, click Socrates from Ethics of Civilization by Sanderson Beck, which includes a comparison of Plato's portrayal of Socrates with the account offered by Xenophon, another of his students. Socrates also makes a comic appearance in Clouds, by Aristophanes; for a text, visit the Perseus Project website on EDSITEment, click on “Classics” from the left sidebar, then select “Texts.” Scroll down to find the English translation of Aristophanes’ Clouds. Look at the section beginning with line 133, where a pupil describes some absurd Socratic arguments, and the section beginning with line 221, where Socrates appears suspended among the clouds, which he explains as the proper way to attain lofty ideas. Such jokes demonstrate that Socrates was well known in ancient Athens, but also show that he and the enterprise of philosophy were not always accorded the respect we might assume they deserve. Before students read Crito, summarize the story, explaining why Socrates was put on trial and condemned to death, why he was not executed immediately, who Crito is and what he wants to do. Spend some time talking about Socrates and Crito as characters. In what sense are they both "good" men? What motivates Crito in his attempt to help Socrates escape from prison? Why would we say that he has "good" intentions? What motivates Socrates in his decision to accept his punishment? What concept of the "good" does he seem to hold? How does this concept compare to Crito's sense of what is good and right? Discuss with students their own sympathies for these two characters and the moral principles they represent. To what extent does Crito equate the good with whatever is good for him and his friends? To what extent does Socrates uphold a standard of goodness beyond the practical demands of human life? In class discussion, lead students through the dialogue in Crito, having them summarize the arguments point by point. Use the chalkboard to diagram the structure and flow of the argument, showing premises, evidence, refutations, etc. For assistance in the analysis of arguments, click "Topics" on the Episteme Links homepage, then scroll down and select “Reasoning and Critical Thinking” to find a link to The Argument Clinic, which includes a page on arguments and their evaluation, and to the Argument Identification Tutorial. As you proceed through the dialogue, remind students that the purpose of the exercise is to practice close reading of argumentation and that their own arguments and opinions should not enter into the discussion at this stage. Once the diagram is finished, have students analyze the argument between Socrates and Crito. What are the weak points? What arguments or refutations would the students make? Have students put themselves into the dialogue as other characters who come to visit Socrates holding different points of view, either by rewriting a passage of the dialogue or by performing a part of the dialogue in class. Point out to students that, in some sense, three characters contribute to the argument in Crito: Socrates, Crito, and the personification of the Law, whom Socrates introduces as an imaginary character. Have the students consider the effect of this personification of The Law upon the argument. Conclude the lesson by having students consider whether this Socratic argument still holds today, finding examples in contemporary American society to demonstrate their point of view. Can this argument be applied to all laws—for example, recycling laws, traffic laws—or does it apply only to major questions of right and wrong? Can this argument be used to justify a change in the laws, or in the enforcement of laws, in order to bring them into alignment with The Law as Socrates envisioned it? Complete the trilogy in which Plato presented the death of Socrates by having students read the Apology, in which Socrates defends himself against charges of immorality and explains the moral purpose behind his questioning of common ethical assumptions, and the Phaedo, which describes his final hours and includes his (or Plato's) argument for the immortality of the human soul based on its capacity for knowledge of eternal truth. Texts of both dialogues, with supporting commentary, are available through EDSITEment at the Episteme Links website; click "Philosophers" on the website's homepage, then select "Plato" for a link to the Clark College "Last Days of Socrates" Project. 1 class periods

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The graph of the equation x 2 + y 2 = 1 is a circle in the rectangular coordinate system. This graph is called the unit circle and has its center at the origin and has a radius of 1 unit. Trigonometric functions are defined so that their domains are sets of angles and their ranges are sets of real numbers. Circular functions are defined such that their domains are sets of numbers that correspond to the measures (in radian units) of the angles of analogous trigonometric functions. The ranges of these circular functions, like their analogous trigonometric functions, are sets of real numbers. These functions are called circular functions because radian measures of angles are determined by the lengths of arcs of circles. In particular, trigonometric functions defined using the unit circle lead directly to these circular functions. Begin with the unit circle x 2 + y 2 = 1 shown in Figure . Point A (1,0) is located at the intersection of the unit circle and the x‐axis. Let q be any real number. Start at point A and measure | q| units along the unit circle in a counterclockwise direction if q > 0 and in a clockwise direction if q < 0, ending up at point P( x, y). Define the sine and cosine of q as the coordinates of point P. The other circular functions (the tangent, cotangent, secant, and cosecant) can be defined in terms of the sine and cosine. Unit circle reference. Sin q and cos q exist for each real number q because (cos q, sin q) are the coordinates of point P located on the unit circle, that corresponds to an arc length of | q |. Because this arc length can be positive (counterclockwise) or negative (clockwise), the domain of each of these circular functions is the set of real numbers. The range is more restricted. The cosine and sine are the abscissa and ordinate of a point that moves around the unit circle, and they vary between −1 and 1. Therefore, the range of each of these functions is a set of real numbers z such that −1 ⩽ z ⩽ 1 (see Figure 2). Range of values of trig functions. Example 1: What value(s) x in the domain of the sine function between −2π and 2π have a range value of 1 (Figure 3 )? Drawing for Example 1. The range value of sin x is 1 when point P has coordinates of (0, 1). This occurs when x = π/2 and x = −3π/2. Example 2: What value(s) x in the domain of the cosine function between −2π and 2π have a range value of − 1 (Figure 4 )? Drawing for Example 2. The range value of cos x is −1 when point P(cos x, sin x) has coordinates of (−1, 0). This occurs when x = π and x = −π. Example 3: The point P is on the unit circle. The length of the arc from point A(1,0) to point P is q units. What are the values of the six circular functions of q? The values of the sine and cosine follow from the definitions and are the coordinates of point P. The other four functions are derived using the sine and cosine. The sign of each of the six circular functions (see Table 1 ) is dependent upon the length of the arc q. Note that the four intervals for q correspond directly to the four quadrants for trigonometric functions.

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Volcanoes are usually found near the borders of tectonic plates that are violently either pushing or pulling at each other. Mysteriously, however, volcanoes sometimes erupt in the middle of these plates instead. The culprits behind these outbursts might be giant pillars of hot molten rock known as mantle plumes, jets of magma rising up from near the Earth’s core to penetrate overlying material like a blowtorch. Still, decades after mantle plumes were first proposed, controversy remains as to whether or not they exist.Superplumes are one of the ideas of what caused the Siberian Traps. They are pretty important to understand, if they exist. The concept of mantle plumes began in 1963 with the enigma of the Hawaiian volcanoes, which dwell more than 2,000 miles (3,200 km) from the nearest plate boundary. Scientists think that as the Pacific plate slid over a “hot spot,” a line of volcanoes blossomed. In 1971, geophysicist W. Jason Morgan proposed that hot spots resulted from plumes of magma originating in the lower mantle near the Earth’s core at depths of more than 1,550 miles (2,500 km). Researchers think these mantle plumes are shaped like mushrooms: narrow streams of molten rock topped with bulbous heads that buoyantly bob upward, like blobs in a lava lamp. The potential importance of mantle plumes may go well beyond explaining volcanism within plates. For example, the mantle plume that may lie under Réunion Island in the Indian Ocean has apparently burned a track of volcanic activity that reaches about 3,400 miles (5,500 km) northward to the Deccan Plateau region of what is now India. Catastrophic volcanism there 65 million years ago gushed lava across 580,000 square miles (1.5 million km2), more than twice the area of Texas, potentially hastening the end of the age of dinosaurs. However, it remains hotly debated whether mantle plumes exist. For example, Massachusetts Institute of Technology seismologist Qin Cao and her colleagues used seismic waves to image activity beneath Hawaii; instead of finding a narrow mantle plume, they discovered that a giant thermal anomaly about 500–1,250 miles (800–2,000 km) wide located far west of the islands is apparently what feeds its volcanoes. The seismologists suggest Hawaiian volcanoes are fueled by a vast pool of hot matter on top of the lower mantle, not at its bottom near Earth’s core by a deep mantle plume. Some researchers suggest hot spots may form in ways besides mantle plumes, such as spreading or cracking within tectonic plates, or “superplumes” that reach up from near the core to the near the base of the upper mantle, where they then give rise to smaller plumes that rise to the surface. Oh, and volcano is the word of the day.

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If there are two numbers we can compare them. One number is either greater than, less than or equal to the other number. If the first number has a higher count than the second number, it is greater than the second number. The symbol ">" is used to mean greater than. In this example, we could say either "15 is greater than 9" or "15 > 9". The greater than symbol can be remembered because the larger open end is near the larger number and the smaller pointed end is near the smaller number. If one number is larger than another, then the second number is smaller than the first. In this example, 9 is less than 15. We would have to count up from 9 to reach 15. We could either write "9 is less than 15" or "9 < 15". Once again the smaller end goes toward the smaller number and the larger end toward the larger number. If both numbers are the same size we say they are equal to each other. We would not need to count up or down from one number to arrive at the second number. We could write "15 is equal to 15" or use the equal symbol "=" and write " 15 = 15". The absolute value of a number is the positive value with the same magnitude. The absolute value is indicated by vertical bars on either side of the number(e.g. |-17| = 17) absolut value of either 17 or -17 is 17.

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History of Congress and the Capitol This is the story of one of the world's great experiments in government by the people. For more than two centuries, a new Congress has convened every two years following elections that determine all the seats in the House and one-third of those in the Senate. While the individuals change, the institution has endured-through civil and world wars, waves of immigration and great migrations, and continuous social and technological change. Following the War of 1812, a stronger sense of national unity emerged in the United States. As America expanded westward, however, attempts to spread slavery into those new territories seriously divided the nation. Conflict and Compromise Free or slave? As America expanded after the War of 1812, new territories began to choose.In the House, slavery foes resisted spreading the South's "peculiar institution" to new states. Southern representatives feared that admitting more free states would tip the delicate balance against them. Missouri’s bid to enter the Union as a slave state, carved from the Louisiana Purchase, sparked controversy in 1819 and 1820. Twenty-six years later, a fight flared over a House amendment banning slavery in all land gained from the Mexican War. Immigration to Northern states meant that with each Federal census, the proportion of free-state representatives in the House grew. Defenders of slavery increasingly felt threatened. A House Divided Slavery tied the House in knots. As the proportion of slave-state representatives dwindled, Southern members frantically tried to defend their interests. First, they changed House rules to keep slavery off the agenda automatically by banning the discussion of antislavery petitions. Later, as the two political parties continued to split into Northern and Southern factions, Southern candidates for House Speaker disrupted both parties so completely that weeks of voting produced no result. Such deadlocks shifted momentum to the Senate, which remained evenly divided between slave states and free, and thus was better able to negotiate compromises between North and South. With an equal number of senators representing slave and free states, the Senate became the setting for explosive issues that increasingly divided the industrialized North, the agricultural South, and the rapidly expanding West. Emerging from the shadow of the House of Representatives, the Senate matured into a creative and active lawmaking body. By 1850, it had grown to 62 members. Yet, unlike the far larger, more crowded House Chamber, the Senate still offered a relatively intimate setting that encouraged extended debate. A Forum for Orators The Senate's tradition of letting senators debate without time limits, and its relatively small size, encouraged great speakers. The even split between North and South inspired the orators. Daniel Webster of Massachusetts delivered two of the most significant speeches in American political history on the Senate floor: his “Second Reply to Hayne” (1830) and the “Seventh of March 1850” address. Passionate words reflected senators' determination to exercise their power. Bitter struggles with President Andrew Jackson and his successors over the economy tested and reinforced the Senate's power, allowing the chamber to evolve into its modern role as a leading forum for setting national policies. A Growing Nation and Capitol As the United States expanded across the continent, laborers in Washington were finishing the Capitol. Early in this period, the building consisted of just two wings, both badly damaged by British attacks in the War of 1812. Congress returned to Washington soon after the fires died down, debating whether to rebuild—or to pack up and move back to Philadelphia. Congress chose to rebuild. It began work reconstructing the two wings, later uniting them with the long-delayed center building. At last, in 1829, the Capitol and its landscaping were complete. But within 20 years, the nation had outgrown the building.

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To get a feel for the process of natural selection, experiment with a population of M&M candy or paper dot “beetles” to test how well each color is adapted to survive on a field of wrapping paper or fabric. You will need a large piece of colorful patterned wrapping paper, and a large bag of M&M candy to represent beetles. Instead of candy, you may create a population of "dot beetles" by punching holes out of five different colors of paper. First, cover a table with a large piece of colorful patterned wrapping paper. This will simulate the environment. - Next count out equal numbers of "beetles" of each color and scatter them across the paper environment. They will represent a population of “beetles” that show variation in the trait of color. - Pretend you are a bird predator and collect half the "beetles" by picking them up and setting them aside. Don’t eat the “beetles” yet! - Turn your eyes away each time you capture a “beetle” and try not to intentionally favor one color over another. Your actions represent a bird searching for the most visible food in its habitat. - Sort the captured "beetles" into piles by color and count them. 1. Which color was the easiest to spot against the colorful background? 2. Which color was best camouflaged? 3. If the surviving camouflaged “beetles” were to reproduce one offspring each, which color of beetle would be most common in the next generation? 4. What do you predict will happen over several generations? How could you test your prediction? 5. What might happen if you altered the environment by using another pattern for the environment or by dimming the lights? 6. Scientists use simulations to test their ideas. What changes would you make in this activity to make it a better simulation of natural selection?

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In our everyday world, we observe all sorts of waves, including sound waves, water waves, and radio waves. But what about gravitational waves? In the antenna of a radio station, electrons surge back and forth and produce electromagnetic waves. Suppose a very massive body like a star moved back and forth. Would it produce gravitational waves? Artist’s drawing of gravitational waves emitted by a rotating system of two massive, tightly bound stars (image courtesy of Caltech/LIGO It may seem far-fetched to think of a star moving like this, but in fact many of the stars we see are members of binary star systems—two stars that circle around each other in a dance of mutual gravitational attraction. If the stars are massive and close together, the stars swing around each other pulled by enormous forces. Einstein, in 1915, predicted that such a system would emit gravitational waves, which would move at the speed of light, but he suspected that the radiation would be too feeble to be detected. The drawing shows a representation of these waves. If two such stars did give off gravitational radiation, their mechanical energy would decrease, they would draw closer together, and their rate of mutual rotation would increase. So if physicists could measure the period of a binary system very precisely, they could look for evidence of gravitational radiation. The physicists who found the evidence, Russell Hulse and Joseph Taylor, were studying pulsars—neutron stars that spin rapidly and emits sharp pulses of radio energy with extraordinary regularity. They found a pulsar whose rate of pulsing oscillated, first speeding up and then slowing down. Careful analysis showed that this variation was a Doppler shift, and that the pulsar was alternately moving towards and away from Earth as it and an unseen companion star orbited each other. The two objects rotate around each other about every eight hours, at a separation of from one to five solar radii. Since they are so close together, the gravitational forces between them are extraordinarily strong. Painstaking, long-term measurements of the pulse arrival times revealed that the rate of rotation of the system was increasing, and in just the way that Einstein predicted 63 years before. In 1993, Hulse and Taylor were awarded the Nobel Prize in physics for this work. They had identified a source of gravitational waves. The next step would be to build a detector to observe these waves directly. Gravitational waves are hard to detect. These waves are actually faint ripples in space-time, the four-dimensional world that Einstein created in his theories of special and general relativity. As a gravitational wave passes by, objects would change their length, but by only about one part in 1021, which for the distance from the sun to Earth is about one atomic diameter. This is an extremely small effect. Niobium resonant mass detector at The University of Western Australia; the niobium cylinder weighs 1.5 tons; the detector is operated at liquid helium temperatures—five degrees above absolute zero. (photo courtesy of the Australian International Gravitational Research Center, The University of Western Australia Here are the three main categories of detectors: 1. Resonant Mass Detectors: These consist of a large suspended metal cylinder, some tens of meters long, instrumented to detect small changes in length. (See photo.) Astrophysical theory predicts that a typical double star system with a pulsar would radiate gravitational waves at a frequency of about 1600 Hz. The length of the cylinder is chosen so the cylinder will resonate at this frequency, enabling the faint gravitational wave to produce a detectable oscillation in the length of the cylinder. A chief limitation on the sensitivity of the resonant detectors is their small size. A different type of detector utilizes laser beams reflected over long distances. 2. Ground-based Interferometers: To increase the magnitude of the oscillation to be measured, these detectors are interferometers with arms several kilometers long. A laser beam is split and travels several kilometers in perpendicular directions to suspended mirrors (see diagram). The reflected beams are combined and interfere, providing a pattern of light and dark that shows the relative phases of the two beams. The Laser Interferometer Gravitational Wave Observatory (LIGO), with one detector in Washington and the other in Louisiana, is currently being constructed and tested. The two detectors will be operated together to reduce the chances that noise at one or the other would mimic a gravitational wave. The photograph shows the Washington detector. Land-based interferometers like LIGO are vulnerable to the effects of seismic noise, especially at low frequencies. This frequency dependence is important, because supermassive black holes and compact binary stars are expected to produce gravitational waves at low frequencies, below 1 cycle per second (Hz). To avoid this noise, the interferometer can be flown in space on three well-separated satellites. Note that, since a gravitational wave changes space itself, no matter is required between the mirrors. Drawing of the interferometer in the LIGO detector; the laser beam splits into two beams that pass down the long arms, reflect back, and then combine and interfere; if the length of one arm changes relative to the other, the phase of the combined light beams changes, changing the intensity at the detector. (images courtesy of Caltech/LIGO Ariel view of the LIGO Hanford Observatory; the long wings contain the interferometer beams. (photo by Gary White, courtesy of LIGO Laboratory) 3. Space-Based Interferometers: Drawing of the formation of three LISA satellites (image courtesy of NASA) The Laser Interferometeric Space Antenna (LISA) system is located on three satellites about five million kilometers apart, in an orbit with a period of about a year. (See drawing.) LISA will be sensitive to gravitational waves from .1 x 10-3 Hz to 1 Hz. It is scheduled for launch sometime near 2011. Since gravitational waves interact so little with matter, they would propagate virtually without change as they pass through interstellar space. Thus they are expected to provide a new window on the universe and a wealth of information very different from what we observe with electromagnetic radiation. National Center for Superconducting Applications (NCSA) University of Illinois The evacuated pipe containing the laser beam in one of the arms in the LIGO detector at Livingston, Louisiana (image courtesy of LIGO

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All About Ratios: Math You Use Everyday Target Audience: Students Hosting Center: Glenn Research Center Subject Category: Math Unit Correlation: Exploring Engineering and Technology Minimum Delivery Time: 030 min(s) Maximum Connection Time: 060 min(s) If you were given a 1:75 scale model of the Space Shuttle, would it fit in your pocket, on your desk, or would it have to stay in your driveway? What are ratios and how do we interpret them? This module is appropriate for videoconference AND web conference presentation. This program focuses on how ratios relate two quantities, how the size of a ratio has meaning in many contexts, how we use ratios in our every day lives, and how they are important to NASA. The Ratios program demonstrates real world applications of math to areas such as velocity of vehicles, the cost of goods, and the consideration of an hourly wage. It shows participants why they are going to need this math skill in their future lives. The learners will decide whether or not to take an easy, legal job for $1,000. The learners will explore a variety of ways that we can compare quantities. The learners will explain different ways that ratios can be expressed. The learners will evaluate their understanding of ratios by discussing their application in scale models. The learners will explain how the size of a ratio can be favorable or unfavorable Sequence of Events What is a ratio? Go to Webmath to find out. You can also ask "Dr. Math" about ratios Ask Dr. Math Learn about writing ratios in different forms at Working with Ratios. Ratio: comparing one quantity to another. An aspect ratio compares a wing's length to its cord. Fraction: comparing one quantity to another, specifically comparing a numerator to a denominator. Numerator: the top number in a fraction. In 3/7, the 3 is the numerator. Denominator: the bottom number in a fraction. In 3/7, the 7 is the denominator. Percent: a number comparison that converts a ratio to parts out of one hundred. Proportion: comparing of two ratios. Two is to nine as four is to eighteen. They can be used to solve problems like “If a hanger can hold four aircraft, how many hangers would be needed to hold thirty-six aircraft?” Lift: an upward force generated by the wings of an aircraft. Drag: a force generated by the air resisting a body moving through it; comparable to friction. Drag keeps as aircraft from moving forward. In this event the presenter will question the students as to what a ratio is and what are some of the ways that they can be expressed. In making the point that almost any quantity can be compared in a ratio, the presenter will show them a water bottle and a wooden dowel and ask the students to come up with a number of different ways that the two can be compared. Decimals, fractions, percents, scale, and proportions will be discussed and examples used to show how they could relate two different quantities. The presenter will demonstrate the many ways that we use ratios in out daily lives. He will ask them is they will take a job that pays $1,000 and then draw out that they need to know the time required as well. Salaries are ratios of time and money. He will discuss how we always use ratios to compare numerous quantities, such as miles per gallon and cost per gallon. He will show how division expresses this mathematically. Models of the Space Shuttle in wind tunnels will be used to illustrate how engineers can collect data from a small-scale model and then use ratios to find out what this would be on a full-scale device without having to build the full-scale device. Using ratios can save large amounts of time, money, and lives. Finally the presenter will discuss what we can know from the size of a ratio. He will ask questions like, "What does it mean if the ratio if nearly one? What can you tell about a ratio that is much greater than one?” Some actual aeronautical engineering ratios like lift to drag are used to exemplify this concept. The engineer wants large lift and little drag, so a large number for the ratio is desirable. Some of the questions that have been asked during this module in the past are: "How are ratios and decimals and percentages the same?" "Why do you need to use ratios? When will you ever use them?" "Can you give me some examples of ratios that you commonly use right now?" "When might it be important for a ratio to have a value larger than one? smaller that one?" Using what you have learned about ratios, now where do you think a 1:75 scale model of the 122-foot tall Space Shuttle would fit in your pocket, on your desk, or would you have to keep it in a parking lot? To extend you knowledge about ratios and how to use them, try some of the following activities: NCTM MATH STANDARDS Number and Operations Standard Understand numbers, ways of representing numbers, relationships among numbers, and number systems GRADES 6-8 understand and use ratios and proportions to represent quantitative relationships Apply appropriate techniques, tools, and formulas to determine measurements. GRADES 6-8 solve problems involving scale factors, using ratio and proportion

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Students will learn about the Lorentz force and how moving particles interact in a magnetic field. In addition, the right hand rule is covered. Students will also solve various types of problems involving particles and magnetic fields using the Lorentz force and the right hand rule. where q is the charge of the particle, v is the velocity of the particle, B is the magnetic field value and is the angle between the velocity vector and the magnetic field vector. Note that for problems where the direction of the particle and the direction of the magnetic field are perpendicular then also, recall that As moving charges create magnetic fields, so they experience forces from magnetic fields generated by other materials. The magnitude of the force experienced by a particle traveling in a magnetic field depends on the charge of the particle , the velocity of the particle , the strength of the field , and, importantly, the angle between their relative directions : There is a second right hand rule that will show the direction of the force on a positive charge in a magnetic field: point your index finger along the direction of the particle’s velocity . If your middle finger points along the magnetic field, your thumb will point in the direction of the force. NOTE: For negative charge reverse the direction of the force (or use your left hand) For instance, if a positively charged particle is moving to the right, and it enters a magnetic field pointing towards the top of your page, it feels a force going out of the page, while if a positively charged particle is moving to the left, and it enters a magnetic field pointing towards the top of your page, it feels a force going into the page: Example 1: Find the Magnetic Field Question : An electron is moving to the east at a speed of . It feels a force in the upward direction with a magnitude of . What is the magnitude and direction of the magnetic field this electron just passed through? Answer : There are two parts to this question, the magnitude of the electric field and the direction. We will first focus on the magnitude. To find the magnitude we will use the equation We were given the force of the magnetic field and the velocity that the electron is traveling . We also know the charge of the electron . Also, because the electron's velocity is perpendicular to the field, we do not have to deal with because of degrees is . Therefore all we have to do is solve for B and plug in the known values to get the answer. Now, plugging the known values we have: Now we will find the direction of the field. We know the direction of the velocity (east) and the direction of the force due to the magnetic field (up, out of the page). Therefore we can use the second right hand rule (we will use the left hand, since an electron's charge is negative). Point the pointer finger to the right to represent the velocity and the thumb up to represent the force. This forces the middle finger, which represents the direction of the magnetic field, to point south. Alternatively, we could recognize that this situation is illustrated for a positive particle in the right half of the drawing above; for a negative particle to experience the same force, the field has to point in the opposite direction: south. Example 2: Circular Motion in Magnetic Fields Consider the following problem: a positively charged particle with an initial velocity of , charge and mass traveling in the plane of this page enters a region with a constant magnetic field pointing into the page. We are interested in finding the trajectory of this particle. Since the force on a charged particle in a magnetic field is always perpendicular to both its velocity vector and the field vector (check this using the second right hand rule above), a constant magnetic field will provide a centripetal force --- that is, a constant force that is always directed perpendicular to the direction of motion. Two such force/velocity combinations are illustrated above. According to our study of rotational motion, this implies that as long as the particle does not leave the region of the magnetic field, it will travel in a circle. To find the radius of the circle, we set the magnitude of the centripetal force equal to the magnitude of the magnetic force and solve for : In the examples above, was conveniently 90 degrees, which made . But that does not really matter; in a constant magnetic fields a different will simply decrease the force by a constant factor and will not change the qualitative behavior of the particle. Watch this Explanation Time for Practice - For each of the arrangements of velocity and magnetic field below, determine the direction of the force. Assume the moving particle has a positive charge. As an electron that is traveling in the positive direction encounters a magnetic field, it begins to turn in the upward direction (positive direction). What is the direction of the magnetic field? - -" "-direction - +" "-direction (towards the top of the page) - -" "-direction (i.e. into the page) - +" "-direction (i.e. out of the page) - none of the above A positively charged hydrogen ion turns upward as it enters a magnetic field that points into the page. What direction was the ion going before it entered the field? - -" "-direction - +" "-direction - -" "-direction (towards the bottom of the page) - +" "-direction (i.e. out of the page) - none of the above - Protons with momentum are magnetically steered clockwise in a circular path. The path is in diameter. (This takes place at the Dann International Accelerator Laboratory, to be built in 2057 in San Francisco.) Find the magnitude and direction of the magnetic field acting on the protons. An electron is accelerated from rest through a potential difference of volts. It then enters a region traveling perpendicular to a magnetic field of - Calculate the velocity of the electron. - Calculate the magnitude of the magnetic force on the electron. - Calculate the radius of the circle of the electron’s path in the region of the magnetic field - A beam of charged particles travel in a straight line through mutually perpendicular electric and magnetic fields. One of the particles has a charge, ; the magnetic field is and the electric field is . Find the velocity of the particle. A positron (same mass, opposite charge as an electron) is accelerated through volts and enters the center of a wide capacitor, which is charged to volts. A magnetic filed is applied to keep the positron in a straight line in the capacitor. The same field is applied to the region (region II) the positron enters after the capacitor. - What is the speed of the positron as it enters the capacitor? - Show all forces on the positron. - Prove that the force of gravity can be safely ignored in this problem. - Calculate the magnitude and direction of the magnetic field necessary. - Show the path and calculate the radius of the positron in region II. - Now the magnetic field is removed; calculate the acceleration of the positron away from the center. - Calculate the angle away from the center with which it would enter region II if the magnetic field were to be removed. An electron is accelerated through and moves along the positive axis through a plate long. A magnetic field of is applied in the - Calculate the velocity with which the electron enters the plate. - Calculate the magnitude and direction of the magnetic force on the electron. - Calculate the acceleration of the electron. - Calculate the deviation in the direction of the electron form the center. - Calculate the electric field necessary to keep the electron on a straight path. - Calculate the necessary voltage that must be applied to the plate. Answers to Selected Problems - a. Into the page b. Down the page c. Right - ; if CCW motion, B is pointed into the ground. - a. b. c. - a. b. d. e. f. g. - a. b. c. d. e. f.

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- Students are encouraged to offer their unique perspectives, share interpretations, and raise questions in classrooms that support discussions. - Discussion provides students with opportunities to explore the layers of possibility individuals bring to each reading, including unique experiences in their lives and differing perspectives based on the books they have read. - Classrooms that support students' developing understandings provide a safe learning community where students feel free to share their range of ideas. They feel respected and learn to respect and trust others in the community. - Writing is an important rehearsal for fruitful classroom - Students are treated as life-long learners in classrooms that support discussion. - Teachers can encourage discussion by: - Providing engaging texts, such as literature that features adolescents and their dilemmas. - Asking questions that help students tap prior knowledge and life experiences. - Choosing a compelling passage and reading it aloud. - Being a good listener to students' ideas. - Setting discussion guidelines in concert with student - Modeling ways to connect to the literature. For instance, share personal experiences that the text makes you recall or similar situations you have encountered in your life. - Using think alouds to demonstrate the ways you are interacting with the literature as you read. - Modeling writing as a way to collect your own ideas about a text. - Inviting students to create their own questions about - Removing yourself as the point from which all conversation - Successful discussions do not occur without careful strategic planning. In planning for discussion: - Consider ways to help students find their way into the text. This is crucial in getting a conversation - Consider ways you can model thinking, writing, and connecting the text to your own life. - Physically arrange your classroom so that it best supports discussion. This may be small groups, pairs, teams, or rows facing one another. Rely on your knowledge of your students, their energy level, their experience with discussion, and your goals for the discussion. It may be necessary to change the configurations often for optimum success. - Know that all groups will not be successful. When this happens, sometimes it is best to allow the group to break off into smaller groups or to allow students to work independently and join the class later in a - Think about which students in your class are more likely to contribute to discussion and which ones are more reluctant. Plan for including all students in the literary discussion. This might include your listening to a group's discussion and directing the conversation towards the quieter students or creating heterogeneous groups with many personalities and temperaments. - Consider ways to respond to the literature, other than discussion, such as the use of art and writing. These opportunities will include some of the quieter - Think about ways you can encourage students to pose their own questions. - Discussion creates a classroom environment where students focus less on recitation and memorization and more on substantial inquiry and analysis. - Questions are a natural part of the literary experience and students are invited to raise thought-provoking questions in a literary community. Questions are never viewed as not knowing or not fully understanding, as in a traditional - Literary concepts are learned in context, as students use this literary lexicon as the fabric of their discussions, developing their understandings and growing their interpretations. Teachers can provide opportunities for literary concept - Asking questions that foreground literary elements in a text. - Modeling the use of literary language in questions and contributions to discussions. - Planning natural connections in the text. If a text lends itself well to "foreshadowing," for instance, find ways to bring this to your students' attention and allow them to take the conversation further. This may include the use of picture books, read alouds,

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Input an integer containing only 0s and 1s (i.e., a “binary” integer) and print its decimal equivalent. Use the modulus and division operators to pick off the “binary” number’s digits one at a time from right to left. Much as in the decimal number system, where the rightmost digit has a positional value of 1, the next digit left has a positional value of 10, then 100, then 1000, and so on, in the binary number system the rightmost digit has a positional value of 1, the next digit left has a positional value of 2, then 4, then 8, and so on. Thus the decimal number 234 can be interpreted as 2 * 100 + 3 * 10 + 4 * 1. The decimal equivalent of binary 1101 is 1 * 1 + 0 * 2 + 1 * 4 + 1 * 8 or 1 + 0 + 4 + 8, or 13. Please explain what the problem is asking. I dont know where to start with this one. What is the program supposed to do step by step? I want to write the code myself but before I do, I need to understand which steps the program will need in order to perform. The program should prompt the user to enter a number. This number should be in binary, so the user should only enter 0's and 1's. Then your program must take this binary number and convert it to a decimal. The program should output this converted number to the screen. Get the input as a string of ones and zeros, e.g. "1101". It would be sensible to verify that the input is valid, that is, no other characters other than '1' or '0' were entered. Next, you need to convert the string of characters into a number (an integer type). This part, while fairly straightforward, will take a few lines of code. As an integer, you can then easily print the decimal value. (just cout << n;). Lastly, you convert your integer into binary digits. The method is to repeatedly divide it by 2. The remainder will be either 1 or 0, which gives the required binary digit. The number will get smaller each time until it is zero. Then you can stop. Thank you for breaking it down for me. Now, I understand what the program should do. I searched how to convert binary numbers to decimal and vice versa. Based on what I understood 010110 would be converted to 22. I'm trying to write the code for the program to do it, but I'm realizing I have no idea how to program each step. Any advice or more suggestions?

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Earth's orbit around the sun is due to the gravitational attraction between the earth and the sun. It follows an elliptical path, similar to an oval, but if viewed from space would look almost circular because the distances between the nearest and most distant points from the sun are not very different. Currently the earth is closest to the sun in the Northern Hemisphere winter. However, the earth's tilt of its rotational axis causes bigger changes in incoming sunlight than the distance from the sun and so it has a bigger effect on the seasons than the distance from the sun itself does. The earth’s orbit around the sun doesn’t always stay the same. Sometimes the shape of the orbit changes, called the eccentricity. Sometimes the tilt of the axis changes, called the obliquity. Sometimes the earth wobbles as it turns, called the precession. All of these have a different effect on climate. Eccentricity is the shape of the earth’s orbit. Over a time period of 100,000 years, the orbit ranges from being a nearly perfect circle to being an oval and back to a near-circle again. Right now, the orbit is almost a perfect circle. This causes the earth to be a little closer to the sun in January than it is in July, which leads to more solar energy reaching the earth in January than in July. But this effect is small compared to the variation in incoming sunlight caused by the tilt of the earth, and so at this point in time the eccentricity has very little effect on the climate over the year. If the orbit became a pronounced oval, it would be warmer when the earth was closer to the sun regardless of tilt, and the length of the seasons would be different. |Figure A||Figure B| |Image from NASA||Image from NASA| Obliquity is the earth’s tilt relative to the earth's orbit around the sun. The earth’s tilt causes the seasons (see Tilt and Latitude under Background and Basics). The tilt away from the axis changes from 22.1° to 24.5° over a period of 41,000 years. The current tilt is 23.5° and is slowly decreasing. When the tilt becomes larger, the seasons are more extreme, with more severe winter and summer weather. When the tilt is smaller, the seasons are milder and less different from each other. |Image from NASA| The precession is how much the earth wobbles on its axis. The earth wobbles like a top that is slowing down. The result is that the North Pole on earth changes where it points to the sky. At present it is pointing at what we call Polaris, the Northern Star. However, 13,000 years ago it was pointing somewhat away from Polaris. The position of the North Pole on the sky forms a circle that is traced out every 26,000 years. The combination of the precession with whether the earth is nearer or farther from the sun can affect the severity of the seasons in one hemisphere compared to the other. |Image from NASA|

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In this lesson we discuss cell references, how to copy or move a formula, and format cells. To begin, let’s clarify what we mean by cell references, which underpin much of the power and versatility of formulas and functions. A concrete grasp on how cell references work will allow you to get the most out of your Excel spreadsheets! Note: we’re just going to assume that you already know that a cell is one of the squares in the spreadsheet, arranged into columns and rows which are referenced by letters and numbers running horizontally and vertically. What is a Cell Reference? A “cell reference” means the cell to which another cell refers. For example, if in cell A1 you have =A2. Then A1 refers to A2. Let’s review what we said in Lesson 2 about rows and columns so that we can explore cell references further. Cells in the spreadsheet are referred to by rows and columns. Columns are vertical and labeled with letters. Rows are horizontal and labeled with numbers. The first cell in the spreadsheet is A1, which means column A, row 1, B3 refers to the cell located on the second column, third row, and so on. For learning purposes about cell references, we will at times write them as row, column, this is not valid notation in the spreadsheet and is simply meant to make things clearer. Types of cell references There are three types of cell references. Absolute – This means the cell reference stays the same if you copy or move the cell to any other cell. This is done by anchoring the row and column, so it does not change when copied or moved. Relative – Relative referencing means that the cell address changes as you copy or move it; i.e. the cell reference is relative to its location. Mixed – This means you can choose to anchor either the row or the column when you copy or move the cell, so that one changes and the other does not. For example, you could anchor the row reference then move a cell down two rows and across four columns and the row reference stays the same. We will explain this further below. Let’s refer to that earlier example – suppose in cell A1 we have a formula that simply says =A2. That means Excel output in cell A1 whatever is inputted into cell A2. In cell A2 we have typed “A2” so Excel displays the value “A2” in cell A1. Now, suppose we need to make room in our spreadsheet for more data. We need to add columns above and rows to the left, so we have to move the cell down and to the right to make room. As you move the cell to the right, the column number increases. As you move it down, the row number increases. The cell that it points to, the cell reference, changes as well. This is illustrated below: Continuing with our example, and looking at the graphic below, if you copy the contents of cell A1 two to the right and four down you have moved it to cell C5. We copied the cell two columns to the right and four down. This means we have changed the cell it refers two across and four down. A1=A2 now is C5=C6. Instead of referring to A2, now cell C5 refers to cell C6. The value shown is 0 because cell C6 is empty. In cell C6 we type “I am C6” and now C5 displays “I am C6.” Example: Text Formula Let’s try another example. Remember from Lesson 2 where we had to split a full name into first and last name? What happens when we copy this formula? Write the formula =RIGHT(A3,LEN(A3) – FIND(“,”,A3) – 1) or copy the text to cell C3. Do not copy the actual cell, only the text, copy the text, otherwise it will update the reference. You can edit the contents of a cell at the top of a spreadsheet in the box next to where is says “fx.” That box is longer than a cell is wide, so it is easier to edit. Now we have: Nothing complicated, we have just written a new formula into cell C3. Now copy C3 to cells C2 and C4. Observe the results below: Now we have Alexander Hamilton and Thomas Jefferson’s first names. Use the cursor to highlight cells C2, C3, and C4. Point the cursor to cell B2 and paste the contents. Look at what happened – we get an error: “#REF.” Why is this? When we copied the cells from column C to column B it updated the reference one column to the left =RIGHT(A2,LEN(A2) – FIND(“,”,A2) – 1). It changed every reference to A2 to the column to the left of A, but there is no column to the left of column A. So the computer does not know what you mean. The new formula in B2 for example, is =RIGHT(#REF!,LEN(#REF!) – FIND(“,”,#REF!) – 1) and the result is #REF: Copying a Formula to a Range of Cells Copying cells is very handy because you can write one formula and copy it to a large area and the reference is updated. This avoids having to edit each cell to ensure it points to the correct place. By “range” we mean more than one cell. For example, (C1:C10) means all the cells from cell C1 to cell C10. So it is a column of cells. Another example (A1:AZ1) is the top row from column A to column AZ. If a range cross five columns and ten rows, then you indicate the range by writing the top-left cell and bottom right one, e.g., A1:E10. This is a square area that cross rows and columns and not just part of a column or part of a row. Here is an example that illustrates how to copy one cell to multiple locations. Suppose we want to show our projected expenses for the month in a spreadsheet so we can make a budget. We make a spreadsheet like this: Now copy the formula in cell C3 (=B3+C2) to the rest of the column to give a running balance for our budget. Excel updates the cell reference as you copy it. The result is shown below: As you can see, each new cell updates relative to the new location, so cell C4 updates its formula to =B4 + C3: Cell C5 updates to =B5 + C4, and so on: An absolute reference does not change when you move or copy a cell. We use the $ sign to make an absolute reference – to remember that, think of a dollar sign as an anchor. For example, enter the formula =$A$1 in any cell. The $ in front of the column A means do not change the column, the $ in front of the row 1 means do not change the column when you copy or move the cell to any other cell. As you can see in the example below, in cell B1 we have a relative reference =A1.When we copy B1 to the four cells below it, the relative reference =A1 changes to the cell to the left, so B2 become A2, B3 become A3, etc. Those cells obviously have no value inputted, so the output is zero. However, if we use =$A1$1, such as in C1 and we copy it to the four cells below it, the reference is absolute, thus it never changes and the output is always equal to the value in cell A1. Suppose you are keeping track of your interest, such as in the example below. The formula in C4 = B4 * B1 is the “interest rate” * “balance” = “interest per year.” Now, you have changed your budget and have saved an additional $2,000 to buy a mutual fund. Suppose it is a fixed rate fund and it pays the same interest rate. Enter the new account and balance into the spreadsheet and then copy the formula = B4 * B1 from cell C4 to cell C5. The new budget looks like this: The new mutual fund earns $0 in interest per year, which can’t be right since the interest rate is clearly 5 percent. Excel highlights the cells to which a formula references. You can see above that the reference to the interest rate (B1) is moved to the empty cell B2. We should have made the reference to B1 absolute by writing $B$1 using the dollars sign to anchor the row and column reference. Rewrite the first calculation in C4 to read =B4 * $B$1 as shown below: Then copy that formula from C4 to C5. The spreadsheet now looks like this: Since we copied the formula one cell down, i.e. increased the row by one, the new formula is =B5*$B$1. The mutual fund interest rate is calculated correctly now, because the interest rate is anchored to cell B1. This is a good example of when you could use a “name” to refer to a cell. A name is an absolute reference. For example, to assign the name “interest rate” to cell B1, right-click the cell and then select “define name.” Names can refer to one cell or a range, and you can use a name in a formula, for example =interest_rate * 8 is the same thing as writing =$B$1 * 8. Mixed references are when either the row or column is anchored. For example, suppose you are a farmer making a budget. You also own a feed store and sell seeds. You are going to plant corn, soybeans, and alfalfa. The spreadsheet below shows the cost per acre. The “cost per acre” = “price per pound” * “pounds of seeds per acre” – that’s what it will cost you to plant an acre. Enter the cost per acre as =$B2 * C2 in cell D2. You are saying you want to anchor the price per pound column. Then copy that formula to the other rows in the same column: Now you want to know the value of your inventory of seeds. You need the price per pound and the number of pounds in inventory to know the value of the inventory. We add two columns: “pound of seed in inventory” and then “value of inventory.” Now, copy the cell D2 to F4 and note that the row reference in the first part of the original formula ($B2) is updated to row 4 but the column remains fixed because the $ anchors it to “B.” This is a mixed reference because the column is absolute and the row is relative. A circular reference is when a formula refers to itself. For example, you cannot write c3 = c3 + 1. This kind of calculation is called “iteration” meaning it repeats itself. Excel does not support iteration because it calculates everything only one time. If you try do this by typing SUM(B1:B5) in cell B5: A warning screen pops up: Excel only tells you that you have a circular reference at the bottom of the screen so you might not notice it. If you do have a circular reference and close a spreadsheet and open it again, Excel will tell you in a pop-up window that you have a circular reference. If you do have a circular reference, every time you open the spreadsheet, Excel will tell you with that pop-up window that you have a circular reference. References to Other Worksheets A “workbook” is a collection of “worksheets.” Simply put, this means you can have multiple spreadsheets (worksheets) in the same Excel file (workbook). As you can see in the example below, our example workbook has many worksheets (in red). Worksheets by default are named Sheet1, Sheet2, and so forth. You create a new one by clicking the “+” at the bottom of the Excel screen. You can change the worksheet name to something useful like “loan” or “budget” by right-clicking on the worksheet tab shown at the bottom of the Excel program screen, selecting rename, and typing in a new name. Or you can simply double-click on the tab and rename it. The syntax for a worksheet reference is =worksheet!cell. You can use this kind of reference when the same value is used in two worksheets, examples of that might be: - Today’s date - Currency conversion rate from Dollars to Euros - Anything that is relevant to all the worksheets in the workbook Below is an example of worksheet “interest” making reference to worksheet “loan,” cell B1. If we look at the “loan” worksheet, we can see the reference to the loan amount: Coming up Next … We hope you now have a firm grasp of cell references including relative, absolute, and mixed. There’s certainly a lot. That’s it for today’s lesson, in Lesson 4, we will discuss some useful functions you may wish to know for daily Excel use.

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Word Analogies allow students to link familiar concepts with new ideasprior experiences with new information. In this strategy, students confront two related words and are challenged to explain the nature of their relationship. Next, students apply this same relationship to other word pairs. Typically, a word analogy exercise takes this form: "Term A is to Term B as Term C is to what word?" Students think critically on two levels: first, in describing the relationship between the first word pair and, second, by suggesting new word pairs with the same relationship. Vacca and Vacca (1996) outline the following word analogy types: Steps to Word Analogies: Prepare students for drawing word analogies in a reading assignment by a detailed discussion of the reasoning process in making analogies and by modeling both positive and negative examples of anologies. Lead students in group exercises to identify the relationship between word pairs and, then, to extend this relationship to a second word pair. Assign students or student groups word analogy worksheets for practice in this complex task. Once students are comfortable building word analogies, choose the key words from a reading selection and create a word analogy exercise to reinforce the meanings of and relationships between these words. Blachowicz, C., & Fisher, P. (2000)." Vocabulary instruction." In M.L. Kamil, P.B. Mosenthal, P.D. Pearson, & R. Barr (Eds.), Handbook of reading research: Vol. 3 (pp. 503-523). Mahwah, NJ: Erlbaum. Hayes, D.A., & Henk, W.A. (1986). "Understanding and remembering complex prose augmented by analogic and pictorial illustration." Journal of Reading Behavior, 18, 63-77. Lenski, Susan D., Wham, Mary Ann, & Johns, Jerry L. (1999). Reading and learning strategies for middle and high school students. Dubuque, IA: Kendall/Hunt. Vacca, R.D., Vacca J. (1995). Content area reading. (5th. Ed.). Glenview, IL: Scott, Foresman.

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Basic Algebra/Working with Numbers/Adding Rational Numbers It is easy to add fractions when the denominators are equal. For example. adding 3/10 and 2/10 is very simple, just add the numerators and you have the numerator of the resulting fraction: Notice the simplification: five parts out of ten is the half of the parts. Unfortunately, it is not always so simple. Sometimes we need to add fractions that have different denominators. Before we can add them, we must alter the fractions so that their denominators are the same. We can do this by multiplying each fraction by the number one which doesn't change the value of the fraction). However, the form of the number one will itself be represented as a fraction whose denominator and numerator are equal, and under our control. For example, all of these fractions are equal to one: Knowing this, we can change the denominators of the fractions so that the denominators of both are the same. For example: In this case we changed both fractions so that they each had a denominator of 6. Practice with simple fractions Calculate the following additions: More complicated fractions In these cases, we can guess which multiplication to do, but sometimes, it is not that easy. For example, adding 123/456 and 234/120. - The simplest general method is to multiply the numerator and denominator of the first fraction by the denominator of the second fraction and vice-versa. The resulting denominators will both be the product of the two original denominators. In this case : - 123/456 + 234/120 = (123 x120)/(456 x120) + (234 x456)/(120 x456) - = 14760/54720 + 106704/54720 = (14760 + 106704)/54720 = 121464/54720 We obtain generally big numbers which is not optimal because the fraction can most of the time be written with smaller numbers. - The second is more subtle. Instead of multiplying by the actual denominators, we multiply by the smallest possible number for each side so that we obtain the same denominator. For example: - 1/6 + 1/4 = (1 x2)/(6 x2) + (1 x3)/(4 x3) = 2/12 + 3/12 = 5/12 We only multiplied by 2 in the first fraction and by 3 in the second fraction. The resulting fraction, 5/12 is optimal, which we call irreducible. Note that 2 is the half of 4=2x2 and 3 the half of 6=3x2. We did not multiply by the given denominators, we avoided to multiply by the factor 2. Let's take the previous example and find the factors composing the numbers... - 123 = 3x41 and 456 = 2x228 = 2x2x114 = 2x2x2x57 = 2x2x2x3x19 - 234 = 2x3x39 = 2x3x3x13 and 120 = 2x2x3x10 = 2x2x3x2x5 We can see that we can simplify 123/456 by 3 which gives 41/(2x2x2x19) and simplify 234/120 by 2x3 which gives 39/(2x2x5). Remember that multiplying by the same number the numerator and the denominator does not change the value. The same is true when dividing by the same number. Now comes a question : which is the smallest integer that contains the factors 2x2x2x19 and the factors 2x2x5. It is the number that has just all these factors in correct number : 2x2x2x5x19 = 760. To attain this number, we must multiply in the first fraction by 5 and in the second by 2x19. So, finally we have: - 123/456 + 234/120 = 41/(2x2x2x19) + 39/(2x2x5) = (41x5)/760 + (39x2x19)/760 - = 205/760 + 1482/760 = 1687/760 This fraction is simpler as the first obtained 121464/54720. Both fractions are equal : 1687/760 = 121464/54720 But the factor between the two fractions is 72 ! put links here to games that reinforce these skills (Note: put answer in parentheses after each problem you write)

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In this worksheet your student will write metaphors and similes about himself. A metaphor is one kind of figurative language. It makes a direct comparison of two unlike things. You can tell the difference between a metaphor and a simile because a simile uses the words “like” or “as”, and a metaphor does not. Metaphors often usually use a form of the verb “to be”. The verb can be in the past tense (was, were), the present tense (am, is, are), or future tense (will be). The printable metaphor worksheets below help students to understand how this kind of figurative language can be used. Each worksheet is free to duplicate for home or classroom use.

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From Wikipedia, the free encyclopedia - View original article A clef (from French: clef “key”) is a musical symbol used to indicate the pitch of written notes. Placed on one of the lines at the beginning of the stave, it indicates the name and pitch of the notes on that line. This line serves as a reference point by which the names of the notes on any other line or space of the stave may be determined. Only one clef that references a note in a space rather than on a line has ever been used. There are three types of clef used in modern music notation: F, C, and G. Each type of clef assigns a different reference note to the line (and in rare cases, the space) on which it is placed. |G-clef||G4||passes through the curl of the clef.| |C-clef||Middle C (C4)||passes through the center of the clef.| |F-clef||F3||passes between the two dots of the clef.| Once one of these clefs has been placed on one of the lines of the stave, the other lines and spaces can be read in relation to it. The use of three different clefs makes it possible to write music for all instruments and voices, even though they may have very different tessituras (that is, even though some sound much higher or lower than others). This would be difficult to do with only one clef, since the modern stave has only five lines, and the number of pitches that can be represented on the stave, even with ledger lines, is not nearly equal to the number of notes the orchestra can produce. The use of different clefs for different instruments and voices allows each part to be written comfortably on the stave with a minimum of ledger lines. To this end, the G-clef is used for high parts, the C-clef for middle parts, and the F-clef for low parts—with the important exception of transposing parts, which are written at a different pitch than they sound, often even in a different octave. In order to facilitate writing for different tessituras, any of the clefs may theoretically be placed on any of the lines of the stave. The further down on the stave a clef is placed, the higher the tessitura it is for; conversely, the higher up the clef, the lower the tessitura. Since there are five lines on the stave, and three clefs, it might seem that there would be fifteen possible clefs. Six of these, however, are redundant clefs (for example, a G-clef on the third line would be exactly the same as a C-clef on the first line). That leaves nine possible distinct clefs, all of which have been used historically: the G-clef on the two bottom lines, the F-clef on the three top lines, and the C-clef on any line of the stave except the topmost, earning the name of "movable C-clef". (The C-clef on the topmost line is redundant because it is exactly equivalent to the F-clef on the third line; both options have been used.) Each of these clefs has a different name based on the tessitura for which it is best suited. Here follows a complete list of the clefs, along with a list of instruments and voice parts notated with them. Each clef is shown in its proper position on the stave, followed by its reference note. An obelisk (†) after the name of a clef indicates that that clef is no longer in common use. When the G-clef is placed on the second line of the stave, it is called the treble clef. This is the most common clef used today, and the only G-clef still in use. For this reason, the terms G-clef and treble clef are often seen as synonymous. The treble clef was historically used to mark a treble, or pre-pubescent, voice part. Among the instruments that use treble clef are the violin, flute, oboe, bagpipe, English horn, all clarinets, all saxophones, horn, trumpet, cornet, vibraphone, xylophone, mandolin, recorder; it is also used for euphonium, baritone horn, and guitar (which sound an octave lower). Treble clef is the upper stave of the grand stave used for harp and keyboard instruments. It is also sometimes used, along with tenor clef, for the highest notes played by bass-clef instruments such as the cello, double bass (which sounds an octave lower), bassoon, and trombone. The viola also sometimes uses treble clef for very high notes. Treble clef is used for the soprano, mezzo-soprano, alto, contralto and tenor voices. The tenor voice sounds an octave lower, and is often written using an octave clef (see below) or double-treble clef. When the G-clef is placed on the first line of the stave, it is called the French clef or French violin clef. It is identical to the bass clef transposed up 2 octaves. When the F-clef is placed on the fourth line, it is called the bass clef. This is the only F-clef used today, so that the terms "F-clef" and "bass clef" are often regarded as synonymous. This clef is used for the cello, euphonium, double bass, bass guitar, bassoon, contrabassoon, trombone, baritone horn, tuba, and timpani. It is also used for the lowest notes of the horn, and for the baritone and bass voices. Tenor voice is notated in bass clef when the tenor and bass are written on the same stave. Bass clef is the bottom clef in the grand stave for harp and keyboard instruments. The contrabassoon, double bass, and electric bass sound an octave lower than the written pitch; no notation is usually made of this fact, but some composers/publishers will place an "8" beneath the clef for these instruments on the conductor's full score to differentiate from instruments that naturally sound within the clef (see "Octave clefs" below). When the F-clef is placed on the third line, it is called the baritone clef. This clef was used for the left hand of keyboard music (particularly in France; see Bauyn manuscript) as well as the baritone part in vocal music. The baritone clef has less common variant as a C clef placed on the 5th line which is exactly equivalent (see below). When the F-clef is placed on the fifth line, it is called the sub-bass clef. It is identical to the treble clef transposed down 2 octaves. When the C-clef is placed on the third line of the stave, it is called the alto clef. This clef (sometimes called the viola clef) is currently used for the viola, the viola da gamba, the alto trombone, and the mandola. It is also associated with the countertenor voice and therefore called the counter-tenor (or countertenor) clef, A vestige of this survives in Sergei Prokofiev's use of the clef for the English horn, as in his symphonies. It occasionally turns up in keyboard music to the present day (Brahms's Organ chorales, John Cage's Dream for piano). When the C-clef is placed on the fourth line of the stave, it is called the tenor clef. This clef is used for the upper ranges of the bassoon, cello, euphonium, double bass, and trombone. These instruments use bass clef for their low- to mid-ranges; treble clef is also used for their upper extremes. When used for the double bass, the sound is an octave lower than the written pitch. The tenor violin parts were also written in this clef (see e.g. Giovanni Battista Vitali's Op. 11). Formerly, it was used by the tenor part in vocal music but its use has been largely supplanted either with an octave version of the treble clef when written alone or the bass clef when combined on one stave with the bass part. When the C-clef is placed on the 5th line of the stave it is called the baritone clef. It is precisely equivalent to the other more common form of the baritone clef, an F clef placed on the 3rd line (see above). When the C-clef is placed on the second line of the stave, it is called the mezzo-soprano clef. When the C-clef occurs on the first line of the stave, it is called the soprano clef. This clef was used for the right hand of keyboard music (particularly in France; see Bauyn manuscript) as well as in vocal music for sopranos. Starting in the 18th century treble clef has been used for transposing instruments that sound an octave lower, such as the guitar; it has also been used for the tenor voice. To avoid ambiguity, modified clefs are sometimes used, especially in the context of choral writing; of those shown, the C clef on the third space, easily confused with the tenor clef, is the rarest. This is most often found in tenor parts in SATB settings, in which a treble clef is written with an eight below it, indicating that the pitches sound an octave below the written value. As the true tenor clef has generally fallen into disuse in vocal writings, this "octave-dropped" treble clef is often called the tenor clef. The same clef is sometimes used for the octave mandolin. In some scores, the same concept is construed by using a double clef—two G-clefs overlapping one another. At the other end of the spectrum, treble clefs with an 8 positioned above the clef may be used in piccolo, penny whistle, soprano recorder, and other high woodwind parts. The F clef can also be notated with an octave marker. The F clef notated to sound an octave lower is used for contrabass instruments such as the double bass and contrabassoon. The F clef notated to sound an octave higher is used for bass recorder. However, both of these are extremely rare (and in fact the countertenor clef is largely intended to be humorous as with the works of P.D.Q. Bach). In Italian scores up to Gioachino Rossini's Overture to William Tell, the English horn was written in bass clef an octave lower than sounding. The unmodified bass clef is so common that performers of instruments and voice parts whose ranges lie below the stave simply learn the number of ledger lines for each note through common use, and if a line's true notes lie significantly above the bass clef the composer or publisher will often simply write the part in either the true treble clef or notated an octave down. The neutral or percussion clef is not a clef in the same sense that the F, C, and G clefs are. It is simply a convention that indicates that the lines and spaces of the stave are each assigned to a percussion instrument with no precise pitch. With the exception of some common drum-kit and marching percussion layouts, the keying of lines and spaces to instruments is not standardized, so a legend or indications above the stave are necessary to indicate what is to be played. Percussion instruments with identifiable pitches do not use the neutral clef, and timpani (notated in bass clef) and mallet percussion (noted in treble clef or on a grand stave) are usually notated on different staves than unpitched percussion. Staves with a neutral clef do not always have five lines. Commonly, percussion staves only have one line, although other configurations can be used. The neutral clef is sometimes used when non-percussion instruments play non-pitched extended techniques, such as hitting the body of a violin, violoncello or acoustic guitar, or when a vocal choir is instructed to clap, stomp, or snap, but more often the rhythms are written with X marks in the instrument's normal stave with a comment placed above as to the appropriate rhythmic action. For guitars and other fretted instruments, it is possible to notate tablature in place of ordinary notes. In this case, a TAB-sign is often written instead of a clef. The number of lines of the stave is not necessarily five: one line is used for each string of the instrument (so, for standard six-stringed guitars, six lines would be used, four lines for the traditional bass guitar). Numbers on the lines show on which fret the string should be played. This Tab-sign, like the Percussion clef, is not a clef in the true sense, but rather a symbol employed instead of a clef. Originally, instead of a special clef symbol, the reference line of the stave was simply labeled with the name of the note it was intended to bear: F and C and, more rarely, G. These were the most often-used 'clefs', or litteræ-clavis (key-letters), in Gregorian chant notation. Over time the shapes of these letters became stylized, leading to their current versions. Many other clefs were used, particularly in the early period of chant notation, including most of the notes from the low Γ (gamma, the note written today on the bottom line of the bass clef) up to the G above middle C, written with a small letter g, and including two forms of lowercase b (for the note just below middle C): round for B♭, and square for B♮. In order of frequency of use, these clefs were: F, c, f, C, D, a, g, e, Γ, B, and the round/square b. In the polyphonic period up to 1600, unusual clefs were used occasionally for parts with extremely high or low written tessituras. For very low bass parts, the Γ clef is found on the middle, fourth, or fifth lines of the stave (e.g., in Pierre de La Rue’s Requiem and in a mid-16th-century dance book published by the Hessen brothers); for very high parts, the high-D clef (d), and the even higher ff clef (e.g., in the Mulliner Book) were used to represent the notes written on the fourth and top lines of the treble clef, respectively. C clefs (along with G, F, Gamma, D, and A clefs) were formerly used to notate vocal music. Nominally, the soprano voice parts were written in first- or second-line C clef (soprano clef or mezzo-soprano clef) or second-line G clef (treble clef), the alto or tenor voices in third-line C clef (alto clef), the tenor voice in fourth-line C clef (tenor clef) and the bass voice in third- fourth- or fifth-line F clef (baritone, bass, or sub-bass clef). However, in practice transposition was applied to fit the range of the music to the available voices, so that almost any clef might be used by all voice types. In more modern publications, four-part harmony on parallel staves is usually written more simply as: This may be reduced to two staves, the soprano/alto stave with a treble clef, and tenor/bass stave marked with the bass clef. Clef combinations played a role in the modal system toward the end of the 16th century, and it has been suggested certain clef combinations in the polyphonic music of 16th-century vocal polyphony are reserved for authentic (odd-numbered) modes, and others for plagal (even-numbered) modes, but the precise implications have been the subject of much scholarly debate. Music can be transposed at sight if a different clef is mentally substituted for the written one. For example, to play an A-clarinet part, a B♭-clarinet player may mentally substitute tenor clef for the written treble clef. Concert-pitch music in bass clef can be read on an E♭ instrument as if it were in treble clef. (Notes will not always sound in the correct octave). The written key signature must always be adjusted to the correct key for the instrument being played. |Wikimedia Commons has media related to Clefs.|

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Sheet: "The Lottery" Discussion Guide Directions: Use this discussion guide to facilitate thoughtful responses to the story "The Lottery." Before students read the story, utilize the "accessing the story" questions to assist students with recalling their prior knowledge. Invite multiple interpretations throughout all discussions, giving the students opportunities to explore a variety of perspectives and pose an array of questions. Accessing the Story This story by Shirley Jackson takes place in a small rural village. The people are gathered for the drawing of a lottery. Consider what you know about small towns. What are some characteristics of a small town or community? Have you ever been to a small town? What was it like? When you think of a lottery, what do you expect to take place? How would you define a lottery? Have you or do you know someone who has participated in a lottery? What was the outcome? Use the following questions to guide students through a post-reading literature discussion. Focus on inviting all students to participate, inviting a variety of interpretations and perspectives. Utilize student comments to probe at the meaning of the story and to move the conversation along. Encourage students' questions and celebrate them. Use students' questions to lead to others, helping students to develop their own unique visions of the text. 1. Why do you think so much time is spent describing the black 2. What do you think the purpose of the lottery is in the village? Why do you think people continue to participate in it? 3. Why do you think the lottery is such a long-standing tradition in the village? 4. Does this compare to anything you know in real life? Explain. 5. How do you think the village people feel about the lottery? 6. What would you have done in Tessie Hutchinson's situation? 7. How did you feel about the lottery at the end of the story? What was your reaction? 8. Do you think this sort of lottery could take place in your own community? Why or why not? Are there any events that have occurred in your community that remind you of the events in 9. How did your initial understanding of the term "lottery" compare to the lottery in the story? How did your initial understandings help or confuse your interpretation of the story? 10. Do you think this story has a message for readers? Explain 11. How have other classmates' interpretations of the story impacted your own understanding of it? Consider how this story would change if it was told from a different point-of-view. How would Bill Hutchinson or Tessie Hutchinson tell the story? What if the reader knew all of their thoughts? Write a news story about the event of the lottery, focusing on an interview with one of the townspeople. What would they say about the event? An alternative to this activity is to conduct a dramatic interview of some of the townspeople, as in a talk Consider using other texts to inform the students' understanding of this one. Students may point out texts on their own, or the teacher may point out texts students have read or ones they are going to read in the future. You might consider the following: Novel: The Giver by Lois Lowry Novel: The Scarlet Letter by Nathaniel Hawthorne Novel: Animal Farm by George Orwell Novel: Lord of the Flies by William Golding Novel: 1984 by George Orwell Novel: Farenheit 451 by Ray Bradbury Short Story: "Charles" by Shirley Jackson Short Story: "A Jury of Her Peers" by Susan Glaspell Short Story: "All Summer in a Day" by Ray Bradbury Short Story: "Harrison Bergeron" by Kurt Vonnegut, Jr. Old Testament: Leviticus 16:22, ritual of purification , and http://etext.lib.virginia.edu/rsv.browse.html, a comprehensive listing of online biblical texts Current events identified by students, and teacher. © Annenberg Foundation 2014. All rights reserved. Legal Policy

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A formal introduction to python Now it's time to write our first python program, a typical hello world! program. You have two choices to write your python program: 1. Using interpreter & 2. Using source file. Here is how to write hello world! program in python- #First python program print "Hello World!" The code starts with # sign indicates that it is a comment line. The output of the program is- Input from user In python, raw_input is used to take input from user end. Look at the bellow example- print "Hi ! What's your name?" name=raw_input("My name is :") print "Nice to meet you %s"%s Indentation is important in python. The statements which go together must have same indentation. Each such set of statements is called a block. Take a look at the following example- #Same indentation & will run successfully i=6 print " The value of i is",i #This will show an error message as indentation level is not same i=6 print "The value of i is",i Control Flow Statement In python, three control flow statements are used: if, for & while. The if statement The if statement is used to check a condition and if the condition is true, a block of statements are executed (called the if-block), else another block of statements (called the else-block) are executed. The else clause is optional. Here is am example of if statement- number=14 guess=int(raw_input("Enter an integer:")) if guess==number: print "Yes! You have guessed the right number." elif guess<number: print "Your guess is little lower than the number!" else: print "Your guess is little higher than the number!" The for loop When we need to do a work repeatedly for a number of times, we can use for loop. Bellow is an example of for loop- for i in range(1,10): print i The output of the above code will be- The while statement The while statement allows you to repeatedly execute a block of statements as long as a condition is true. It is also another looping statement. A while statement can have an optional else clause. Take a look at the example given below- stop=False password="atik" while not stop: guess=raw_input("Enter password:") if guess==password: print "Hello atik! Nice to see you" stop=True else: print "Hello guest! Try once again" The break Statement The break statement is used to break out of a loop statement even if the loop condition has not become False. Here is an example- stop=False while not stop: something=raw_input("Enter something:") if something=="quit": break Comments in Python Comment s are used as the documentation of your work. They explains your code, which is helpful when someone else want to work with your code. Or they can be useful to you also at a later date to understand easily what you have done. Comments are not executed, so they have no effect when a program runs. In Python use can comment using # sign. Anything right to # sign will be treated as comment. So take a look at the example below how to make a comment- Example:Comments in python #This will print Hello World print "Hello World!" Constants are used to store some piece of data. But their values are fixed , which means their values are never changed. A constant can be either numeric constant or string constant. Numeric constants are just numbers like 4, 2.6 etc. String constant is a sequence of characters like "This is a string constant" or "Hello World!" and so on. Variables are used to store some information and manipulate it. It’s value can vary. Variables are just parts of your computers memory where you can store some information. To access a variable you need to give them name. There are some rules for naming variable- 1.First character must be a letter or underscore(_). 2.Other characters should be letter, digit or underscore. 3.Variable names are case-sensitive. For example- myname is not same as myName. Example:Use of Variables i=5 print i i=i+1 print i Basic Data Types Now we will discuss about the basic data types in Python. The basic data types used in Python are- b)Long Integer Number c)Floating Point Number Integer numbers are just whole numbers. Example of integers are- 3,6,-11 etc. Long Integer Number Long integers are nothing than bigger numbers. Floating Point Number Floating point numbers are numbers with decimal points. For example- 4.25,5.3E-2 etc. Examples of complex numbers are (2+3j),(-4+6j) etc. A string is just simply sequence of characters. You can use string in Python as following ways- 1.Using single quotes->’This is a string’ 2.Using double quotes->”This is a string enclosed in double quotes” 3.Using triple quotes->’’’This is a string enclosed in triple quotes’’’ Note:Triple quotes are generally used in multi-line strings. For example- ‘’’This is a multi-line string. This is the second line. Here comes the last line.’’’ In order to use you native language in python, you need to use unicode enabled editor. You can use unicode string in this way- u’This is a unicode string’ If you need to use a special character in your string and you don’t want any special processing, then you need to use raw string. Here is how can you do it- r”New lines are represented by\n” Let you want to use a string which itself contains a single quotation mark such as What’s your name? You cann’t use ‘What’s your name?’. In that case you need to do a special process called escape sequence. It is done by- ‘What\’s your name?’. You can also use double quotation mark- “What’s your name?”. In case of string containing double quote you need to do the same thing.

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|Lesson Plan ID: Pythagorean Theorem: Prove It During this lesson, eighth grade students will be introduced to the Pythagorean Theorem: a2+b2=c2. They will construct a right triangle on graph paper and draw squares on each side of the triangle. |MA2013(8) ||21. Explain a proof of the Pythagorean Theorem and its converse. [8-G6] | |MA2013(8) ||22. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. [8-G7] | |Primary Learning Objective(s): At the end of this lesson, students should know and be able to explain the attributes of a right triangle. They should be able to apply their new found knowledge of the Pythagorean Theorem to a real life scenario. |Additional Learning Objective(s): |Approximate Duration of the Lesson: || Time Not Specified| |Materials and Equipment: - graph paper (1 cm) - colored pencils - copies of Pythagorean assignment (one per student) - Each group of three needs one of the triangle lengths. |Technology Resources Needed: - Interactive Whiteboard - Computer with access to the following video: Pythagorean Theorem demo (attached) - Access to the following Internet website: http://www.quia.com/cc/65631.html Student Prerequisite Knowledge needed: Students need to understand how to square numbers as well as the inverse operation: square roots. Students should have a list of perfect squares through 225. Students should understand that the hypotenuse is the longest side in a right triangle. It is also opposite the largest angle. Cut out triangle side lengths attachment. Make sure that you have one for each group of students. 1.) To begin, review how to find the perfect square of a number by playing the following interactive game: http://www.quia.com/cc/65631.html. If using an interactive whiteboard, students may come up to the board and tap to find matching pairs. 2.) Students will watch the demo video on the Pythagorean Theorem (attached) 3.) Use an interactive whiteboard to display the Pythagorean Theorem. Lead a class discussion to see what conclusions the students can draw about the relationship between the sum of the squares of the legs and the square of the hypotenuse. 4.) Divide students into mixed-ability cooperative groups. Groups of three would be ideal for this lesson. 5.) Remind the students that the hypotenuse is the longest length because it is opposite the largest angle. The "right" angle should be between the other two side lengths. 6.) Students will test this theory with different size triangles. Hand out a slip of paper with three lengths on it to each group. Students will use these lengths to build a triangle. They will apply what they saw in the video to this particular lesson. They will build squares off of each side of the triangle and see if it does prove to be a right triangle. 7.) Students will complete attached assignment to assess their understanding of the application of the Pythagorean Theorem. |Attachments:**Some files will display in a new window. Others will prompt you to download. Students will complete the attached assignment. This assignment requires them to read and interpret a real life scenario. They will need to be able to represent their mathematical thinking in words as well as pictorially. Each area below is a direct link to general teaching strategies/classroom for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems. |Presentation of Material ||Using Groups and Peers |Assisting the Reluctant Starter ||Dealing with Inappropriate Be sure to check the student's IEP for specific accommodations. |Variations Submitted by ALEX Users:

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The surface temperature of the Moon varies considerably with location and the relative position of the Sun. Unlike geologically active bodies, the Moon no longer has an internal heat source, so heating comes almost entirely from the Sun (at night the lunar surface is warmed slightly by Earth). With no atmosphere and a surface made up almost entirely of rocky materials with low thermal conductivity and relatively low heat capacity, during the lunar day the surface temperature quickly reaches equilibrium with incoming solar radiation. The Stefan-Boltzmann equation sets the numbers: I = εσT4 where I represents absorbed solar energy per unit area, T is the absolute surface temperature (kelvins), ε is the emissivity, and σ is Stefan's constant, 5.67x10^-8 in metric units. For a surface with the sun directly overhead, for example a horizontal region near the equator at lunar noon, I is the solar constant in Earth's neighborhood, about 1366 W/m^2, minus the portion reflected. Since the emissivity is close to 1 minus the reflectance, those two terms cancel out, and inverting the equation gives the maximum day-time high on the Moon: 394 K or about 120 degrees C. When the sun's not directly overhead whether you are at the equator during lunar morning or evening, near the poles, or looking at a rock face sharply angled to the horizontal, the surface temperature will be lowered because the same solar energy is spread over a larger area. I = 1366cos(θ)W / m2 where θ is the angle of the Sun's position relative to a line perpendicular to the surface. Because the lunar rotational axis is tilted only 1.5 degrees from the ecliptic, solar angles at noon are always within 1.5 degrees of the lunar latitude value. For an angle of 30 degrees, (maximum temperature for a horizontal surface at latitude 30 degrees N or S, or equatorial temperature at roughly plus or minus two Earth days from lunar "noon"), T is then 380 K, or 107 degrees C. At 60 degrees, the temperature is still 331 K or 58 degrees C. At 75 degrees we reach about 281 K or 8 degrees C. At 85 degrees the equilibrated temperature drops to 214 K or -59 degrees C. At the lunar poles there are believed to be regions which never receive direct sunlight. If they don't receive significant warming from higher elevation surfaces that are in direct sunlight, they would be equilibrated only with the thermal background radiation of deep space at 2-3 K (-270 degrees C), and would likely form cold traps holding volatile materials. During the night the surface temperature drops further as the rocks radiate away the energy they've absorbed during the day time, with regions near the lunar equator dropping to about 120 K or -150 degrees C by the end of the night. The temperature drop is limited by conduction of heat from layers several meters below the surface, which maintain a roughly steady average temperature that can also be determined from the Stefan-Boltzmann law. In this case 'I' represents the incoming solar energy averaged over a full day-night cycle Iave = 1366cos(θ) / πW / m2 so at the equator T is about 296 K, or a comfortable 23 degrees C if you bury yourself sufficiently. At 60 degrees that drops to 249 K or -24 degrees C. The average subsurface temperature near the poles (85 degrees and higher) would be below 160 K or -110 degrees C. This article is a physics stub. You can help Lunarpedia byit.

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Convection is the way heat travels through liquids and gases. The molecules of liquids and gases are not tightly packed. There are spaces between the molecules. This means that the molecules can move from place to place. The molecules closest to the heat get hot first. They vibrate faster. They also move. They move away from the heat. Cooler molecules move in and take their place. The cooler molecules are heated. then they move away. Other molecules move in to take their place. This happens over and over again. Little by little, all the molecules in the gas or liquid are heated . The molecules that were first heated cool a bit. Then they move back toward the heat and are heated again. This happens over and over - heating, cooling, and then re-heating. The passing along of heat by moving molecules is called convection. Only gases and liquids are heated by convection. The up-and-down movements of gases and liquids due to uneven heating are called convection currents. Convection currents are responsible for our weather. In addition, convection occurs deep within the earth helping to shape our earth. We did the "Convection Snake" and the "Spot Drop" activity in class to help explore convection.

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Axial tilt is an astronomical term regarding the inclination angle of a planet's rotational axis in relation to a perpendicular to its orbital plane. It is also called axial inclination or obliquity. The axial tilt is expressed as the angle made by the planet's axis and a line drawn through the planet's center perpendicular to the orbital plane. The axial tilt may equivalently be expressed in terms of the planet's orbital plane and a plane perpendicular to its axis. In our solar system, the Earth's orbital plane is known as the ecliptic, and so the Earth's axial tilt is officially called the obliquity of the ecliptic. The Earth has an axial tilt of about 23 degrees 27’. The axis is tilted in the same direction throughout a year; however, as the Earth orbits the Sun, the hemisphere (half part of earth) tilted away from the Sun will gradually come to be tilted towards the Sun, and vice versa. This effect is the main cause of the seasons (see effect of sun angle on climate). Whichever hemisphere is currently tilted toward the Sun experiences more hours of sunlight each day, and the sunlight at midday also strikes the ground at an angle nearer the vertical and thus delivers more heat.

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What are Riparian Zones and Vegetation? The edges of wetlands, creeks and drainage lines are commonly referred to as riparian zones. Riparian zones adjoin or directly influence a body of water and include land alongside small creeks and rivers, river banks, gullies and dips (which sometimes flow with water), as well as around lakes, wetlands and river floodplains that interact with the river in times of flood. The riparian zone can extend from several to hundreds of metres, depending on the water body. Riparian zones occur whether the water bodies are both permanent or temporary (for example many wetlands experience natural drying out periods). They also occur whether the water body is natural or artificial (a farm dam). Riparian areas contain specialised vegetation communities adapted to the moist conditions (eg. rainforest species, sedges, and species such as mangroves and saltmarsh that are adapted to flooding of freshwater or saline water). Many of these vegetation communities are sensitive to disturbance, vulnerable to weed invasion and are not well adapted to fire. The Importance of Riparian Zones and Vegetation Riparian zones are important habitat and breeding areas for native animals and plants. In a predominantly cleared landscape, riparian lands also provide wildlife corridors and refuge for animals in times of drought. Forming a link between land and water ecosystems, riparian lands are very important in slowing water velocity, stablising streambanks, and reducing erosion. Riparian vegetation acts as a water filter and is important in maintaining water quality, and nutrient and algal growth. Special attention should be given to the protection and management of riparian zones to prevent soil erosion and to protect and improve water quality. Environmental Issues and Riparian Zones Creeks, streams and rivers are dynamic entities that are continually changing in response to natural and human activities. Waterways are constantly shifting within their current channels and making adjustments across their floodplains. Use of riparian lands should recognise that it can be financially or physically impractical to stop these natural changes. The removal of native vegetation within catchments has caused major change to the way water moves through the landscape. Native vegetation once slowed the flow of water, allowing it to percolate through the soil and feed streams between rainfall events. The loss of native vegetation however has caused water to move quickly to drainage lines (including creeks and rivers) during rainfall. This increases the volume and velocity of flows during and shortly after rainfall events leading to higher rates of erosion including bank under-cutting and slumping, and stream bed erosion. These processes are particularly severe in areas where riparian vegetation has been degraded by clearing, stock grazing, and weed invasion. The removal of large woody debris in many streams, undertaken in the belief that this would reduce flooding, has also contributed to unstable streambanks. Large woody debris include masses of vegetation such as full trees, shrubs, trunks, branches, tree heads or root masses, which have been washed into rivers, streams, or onto the floodplain. Large woody debris is very important in slowing the velocity of streams, reducing overall erosion and improving structural stability. The localised erosion that can occur around large woody debris is important for the ecology and structural diversity of streams and rivers, and forms essential habitat and breeding areas for aquatic animals such as fish and terrestrial animals such as birds. Protecting Riparian Zones and Vegetation There are a number of ways you can protect riparian lands and riparian vegetation, to benefit native wildlife and property productivity. They include: - Revegetating banks and riparian areas, using a variety of native plant species (trees, shrubs, herbs and grasses) - Fencing to restrict stock access to waterways and drainage lines using fencing. Stock watering can be provided through alternative off-stream watering points - Controlling noxious and environmental weeds - Seeking professional advice prior to attempting any works to prevent or repair erosion. This can be provided through the Hunter-Central Rivers Catchment Management Authority, Local Council, Landcare, or the Department of Environment and Climate Change - Not removing sand or gravel (any such activity requires permission from the New South Wales Department of Environment and Climate Change)

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A science fair is a competition where students present their results from their science fair projects . Results can be shown in a number of different ways such as in a report, with a model or display board or using whatever else the student may have created. Science fair projects are wonderful opportunities for you to let your imagination soar. You conduct the research and learn about things that you find interesting. For example, how does a volcano erupt? You can actually build a volcano and make it erupt. Science can be fun and it is all around us. It is important for you to choose a science fair topic that really interests and excites you. You will have more fun and you will be more motivated to do the necessary work in order to do a good job. When you plan your project you need to give yourself plenty of time to conduct the research as well as to observe and analyze things. It is good to ask questions about your project but make sure you actually do the work yourself. Doing your own work provides you with a much greater understanding of what actually occurred during the experiment. Finally don't worry if your hypothesis is not correct. Some of the most important experiments throughout history did not prove the original hypothesis. What is a Science Fair Project? A science fair project uses research and planning followed by a scientific method to discover the answer to a specific question. Scientists use different scientific methods as tools to answer questions. Steps involved with scientific methods include: the identification of a problem; declaring a hypothesis; researching the question; doing the experimentation for the project; and determining a conclusion. Research begins as soon as your topic has been selected. It is best to create a catchy yet specific title in order to gain people's attention. Questions make good titles as well the following suggestions: The Study of; An Investigation of; The Observation of; The Effects of; or The Comparative Study of. The problem you are studying is the question which you are seeking the answer to. Your hypothesis is your guess as to what you believe is going to happen. Project experimentation involves actually testing your hypothesis. You experiment to test to see if your hypothesis is correct. Everything you do should be recorded. You need to make observations and then write down the results. Graphs, charts and photographs are all good ways to document things you have done in a way that others can easily understand. Variables are things which affect your experiment. There are different kinds of variables. Controlled variables are ones that do not change. A variable which you change on purpose is an independent variable. A variable that you are observing which changes because of the independent variable is called a dependent variable. Finally, your conclusion sums up everything that you have learned through your experiment. You thoroughly examine the data and decide if you were correct with your hypothesis. You also determine if more work is necessary and what else you could do to investigate this problem. How to Choose a Science Fair Project A great way to decide on a science fair project topic is to create a list of your favorite subjects and activities. Choose your topic from one of these favorite areas. Try to find inexpensive and easy to find materials for your project. It is good to use materials that you can find in your home. Where are good places to research your project? The public library and your school library are both great options for research. Tips for a Great Display It is a good idea to talk to your teacher to find out if there are special guidelines for your school regarding the shape, style and size of your display. Try to keep your displays as simple as possible with only the essentials. Try not to include lengthy descriptions. Let your headlines tell the story and peak interest in your viewers. Checking your spelling is important because you don't want any spelling errors to take away from your project and your hard work. Be as neat as you can and use a computer if possible to print things such as labels, charts and graphs. If using a computer is not an option merely use a stencil and a ruler to make your project neater. If you use a pencil be sure to use a dark marker to go over the lines so people can easily see them. If you can it is a good idea to use color in order to clarify or highlight information such as in graphs, diagrams or charts. Drawings and photographs are very helpful to document exactly what you did. If your project needs anything special such as electricity make certain you let your teacher or the chairperson for the science fair know as early as possible so they can plan accordingly. Be sure that all of your project materials meet school safety standards. Only use materials that are durable and safe. It is also a good idea to have brochures or magazine articles relating to your project in front of your display. If you follow these tips your science fair project will truly be exceptional. The following links all have to do with things such as how to create quality science projects, ideas for experiments and other important and relevant information. - Make a Science Fair Splash: The Dragonfly TV website is filled with great science fair project ideas and includes questions asked, experiments tried and conclusions. - Try Science Experiments: The Try Science website provides experiment ideas such as animal attraction. - Google Science Fair: This website is actually an online science competition with prizes for children ages 13 to 18. - Reeko's Mad Scientist Lab: The website offers science experiment ideas such as a homemade volcano or a hover craft, science resources and other fun stuff. - Science Fair Project Resource Guide: The website provides information and links on each step of the project process as well as hints, tips, tools and research. - Science Fair Adventure: This website not only provides experiment ideas but also allows you to search topics by science category such as chemistry, biology or physics among many others. - Science Fair-An Experiment in Science, Space and Discovery: Science Fair is by USA Today and discusses scientific news such as planets bouncing between two stars. - Science Projects: The website explains what is needed for a good science project and then offers project ideas according to categories such as solar projects or wind energy projects. - Crystal Clear Science Fair Projects: The website provides information on where to begin, topic ideas, planning, completion and where to find science kits. - What Makes a Good Science Fair Project?: The article discusses what goes into making a science project an exceptional one. - Science Fair Resources: The website provides great links to information you can use for science fair projects. - Clubs and Science Fairs: The website focuses on psychological research for science fairs as well as providing different science fair information and resources. - Do Science: The website offers science activity ideas and science assistance. - Selected Internet Resources-Science Fair Projects: The website provides links to science fair related websites. - Science Fair Projects 13.01: The article explains how to do a science project, plan the project, choose a topic, use literature to search for a topic and many other important subject areas. - Science Fair Project Ideas: The website provides project ideas by grade or by subject area. - Science Fair Ideas by Science Bob: The website offers science fair ideas, information on the scientific method, resources and advice. - Science Project by Grade: The website has many science project ideas listed by grade or by subject matter. - Science Experiments: The website provides science experiment ideas such as how your lungs work. - Over 400 Science Fair Projects: The website offers science fair projects which include: material's list, scientific method overview, judge's insights, display guide and presentation tips. - Science Fair Project Ideas by USGS: The website provides information on earthquake science project ideas such as earthquakes on other planets. - Sci4Kids: The website features agricultural science fair projects from beginning to end. - Goddard Space Flight Center: The NASA website features information on earth science, flight projects and sciences and exploration. - Science Experiments You Can Do: The website provides fun project ideas such as making slime, a lumina box and a giant air cannon. - Science Fair Projects-Government Sites: The website offers links to different government sites with science projects as well as other resources. - Exploratorium Science Snacks: Exploratorium's Science Snacks are actually miniature versions of some of their most popular exhibits such as the anti-gravity mirror. - Science Fair Experiments: The website offers a guide to planning a science fair project, a cartoon about preparing for a science fair, and experiments according to grade. - Science Fair Projects-A Resource For Students and Teachers: The website provides links regarding science fair projects along with useful tool links. - Free Science Fair Projects: The website provides project information by category and offers a miscellaneous section with projects such as making electricity from fruits. - Science Fair Central: The website explains how to get started, different types of projects, presentations and provides parental resources. - Science Fair Projects Online: Projects are separated into grades K through 7 and 8 to 12. The website provides step-by-step blueprints, suggested materials, instructions, tips and scientific method. - Steps of the Scientific Method: The website discusses the various steps of the scientific method and also offers project ideas and other information. - Science Fair Project Guidebook (PDF): The PDF explains what a science fair project is and provides tips regarding projects as well as offering individual energy project instructions. - Basic Projects: The Sloan Digital Sky Survey/SkyServer website offers numerous astronomy-related project ideas such as types of stars. - Science Projects by the U.S. Department of Energy: The science project ideas on this website are nuclear science experiments such as radioactive or not.

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Stars like our Sun don't die through a supernova. Instead, after they exhaust their usable nuclear fuel, they shed their outer layers. This forms the beautiful clouds known as planetary nebulae, while the remaining core becomes a white dwarf. The mechanism by which stars jettison most of their mass has proven difficult to measure, since obtaining good data on the region close to stars is technically very challenging. Using the Very Large Telescope (VLT) in Chile, astronomers have now measured the light scattered off the ejected matter from three stars nearing the end of their lives. As they describe in Nature, Barnaby R. M. Norris et al. found that huge, late-life stars known as asymptotic giants form large dust grains close to their surfaces, which are then driven outward by photon scattering. This finding has interesting implications for the seeding of interstellar space with the raw ingredients for forming new star systems. When a star like our Sun nears the end of its life, the nuclear fusion that makes it shine runs at an accelerated rate. This excess energy inflates the outer layers of the star—called the envelope—so that it becomes huge, even as the surface temperature drops. While in this asymptotic giant (sometimes known as red supergiant) phase, stars are unstable: their surfaces pulse in and out. When the star is at its largest, standard astronomical models indicate that the temperature is low enough that heavier atoms (notably silicon) in the envelope can cluster to form dust grains. Lower-mass stars (including the Sun) aren't able to create elements more massive than oxygen in their cores. However, the envelopes of typical stars contain heavier elements including magnesium, silicon, calcium, and iron, that were produced in earlier, much more massive stars that then exploded. But there aren't enough supernovas going off to create the distribution of stuff we see, so mass shed by lower-mass stars must be responsible for the remainder. The dust clouds produced by these stars are an important part of the continuing cycle of star birth: cold dust clouds form the environment in which new stars can form. However, the mechanism that liberates the dust from the dying star that produced it isn't clear. Dust grains containing iron don't move much when they absorb photons, meaning they stick close to the star rather than spreading out into interstellar space. The new observations by Norris et al. provide a way out of this difficulty. They measured light from three asymptotic giant stars (W Hydrae, R Doradus, and R Leonis). The polarization of the light enabled them to separate the light from the star itself (which is unpolarized) from photons scattered off dust grains near the surfaces (which is polarized). They determined that there are shells of dust very close to the surface, with grains of relatively large size: approximately 600 nanometers in diameter. Since these grains aren't obscuring the star's light, they must be mostly transparent in visible wavelengths, which limits the possibilities for their chemical composition. Putting all this information together, the astronomers concluded that the grains must be iron-free silicates such as forsterite (Mg2SiO4) and enstatite (Mg2SiO4), found in interstellar dust clouds. Even though dust formed from these molecules is transparent to visible light, photons still scatter off them, giving them a bit of momentum, which they pass along to lighter gas molecules. This phenomenon provides a good understanding of the flow of particles away from the surface of stars. Since mass loss by stars like our Sun contributes to the environment of interstellar space, knowing how asymptotic giants shed their envelopes is an important part of comprehending the cycle of star birth and death. The new observations by Norris et al. help enhance this comprehension.

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Unlike Earth, Mars lacks a thick atmosphere and a magnetic field. This leaves the planet totally vulnerable to radiation from space. The Mars radiation comes from many sources: the Sun’s solar wind, cosmic rays from the Sun, and other stars. Life on the surface of Mars would be exposed to a constantly high dose of radiation, and the occasional lethal blasts that come regularly from strong solar flares. NASA’s 2001 Mars Odyssey spacecraft was equipped with a special instrument called the Martian Radiation Experiment (or MARIE), designed to measure the radiation environment around Mars. Since Mars has that thin atmosphere, radiation detected by Mars Odyssey would be roughly the same as the surface. Over the course of about 18 months, Mars Odyssey detected ongoing radiation levels which are 2.5 times higher than the astronauts experience on the International Space Station – 22 millirad per day. The spacecraft also detected 2 solar proton events, where radiation levels peaked about 2,000 millirads in a day, and a few other events that got up to about 100 millirads. Human explorers to Mars will definitely need to deal with the increased radiation levels on the surface of Mars. To protect against the radiation, long term colonists on Mars will need to build their bases underground – just a little Martian soil will prevent the Mars radiation exposure. If you want, learn more about the MARIE instrument on board NASA’s Mars Odyssey spacecraft, and the radiation risks humans will face trying to go to Mars. Finally, if you’d like to learn more about Mars in general, we have done several podcast episodes about the Red Planet at Astronomy Cast. Episode 52: Mars, and Episode 91: The Search for Water on Mars.

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A force may be thought of as a push or pull in a specific direction. This slide shows the forces that act on the Wright airplane in flight. Weight is a force that is always directed toward the center of the earth. The of the force depends on the mass of all the airplane parts, plus the amount of fuel, plus the pilot. The weight is distributed throughout the airplane. But we can often think of it as collected and acting through a single point called the center of gravity. In flight, the airplane about the center of gravity, but the direction of the weight force always remains toward the center of the earth. During a flight, the airplane's weight constantly changes as the aircraft consumes fuel. To make an airplane fly, we must generate a force to overcome the weight. This force is called the lift and is generated by the motion of the airplane through the air. Lift is an aerodynamic force ("aero" stands for the air, and "dynamic" denotes motion). Lift is directed perpendicular (at right angle) to the flight direction. As with weight, each part of the aircraft contributes to a single aircraft lift force. But most aircraft lift is generated by the wings. Aircraft lift acts through a single point called the center of pressure. center of pressure is defined just like the center of gravity, but distribution around the body instead of the As the airplane moves through the air, there is another aerodynamic force present. The air resists the motion of the aircraft; this resistance force is called the drag of the airplane. Like lift, there are many factors that affect the magnitude of the drag force including: And like lift, we often collect all of the individual components' drags and combine them into a single aircraft drag magnitude. The direction of the drag force is always opposed to the flight direction, and drag acts through the center of pressure. To overcome drag this airplane has a pair of propellers to generate a force called thrust. The propellers are turned by a small mounted on the top of the It is often confusing to remember that aircraft thrust is a reaction to the air being pushed to the rear by the propellers. The air goes to the back, but the thrust pushes towards the front. Action <--> reaction is explained by Newton's Third Law of Motion. of the airplane through the air depends on the relative strength and direction of the forces shown above. If the forces are balanced, the aircraft velocity. If the forces are unbalanced, the aircraft accelerates in the direction of the largest force. You can view a short of "Orville and Wilbur Wright" explaining how the four forces of weight, lift, drag and thrust affected the flight of their aircraft. The movie file can be saved to your computer and viewed as a Podcast on your podcast player. - Re-Living the Wright Way - Beginner's Guide to Aeronautics - NASA Home Page

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8th Grade Worksheets The worksheets below will help you when you are tutoring your children on 8th Grade Math where the focus is on three main areas: and reasoning with expressions and equations; - understanding and using functions; - geometry including similarity, congruence, angles, and Pythagoras' Theorem. The math worksheets and other resources below are listed by subject. They have been categorized at the 8th Grade level based on the Common Core Standards For Mathematics. You can learn more about these standards here. 8th Grade Math Worksheets Expressions and equations Other 8th Grade Related Math Resources Click below for more math worksheets at adjacent grade levels. You'll find help with fractions, including games and a fraction calculator in the fraction section.

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You have been familiar with binary operations since the early days of school. A binary operation is simply a rule for combining two objects of a given type, to obtain another object of that type. Through elementary school and most of high school, the objects are numbers, and the rule for combining numbers is addition, subtraction, multiplication or division. In your precalculus and calculus courses, you encountered a situation where the objects were functions, and composition was the rule for combining two functions. The concept of a binary operation is a very general one, and need not be restricted to sets of numbers. In fact, an operation can be specified on any finite set simply by presenting a table that shows how the operation is performed, when your are given two elements of the set. For example, consider the set and an operation, denoted by *, defined by the following table: Not All Operations Have the Same Properties You should be familiar with various properties of the arithmetic operations on numbers. Addition of numbers, for instance, is a commutative operation -- meaning that for all numbers x and y. The operation on the set A defined by the operation table above, however, is not commutative, and there are several instances of this lack of commutativity. For instance, since the table shows that . In general, commutativity is a property of an operation, so it takes only one instance of lack of commutativity to spoil that property for the operation. It is easy to check whether an operation defined by a table is commutative. Sinply draw the diagonal line from upper left to lower right, and then look to see if the table is symmetric about this line. In the illustration below, we see a lack of symmetry: the table entries colored yellow do not match, and the table entries colored blue do not match. Addition of numbers is an associative operation, meaning that for all numbers x, y and z. To check to see whether the operation * defined above is associative, however, is a somewhat tedious task. We would need to compute all combinations of the form in two ways -- once as shown, and then again in the form -- and then check to see that they are equal. This must be done for each selection of elements to fill the placeholders. In the case of a 4-element set such as A above, there are choices of the elements to be used, and each must be computed in two ways. Thus, to verify that a binary operation on a 4-element set is associative, we would have to do 128 computations! There is no easy shortcut as there is for checking commutativity. On the other hand, if a given operation fails to be associative, all we need to do to verify this is to find one instance of the lack of associativity. For the operation * defined on the set above, we find that , while . Thus , so the operation * is not associative. An additional property that a binary operation may or may not have is the existence of an identity element. Given a binary operation on a set S, an element e of S is called an identity element for if for every element x of S. (We are using the symbol to represent a generic binary operation here.) As examples, 0 is an identity element for the operation of addition on the set of real numbers, and 1 is an identity element for the operation of multiplication on the set of real numbers. For the operation * on the set A above, the element a is an identity element. As another example, let denote the set of all functions from to (where denotes the set of real numbers), and let be the operation of composition of functions in . Then is an associative operation, since for all functions f, g and h in . But is not a commutative operation; there are many examples of functions f and g for which . (Can you find such an example?) Does the operation on have an identity element? The function defined by f(x) = x for all real numbers x (which happens to be called the identity function) has the property that for all functions g in , and therefore f is an identity element for the operation on . One easy fact about identity elements is that if an operation has an identity element, then that identity element must be unique -- that is, there is only one such identity element. To see why this is true, we suppose that there are two identity elements for the operation on the set S, say e and . Then consider the element . Since is an identity, we have , and since e is an identity, we have . Thus , so there is only one identity for . The field of mathematics in which binary operations and their properties are studied is called abstract algebra. In abstract algebra, a semigroup is defined to be a set, along with a binary operation that is associative. Examples of semigroups include the following: Examples of sets that are not semigroups include

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In this Lesson, we will answer the following: Here is an elementary example: one half of 1. As fractions of a unit of measure, equivalent fractions are equal measurements. (Compare the theorem of the same multiple; for, a numerator has a ratio to the denominator. Every property of ratios applies to fractions. From the viewpoint of comparing fractions, however, see Problem 2 of that lesson.) Answer. For example, To create them, we multiplied both 5 and 6 by the same number. First by 2, then by 3, then by 10. (Compare Lesson 20, Problem 2c.) Example 2. Write the missing numerator: Answer. To make 7 into 28, we have to multiply it by 4. Therefore, we must also multiply 6 by 4: In practice, to find the multiplier, mentally divide the original denominator into the new denominator, and then multiply the numerator by that quotient. That is, say: "7 goes into 28 four times. Four times 6 is 24." The student who has studied ratio and proportion Example 3. Write the missing numerator: Answer. "8 goes into 48 six times. Six times 5 is 30." In actual problems, we convert two (or more) fractions so that they have equal denominators. When we do that, it is easy to compare them (see the next Lesson, Question 3), and equal denominators are necessary in order to add or subtract them (Lesson 25). For we can only add or subtract quantities that have the same name, that is, that are units of the same kind; and it is the denominator of a fraction that names the unit. (Lesson 21.) Now, since 15, for example, is a multiple of 5, we say that 5 is a divisor of 15. (5 is not a divisor of 14, because 14 is not a multiple of 5.) 5 is also a divisor of 20. 5 is a common divisor of 15 and 20. (15 and 14 have no common divisors, except 1, which is a divisor of every number.) Answer. The denominators 3 and 5 have no common divisors (except 1). Therefore, as a common denominator, choose 15. Once we convert to a common denominator, we could then know denominators, then the larger the numerator, the larger the fraction. (Lesson 20, Question 11.) Also, we could now add those fractions: See Lesson 21, Example 3. We can choose the product of denominators even when the denominators have a common divisor. But their product will not then be their lowest common multiple (Lesson 23). The student should prefer the lowest common multiple because smaller numbers make for simpler calculations. When fractions are equivalent, their numerators and denominators are in the same ratio. That in fact is the best definition of equivalent fractions. 1 is half of 2. 2 is half of 4. In fact, any fraction where the 1 is half of 2. 2 is half of 4. 3 is half of 6. 5 is half of 10. And so on. These are all at the same place on the number line. a third of its denominator. Example 6. Write the missing numerator: Answer. 7 is a quarter of 28. And a quarter of 16 is 4. 7 is to 28 as 4 is to 16. How to simplify, or reduce, a fraction The numerator and denominator of a fraction are called its terms. To simplify or reduce a fraction means to make the terms smaller. To accomplish that, we divide both terms by a common divisor. We like to express a fraction with its lowest terms because it gives a better sense of its value, and it makes for simpler calculations. Answer. 15 and 21 have a common divisor, 3. Or, take a third of both 15 and 21. Answer. When the terms have the same number of 0's, we may ignore them. Effectively, we have divided 200 and 1200 by 100. (Lesson 2, Question 10.) Solution. Divide 20 by 8. "8 goes into 20 two (2) times (16) with 4 left over." Or, we could reduce first. 20 and 8 have a common divisor 4: Notice that we are free to interpret the same symbol "the ratio of 20 to 8." Any fraction in which the numerator and denominator are equal, is equal to 1. At this point, please "turn" the page and do some Problems. Continue on to the next Section. Please make a donation to keep TheMathPage online. Copyright © 2015 Lawrence Spector Questions or comments?

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Here you'll review how to perform the basic operations of addition, subtraction, multiplication and division with real numbers. All of these operations will then be applied to the order of operations. You will also learn how to express a fraction as a decimal and a decimal number as a fraction. Finally, you will represent real numbers on a number line. You reviewed how to add real numbers using two rules: - Real numbers with unlike signs must be subtracted and the answer will have a sign the same as that of the higher number. - Real numbers with the same sign must be added and the answer will have a sign the same as that of the numbers being added. Then you reviewed how to subtract real numbers by adding the opposite. You learned that a number has both direction and magnitude. The direction of a positive number is to the right and that of a negative number is to the left. This direction is determined by the numbers location with respect to zero on the number line. The magnitude of a number is simply its size with no regard to its sign. Next you reviewed multiplication and division of real numbers using the following rules: - The product/quotient of two positive numbers is always positive. - The product/quotient of two negative numbers is always positive. - The product/quotient of a positive number and a negative number is always negative. You reviewed the standard order of operations represented by the letters PEMDAS. - P – Parenthesis – Do all the calculations within parenthesis. - E – Exponents – Do all calculations that involve exponents. - M/D – Multiplication/Division – Do all multiplication/division, in the order it occurs, working from left to right. - A/S – Addition/Subtraction – Do all addition/subtraction, in the order it occurs, working from left to right. - S – Subtraction – Do all subtraction, in the order it occurs, working from left to right. Next you learned how to distinguish between a terminating decimal number and a periodic decimal number. You were also shown that a given fraction can be changed to a decimal number by long division. Last you revisited the real number system . The real number system is made up of rational and irrational numbers. The rational numbers include the natural numbers, whole numbers, integers and rational numbers. The natural numbers are the counting numbers and consist of all positive, whole numbers.

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The covalent bonds that hold complex molecules together can come in different forms. Atoms like carbon, nitrogen, and oxygen can form both single and double bonds, sharing two or four electrons. Nitrogen and carbon can even form a triple bond, sharing six. And those are some of the simpler ones. A mixed series of single and double bonds, like those found in benzene, can end up creating a diffuse electron cloud, so that each of the bonds has an odd number of electrons. The exact strength of these bonds depends strongly on the context of the surrounding molecule. It's possible to get a variety of information about these bonds. We could calculate what their energy is, probe them with chemical reactions, and could even detect the difference in bond strength by imaging the structure of a crystalized population of molecules. But now, a consortium of researchers in Europe have figured out how to use a modified form of atomic force microscopy to examine the strength of chemical bonds in a single molecule. The rules of covalent bonds are, at least on the surface, quite simple. The more electrons that are shared, the stronger the bond. And the stronger the bond, the closer together the two atoms on either end of it will be. As we said above, though, things get complicated when there is a mixture of single and double bonds, which can create a set of delocalized electrons. The simplest form of this is a benzene ring, which has six carbon atoms arranged in a circle, linked by three single and three double bonds. In this case, the bonds all become equivalent, and each atom is linked by what you could consider 1.5 bonds, instead of a single or double. Things get even more complex when a benzene ring is embedded in a larger molecule, with other single and double bonds surrounding it. Take a buckyball, in which carbon atoms are linked in a set of interconnected five- and six-atom rings. The six atom rings have benzene-style alternating bonds, while the five atom ones are all linked through single bonds. So a given atom may be part of two benzene rings and a pentagon, all at the same time. Instead of nice, clean 1.5 bonds, these arrangements create fractional shared electrons, leading to very small differences in energy and distance between adjacent atoms. All of which makes detecting the difference that much more of an achievement. Standard atomic force microscopy relies on a needle with a single atom as a tip, and that's able to probe the electronic conditions in a molecule or surface. But it doesn't have enough resolution to detect differences in bond length. Instead, the team behind the new paper used a modified form, in which that single atom is capped by a carbon monoxide molecule, meaning the tip of the needle juts out by two extra atoms. This turned out to be critical. In a number of the samples, the difference in bond length is expected to be at or below the best resolution of atomic force microscopy. As the tip gets pressed down, the carbon monoxide molecule can flex out of the way, behavior that appears to amplify the length of the bond. As a result, the authors were able to discriminate down to bonds that differed by only 0.03 Angstroms (3.0 × 10-12 meters). The team started by imaging a buckyball, where they could see the difference in bonds between those in five and six membered rings. They then moved on to more complex molecules, such as the one shown on top. Aside from being an impressive technical achievement, the technique should open up a number of potential opportunities. Molecules that don't form crystals easily could be imaged with this technique, and the extremely precise control could allow researchers to inject electrons or probe chemical conditions at specific points in a single molecule. All of which could help provide a better understanding of the reactions and catalysts that we rely on for many of the basic materials we use every day.

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One big advantage to a helicopter’s rotor system is the vertical thrust that allows the aircraft to hover. However, when this same rotor system is flown edge wise through the air it creates an aerodynamic problem that limits the helicopter’s forward speed. The term used to describe this is dissymmetry of lift. To generate lift a helicopter’s rotor blades spin to create airflow. A rotor system’s RPM is fixed at a certain value for all phases of normal flight and increasing the blade’s angle of attack (the angle between the relative wind and the blade’s cord line.) with the collective control generates lift. In a hover with no wind, lift is essentially equal across the entire rotor disc. However, as the helicopter begins to move forward it creates a relative wind. One side of the rotor disc has a blade that is advancing into the relative wind (think headwind) and the other side has a blade that is retreating (think tailwind). The difference in airspeed each blade encounters between the two sides grows as the helicopter gains forward speed. This creates an imbalance of lift problem that early helicopter engineers had to solve to maintain controllability. To help understand how they did it, consider the equation for lift. Lift = CL ½ p S V2 CL = Coefficient of Lift, which is a function of angle of attack and blade shape p = air density S = total blade area V = airspeed At a given moment in time, air density, total blade area and blade shape are all fixed values, so as each blade’s airspeed changes the rotor system must respond by changing the blade’s angle of attack to keep total lift constant. This is done primarily by allowing the blades to move up or down in a process known as flapping. Two bladed rotor systems (known as semi-rigid) use a single teetering hinge that allows the blades to flap as a unit (one go up, the other goes down). Rotor systems with more than two blades (typically known as fully articulated) use a flapping hinge on each blade allowing the blades to move up or down independently of each other. How flapping works is by changing the angle of attack in response to the varying airspeeds the blade encounters as it moves around the rotor disc. When the advancing blade experiences a higher airspeed, the lift on that blade increases forcing it to move up. This upward movement changes the direction of the blade’s relative wind reducing its angle of attack. On the retreating side just the opposite happens. The reduced airspeed causes a decrease in lift causing the blade to move down, increasing its angle of attack. Each blade’s angle of attack changes in direct relation to its relative airspeed. As each blade’s relative airspeed increases, angle of attack decreases and vice versa to maintain equal lift across the disc as the helicopter’s airspeed increases. As you might have guessed, this creates a problem on the retreating side. You can only increase an airfoil’s angle of attack so much before it stalls. As the helicopter continues to fly faster the retreating side must continue to increase its angle of attack to compensate. At some airspeed the retreating blade stalls and this is what limits the helicopter’s forward airspeed. This is referred to as retreating blade stall. There is more to discuss on this subject so part 2 is coming up next time.

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Look at the pictures of the scales below. Can you write equations to represent what you see on each scale? Can you figure out the weight of the green block? Can you figure out the weight of the blue block? In this concept, we will learn how to work with equations that represent what we see on scales. In order to solve the problem above, we can write equations to represent what we see on each scale. We know that if we add the weights of each of the blocks on one scale together, the total weight must be the same as the number on the scale. If we look at the scale on the left, we see that there are two green blocks that weigh 8 pounds total. An equation would be: There is another way to think about the equation. This means, I could also write the equation as: In the following examples, we will practice writing equations in different ways and matching equations with scales. Fill in the number to finish the equation: On the left side of the equation we see three 3 blocks. This means, we need a 3 on the right side of the equation next to the red block. The equation should look like this: Circle the equation that matches the scale: On the scale we see two red blocks and one yellow block. They add up to 20 pounds. The correct equation should have 2 red blocks and one yellow block. The correct equation is Eric wrote these equations from pictures of scales. Use Eric’s equations. Find the weight of each block. From the first equation we can see that 2 blue blocks weigh 6 pounds. This means that each blue block is 3 pounds. From the second equation we can see that one yellow block and one blue block together weigh eight pounds. Since we know that the blue block is 3 pounds, we have this equation: , we know that the yellow block must be 5 pounds. Here is our final answer: Concept Problem Revisited We can use problem solving steps to help: In math, an is a letter that stands for a number that we do not yet know the value of. In this concept, the blocks that we did not know the weights of were is a math sentence that tells us two quantities that are equal. In this concept, we wrote with unknowns to represent what we saw on the scales. 1. Write equations for each scale. Figure out the weight of each block. 2. Fill in the numbers to make an equation. 3. Circle the equation that matches the scale. 4. Eric wrote these equations from pictures of scales. Use Eric’s equations. Find the weight of each block. For each of the following, write equations. Figure out the weights of the blocks. Fill in the numbers for problems 6-9. Circle the equation that matches the scale for problems 10 and 11. Eric wrote these equations in problems 12 and 13 from pictures of scales. Use Eric’s equations. Find the weight of each block. For problems 14-16, write the block equation for each scale. Figure out the weights of the blocks.

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It's not surprising that it took so long. The stars are so far away that even the light from our hundred nearest neighbors takes up to twenty years to get here. In addition, we have to remember that we see Solar System planets by reflected sunlight. If we were 24 trillion miles away - the distance to the next star - even Jupiter would be submerged in the Sun's light. This means astronomers don't find extrasolar planets simply by pointing their telescopes at nearby stars. In fact, it was only in 2005 that we had the first image of an extrasolar planet. The technology for imaging has improved to the point that some three dozen extrasolar planets have been discovered by direct imaging. However that isn't many out of nearly two thousand. So how do they find the planets if they can't see them? Usually by detecting a planet's influence on its star. The method which had enabled the discovery of most of the extrasolar planets in the first fifteen years of discoveries is Doppler spectroscopy. It's also called the radial velocity method or, popularly, the wobble method. Think how the note of an emergency vehicle's siren changes as it approaches and then passes you. When approaching, the vehicle overtakes the sound waves. This increases the frequency you hear, making the note higher. After it passes, the opposite occurs and the pitch drops. This is The Doppler effect applies to light waves too. The spectrum of approaching objects is blue-shifted, i.e., it's detected at a higher frequency. Objects moving away are red-shifted. Strictly speaking, planets don't orbit stars. There is a mutual gravitational attraction so that star and planet orbit their common center of gravity. This center is inside the star, so the interaction makes the star wobble slightly. If the orbiting planet causes the star to move alternately towards and away from us, a sensitive telescope may detect alternating blue and red shifts in the light spectrum. The frequency of the shifts shows the planet's orbital period and the size of the shifts tells us about the mass. In 1995 Swiss astronomers Michel Mayor and Didier Queloz discovered the first extrasolar planet orbiting a sun-like star. It was quite a surprise, for it had at least half the mass of Jupiter, but was in an closer orbit than Mercury's is to the Sun. This was the first of the "hot Jupiters". Hot Jupiters aren't the most common planets in the Galaxy, but they were the easiest to find. Massive and close to the star, their gravitational influence is maximized. And it doesn't take long for repeated observations to establish the orbital time. By contrast, Jupiter itself takes twelve years to orbit the Sun. However in 2010 half the discoveries were made by a different method - the transit method. A transit occurs when a planet crosses the disc of its star. This causes a tiny dip in the star's brightness. The size of the dip provides evidence of the planet's diameter, and the orbital period is determined from the timing of the dips. As there are many causes for variation in starlight, transits are confirmed by various follow-up methods. Ever since 2011 most of the discoveries have been through the transit method and most of these were made from data collected by the Kepler mission. In January 2015 the 1000th extrasolar planet discovery by Kepler was confirmed. NASA's Kepler mission, launched in March 2009, monitored a small, populous star field. Not being subject to distortion by Earth's atmosphere, its sensitive photometer was able to detect the transits of smaller planets. One of the mission goals was to find Earth-sized planets, and there are some possibles. Kepler's main mission ended in 2013 when a second stabilizer failed, leaving it unable to carry out precision targeting. However the vast amount of data collected is still being analyzed, and new discoveries continue to be made. In addition, in 2014 an ingenious solution was found that has allowed Kepler to start a new mission. There are images related to this article on my Pinterest board Extrasolar Planets.

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This lesson is the 3rd lesson for the unit outline which centers on of the necessity for rules. Students have had the opportunity to play a variety of games: physical, social, intellectual all the while discussing what makes a quality game. 5.7.5 Discuss the meaning of the American creed that calls on citizens to safeguard the liberty of individual Americans within a unified nation, to respect the rule of law, and to preserve the Constitution 5.7.3 Understand the fundamental principles of American constitutional democracy, including how the government derives its power from the people and the primacy of individual liberty. Students apply what they learn in the visual arts across subject areas. They develop competencies and creative skills in problem solving, communication, and management of time and resources that contribute to lifelong learning and career skills Common Core State Standards for ENGLISH LANGUAGE ARTS & Literacy in History/Social Studies, Science, and Technical Subjects K-5 College and Career Readiness Anchor Standards for Speaking and Listening K-5 Comprehension and Collaboration 1. Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively. 2. Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally. 3. Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric. After having the opportunity to play all the games, students will respond to the following question: Write about a rule that recurs throughout the games. What rules were the most important as well as what rules were unnecessary and why. Were there any unfair rules? If so, why was it unfair? Students might also write a letter to another group … 1. Teacher reviews types of games played over the past days and/or in their past focusing on what makes games successful. Chart 2. Teacher breaks students into groups (selective homogenous grouping by teacher). 3. Teacher hands out a prepared box of materials (dice, scarf, yarn, measurement tool, bin ) to each group of students. Allow exploration time. Teacher should be actively listening for comments to share with entire group. 4. Pose questions: What might I have given you these materials? Accept responses. Think about what we have been discussing and doing these past few days. Accept all responses. 5. Teacher then brings groups together. Invites students to create a game of their choice using 4/5 objects. Each group will follow the same guidelines but all will have different outcomes. Refer to chart in #1. 6. Show game guideline (see attached) 7. Students will need plenty of time to explore, discuss, create, brainstorm, review, revise. Teacher moves from group-group gauging progress, facilitating as needed. 8. It may be wise to continue lesson over two days in order to let students have quality time to think about the project (Rome wasn’t built in a day!) 9. Students complete game plan, share among the class with each group having the opportunity to play everyone else’s game. Special Needs of students are considered in this lesson: Teacher model, visual aids Outline of Unit Plan: Unit Name: Out of Many, One

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Region 8 Curriculum Unit 5th Grade Social Studies Enduring Understandings: Essential Questions: Freedom is not free, it is achieved through struggle and carries responsibilities. • What do you mean when you say you want to be free? • What are the responsibilities of freedom? • Who is responsible for bringing about change? A revolution is not always political or violent. • What is a “revolution”? It is usually the minority, not the majority who initiate change • Why do revolutions happen? Freedom of expression can bring about revolution • How do people achieve political freedom? • How do people achieve personal freedom? • Can you be free without freedom of expression?.back State Standards Learned: 1.2 LA: Answers literal and inferential questions about grade-appropriate books read aloud by the teacher and about own reading in context (at instructional level) 1.3 LA: Interprets text according to such features as character development, conflict/theme, and supports with data from the text. 3.3 LA: With some guidance, uses all aspects of a writing process in producing fluent compositions and reports, including taking responsibility for editing of spelling and mechanics 3.3 LA: Writes in complete and varied sentences 1.1 LA: Applies comprehension strategies when reading grade appropriate text (narrative, expository, poetry) and text structures (1.1) 1,2,4,SS: Read or locate primary sources of historical data, identify main ideas, and analyze their quality and meaning (1,2,4) 5.5 SS: Outline and detail the relationship between rights and responsibilities and the role of citizens and citizenship in that system 5 SS: Identify and explain the key documents that guide and outline our system of state and national government. 7 SS: Describe the role the Constitution plays in limiting the power of the government. . .........back Key Knowledge and Skills Learned: • The underlying causes of the American Revolution, including prior events that helped to bring about revolution. • The Boston Tea Party did not cause the American Revolution • The definition of revolution. • That there have been a variety of revolutions, including in industry, technology and the arts. • We have personal revolutions. • Opposing views of Whigs and Tories. • Meaning and intent of the 1st amendment to the U.S. Constitution • Who the “framers” were of the U.S. Constitution. • Why the Bill of Rights was added to the U.S. Constitution. • Discuss the personal responsibilities of freedom. • Read critically, and interpret, diverse points of view. • Empathize with and defend both the Whig and Tory viewpoints. • Identify Johnny Tremain’s character traits. • Identify and describe personal revolution • Empathize with Johnny. • Integrate new vocabulary into their writing. • Locate primary resources in print and on-line. .........back Performance Tasks/Authentic Assessments: Over the years, historians have learned quite a bit of history from personal journals left behind in attics, old trunks, and dresser drawers. These primary resources give us a firsthand look at the lives and history of people during other historical times. You are going to recreate such a journal. You are Johnny Tremain. Throughout your reading of the novel you will keep a journal of your (Johnny’s) experiences. The experiences that you describe should include those that are related to your personal life and those that are related to the political environment of pre-revolution Boston. Sometimes your personal experiences will be caused by the political environment. You should write these journal entries as if you are in Johnny’s shoes – write from your heart and show Johnny’s reactions to his experiences. Do not simply summarize events. Your journal entries should include specific examples of Johnny’s struggles for both personal and political freedom. You may include illustrations if they enhance Johnny’s sharing of his feelings. Once all of your journal entries are written, a classmate, friend, or other person who reads your journal should be able to understand the struggles that Johnny endured to become the person he is at the end of the book. Your journal should also reflect the historic period in which Johnny lived. You may use any font or style of presentation, but you must meet the guidelines of this assignment. If you type, please double space. If you hand write, please skip lines. Always keep the image in your mind of your journal being discovered in the dusty corner of an old colonial home. Perhaps in the attic, perhaps on a bookcase. What would you like the child who discovers your words on the yellowed and brittle pages to know about you/Johnny? Save all of your journal entries as they are returned to you. We will review them as a whole at the end of the unit. When you read them as a whole you will get to see the full picture of how you have interpreted Johnny’s development and the historical period. Your journal will be scored according to this rubric. Task #2 Final Essay Assignment: Select one of the essay assignments below. This essay assignment is an opportunity for you to reflect upon the Johnny Tremain novel as a whole. You should approach this assignment with much thought. Your essay should show that you understand Johnny and/or the historical period well. If you type this assignment, please double space. If you handwrite the assignment, please skip lines. We have spent time in class discussing Johnny’s personal struggle for freedom from the negative influences of personal pride. In chapter VII, scene 4, Johnny realizes that “the bright little silversmith’s apprentice was no more”. How do you think Johnny has changed by the end of the book? Has he achieved the personal freedom for which he struggled? Be sure to show how events and people in the novel contributed to the changes in Johnny. For instance, how does the injury to his hand help him to change? How does Rab help him to change? How does the political climate affect Johnny? You should look back through your journal entries to help you with this essay. Once again, take on the character of Johnny Tremain and write in the first person narrative. Use a friendly letter format and have Johnny write to one of the following people for the reason listed: • Priscilla: trying to convince her to marry him. • Paul Revere: trying to convince him to hire him. • His diary: as a final, reflective journal entry During class we discussed Sam Adams’ comment that “. . . without you printers the cause of liberty would be lost.” Please explain what you think Sam Adams means by this. How do you think beliefs such as his influenced the writing of the first amendment to the United States Constitution? Use specific examples from the book and from history. Please end your essay by describing two issues about which you feel very strongly and would be willing to speak out about despite obstacle or difficult consequences that might result. You should look back at the assignment called “That A Man Can Stand Up” to help you with ideas for this essay. Make sure that your essay reflects your feelings about free speech. You might want to write a letter to the editor of one of our local papers as a follow up to this assignment!Choice #3: We have talked in class about the conflict Johnny feels between his support for the Sons of Liberty and his ability to see the British soldiers as individuals, not just as targets. On page 201 is the following paragraph: That night, for one horrible moment he was glad his hand was crippled. He would never have to face the round eye of death at the end of a musket. For days he felt his own inadequacy. Was the ‘bold Johnny Tremain’ really a coward at heart? Please answer the question, was Johnny Tremain “really a coward at heart?”. When you write this essay, use a friendly letter format. Write either from your own perspective or from the perspective of one of the characters in the novel. Make sure you use examples from the book to support your ideas..........back Other Evidence of Learning: Letter to the Editor (perspective) Oral and written responses to essential questions Worksheets e.g. That a Man Can Stand Up. .........back - Have tea served for each student upon arrival for first class. Pose question: What caused the American Revolution? - Have the essential questions mounted on colorful paper and posted on bulletin board. - Work in small groups to brainstorm definition of “revolution” and types of revolutions. Have Beatles’ song “Revolution 1” playing. As a whole group, discuss responses. Ask, “Why do we have revolutions?” - Distribute the performance task assessments (journal, final essay) and rubrics. Review program expectations. - Review extra credit project choices, including researching and planning a Colonial Era tea party for the class. - Vocabulary worksheets for each weekly assignment. This is for purpose of expanding ability to communicate effectively ideas and feelings in journal entries. - Brainstorm pros and cons of personal pride. Discuss within small groups. Relate to Johnny Tremain and to personal experiences. - Literary elements worksheet discussion of character development. - Use literature circle format for some chapter discussions - Students write Letter to the Editor about the Boston Tea Party. Must write from either the Tory or the Whig perspective, as assigned by the teacher. Discuss tea party and its place in pre-revolution events. Ask, did you ever stop to consider yourself as a taxpayer? What can you do to have a say in the taxes you pay? - Mount a few words about contributing factors to the American Revolution on oak tag. Have students work in small groups to find out what each event was, put them in chronological order, and explain the event’s role in spurring the Revolution. (Seven Years’ War/French & Indian War; expulsion of French from N. America and India; political instability of King George III coupled with British debt; Stamp Act; establishment of colonial assemblies; Townshend Acts; Naviagation Acts/American Board of Customs; riot on June 21, 1768 in Boston; Boston Massacre; Tea Act; Coercive Acts – Boston Port Act, Quartering Act; alteration of colony’s charter; - enforced by Lt. Gage; Boston Tea Party; 1st Continental Congress; - Assign worksheet “That A Man Can Stand Up”, interpretation of quote by James Otis (historical character) in the novel. During class discussion, use to introduce reading and interpretation of the first amendment. - Use of primary resources and local history: role of Hebron native, Benjamin Trumbull during Revolutionary time; excerpt on American Revolution from Noah Webster’s 1797 publication, American Selection of Lessons in Reading and Speaking. Ninth Edition. (Chapter XXV, “A Sketch of the History of the late War in America); George Hewes’ first person description of the Boston Tea Party events and his involvement with it; In The Path of War: Children of the American Revolution and their Stories. - Have each student make a list of up to 4 things from which he or she would like to be free. Share within a small group and get ideas for “freeing yourself”.. .........back Teaching materials/Technology Integration:

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Introduction to Coordinate Geometry A system of geometry where the position of is described using an ordered pair of numbers. Recall that a plane is a flat surface that goes on forever in both directions. If we were to place a point on the plane, coordinate geometry gives us a way to describe exactly where it is by using two numbers. What are coordinates? To introduce the idea, consider the grid on the right. The columns of the grid are lettered A,B,C etc. The rows are numbered 1,2,3 etc from the top. We can see that the X is in box D3; that is, column D, row 3. D and 3 are called the coordinates of the box. It has two parts: the row and the column. There are many boxes in each row and many boxes in each column. But by having both we can find one single box, where the row and column intersect. The Coordinate Plane In coordinate geometry, points are placed on the "coordinate plane" as shown below. It has two scales - one running across the plane called the "x axis" and another a right angles to it called the y axis. (These can be thought of as similar to the column and row in the paragraph above.) The point where the axes cross is called the origin and is where both x and y are zero. On the x-axis, values to the right are positive and those to the left are negative. On the y-axis, values above the origin are positive and those below are negative. A point's location on the plane is given by two numbers,the first tells where it is on the x-axis and the second which tells where it is on the y-axis. Together, they define a single, unique position on the plane. So in the diagram above, the point A has an x value of 20 and a y value of 15. These are the coordinates of the point A, sometimes referred to as its "rectangular coordinates". Note that the order is important; the x coordinate is always the first one of the pair. For a more in-depth explanation of the coordinate plane see The Coordinate Plane. For more on the coordinates of a point see Coordinates of a Point Things you can do in Coordinate Geometry If you know the coordinates of a group of points you can: Information on all these and more can be found in the pages listed below. - Determine the distance between them - Find the midpoint, slope and equation of a line segment - Determine if lines are parallel or perpendicular - Find the area and perimeter of a polygon defined by the points - Transform a shape by moving, rotating and reflecting it. - Define the equations of curves, circles and ellipses. The method of describing the location of points in this way was proposed by the French mathematician René Descartes (1596 - 1650). (Pronounced "day CART"). He proposed further that curves and lines could be described by equations using this technique, thus being the first to link algebra and geometry. In honor of his work, the coordinates of a point are often referred to as its Cartesian coordinates, and the coordinate plane as the Cartesian Coordinate Plane. Other Coordinate Geometry entries (C) 2009 Copyright Math Open Reference. All rights reserved

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In fiction, the first-person narrator is usually distinct from the author. Understanding the differences, subtle or pronounced, between an author and the narrator he or she creates is essential to understanding a work of fiction. Help students understand how the point of view of the narrator and the point of view of the author are not the same. How does the author represent the narrator? Do they necessarily share common opinions, beliefs, or characteristics? Have students write a short description of the narrator of "The Scarlet Letter," drawing evidence from the introductory chapter and elsewhere in the book. Or you might have students write a short description of school life in the style of the novel's narrator. Another way to understand narrative perspective is to think about how "The Scarlet Letter" would be different if one of the other characters, such as Hester, Dimmsdale, or Pearl, were the narrator. Have students write a passage from the story from the perspective of one of these other characters. Help students to see Hawthorne in the context of his times, as a contemporary of Henry David Thoreau, Ralph Waldo Emerson, Louisa May Alcott, Frederick Douglass, Elizabeth Cady Stanton, Herman Melville, Margaret Fuller, Walt Whitman, and Abraham Lincoln. To what extent was he engaged by the transforming political and technological forces at work in his society, and to what extent was he (like the narrator of The Scarlet Letter) estranged from his times by an overriding attachment to the American past? To complete this study of Hawthorne's literary and literal lives, have small groups of students each read a Hawthorne short story from different periods in his later life. (Students can find appropriate stories on the Nathaniel Hawthorne website or in the library.) Ask each group to report on the narrative point of view represented in their story, citing passages from the text to support their views. Compare narrators from The Scarlet Letter and a short story. What is the point of view of each narrator? Why did Hawthorne choose these narrators? 2-3 class periods

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All conductors contain charge]]s which will move when an electric potential difference (measured in volts) is applied across separate points on the material. This flow of charge (measured in amperes) is what is meant by electric current. In most materials, the rate of current is proportional to the voltage (Ohm's law,) provided the temperature remains constant and the material remains in the same shape and state. The ratio between the voltage and the current is called the resistance (measured in ohms) of the object between the points where the voltage was applied. The resistance across a standard mass (and shape) of a material at a given temperature is called the resistivity of the material. The inverse of resistance and resistivity is conductance and conductivity. Some good examples of conductors are metal. Most familiar conductors are metallic. Copper is the most common material for electrical wiring (silver is the best but expensive), and gold for high-quality surface-to-surface contacts. However, there are also many non-metallic conductors, including graphite, solutions of salts, and all plasmas. See electrical conduction for more information on the physical mechanism for charge flow in materials. Non-conducting materials lack mobile charges, and so resist the flow of electric current, generating heat. In fact, all materials offer some resistance and warm up when a current flows. Thus, proper design of an electrical conductor takes into account the temperature that the conductor needs to be able to endure without damage, as well as the quantity of electrical current. The motion of charges also creates an electromagnetic field around the conductor that exerts a mechanical radial squeezing force on the conductor. A conductor of a given material and volume (length x cross-sectional area) has no real limit to the current it can carry without being destroyed as long as the heat generated by the resistive loss is removed and the conductor can withstand the radial forces. This effect is especially critical in printed circuits, where conductors are relatively small and close together, and inside an enclosure: the heat produced, if not properly removed, can cause fusing (melting) of the tracks. Since all conductors have some resistance, and all insulators will carry some current, there is no theoretical dividing line between conductors and insulators. However, there is a large gap between the conductance of materials that will carry a useful current at working voltages and those that will carry a negligible current for the purpose in hand, so the categories of insulator and conductor do have practical utility. Thermal and electrical conductivity often go together (for instance, most metals are both electrical and thermal conductors). However, some materials are practical electrical conductors without being a good thermal conductor. In many countries, conductors are measured by their cross section in square millimeters. However, in the United States, conductors are measured by American wire gauge for smaller ones, and circular mils for larger ones. In some poor countries they have overloaded wires going into one circuit. Of the metals commonly used for conductors, copper, has a high conductivity. Silver is more conductive, but due to cost it is not practical in most cases. However, it is used in specialized equipment, such as satellites, and as a thin plating to mitigate skin effect losses at high frequencies. Because of its ease of connection by soldering or clamping, copper is still the most common choice for most light-gauge wires. Aluminum has been used as a conductor in housing applications for cost reasons. It is actually more conductive than copper when compared by unit weight, but it has technical problems related to heat and compatibility of metals. The voltage on a conductor is determined by the connected circuitry and has nothing to do with the conductor itself. Conductors are usually surrounded by and/or supported by insulators and the insulation determines the maximum voltage that can be applied to any given conductor. Voltage of a conductor "V" is given by The ampacity of a conductor, that is, the amount of current it can carry, is related to its electrical resistance: a lower-resistance conductor can carry more current. The resistance, in turn, is determined by the material the conductor is made from (as described above) and the conductor's size. For a given material, conductors with a larger cross-sectional area have less resistance than conductors with a smaller cross-sectional area. For bare conductors, the ultimate limit is the point at which power lost to resistance causes the conductor to melt. Aside from fuses, most conductors in the real world are operated far below this limit, however. For example, household wiring is usually insulated with PVC insulation that is only rated to operate to about 60 °C, therefore, the current flowing in such wires must be limited so that it never heats the copper conductor above 60 °C, causing a risk of fire. Other, more expensive insulations such as Teflon or fiberglass may allow operation at much higher temperatures. The American wire gauge article contains a table showing allowable ampacities for a variety of copper wire sizes. If an electric field is applied to a material, and the resulting induced electric current is in the same direction, the material is said to be an isotropic electrical conductor. If the resulting electric current is in a different direction from the applied electric field, the material is said to be an anisotropic electrical conductor!.

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The internal temperatures of the planets cannot be directly measured, but they can be inferred in a variety of ways. For the Earth we can combine seismic studies and laboratory experiments to estimate the temperatures at various depths. For other planets we rely on heat radiated from their surfaces, surface features which suggest one kind of geologic history or another, theories of the origin and evolution of the planets, and theories of the origin of planetary magnetic fields. Sometimes different lines of evidence yield different estimates of planetary temperatures, but the range of temperatures given below are probably closer to the actual temperatures than not. Theories of Planetary Formation and Evolution From a number of lines of evidence, we know that the inner Solar System was very hot at the time the planets were forming, and that large amounts of rapidly-decaying radioactive materials were mixed into the rocky bodies that formed close to the Sun. As a result all of the inner planets must have been mostly or entirely molten during the last stages of their formation (see The Melting and Differentiation of the Planets The heat sources which melted the inner planets must have disappeared very early on. The Sun, which was a major source of heat at the start of things, rapidly shrank in size and brightness and became an insignificant factor within a few millions of years. The most important radioactive materials decayed to nonexistence within a few tens of millions of years. And collisional heating, which was once thought to be the most important factor, is now believed to have been a relatively minor factor, especially by the time the planets more or less reached their final size, and there was little left for them to run into. As a result the planets would have begun to resolidify almost as soon as they melted, and as the heat stored inside them gradually made its way to the surface, they would have slowly cooled off. As heat leaked from their interiors, larger planets should have cooled more slowly than smaller ones, because with larger masses they had more heat stored inside them in comparison to their surface areas (doubling the size of a planet increases the ratio of mass to surface area by a factor of two), which means more heat has to escape to reduce their temperature by a given amount. But even if the internal heat of a smaller planet caused internal temperatures to rise just as rapidly as you go downward as in larger planets, the smaller distance between the surface and center should result in lower central temperatures for the smaller planets. Both factors suggest that smaller planets should have cooled off considerably more than larger ones in the four and a half billion years since they were formed. Based on this we would expect the Earth, as the largest of the Terrestrial planets, to have the highest internal temperatures. Venus, with a slightly smaller mass and size, should have comparable temperatures. But Mars and Mercury, being much smaller, should be considerably cooler than either the Earth or Venus. For the Jovian planets, the gravitational compression of the huge amounts of gaseous materials which make up their structure should have produced far higher internal temperatures early on than for the Terrestrial planets. As a result, if they had similar structures they should be much hotter. However, they are made of fluids (primarily gases compressed to densities even higher than those of typical liquids), and heat flow in fluids can be much faster than in the solid rock which makes up the outer layers of the Terrestrial planets. So although the Jovian planets were probably once much hotter than the Terrestrial planets, that cannot ensure that they are still hotter than the inner planets. All we can say based on this theory alone, is that Jupiter, being by far the largest and most massive Jovian planet, should be substantially hotter than Saturn, which should be much hotter than the smaller Jovian planets, Uranus and Neptune. Although this theory of heating and cooling suggests relative temperatures within a given group of planets, for any given planet accurate temperature estimates depend on additional lines of evidence. Heat Radiated By the Planets At the current time most of the heat once stored inside the planets has leaked to their surfaces, and been radiated away. As a result, the heat of the Sun is the primary source of heat at their surfaces. In fact for the Terrestrial planets, the heat absorbed from the Sun and the heat radiated by the planets is so nearly identical that uncertainties in the two values, small though they are, are much larger than any heat still leaking from their interiors. For the Jovian planets, however, this is not true. Jupiter radiates nearly three times as much heat as it absorbs from sunlight, meaning that two-thirds of its surface heat budget is derived from heat leaking out of its interior. For Saturn, heat leaking from the interior is considerably smaller than for Jupiter, but is still about half of the surface heat budget. As discussed in the (relatively old, relatively brief) planet by planet discussion below, this implies that Jupiter is still extraordinarily hot inside, and Saturn, though not as hot as Jupiter, is probably twice as hot (in the deep interior) as the Earth. For Uranus and Neptune the heat flow from the interior is much smaller, and they probably have lower internal temperatures than the Earth, but not as much lower as might have been thought forty or fifty years ago. (Author's Note to Self: Need to discuss (1) the relationship of surface features to internal thermal history, (2) the relationship of magnetic fields to internal temperatures, (3) seismic studies of the Earth, and (4) "flex" measurements of Mercury and Mars) (The following discussion, based on lecture notes now several years old, is relatively correct and complete, but needs some additions and revisions in the light of recent discoveries. A few minor updates have been inserted as indicated at various places; but a considerable revision will be made in the next iteration of this page.) The Internal Temperatures of The Terrestrial Planets Its extremely cratered surface implies little if any geological activity since the end of the heavy bombardment of the Solar System around 4 billion years ago. (Note added 2014: Gravimetric studies and images taken by the MESSENGER spacecraft indicate that despite its relative lack of geological activity in recent aeons, Mercury has had a more interesting geological history than suggested by earlier studies.) In addition, the small size of the planet should allow any heat left over from its formation to escape quickly. Both these factors would lead to a prediction of a low internal temperature, probably less than 4000 Fahrenheit degrees, and most likely, a completely solid interior. (Note added 2014: Although the temperature estimate is probably still in the right ballpark, the aforementioned MESSENGER observations indicate that at least a portion of Mercury's core is still molten.) Radar imaging seems to show an extremely volcanic and otherwise substantially changed surface, with an almost complete destruction of the cratering which would have occurred in its early history, implying a substantial amount of geological activity throughout its history. The large size of the planet should allow much of the heat left over from its formation to be easily retained. However, there are also a large number of large craters which would have taken the best part of half a billion years or more to be formed by random collisions, implying that the geological activity otherwise so apparent on the planet's surface probably ceased or at least greatly decreased at some time in the past. This implies that the planet is somewhat cooler than the Earth, probably less than 10000 Fahrenheit degrees in the central core, and may be entirely solid, although substantial molten regions cannot be ruled out on this basis alone. Shows extreme geological activity, so that major surface features such as continents almost completely change in time scales of only a few hundred million years (this is in addition to weathering and erosion, which act on much shorter time scales). In addition, its size, the largest of the Terrestrial planets, should allow it to hold in more heat than the smaller planets. Finally, earthquake studies absolutely prove the existence of a mostly molten core. As a result of laboratory studies of the behavior or materials at high temperature and pressure, its internal temperature is believed to be in excess of 12000 Fahrenheit degrees, and the central core is probably closer to 14000 degrees. Half of its surface contains huge, partially weathered craters almost certainly dating back to over 4 billion years ago, whereas the other half has many volcanoes and stress fractures, implying at least some internal activity, although not on the same scale as Venus or the Earth, continuing to within a few million years of the present time. The small size of the planet should allow heat to escape fairly easily, and with its looks being intermediate between those of Mercury and the larger Terrestrial planets, it would be expected to have internal temperatures between 5000 and 7000 Fahrenheit degrees. This might lead to partial melting of the interior, depending upon the composition of the central regions. (Note added 2014: It is now certain that at least a portion of the outer core is molten, or partially molten; but temperature estimates remain the same, differences in composition compared to the Earth being thought to be the main cause of the unexpected difference in structure.) The Magnetic Fields of the Terrestrial Planets and of The Moon The magnetic fields of the Terrestrial planets should be created by convective motions within molten metallic cores. In some theories this motion alone is capable of causing a net planetary field. In others theories a relatively fast rotation of the planet is also necessary, so that the Coriolis effect of the rotation can organize the internal convection parallel to (and/or anti-parallel to) the rotation axis of the planet. Known to have a molten core, s rapid rotation, and a fairly strong magnetic field (strongest of the Terrestrial planets), nearly parallel to its axis of rotation (although it does move around a bit over long periods of time). Theory predicts a strong magnetic field under these circumstances, which agrees with observation. Its heavily cratered, presumably ancient surface, slow rotation, and probably solid core (based on very limited seismic studies) predict that it should have no magnetic field. No magnetic field is observed, again in agreement with theory. Its in-between geology suggests it is probably too cool for a large molten core (2014: Although now almost certain to have a partially molten outer core, the size of the molten region is probably too small to support extensive convective motion). Because of its relatively rapid rotation (almost as fast as the Earth's), a molten core should producea magnetic field, but only a minuscule field is observed, which implies that it may be too cool (probably less than 5000 Fahrenheit degrees) to have a molten core. (following added 2005) However, fossil magnetism at the surface suggests that the rocks which contain fossil magnetism were formed at a time, 4+ billion years ago, when Mars had a substantial magnetic field; and parallel striping of that fossil magnetism in certain areas suggests that in that same time frame something occurred similar to the seafloor spreading and magnetic striping caused by magnetic field reversals in the Earth. So although Mars' core must be relatively cool and almost totally solid now, it was undoubtedly hot enough to create an active magnetic field and drive some mantle activity in the very early days of the planet's history. Its once-active geology suggests it probably had a molten core, but its large number of more recent craters suggests that the geological activity has ceased, so that the core may have cooled off and solidified, and in any event its extremely slow rotation makes it possible that it might not have a magnetic field even if it did have a molten core. NO FIELD IS OBSERVED. This means either that it does have a solid core, or that those theories which require a rapid rotation to create a magnetic field are more likely to be correct, and those which do not require a rapid rotation are wrong. An ancient, heavily cratered surface implies relatively little geological activity, particularly in recent times, probably low internal temperatures, and therefore probably no molten core of significant size. In addition, it has a slow rotation, so even if it had a molten core it might not have a magnetic field. HOWEVER, it does have a magnetic field, albeit only about 1% as strong as ours. (Modified in 2014) The presence of a magnetic field, combined with the absence of geological activity, was a longtime puzzle; however, MESSENGER studies that show the planet has a partially molten core, so its weak magnetic field can be explained by convective motions in the partially molten region. The Internal Temperatures of the Jovian Planets Heat leaking from its surface is almost three times as much as that absorbed from sunlight, implying that almost twice as much heat is leaking out of planet as is coming from the Sun. This is partly due to large distance from the Sun (a little over 5 AU's), which causes it to receive less than 4% of the heat that we do, but this still requires a very large internal heat flow. In the case of the Earth a temperature rise of 100 degrees (F) per mile near the surface produces very little heat flow (except at unusually warm places such as volcanoes), but the crust and mantle of the Earth are made of'solid rock, and heat flows very slowly through such material. Jupiter is made of liquid hydrogen, and convective motions in such a liquid should be capable of moving heat outwards fairly easily. Estimates based on theory and lab experiments suggest that a temperature rise of only 1 Fahrenheit degree per mile might be adequate to explain such a heat flow, but since Jupiter is 44000 miles in radius, its central temperature is probably more than 50000 Fahrenheit degrees. (Despite this, the central core of ice and rocks, being compressed by incredible weights, is almost certainly solid.) This planet has only half its heat coming from the interior, and being further from the Sun than Jupiter, only needs 1/4 to 1/8 as much interior heat flow to produce this result. It is therefore thought that its internal temperature rises only about half as fast as in Jupiter, resulting in central temperatures of only 25000 to 35000 Fahrenheit degrees. Uranus and Neptune are so far from us and the Sun, and have so little internal heat flow that measurements prior to the Voyager 2 flybys were almost useless. Some heat flow has now been observed, but central temperatures are still very uncertain, are probably less than 15000 degrees, and possibly less than 10000 degrees. The Magnetic Fields of the Jovian Planets The basic theory is the same as for the Terrestrial planets, but since there is very little rock, let alone metal in the Jovian planets, even completely molten cores and very rapid rotations would not produce fields strong enough to reach their surfaces with any substantial strength. Despite this, Jupiter has a VERY strong field, 10 times stronger at the surface than ours, which extends into space many times further than ours, and has a total energy 1000 times greater than ours. Saturn has a relatively strong field (divide Jupiter's numbers by 10), which also requires a substantial energy to create it, and Uranus and Neptune, although their fields are only a fraction of the strength of the Earth's field, still require a substantial source of magnetic energy. For Jupiter and Saturn the answer to the creation of their magnetic fields is believed to be metallic hydrogen . Normally, hydrogen is a non-metal, which tightly holds onto its lone electron. (Metallic properties are produced by atoms which have so many electrons that the outermost one can easily be detached and wander freely between the atoms in a liquid or solid state.) Under the tremendous ressures inside Jupiter and Saturn, hydrogen is compressed so much (perhaps 30 to 40 times denser than normal inside Jupiter) that many atoms occupy the space normally filled by only a single atom, and although each electron is closer to its own nucleus than to other atoms' nuclei, being so close to so many nuclei can "confuse" some of the electrons, allowing them to wander from atom to atom, producing a metallic form of hydrogen. Recent lab experiments (testing the properties of hydrogen under high pressure) and theoretical calculations (involving the pressures inside the Jovian planets) suggest that although Uranus and Neptune are not likely to contain such a form of hydrogen, Saturn should have substantial amounts, and Jupiter may be mostly made of this strange liquid. If this is correct it would easily explain the magnetic fields of Jupiter and Saturn, but for Uranus and Neptune the magnetic fields are probably caused by convective motions in an outer core made mostly of electrically conductive liquids such as seawater mixed with gases (such as methane and ammonia) compressed to the density of a liquid.

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Digital Electronics: Binary Basics Digital electronic circuits rely on the binary number system. Thus, before you can understand the details of how digital circuits work, you need to understand how the binary numbering system works. Binary is one of the simplest of all number systems because it has only two numerals: 0 and 1. In the decimal system (with which most people are accustomed), you use 10 numerals: 0 through 9. In an ordinary decimal number, such as 3,482, the rightmost digit represents ones; the next digit to the left, tens; the next, hundreds; the next, thousands; and so on. These digits represent powers of ten: first 100 (which is 1); next, 101 (10); then 102 (100); then 103 (1,000); and so on. In binary, you have only two numerals rather than ten, which is why binary numbers look somewhat monotonous, as in 110011, 101111, and 100001. The positions in a binary number (called bits rather than digits) represent powers of two rather than powers of ten: 1, 2, 4, 8, 16, 32, and so on. To figure the decimal value of a binary number, you multiply each bit by its corresponding power of two and then add the results. The decimal value of binary 10111, for example, is calculated as follows: Fortunately, converting a number between binary and decimal is something that a computer is good at — so good, in fact, that you’re unlikely ever to need to do any conversions yourself. The point of learning binary is not to be able to look at a number such as 1110110110110 and say instantly, Ah! Decimal 7,606! Here are some of the most interesting characteristics of binary, which explain how the system is similar to and different from the decimal system: In decimal, the number of decimal places allotted for a number determines how large the number can be. If you allot six digits, for example, the largest number possible is 999,999. Because 0 is itself a number, however, a 6-digit number can have any of 1 million different values. Similarly, the number of bits allotted for a binary number determines how large that number can be. If you allot 8 bits, the largest value that number can store is 11111111, which happens to be 255 in decimal. Thus, a binary number that is 8 bits long can have any of 256 different values (including 0). To quickly figure how many different values you can store in a binary number of a given length, use the number of bits as an exponent of two. An 8-bit binary number, for example, can hold 28 values. Because 28 is 256, an 8-bit number can have any of 256 different values. This is why a byte — 8 bits — can have 256 different values. This powers of two thing is why digital systems don’t use nice, even round numbers for measuring such values as memory capacity. A value of 1k, for example, isn’t an even 1,000 bytes: It’s actually 1,024 bytes, because 1,024 is 210. Similarly, 1MB isn’t an even 1,000,000 bytes, but 1,048,576 bytes, which happens to be 220. Power Bytes Kilobytes Power Bytes k, MB, or GB 21 2 217 131,072 128k 22 4 218 262,144 256k 23 8 219 524,288 512k 24 16 220 1,048,576 1MB 25 32 221 2,097,152 2MB 26 64 222 4,194,304 4MB 27 128 223 8,388,608 8MB 28 256 224 16,777,216 16MB 29 512 225 33,554,432 32MB 210 1,024 1k 226 67,108,864 64MB 211 2,048 2k 227 134,217,728 128MB 212 4,096 4k 228 268,435,456 256MB 213 8,192 8k 229 536,870,912 512MB 214 16,384 16k 230 1,073,741,824 1GB 215 32,768 32k 231 2,147,483,648 2GB 216 65,536 64k 232 4,294,967,296 4GB

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What Are Forces? Whenever we lift something, push something, or otherwise manipulate an object, we are exerting a force. A force is defined very practically as a push or a pull—essentially it’s what makes things move. A force is a vector quantity, as it has both a magnitude and a direction. In this chapter, we will use the example of pushing a box along the floor to illustrate many concepts about forces, with the assumption that it’s a pretty intuitive model that you will have little trouble imagining. Physicists use simple pictures called free-body diagrams to illustrate the forces acting on an object. In these diagrams, the forces acting on a body are drawn as vectors originating from the center of the object. Following is a free-body diagram of you pushing a box into your new college dorm with force F. Because force is a vector quantity, it follows the rules of vector addition. If your evil roommate comes and pushes the box in the opposite direction with exactly the same magnitude of force (force –F), the net force on the box is zero

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Many analysis tools that are used for hypothesis testing in STATISTICA give a calculated test statistic and a p-value. (For more information about hypothesis testing, see the article, How to Interpret Statistical Analysis Results.) At times, it may be necessary in your hypothesis test to report the test’s critical value. This article describes how to find the critical value for a statistical test. In statistical hypothesis testing, a critical value is the cut-off value for the computed test statistics that defines statistical significance of the test. This statistical test follows a known distribution, and the analyst will have selectedalpha, the type I error rate. The critical value is the value from the distribution of the test for which P(X>X critical value) = alpha, where X is the observed test statistic and X critical value is the critical value for the test. Statistical tests can be either one or two-sided, and this is important for finding the critical value of a test. Below are three possible null and alternative hypotheses for a single sample mean test. Given the same alpha, each of the three tests would have a different critical value (or values). The distribution a test follows is an important piece of finding the critical value. Tests comparing population means may follow a standard Normal or Studentized T distribution. ANOVA significance tests follow the F distribution. Chi Square is another common distribution of test statistics. T, F, and Chi Square all have one or more degree of freedom parameters that are needed to find the critical value. You can use STATISTICA's Probability Distribution Calculator to find values or areas from various distributions. This tool can be used to find the critical value for a test. Once the distribution is selected, alpha is entered as well as any other required parameters such as degrees of freedom. Then the tool computes the critical value of the test. For these examples, reading comprehension was measured for students in three grade levels who were administered one of two teaching methods. In this one-sample t-test, researchers hypothesized that the average reading comprehension score is significantly different from 55. This is a two-sided test. Data was collected and the one-sample t-test was calculated with the results shown below. The calculated test statistic is -1.96166 and p=0.054526. At alpha = 0.05, this two-sided test is not statistically significant, p-value = 0.054526 > 0.05 = alpha. Let’s find the critical value of the test. On the Statistics tab in the Base group, click Basic Statistics to display the Basic Statistics and Tables dialog box. Select Probability calculator. Click the OK button to display the Probability Distribution Calculator. Since the test follows the t (Student) distribution, select this in the Distribution list. Select the Inverse, Two-tailedand (1-Cumulative p) check boxes. Enter 59 as df, which comes from the t-test output above. We are using alpha = 0.05, so enter this value for p. Click the Compute button to calculate the t critical value. It is found to be 2.000995. Since the test has a two-sided alternative, the critical region is -2.000995 < t calc < 2.000995. The computed test statistic is -1.96166, which is between -2.000995 and 2.000995, so the conclusion is to fail to reject the null hypothesis. There is insufficient evidence to conclude that the average reading comprehension score is significantly different from 55. Now let’s assume that the test had a one-sided alternative, i.e. we hypothesize that average reading comprehension scores are significantly less than 55. (Note that this example is for illustrating the calculation of critical values only. It is not an acceptable statistical practice to change your hypothesis to suit the data. The one-sided alternative critical values are calculated slightly different and this example aims to highlight this difference.) The critical value for this test is very similar, but the Two-tailed check box is cleared. Additionally, depending on the direction of the hypothesis, the (1-Cumulative p) check box may also be cleared. The alternative hypothesis is that µ<55. The direction of the inequality also tells the direction of the test. For this test, the (1-Cumulative p) check box should be cleared. For the one-sided test, the critical value is -1.671093. If t calc < -1.671093, reject H0. Thus, -1.96166<-1.671093, so reject H0. The conclusion for this test is different from the two-sided test, which failed to reject the null. Here, the conclusion would be that the average reading comprehension scores are significantly less than 55. (Note that the t-test output from STATISTICA gives p-values based on the two-sided alternative. For a one-sided alternative test, the p-value should be divided by 2.) Using an example from an ANOVA analysis, let’s compute the critical F value for the significance test for an effect. The ANOVA table below tests for a significant effect of Method, Grade, and the interaction between the two on a student’s reading comprehension. This ANOVA output table gives the calculated F statistics, the associated p-values, and degrees of freedom for each test. (The F distribution requires 2 degrees of freedom parameters, nominator and denominator. The F statistics are calculated as MEeffect/MSerror. The degrees of freedom for the numerator and denominator come from the effect and error respectively. Additionally, F tests are always one-sided tests.) Using this information and the Probability Distribution Calculator, we can find the critical values of each test for a givenalpha. In the Probability Distribution Calculator, select F (Fisher) in the Distribution list. Select the (1-Cumulative p)check box. Enter numerator and denominator degrees of freedom, df1 =1 and df2 =54. We are using alpha = 0.05, so enter this value for p. Click Compute to compute the F statistic: 4.019541. This is the critical value for the significance test for the METHODeffect. Given that the null hypothesis is true, P(F calc >4.019541)=0.05, so if F calc > F critical = 4.019541, reject H0. The computed test statistic is 1.884, which is less than 4.019541, so the conclusion is to fail to reject the null hypothesis. There is insufficient evidence to conclude that there is a significant difference in the teaching methods. Critical values can be calculated for any statistical test that follows a known distribution. The Probability Distribution Calculator makes it easy to find these test critical values.

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3D Glossary-- Normal A flat polygon situated in 3-D Coordinate Space necessarily has an orientation. It faces some unique direction. An imaginary ray pointing out from the surface of the polygon, and perpendicular to that surface, is called the normal of the polygon. As there will always be two normals, one on each side of the surface, and pointing in opposing directions, the choice of the side from which the normal projects defines the front or "face" of the polygon. In 3-D computer graphics, as opposed to the physical world, it is usual for a polygon to have only one face or side, and therefore only one normal. This is because polygons are typically used to create a closed mesh representing the surface of a 3-D object and the back side of the polygon is therefore hidden inside the object. To save render time, polygons are kept single-sided and the normal projects from only the exposed face. However, occasionally it is necessary to create double-sided polygons that have normals pointing from both sides, and which therefore can be rendered from both sides as the different sides come into view during the course of an animation. The face side of a polygon is typically established in a Model file by the order in which the vertices of the polygon are listed, clockwise or counterclockwise around the facing (normal) side. Normals can be associated not only with the flat surfaces of the polygons, but also with the individual points that make up the vertices where polygons meet on the surface of a model. This technique is used in rendering to create the appearance of curved surfaces rather that flat, faceted sides. Such vertex normals can be directly assigned in the model file, but are usually computed during rendering by averaging the normals of the adjacent polygons. This rather subtle idea is described and illustrated in the Lesson 3 tutorial. Comments are welcome Created: Mar. 11, 1997 Revised: Mar. 11, 1997

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How to Identify the Min and Max on Vertical Parabolas Vertical parabolas give an important piece of information: When the parabola opens up, the vertex is the lowest point on the graph — called the minimum, or min. When the parabola opens down, the vertex is the highest point on the graph — called the maximum, or max. Only vertical parabolas can have minimum or maximum values, because horizontal parabolas have no limit on how high or how low they can go. Finding the maximum of a parabola can tell you the maximum height of a ball thrown into the air, the maximum area of a rectangle, the minimum value of a company's profit, and so on. For example, say that a problem asks you to find two numbers whose sum is 10 and whose product is a maximum. You can identify two different equations hidden in this one sentence: x + y = 10 xy = MAX If you're like most people, you don't like to mix variables when you don't have to, so you should solve one equation for one variable to substitute into the other one. This process is easiest if you solve the equation that doesn't include min or max at all. So if x + y = 10, you can say y = 10 – x. You can plug this value into the other equation to get the following: (10 – x)x = MAX If you distribute the x on the outside, you get 10x – x2 = MAX. This result is a quadratic equation for which you need to find the vertex by completing the square (which puts the equation into the form you're used to seeing that identifies the vertex). Finding the vertex by completing the square gives you the maximum value. To do that, follow these steps: Rearrange the terms in descending order. This step gives you –x2 + 10x = MAX. Factor out the leading term. You now have –1(x2 – 10x) = MAX. Complete the square. This step expands the equation to –1(x2 – 10x + 25) = MAX – 25. Notice that –1 in front of the parentheses turned the 25 into –25, which is why you must add –25 to the right side as well. Factor the information inside the parentheses. This gives you –1(x – 5)2 = MAX – 25. Move the constant to the other side of the equation. You end up with –1(x – 5)2 + 25 = MAX. The vertex of the parabola is (5, 25). Therefore, the number you're looking for (x) is 5, and the maximum product is 25. You can plug 5 in for x to get y in either equation: 5 + y = 10, or y = 5. This figure shows the graph of the maximum function to illustrate that the vertex, in this case, is the maximum point.

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Negative numbers can be confusing at first. Some simple models and analogies help make them clearer. Introduce your students to prime factors, the basic building blocks of numbers. Graphing is a way to visualize relationships between two quantities. Help your students understand ordered pairs and graphing linear equations. Explore the formula for the area of a triangle and a parallelogram. Refresh your memory with this overview of the topic. Here you'll find at least two complete lesson scripts to use with your class. Share your ideas for ways to manage your classroom, speed learning, and handle difficulties. Find answers to common questions students ask.

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Related Information Links A chemical reaction is a process in which the identity of at least one substance changes. A chemical equation represents the total chemical change that occurs in a chemical reaction using symbols and chemical formulas for the substances involved. Reactants are the substances that are changed and products are the substances that are produced in a chemical reaction. The general format for writing a chemical equation is reactant1 + reactant2 + … → product1 + product2 + … With the exception of nuclear reactions, the Law of Conservation of Mass–matter is neither created nor destroyed during a chemical reaction– is obeyed in “ordinary” chemical reactions. For this reason a chemical equation must be balanced–the number of atoms of each element must be the same on the reactants side of the reaction arrow as on the products side. Details on balancing chemical equations are found in the units on Stoichiometry and Redox Reactions. The general format for writing a chemical equation can be written in a short-hand version as a A + b B + … → c C + d D + … where the lower case letters are the stoichiometric coefficients needed to balance a specific equation. The units on Stoichiometry, Redox Reactions, and Acid-Base Chemistry contain additional background reading, example problems, and information on the topics covered in this unit. Chemists classify chemical reactions in various ways. Often a major classification is based on whether or not the reaction involves oxidation-reduction. A reaction may be classified as redox in which oxidation and reduction occur or nonredox in which there is no oxidation and reduction occurring. A redox reaction can be recognized by observing whether or not the oxidation numbers of any of the elements change during the reaction. Example Problem: Classify the reactions as either redox or nonredox. (1) 4 Fe(s) + 3 O2(g) → 2 Fe2O3(s) (2) NaOH(aq) + HCl(aq) → NaCl(aq) + H2O(l) (3) Cl2(g) + H2O(l) → HCl(aq) + HClO(aq) Answer: In equation (1), the iron changes oxidation numbers from 0 to +3 and oxygen changes from 0 to -2. Equation (1) represents a redox reaction. In equation (2), there is no change in oxidation numbers for the elements involved: sodium is +1, oxygen is -2, hydrogen is +1, and chlorine is -1 on both the reactants and products sides. Equation (2) represents a nonredox reaction. In equation (3), the chlorine changes from 0 to -1 in HCl and to +1 in HClO. There is no change in the oxidation numbers of hydrogen (+1 in H2O, HCl, and HClO) and oxygen (-2 in H2O and HClO). Because chlorine is oxidized and reduced, equation (3) represents a redox reaction. The reaction described in equation (3) is interesting in that an element in one oxidation state undergoes both oxidation and reduction. Such a redox process is known as a disproportionation reaction. The element undergoing disproportionation must have at least three different oxidation states–the initial one in the reactant and one higher plus one lower in the products. Most simple redox reactions may be classified as combination, decomposition, or single displacement reactions. In a combinations reaction two reactants react to give a single product. The general format of the chemical equation is a A + b B + … → c C A special case of a combination reaction in which the reactants are only elements in their naturally occurring forms and physical states at the temperature and pressure of the reaction is known as a formation reaction. Example Problem: Identify which reactions are redox combination reactions. (4) 6 Li2O(s) + P4O10(g) → 4 Li3PO4(s) (5) CaO(s) + H2O(l) → Ca(OH)2(s) (6) S(s) + 3 F2(g) → SF6(g) (7) ZnS(s) + 2 O2(g) → ZnSO4(s) (8) SO2(g) + Cl2(g) → SO2Cl2(g) Answer: All of the reaction are classified as combination reactions because they involved two or more reactants producing a single product. However, redox is occurring only in equations (6), (7), and (8). In equation (6), S is oxidized from 0 to +6 and F is reduced from 0 to -1; in equation (7), S is oxidized from -2 to +6 and O is reduced from 0 to -2; and in equation (8), S is oxidized from +4 to +6 and Cl is reduced from 0 to -1. In a decomposition reaction a single reactant breaks down to give two or more substances. The general format of the chemical equation is a A → b B + c C + … If the decomposition reaction involves oxidation-reduction, the reaction is often called an internal redox reaction because the oxidized and reduced elements originate in the same compound. Example Problem: Identify which reactions are redox decomposition reactions. (9) CuSO4⋅5H2O(s) → CuSO4(s) + 5 H2O(g) (10) SnCl4⋅6H2O(s) → SnO2(s) + 4 HCl(g) + 4 H2O(g) (11) NH4NO2(s) → N2(g) + 2 H2O(g) (12) (NH4)2Cr2O7(s) → N2(g) + Cr2O3(s) + 4 H2O(g) Answer: All of the reactions are classified as decomposition reactions because they involve a single reactant producing two or more substances. However, redox is occurring only in equations (11) and (12). In equation (11), the N in NH4+ is oxidized from -3 to 0 and the N in NO2- is reduced from +3 to 0. In equation (12), the N is oxidized from -3 to 0 and the Cr is reduced from +6 to +3. In a single displacement reaction the atoms or ions of one reactant replace the atoms or ions in another reactant. Single displacement reactions are also known as displacement, single replacement, and replacement reactions. The general format of the chemical equation is a A + b BC → c AC + d B Whether or not a redox single displacement reaction occurs will depend on the relative reducing strengths of A and B. Example Problem: Identify which reactions are redox single displacement reactions. (13) 2 Al(s) + Fe2O3(s) → 2 Fe(s) + Al2O3(s) (14) 2 NaI(aq) + Br2(aq) → 2 NaBr(aq) + I2(aq) (15) Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s) Answer: All three reactions are redox. Both equations (13) and (14) fit the general format of the single displacement reaction by assigning A as Al, B as Fe, and C as O in equation (13) and A as Br, B as I, and C as Na in equation (14). To classify equation (15) is a little more difficult. The reaction has been represented by a net ionic equation in which the anion has been omitted. If an anion X is added to generate the overall equation, Zn(s) + CuX(aq) → ZnX(aq) + Cu(s), then assigning A as Zn, B as Cu, and C as X shows that this is also a redox single displacement reaction. In addition to the single redox reactions described above, a redox reaction may be classified as a simple redox electron transfer reaction in which the oxidation numbers of ionic reactants are changed by the direct transfer of electrons from one ion to the other–typically in aqueous solutions. For example 2 Fe3+(aq) + Sn2+(aq) → 2 Fe2+(aq) + Sn4+(aq) Many redox reactions do not fit into the classifications described above. For example, redox reactions involving oxygen-containing reactants in aqueous acidic or basic solutions such as 3 Cu(s) + 8 HNO3(aq, dil) → 3 Cu(NO3)2(aq) + 2 NO(g) + 4 H2O(l) Cu(s) + 4 HNO3(aq, conc) → Cu(NO3)2(aq) + 2 NO2(g) + 2 H2O(l) or the combustion of oxygen with more than one element in a reactant 2 CH3OH(g) + 3 O2(g) → 2 CO2(g) + 4 H2O(l) These types of reactions are classified as complex redox reactions. There are several classifications of nonredox reactions–including combination, decomposition, single displacement, and double displacement reactions. The general format of the chemical equation for a nonredox combination reaction is the same as for a redox combination reaction a A + b B + … → c C However, all reactants and the product must be compounds and no changes in oxidation numbers of the elements occur. Usually these reactions involve reactants that are acidic and basic anhydrides. Example Problem: Identify which reactions are nonredox combination reactions. (16) 2 Na(s) + Cl2(g) → 2 NaCl(s) (17) SO3(g) + CaO(s) → CaSO4(s) (18) SO2(g) + H2O(l) → H2SO3(aq) Answer: All three equations are combination reactions, but only equations (17) and (18) are nonredox. The general format of the chemical equation for a nonredox decomposition reaction is the same as for a redox decomposition reaction a A → b B + c C + … However, the reactant and all products must be compounds and no changes in oxidation numbers occur. Quite often one of the products formed will be a gas. Example Problem: Identify which reactions are nonredox decomposition reactions. (19) NH4HCO3(s) → NH3(g) + CO2(g) + H2O(g) (20) NH4NO2(s) → N2(g) + 2 H2O(g) (21) CaCO3(s) → CaO(s) + CO2(g) Answer: All three equations are decomposition reactions, but only equations (19) and (21) are nonredox. The general format of the chemical equation for a nonredox single displacement reaction is the same as for a redox single displacement reaction a A + b BC → c AC + d B However, there are no changes in the oxidation numbers of the elements during the reaction. Common nonredox single displacement reactions include ligand substitution in complexes and formation of more stable oxygen-containing compounds from less stable oxygen-containing compounds. Example Problem: Identify which reactions are nonredox single displacement reactions. (22) [PtCl4]2-(aq) + 2 NH3(aq) → [Pt(NH3)Cl2](s) + 2 Cl-(aq) (23) Na2CO3(s) + SiO2(s) → Na2SiO3(l) + CO2(g) (24) 2 AgNO3(aq) + Cu(s) → Cu(NO3)2(aq) + 2 Ag(s) Answer: All three equations are single displacement reactions, but only equations (22) and (23) are nonredox. Finally, the last classification of nonredox reactions is that of nonredox double displacement reactions. The general format of the chemical equation is a AC + b BD → c AD + d BC with no oxidation or reduction of A, B, C, or D occurring. These reactions are also known as double replacement, “partner” exchange, and metathesis reactions. Usually one or more of the products will be a gas, a precipitate, a weak electrolyte, or water. An important example of a nonredox double displacement reaction is the reaction of an acid with a base under aqueous conditions. Example Problem: Identify the nonredox double displacement reactions. (25) CaCO3(s) + 2 HCl(aq) → CaCl2(aq) + H2O(l) + CO2(g) (26) HCl(aq) + KOH(aq) → KCl(aq) + H2O(l) (27) AgNO3(aq) + KCl(aq) → AgCl(s) + KNO3(aq) Answer: All three reactions are nonredox double displacement reactions. Most experienced chemists can classify a given chemical reaction rather easily and quickly by “inspection” of the formulas of the reactants and products in the chemical equation. The first decision most chemists make is to determine whether or not the reaction involves redox. Based on this decision, the answers to a few more specific questions will readily lead to the reaction classification. These specific questions are based on the general formats of the chemical equations for the different classifications of the reactions described above. To begin learning what these questions are, you might consider using the online analysis program that is available at http://www.xxx.yyy to classify the reactions given in the Example Problem. The basis of this analysis program is outlined by the flow charts given in Figures (1) and (2). Please do not memorize this flow chart–it is simply a tool to help you learn what to look for and what questions should be asked as you classify a given reaction. Example Problem: Classify each reaction. (28) XeF6(s) → XeF4(s) + F2(g) (29) Zn(s) + 2 AgNO3(aq) → Zn(NO3)2(aq) + Ag(s) (30) H2SO4(aq) + Ba(OH)2 → BaSO4(s) + 2 H2O(l) (31) XeF6(s) + RbF(s) → RbXeF7(s) (32) 2 Cs(s) + I2(g) → 2 CsI(s) Answer: In equation (28), Xe is reduced from +6 to +4 and some of the F is oxidized from -1 to 0. This reaction would be classified as a redox decomposition reaction. In equation (29), Zn is oxidized from 0 to +2 and Ag is reduced from +1 to 0. One of the reactants is an element and one of the products is an element. This reaction would be classified as a redox single displacement reaction. In equation (30), there is no redox occurring. Both reactants are in the form of aqueous ions, but are not complex ions. This acid-base reaction is classified as nonredox double displacement. In equation (31), there is no redox occurring. Because there is one product formed, this reaction is classified as a nonredox combination reaction. In equation (32), Cs is oxidized from 0 to +1 and I is reduced from 0 to -1. Both reactants are elements and there is only one product formed. The reaction is classified as a (redox) formation reaction. Try It Out Classify each reaction. (33) Na2CO3(s) + SiO2(s) → Na2SiO3(l) + CO2(g) (34) 2 Mg(NO3)2(s) → 2 Mg(NO2)2(s) + O2(g) (35) 3 HNO2(aq) → 2 NO(g) + NO3-(aq) + H3O+(aq) (36) BaCO3(s) → BaO(s) + CO2(g) (37) 2 Eu2+(aq) + 2 H+(aq) → 2 Eu3+(aq) + H2(g) (38) [Ag(NH3)2]+(aq) + 2 CN-(aq) → [Ag(CN)2]-(aq) + 2 NH3(aq) (39) MgO(s) + 2 HCl(aq) → MgCl2(aq) + H2O(l) (40) CaO(s) + SO2(g) → CaSO3(s) (41) 2 NO(g) + O2(g) → 2 NO2(g) (42) N2(g) + 2 O2(g) → 2 NO2(g) Additional Information Available on the Web Copyright © 1996-2008 Shodor Last Update: Sunday, 06-Oct-2002 13:08:39 EDT Please direct questions and comments about this page to

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Recent tests aboard the International Space Station have shown that fire in space can be less predictable and potentially more lethal than it is on Earth. “There have been experiments,” says NASA aerospace engineer Dan Dietrich, “where we observed fires that we didn’t think could exist, but did.” From This Story That fire continues to surprise us is itself surprising when you consider that combustion is likely humanity’s oldest chemistry experiment, consisting of just three basic ingredients: oxygen, heat and fuel. Here on Earth, when a flame burns, it heats the surrounding atmosphere, causing the air to expand and become less dense. The pull of gravity draws colder, denser air down to the base of the flame, displacing the hot air, which rises. This convection process feeds fresh oxygen to the fire, which burns until it runs out of fuel. The upward flow of air is what gives a flame its teardrop shape and causes it to flicker. But odd things happen in space, where gravity loses its grip on solids, liquids and gases. Without gravity, hot air expands but doesn’t move upward. The flame persists because of the diffusion of oxygen, with random oxygen molecules drifting into the fire. Absent the upward flow of hot air, fires in microgravity are dome-shaped or spherical—and sluggish, thanks to meager oxygen flow. “If you ignite a piece of paper in microgravity, the fire will just slowly creep along from one end to the other,” says Dietrich. “Astronauts are all very excited to do our experiments because space fires really do look quite alien.” Such fires might appear eerily tranquil to people accustomed to the capricious nature of earthly flames. But a flame in microgravity can be more tenacious, capable of surviving on less oxygen and burning for longer periods of time. NASA has practical applications in mind with its research. Scientists hope to learn if certain materials are more flammable in space, and thus to be avoided. Experiments suggest that space station fire extinguishers that squirt gases at a flame are less effective than on terra firma, since they direct air (and oxygen) to the fire, providing additional fuel. Moreover, the data obtained aboard the space station—through experiments such as comparing how fire spreads on flat objects versus spherical ones—will help engineers better understand the behavior of fuel and flames on Earth, where approximately 75 percent of our power comes from some form of combustion. NASA scientists are especially excited about the potential applications for a bizarre, unprecedented type of combustion they observed in space this past spring: When certain types of liquid fuel catch fire, they continue to burn even when the flames appear to have been extinguished. The fuel combustion occurs in two stages. The first fire burns with a visible flame that eventually goes out. But shortly afterward, the fuel reignites, taking the form of “cool flames” that burn at lower temperatures and are invisible to the naked eye. Scientists do not yet have an explanation for this phenomenon. But engineers say that if this chemical process could be duplicated on Earth, the result could be diesel engines that use cool flames to produce fewer air pollutants. NASA researcher Paul Ferkul says the microgravity experiments provide a unique opportunity to study the underlying dynamics of fire “from a more fundamental point of view” by looking at combustion processes “that would otherwise be masked or at least complicated by gravity.”

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by Roberta Sue Alexander, Rodney D. Barfield, and Steven E. Nash, 2006. Additional research provided by Joseph W.Wescott II and Wiley J. Williams. See Also: Emancipation Part i: Introduction; Part ii: Life under slavery and the achievements of free blacks; Part iii: Emancipation and the Freedmen's Fight for Civil Rights; Part iv: Segregation and the struggle for equality; Part v: Emerging roles and new challenges; Part vi: References Part iii: Emancipation and the Freedmen's Fight for Civil Rights The conditions of African Americans changed dramatically after the outbreak of the Civil War. The Confederates used black slave labor to operate railroads, to construct earthworks and fortifications, and—in the closing days of the conflict—to fight in their army. Many slaves defected to Union forces in eastern North Carolina. A sizable number joined the African Brigade, first organized in New Bern, to bear arms for the Federal army. Perhaps as many as 5,000 black North Carolinians fought for the Union. With the Emancipation Proclamation of 1863, nearly 4 million slaves were free people by the end of the war, more than 360,000 of them in North Carolina. Despite their lack of schooling, these African Americans demonstrated a clear vision of what they wanted and a strong determination to get it. Like their fellow citizens, they demanded independence and the opportunity to own their own farms, businesses, and homes, and they were willing to work as hard as necessary to achieve these goals. They also desired education for themselves and their children, making great sacrifices toward this end; a full and rewarding social life, surrounded by family and friends; and protection from physical abuse, intimidation, and discriminatory laws. The majority of North Carolina’s white population sought to keep African Americans in a subservient position, politically and economically. The state’s 1865 black code restricted their movements, economic opportunities, and civil rights. Blacks were limited in their right to testify in court, received discriminatory penalties for crimes, and could not vote. Planters sought a stable labor force through restrictive contracts, low wages, apprenticeship, physical intimidation, and, in some cases, abuse of the court system. Most blacks worked peacefully but with determination to change attitudes and policies. Socially, thousands of the state’s African Americans reunited their families and married the person with whom they had previously cohabited. They deserted white churches and formed new ones, either affiliating with white northern or African Methodist Episcopal churches. Black churches quickly became the center not only for religious worship but also for educational instruction and community pride. Blacks also organized a rich cultural life, forming bands and lodges, sponsoring parades and exhibits, holding balls and dances, and establishing a few newspapers to serve their communities. Moreover, North Carolina’s freedpeople exhibited a ‘‘mania’’ for education. Almost immediately after the war, blacks in many areas began to raise money to build schools, buy books, and pay teachers. Within two years, more than 150 schools taught approximately 13,000 black children. Freedmen held two statewide conventions (1865 and 1866), in addition to numerous mass meetings throughout the state. At these gatherings, they praised the work of congressional Republicans and the Freedmen’s Bureau and called for full civil and political rights. They also pressed for more economic equality, complaining of physical abuse and intimidation, nonpayment of wages, mistreatment by their former masters, low pay, and the unavailability of land for them to purchase. Blacks established the Freedmen’s Educational Association of North Carolina to promote black education and an Equal Rights League to advance their civil rights. Many of the state’s traditionally black colleges were established in this era. Freedmen also organized one of the South’s most successful Union Leagues, which became the basis for political education once black suffrage was instituted. They protested abuse of the apprenticeship system, whereby children were removed from their parents and apprenticed to their former owners. Taking their grievances to the Freedmen’s Bureau and to state courts, they finally won a victory in 1867, when the North Carolina Supreme Court voided the apprenticeship contracts of Harriet and Eliza Ambrose to Daniel L. Russell and delivered a strong censure of those who violated due process of law. When black men gained the vote in 1867, their political activity increased in North Carolina. Between 1876 and 1894, 52 African Americans were sent to the Lower House of the General Assembly. The Second Congressional District, known as the ‘‘Black Second,’’ served as a political stronghold between 1872 and 1900, electing such representatives as John A. Hyman, the first African American in North Carolina to sit in the U.S. Congress; James E. O’Hara, the state’s second black congressman; and George H. White, the last former slave to serve in Congress. Life for black North Carolinians following Reconstruction appeared to be liberal by late nineteenth-century standards. After the passage of the national Civil Rights Act of 1875, many African Americans exercised their new freedom in railroad cars, steamboats, hotels, theaters, and other public venues. Their political gains came at great cost, however, and were muted by the return of Democrats to power in 1876. The newfound freedoms enjoyed by blacks fueled a brutal backlash by angry whites. North Carolina saw the eruption of widespread violence by groups such as the Ku Klux Klan, whose purpose was to terrorize blacks and diminish their newly won political rights. When the Republican and Populist Parties collaborated in the mid-1890s to again oust the Democrats, their ‘‘Fusion’’ government yielded blacks more funds for education and direct election of local officials, as well as a wealth-based tax system. In response, brutal white supremacy campaigns in 1898 and 1900 enabled the Democratic Party—through fraud, intimidation, violence, and racist rhetoric—to return to power in North Carolina. The Democrats then set out to prevent any future challenges to white supremacy, amove grounded in African American disfranchisement. Building on the ‘‘separate but equal’’ doctrine established in the 1896 U.S. Supreme Court decision in Plessy v. Ferguson, North Carolina Democrats in 1899 passed JimCrow laws instituting a system of legal segregation. The next year, white citizens approved a state constitutional amendment requiring all voters to pay a poll tax and pass a literacy test unless an ancestor had voted in an election prior to 1 Jan. 1867. Intended to disfranchise the African American population, the amendment succeeded in eliminating black North Carolinians from traditional politics. Keep reading >> Part IV: Segregation and the struggle for equality 1 January 2006 | Alexander, Roberta Sue; Barfield, Rodney D.; Nash, Steven E.

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When using if statements, you will often wish to check multiple different conditions. You must understand the Boolean operators OR, NOT, and AND. The boolean operators function in a similar way to the comparison operators: each returns 0 if evaluates to FALSE or 1 if it evaluates to TRUE. NOT: The NOT operator accepts one input. If that input is TRUE, it returns FALSE, and if that input is FALSE, it returns TRUE. For example, NOT (1) evalutes to 0, and NOT (0) evalutes to 1. NOT (any number but zero) evaluates to 0. In C and C++ NOT is written as !. NOT is evaluated prior to both AND and OR. AND: This is another important command. AND returns TRUE if both inputs are TRUE (if 'this' AND 'that' are true). (1) AND (0) would evaluate to zero because one of the inputs is false (both must be TRUE for it to evaluate to TRUE). (1) AND (1) evaluates to 1. (any number but 0) AND (0) evaluates to 0. The AND operator is written && in C++. Do not be confused by thinking it checks equality between numbers: it does not. Keep in mind that the AND operator is evaluated before the OR operator. OR: Very useful is the OR statement! If either (or both) of the two values it checks are TRUE then it returns TRUE. For example, (1) OR (0) evaluates to 1. (0) OR (0) evaluates to 0. The OR is written as || in C++. Those are the pipe characters. On your keyboard, they may look like a stretched colon. On my computer the pipe shares its key with \. Keep in mind that OR will be evaluated after AND. It is possible to combine several boolean operators in a single statement; often you will find doing so to be of great value when creating complex expressions for if statements. What is !(1 && 0)? Of course, it would be TRUE. It is true is because 1 && 0 evaluates to 0 and !0 evaluates to TRUE (ie, 1). Try some of these - they're not too hard. If you have questions about them, feel free to stop by our forums. A. !( 1 || 0 ) ANSWER: 0 B. !( 1 || 1 && 0 ) ANSWER: 0 (AND is evaluated before OR) C. !( ( 1 || 0 ) && 0 ) ANSWER: 1 (Parenthesis are useful) Why does not false evaluate to true and vice versa??? What the heck do those questions mean??

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Before a number can be displayed it has to be converted to a string - more on strings in the next chapter. The simplest way to get numeric output is to use the println or print methods of out double myDouble=1.523454565; int myInt=2; System.out.println(myInt); System.out.println(myDouble); In each case the printlin method performs a default conversion of the numeric value to a string. What if we want to control the conversion? The answer is that you can use the format or printf methods in place of print or println. The way that this works is that you specify a format and the variables to be printed. The rules for the format can be complicated but the first rule is that any regular character in the format is just displayed. So for example: System.out.printf("this is my number",myDouble); just displays "this is my number" the value in myDouble isn't displayed. To get a the value in a variable displayed you have to include a format specifier which all start with %. How the number is displayed depends on the format specifier you choose. System.out.printf( "this is my number %f",myDouble); this is my number 1.523455 Notice that the value of the variable is displayed where the format specifier occurs - the value replaces the format specifier in the output. If you want to specify the number total number of characters and the digits after the decimal point to use then you can precede the f by two numbers c.d which gives the total number of characters including the decimal point and fractional digits f, For example: System.out.printf( "this is my number %5.2f",myDouble); displays the floating point number using a total of 5 characters with 2 digits after the decimal point i.e. this is my number 1.5 You can use other format specifiers for other numeric types and for general formatting: %d is a decimal integer %f is a floating point value %n is a newline If you add a leading + you get a sign printed, a comma includes a locale specific grouping character and a - left justified the value in the space. System.out.printf( "this is my number %+-10.2f",myDouble); this is my number +1.52 There are a lot more ways to format numbers and you should lookup the DecimalFormat class if you want to control the way values are displayed even more.

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On this page... (hide) Middle English is the name given by historical linguistics to the diverse forms of the English language spoken between the Norman invasion of 1066 and the mid-to-late 15th century, when the Chancery Standard, a form of London-based English, began to become widespread, a process aided by the introduction of the printing press. By this time the Northumbrian dialect spoken in south east Scotland was developing into the Scots language. The language of England as spoken after this time, up to 1650, is known as Early Modern English. The Middle English verb has the following independent forms: - one voice (active) - 3 moods; indicative, subjunctive, and imperative - 2 tenses; present and preterite - 2 numbers and 3 persons - verbal noun (infinitive), present participle, and verbal adjective (past participle) Verbs are divided in two major groups according to how preterite and past participle is formed: - weak verbs; preterite formed with a dental suffix (-de/-te) - strong verbs; preterite formed with an ablaut. Weak verbs form the majority of Middle English verbs. In Old English there existed three classes of weak verbs, but in Middle English these fell together. Weak verb, class I |Sg.2||lern(e)st1 / lernest2 / lern(e)st3 / lernes4||lernedest||lerne!| |Sg.3||lern(e)þ1 / lerneþ2 / lernes3,4||lerned(e)||-| |Pl.1||lerneþ1 / lernen2,3 / lernes3, 4||lernen||lernen||lerned(en)||-| |Pl.2||lerneþ!1,2,3 / lernes!4| - Southern and Kentish - East Midland - West Midland Click verbs to conjugate them in the table above! - þanken to thank, - asken to ask, - clensen to ?, - enden to end, - lernen to learn, - wę̄ren to defend, - hāten to hate. - Wright, Joseph & Wright, Elizabeth Mary. An Elementary Middle English Grammar. Oxford University Press. 2 edition. Oxford. 1979. - http://astrolabe.vidmo.net/(approve sites)

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Imagine a system of molten silicate material, where low-density minerals float and higher density minerals sink. Minerals rich in iron and magnesium (such as olivine and pyroxene) will settle toward the bottom of the magma body while those rich in the elements aluminum and calcium (such as plagioclase feldspar) will float. Just such a scenario – on a global basis – is thought to have created the crust of the Moon. Before Apollo, many believed that the Moon was a primitive, undifferentiated lump of cosmic debris. By studying the samples returned by Apollo 11, scientists identified small fragments of white, plagioclase-rich rocks (anorthosite). There are no known magma compositions corresponding to this rock type – anorthosite is created by removing low-density plagioclase from a crystallizing system and concentrating it by floatation. From the evidence of fragments in the lunar soil, large amounts of anorthosite were inferred to be present in the nearby highlands of the Moon. As the highlands make up more than 85% of the surface of the Moon, it was postulated that the crust of the Moon formed early in its history by global melting, an episode termed the “magma ocean.” Expecting only minor volcanic activity and perhaps a local igneous intrusion, the concept of a global ocean of magma was surprising to most scientists. Given its small size and consequent paucity of radioactive heat-producing elements, the idea that most of the Moon might have melted and differentiated was astounding. The existence of an early magma ocean, which implied high-energy processes, provided us with clues to lunar origin. Once it was recognized that the Moon had a crust, it was important to gain an understanding of its composition and physical nature. On subsequent missions, Apollo astronauts were tasked with laying out a series of seismic stations across the near side. These stations allowed us to measure “moonquakes” – both natural events as well as those created artificially by slamming spent rocket stages and satellites into the Moon. Seismic recording allowed us to infer the speed at which seismic waves traveled through the lunar interior. These estimated speeds indicated densities that implied composition, allowing us to deduce the probable chemical and mineral composition of the lunar interior. The Apollo seismic network indicated that the crust of the Moon was about 50-60 km thick in the central near side, a surprisingly large value, especially compared to the thickness of the crust of the Earth (which varies from as thin as 5-10 km under the ocean basins to over 30 km in continental areas). Such a thick crust for the Moon led to the postulation of a global magma ocean, as so much anorthosite could only be produced under the conditions of near global melting. Subsequent studies incorporating gravity data from Lunar Orbiter and other missions suggested that the lunar crust is variable in thickness, with values exceeding 100 km in some regions of the far side highlands. Re-analysis of the Apollo seismic data gave the first indication that those values might be overestimated. Using modern techniques on these old data, new analysis revealed that the crust might be thinner than we had originally thought, on the order of 40-50 km thick. This lower value of crustal thickness had some implications for estimating the bulk chemical composition of the Moon, but because it was considered to be a relatively minor adjustment, it caused no major difficulties for the rest of lunar science. However, the recent GRAIL mission to the Moon (using high precision gravity mapping) ascertained the thickness of its crust to be 34-43 km. Why should this new value worry some scientists? Because we are now entering realms in which the new estimates of crustal thickness create consistency problems for other aspects of lunar science. A crust as thin as 35 km on the near side of the Moon implies that the largest impacts – the multi-ring basins – should have excavated considerable amounts of material from the layer below the crust, the mantle of the Moon. One might object that, as this region of the interior is inaccessible, we don’t know what the mantle would look like. But in fact, the density constraints imposed by the seismic and gravity data dictate that it must be a rock type rich in iron and magnesium, made up mostly of the minerals olivine and pyroxene. Such rocks are not unknown in the lunar collections, but they possess chemical and mineralogical characteristics indicating their origins at much shallower (crustal) depths. In other words, there does not appear to be any material from the lunar mantle in the Apollo collections. Given our obviously incomplete sampling of the Moon, should this be a problem? Several Apollo landing sites (e.g., Apollo 14 and 15) were specifically chosen to maximize the chances of sampling ejecta from the enormous 1100 km diameter Imbrium basin (one of the biggest impact features on the Moon). Virtually any reconstruction of the dimensions of the excavation cavity of this basin indicates that it should have dug up material from tens of kilometers depth, much deeper than the new value of crustal thickness implied by the GRAIL data. So where is this debris from the mantle of the Moon? True enough, it is possible that it may have been missed during the limited exploration time available to the Apollo crews, but the astronauts were trained to recognize such rocks and none were found. Additionally, because we can map rock types by remote sensing (both from spacecraft and from Earth), we have an understanding of the regional distribution of rocks around these large impact features. Despite a 30-year, exhaustively detailed search of the Imbrium impact basin (an area larger than Texas), we have found no convincing evidence for mantle material on the surface of the Moon. So where does this leave us? In science, new data can solve some problems but at the same time, it may also create new ones. Modern analyses of the old seismic data and new information on the Moon’s gravity field both suggest a relatively thin crust, with mantle material being very close to the surface (a few km) in some areas. On the other hand, none of the ubiquitous impact basins and large craters of the Moon show evidence for mantle material in their ejecta, either in the Apollo collections or in remote sensing data. Could our understanding of impact mechanics be completely wrong? Or are we misunderstanding the new gravity data? How could an event that formed an impact crater thousands of kilometers across excavate only a few kilometers deep?

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Overview of Section Resources - Section 1: What Is Sound? - Students begin their investigation of sound by listening to sounds and noting differences in pitch and volume. They experiment to find out what makes a loud sound and what makes a soft sound. Students also learn that sounds are made by vibrating objects. They are given the opportunity to feel the vibrations of the tines of a tuning fork and see the vibrations make ripples in water. - Section 2: Speaking and Hearing - Students learn that their vocal chords vibrate as air passes through them, producing sound. Students practice varying the pitch and volume of their voices. Using a homemade kazoo, they feel the vibrations of the membrane that create the sound. They also construct a model of the ear canal and ear drum and use it to learn how we hear sounds. - Section 3: Changing Pitch - Students learn about the variables that affect pitch. They pluck a string and observe what happens to the pitch as the length and tension of the string change. Then they compare the pitch of sounds produced by plucked rubber bands of different widths. They look inside a stringed instrument to see how the instrument is able to produce a wide variety of pitched notes. Finally, they tap glass bottles filled with varying amounts of water and see how the amount of water in the bottles affects the pitch of the sound produced. - Section 4: How Sound Travels - In this section, students learn that sounds travel differently through solids, liquids, and gases. Students compare the quality of sound traveling through solids, liquids, and gases and conclude that sound travels best through solids and least well through gases.

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How does the accelerator work? Jefferson Lab's accelerator makes electrons go faster by placing negative charges behind them and positive charges in front of them. Since electrons have a negative electrical charge, they are repelled by the other negative charges and are attracted towards the positive charges. Devices called cavities, like the two shown in the photo, are used to place positive and negative charges around the electrons in the beam. Cavities are hollow shells made from the element niobium. Jefferson Lab's accelerator uses 338 cavities, mostly in the two long, straight sections. Microwaves are directed into the cavities and cause the electrons in the niobium metal to concentrate in certain areas. Since these areas have extra electrons, they become negatively charged. Other areas of the cavities have too few electrons, so they become positively charged. The electrons in the beam are pulled towards the positively charged areas and are pushed away from the negatively charged areas. [See Diagram] Since the electrons in the beam are moving at nearly the speed of light, the microwaves must cycle the positions of the charged areas 1.5 billion times a second. This ensures that the electrons in the beam will always have a positively charged area ahead of them and a negatively charged area behind them.

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Along the margin of the Greenland Ice Sheet, outlet glaciers flow as icy rivers through narrow fjords and out to sea. As long as the thickness of the glacier and the depth of the water allow the ice to remain grounded, it stays intact. Where the ice becomes too thin or the water too deep, the edge floats and rapidly crumbles into icebergs. Satellite observations of eastern Greenland’s Helheim Glacier show that the position of the iceberg’s calving front, or margin, has undergone rapid and dramatic change since 2001, and the glacier’s flow to the sea has sped up as well. These images from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) on NASA’s Terra satellite show the Helheim glacier in June 2005 (top), July 2003 (middle), and May 2001 (bottom). The glacier occupies the left part of the images, while large and small icebergs pack the narrow fjord in the right part of the images. Bare ground appears brown or tan, while vegetation appears in shades of red. From the 1970s until about 2001, the position of the glacier’s margin changed little. But between 2001 and 2005, the margin retreated landward about 7.5 kilometers (4.7 miles), and its speed increased from 8 to 11 kilometers per year. Between 2001 and 2003, the glacier also thinned by up to 40 meters (about 131 feet). Scientists believe the retreat of the ice margin plays a big role in the glacier’s acceleration. As the margin of the glacier retreats back toward land, the mass of grounded ice that once acted like a brake on the glacier’s speed is released, allowing the glacier to speed up. Overall, the margins of the Greenland Ice Sheet have been thinning by tens of meters over the last decade. At least part of the thinning is because warmer temperatures are causing the ice sheet to melt. But the other part of the thinning may be due to changes such as glacier acceleration like that seen at Helheim. Initial melting due to warming may set up a chain reaction that leads to further thinning: the edge of the glacier melts and thins, becomes ungrounded and rapidly disintegrates. The ice margin retreats, the glacier speeds up, and increased calving causes additional thinning. Understanding the dynamic interactions between temperature, glacier flow rates, and ice thickness is crucial for scientists trying to predict how the Greenland Ice Sheet will respond to continued climate change. - Howat, I. M., I. Joughin, S. Tulaczyk, and S. Gogineni (2005). Rapid retreat and acceleration of Helheim Glacier, east Greenland. Geophysical Research Letters, 32, L22502, doi:10.1029/2005GL024737. NASA images created by Jesse Allen, Earth Observatory, using data provided courtesy of NASA/GSFC/METI/ERSDAC/JAROS, and the U.S./Japan ASTER Science Team.

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History of Slavery in North Carolina This illustration shows white children playing with a black child, and "represents the old Negro servants of the planter's family among his children. The children of the [white] family grow up among the Negro domestic servants, and often learn to regard them with as much affection as they show their own parents." Source: The Illustrated London News Many of the first slaves in North Carolina were brought to the colony from the West Indies or other surrounding colonies, but a significant number were brought from Africa. Most of the English colonists arrived as indentrued servants, hiring themselves out as laborers for a fixed period to pay for their passage. In the early years the line between indentured servants and African slaves or laborers was fluid. Some Africans were allowed to earn their freedom before slavery became a lifelong status. As the flow of indentured laborers from England to the colony decreased with improving economic conditions in Great Britain, more slaves were imported and the state's restrictions on slavery hardened. The economy's growth and prosperity was based on slave labor, devoted first to the production of tobacco. Colonial laws were enacted to allow whites to control their slaves. The first of these was the North Carolina Slave Code of 1715. Under these laws, whenever slaves left the plantation they were required to carry a ticket from their master, which stated their destination and the reason for their travel. The 1715 code also prevented slaves from gathering in groups for any reason, including religious worship, and required whites to help capture runaway slaves. The colony lacked the extensive plantation system of the Lower South, and when Carolina split into the North and South Carolina in 1729, North Carolina had about 6000 slaves, only a fraction of the slave population of South Carolina. As the plantation system expanded across the Lower South, many North Carolina slaves were "sold south" to work on large plantations. Slaves deeply feared this fate because it usually meant permanent separation from friends and family. A second set of even stricter laws was put into place in 1741, which prevented slaves from raising their own livestock and from carrying guns without their master's permission, even for hunting. The law also limited manumission – the freeing of slaves. A master could only free a slave for meritorious service, and even then the decision had to be approved by the county court. Perhaps the most ominous of all the laws was the one regarding runaway slaves: If runaways refused to surrender immediately, they could be killed and there would be no legal consequences. By 1767, there were about 40,000 slaves in the North Carolina colony. About 90 percent of these slaves were field workers who performed agricultural jobs. The remaining 10 percent were mainly domestic workers, and a small number worked as artisans in skilled trades, such as butchering, carpentry, and tanning. Because of its geography, North Carolina did not play a large part in the early slave trade. The string of islands that make up its Outer Banks made it dangerous for slave ships to land on most of North Carolina's coast, and most slave traders chose to land in ports to the north or south of the colony. The one major exception is Wilmington – located on the Cape Fear River, it became a port for slave ships because of its accessibility. By the 1800s, blacks in Wilmington outnumbered whites 2 to 1. The town relied on slaves' abilities in carpentry, masonry, and construction, as well as their skill in sailing and boating, for its growth and success. Most of the free black families formed in North Carolina before the Revolution were descended from unions or marriages between free white women and enslaved or free African American men. Because the mothers were free, their children were born free. Many had migrated or were descendants of migrants from colonial Virginia. The North Carolina Provincial Congress passed a ban on importing slaves in 1774, because they felt increasing the number of slaves in the colony would increase the number of runaways and free blacks. The fear of slave uprisings only increased with the advent of the Revolutionary War in 1775. The British offered to help slaves escape if they would fight against the colonists, and a number of North Carolina slaves accepted. After the war ended and the new country was founded, tensions between whites and blacks in the state continued to increase. Besides slaves, there were a number of free people of color in the state. Most were descended from free African Americans who had migrated from Virginia during the eighteenth century. After the Revolution, Quakers and Mennonites worked to persuade slaveholders to free their slaves. Some were inspired by their efforts, and the language of men's rights, to arrange for manumission of their slaves. The number of free people of color rose markedly in the first couple of decades after the Revolution. Hauling the Seine This scene is of the fisheries of Albemarle and Pamlico Sounds in North Carolina, which were known to employ a considerable number of Free Negroes from neighboring counties. The huge seines (nets) could measure up to two miles in length. The ban on importing slaves to North Carolina was lifted in 1790, and the state's slave population quickly increased. By 1800, there were around 140,000 blacks living in the state. A small number of these were free blacks, who mostly farmed or worked in skilled trades. The majority were slaves working in agriculture on small- to medium-sized farms. After 1800, cotton and tobacco became important export crops, and the eastern half of the state developed a plantation system based on slavery, while the western areas were dominated by white families who operated small farms. Most of North Carolina's slave owners and large plantations were located in the eastern portion of the state. Although North Carolina's plantation system was smaller and less cohesive than those of Virginia, Georgia or South Carolina, there were significant numbers of planters concentrated in the counties around the port cities of Wilmington and Edenton, as well as suburban planters around the cities of Raleigh, Charlotte and Durham. In addition, 30,463 free people of color lived in the state. They were also concentrated in the eastern coastal plain, especially at port cities such as Wilmington and New Bern where they had access to a variety of jobs. Free African Americans were allowed to vote until 1835, when the state rescinded their suffrage. As in the colonial period, few North Carolina slaves lived on huge plantations. Fifty-three percent of slave owners in the state owned five or fewer slaves, and only 2.6 percent of slaves lived on farms with over 50 other slaves during the antebellum period. In fact, by 1850, only 91 slave owners in the whole state owned over 100 slaves. Because they lived on farms with smaller groups of slaves, the social dynamic of slaves in North Carolina was somewhat different from their counterparts in other states, who often worked on plantations with hundreds of other slaves. In North Carolina, the hierarchy of domestic workers and field workers was not as developed as in the plantation system. There were fewer numbers of slaves to specialize in each job, so on small farms, slaves may have been required to work both in the fields and at a variety of other jobs at different times of the year. Another result of working in smaller groups was that North Carolina slaves generally had more interaction with slaves on other farms. Slaves often looked to other farms to find a spouse, and traveled to different farms to court or visit during their limited free time. The slave codes passed in the colonial period continued to be enforced during the antebellum years. Whites hoped these laws would prevent threats of slave uprisings. In 1829, David Walker, a free black author born in Wilmington, gave whites in North Carolina another reason to fear their slaves turning against them. Walker was an avid abolitionist who moved from his home state of North Carolina to Boston, where he helped escaped slaves establish new lives. He wrote and published a pamphlet, Walker’s Appeal, calling for immediate freedom for all slaves and urging slaves to rebel as a group. Copies of the pamphlet were smuggled into Wilmington via ships from the Northern US, and then spread throughout the state. Whites reacted to Walker’s Appeal by passing increasingly restrictive slave laws. Nervous leaders in North Carolina passed legislation in 1830 making it illegal to distribute the pamphlet in hopes of quelling Walker's radical ideas about abolishing slavery. Another North Carolina law passed in 1830 made it a crime to teach a slave to read or write. Laws were even extended to restrict the rights of free blacks. An 1835 law prevented free blacks from voting, attending school, or preaching in public. These restrictive laws were also passed in response to the increase in slave uprisings in nearby states, such as the Nat Turner Rebellion just across the border in Virginia. In 1831, Nat Turner led a group of 75 escaped slaves in an uprising, during which the group killed about 60 white people before being captured by the state militia. Whites in North Carolina were appalled at the thought of a similar rebellion happening in their state, and hoped severe slave laws would prevent such bloody uprisings. The Life of a Slave Daily life for a slave in North Carolina was incredibly difficult. Slaves, especially those in the field, worked from sunrise until sunset. Even small children and the elderly were not exempt from these long hours. Slaves were generally allowed a day off on Sunday, and on holidays such as Christmas or the Fourth of July. During their few hours of free time, most slaves performed their own personal work. The diet supplied by slaveholders was generally poor, and slaves often supplemented it by tending small gardens or fishing. Although there were exceptions, the prevailing attitude among slave owners was to allot their slaves the bare minimum of food and clothing. Shelter provided by slave owners was also meager. Many slaves lived in small stick houses with dirt floors, not the log slave cabins often depicted in books and films. These shelters had cracks in the walls that let in cold and wind, and had only thin coverings over the windows. One area of their lives in which slaves were able to exercise some autonomy from their masters was creating a family. Slave owners felt it was to their advantage to allow slaves to marry, because any children from the marriage would add to their wealth. According to law, a child took on the legal status of its mother; a child born to a slave mother would in turn become a slave, even if the father was free. Because the large plantations of the Lower South needed more slaves than the smaller farms of North Carolina, it was not uncommon for slaves in the state to be sold to slave traders who took them south to Georgia, South Carolina, Mississippi, Louisiana, or Alabama. Once a family member was sold and taken to the Deep South, they became almost impossible to locate or contact. Although slaves had no way to publicly or legally complain about unfair treatment and abuse, they developed other methods of resistance. Slaves could slow down, pretend to be sick, or sabotage their work as a way to object against long hours of backbreaking labor. Slaves could also steal small amounts of food as a method of protesting their inadequate diet and providing for their families. The Great Dismal Swamp, which is located in the northeastern part of the state and stretches from Edenton, North Carolina to Norfolk, Virginia, was a common destination for North Carolina runaways. The swamp was an ideal spot in which to hide and forage for food, and some escaped slaves chose to stay and make their homes there. The swamp was also known as a destination for escaped slaves from other states. As in other states, the Underground Railroad developed in North Carolina to help escaped slaves reach safety. The North Carolina stops were primarily organized by members of the Religious Society of Friends, also known as the Quakers. Levi Coffin was well-known for assisting escaped slaves in Guilford County, North Carolina. The North and the South clashed over the issue of slavery throughout the 1850s, and the conflict soon boiled over into Civil War. Southern slave owners felt they would quickly defeat the Union. The Union states had about 21 million people, while the Confederate states had approximately 9 million, and over three and a half million of those Southerners were slaves. President Abraham Lincoln had issued the Emancipation Proclamation on January 1, 1863, stating that slaves in the Confederate states were freed. The proclamation had little immediate effect, but served as a promise that the government would free slaves after the war. Slaves in the Confederate states were officially freed by the passage of the Thirteenth Amendment of the U.S. Constitution in December of 1865. Slavery in North Carolina Slavery and Servitude in the Colony of North Carolina

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Beginning in the eighteenth century, free and enslaved African Americans used public spaces for celebrations, such as Negro Election Day, Militia Training Day, and Pinkster festivals throughout the New England and Mid-Atlantic states. In 1808, African Americans began to celebrate the United States' abolition of the Atlantic slave trade on January 1, 1808. These early examples of black holidays helped lay the foundation for future commemorative traditions important to African American culture. Following emancipation African Americans expanded their commemorative traditions in a way that had been impossible during slavery. Such observances were important in part because they represented a form of cultural resistance and autonomy. Because black holidays took place in very public spaces, like main streets and thoroughfares, white Americans could not ignore their lively festivities. In some cases, the mayors and governors delivered speeches at black parades and attractions. By the end of the nineteenth century, the African American calendar was filled with holidays and other events that celebrated prominent and renowned African Americans of their time. Even though blacks practiced commemorative traditions decades before the Emancipation Proclamation, Emancipation Day celebrations are one of the most important African American holidays. President Abraham Lincoln's Emancipation Proclamation stated that all enslaved Americans living in the Confederate states would be free beginning on January 1, 1863, which represented the first of several incremental steps toward total abolition of slavery in the United States. Blacks held celebrations all over the North and in portions of the South the first few days after January 1. This extraordinarily important event inspired African Americans to celebrate and rejoice through local festive gatherings such at watch night services, musical concerts, and national conventions and expositions after the Civil War. Local festive gatherings included mainly religious services, speeches, and the reciting of the Emancipation Proclamation. Larger events, like national conventions and expositions, lasted several days and included plantation melodies, jubilee songs, parades, games, and large-scale attractions. There is no one, official day African Americans celebrated Emancipation Day. In fact, as an article about the National Thanksgiving Day for Freedom celebration that ran in the Richmond Planet outlined, there was a great deal of disagreement over the proper date for the observance. Many felt that January 1 was the appropriate date, while other African Americans in the community thought that April 3, the date that Richmond fell, or April 9, the date of Lee's surrender, were more appropriate. In Purcellville and Hamilton, Virginia, the Loudoun County Emancipation Association organized in 1890 an annual Freedom Day celebration on September 22, the day President Lincoln announced the Emancipation Proclamation to the country. Other localities throughout the South continue to celebrate emancipation at different times in the calendar year, often related to the date when Union troops brought news of the Emancipation Proclamation to the area. In San Antonio, Texas, blacks celebrated emancipation on June 19, also known as Juneteenth. From October 15 to 17, 1890, Richmond, Virginia, hosted emancipation festivities advertised on this broadside, or poster, publicizing a National Thanksgiving Day for Freedom. Events included speeches by then–Virginia governor Philip Watkins McKinney and the mayor of Richmond, James Taylor Ellyson, on the first day. Among the other notable participants were Branch K. Bruce of Mississippi, the first African American to be elected to the U.S. Senate; U.S. representative John Mercer Langston, the only African American to represent Virginia in the U.S. Congress (then serving in his short, six month tenure in that position); Joseph Charles Price, the president of the National Afro-American League, and founder and president of the Zion Wesley Institute, now Livingstone College, in Salisbury, North Carolina; William Washington Browne, founder of the United Order of True Reformers and the True Reformers Bank in Richmond Virginia, the first African American–operated bank in the nation. The second day featured a grand parade through parts of Richmond, the former capital of the Confederacy, and religious praise and orations on the last day. In these and many other instances, African Americans used racially contested public spaces to expand and strengthen the influence of their own rituals throughout the United States. 1. Why did Richmond's Freedom Day organizers include important white politicians and business leaders? 2. What can this broadside tell us about Richmond's black population? 3. What role would you play in the Emancipation Day festivities? The Juneteenth tradition is thought to have begun on June 19, 1865, when General Gordon Granger arrived in Galveston, Texas, and read the governmental decree freeing all slaves east of Texas. By the late twentieth century, Juneteenth celebrations had gained recognition throughout the United States because of popular media and intellectual attention. Today, Juneteenth is celebrated throughout the United States to honor the freedom of African Americans. Berrett, Joshua. “The Golden Anniversary of the Emancipation Proclamation.” Black Perspective in Music 16, no. 1 (1988): 63–80. Brundage, W. Fitzhugh. The Southern Past: A Clash of Race and Memory. Cambridge, Massachusetts: The Belkap Press of Harvard University Press, 2005. Kachun, Mitch. Festivals of Freedom: Memory and Meaning in African American Emancipation Celebrations, 1808–1915. Amherst: University of Massachusetts Press, 2003. Wiggins, William H. O Freedom! Afro-American Emancipation Celebrations. Knoxville: University of Tennessee Press, 1987.

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The objective of this lesson is to introduce the parts of the heart and the flow of blood through the heart. - diagram of the heart - a model of the heart - masking tape - small pieces of paper or index - floor space - Before class, the teacher should draw a large diagram of the heart on the floor (this diagram should include the four chambers of the heart, valves, major veins and arteries) and also make labels of the parts of the heart. - When the students arrive, vocabulary should be discussed and then students should be chosen to place the labels in the appropriate places on the heart diagram on the floor. - The flow of blood through the heart should then be discussed. Arrows may also be placed on the diagram. - Students can then “become” a drop of blood, walk through the heart and trace the flow of blood. Oxygenated and deoxygenated blood may also be discussed. - The diagram may then be left on the floor for several days and used for review. A good follow up homework activity is to have students write a journal entry about a drop of blood traveling through the body. I used this lesson with deaf and hard of hearing students in a high school biology class. This activity is very interactive and fun. It is a great alternative to memorizing parts of the heart from a book. Also, be patient when working with the tape… becoming skilled at drawing a heart may take some practice! Using color coordinated cards for the labels is also a good idea-red markers for parts of the heart with oxygenated blood and arrows, and blue for parts with deoxygenated blood and arrows. Grade Level(s): 9-12 By: Amy, 9th and 10th grade biology teacher Related lesson plans: - Halloween Candy Sort Share/BookmarkA post-Halloween math activity that uses sorting, classification, and a Venn Diagram. Materials: a large piece of butcher paper candy wrappers Lesson Plan: Have students bring in a variety of candy wrappers after Halloween. As a class, sort the candy... - Complete Sentences Share/BookmarkStudents will be able to put parts of a sentence together to make a complete sentence. Materials: sentence strips paper sentence parts Lesson Plan: Do some warm up exercises with parts of a sentences using pieces of sentences strips. Have... - It’s Time to Get Organ-Wised Share/BookmarkSeveral activities & printables for a unit on the body and body organs. GET TO KNOW YOUR MAJOR ORGANS Printables: Organ Cards - color • black & white • facts For younger children, copy the colorful organs onto card stock. Cut out and paste on... - The Kissing Hand Activity for the First Week of School Share/BookmarkActivities to go along with the book The Kissing Hand. Materials: Put the following items in a book bag or backpack or shoebox: Book: The Kissing Hand by Audrey Penn Heart shaped stickers Hand cut outs Journal book Pencils or crayons Lesson... - Dinofours My Seeds Won’t Grow Book Activity Share/BookmarkStudents will be able to identify what plants need to grow. Materials: Book: Dinofours My Seeds Won’t Grow clear plastic cups seeds- Lima Beans or marigolds water potting soil Lesson Plan: Read and discuss the story including talking about what...

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are stony meteorites that have not been modified due to melting of the parent body. They formed when various types of dust and small grains that were present in the early solar system accreted to form primitive asteroids . Prominent among the components present in chondrites are the enigmatic chondrules , millimeter-sized objects that originated as freely floating, molten or partially molten droplets in space; most chondrules are rich in the silicate . Chondrites also contain refractory inclusions (including Ca-Al Inclusions ), which are among the oldest objects to form in the solar system, particles rich in metallic Fe-Ni and sulfides, and isolated grains of silicate minerals. The remainder of chondrites consists of fine-grained (micrometer-sized or smaller) dust, which may either be present as the matrix of the rock or may form rims or mantles around individual chondrules and refractory inclusions. Embedded in this dust are presolar grains , which predate the formation of our solar system and originated elsewhere in the galaxy. Most meteorites that are recovered on Earth are chondrites: ~86% of witnessed falls are chondrites, as are the overwhelming majority of meteorites that are found. There are currently over 27,000 chondrites in the world's collections. The largest individual stone ever recovered, weighing 1770 kg, was part of the Jilin meteorite shower of 1976. Chondrite falls range from single stones to extraordinary showers consisting of thousands of individual stones, as occurred in the Holbrook fall of 1912, where an estimated 14,000 stones rained down on northern Arizona. Origin and history The parent bodies of chondrites are (or were) small to medium sized asteroids that were never part of any body large enough to undergo melting and planetary differentiation . These bodies accreted shortly after the beginning of the Solar System's history, about 4.55 billion years ago. Although chondritic asteroids never became hot enough to melt, many of them reached high enough temperatures that they experienced significant thermal metamorphism in their interiors. The source of the heat was most likely energy coming from the decay of short-lived radioisotopes (half-lives less than a few million years) that were present in the newly formed solar system, especially 26Al , although heating may have been caused by impacts onto the asteroids as well. Many chondritic asteroids also contained significant amounts of water, possibly due to the accretion of ice along with rocky material. As a result, many chondrites contain hydrous minerals, such as clays, that formed when the water interacted with the rock on the asteroid in a process known as aqueous alteration . In addition, all chondritic asteroids were affected by impact and shock processes due to collisions with other asteroids. These events caused a variety of effects, ranging from simple compaction to brecciation , veining, localized melting, and formation of high-pressure minerals. The net result of these secondary thermal, aqueous, and shock processes is that only a few known chondrites preserve in pristine form the original dust, chondrules, and inclusions from which they formed. Types of chondrites Chondrites are divided into about 15 distinct groups (see Meteorites classification) on the basis of their mineralogy, bulk chemical and oxygen isotopic compositions (see below). The various chondrite groups likely originated on separate asteroids or groups of related asteroids. Each chondrite group has a distinctive mixture of chondrules, refractory inclusions, matrix (dust), and other components and a characteristic grain size. are by far the most common type of meteorite to fall on Earth: about 80% of all meteorites and over 90% of chondrites are ordinary chondrites. They contain abundant chondrules, sparse matrix (10-15% of the rock), few refractory inclusions, and variable amounts of Fe-Ni metal and troilite (FeS). Their chondrules are generally in the range of 0.5 to 1 mm in diameter. Ordinary chondrites are distinguished chemically by their depletions in refractory lithophile elements, such as Ca, Al, Ti, and rare earths , relative to Si, and isotopically by their unusually high 17 O ratios relative to 18 O compared to Earth rocks. Most, but not all, ordinary chondrites have experienced significant degrees of metamorphism, having reached temperatures well above 500°C on the parent asteroids. They are divided into three groups, which have different amounts of metal and different amounts of total iron: - H chondrite have High iron contents, and smaller chondrules than L and LL chondrites. ~40% of ordinary chondrite falls belong to this group. - L chondrites have Low iron contents. About half of ordinary chondrite falls are L chondrites, which makes them the most common type of meteorite to fall on Earth. - LL chondrites have Low iron and Low metal contents. Only 1 in 10 ordinary chondrites is LL. make up less than 5% of the chondrites that fall on earth. There are many groups of carbonaceous chondrites, but most of them are distinguished chemically by enrichments in refractory lithophile elements relative to Si and isotopically by unusually low 17 O ratios relative to 18 O compared to Earth rocks. All groups of carbonaceous chondrites except the CH group are named for a characteristic type specimen: - CI (Ivuna type) chondrites entirely lack chondrules and refractory inclusions; they are composed almost exclusively of fine-grained material that has experienced a high degree of aqueous alteration on the parent asteroid. CI chondrites are highly oxidized, brecciated rocks, containing abundant magnetite and sulfate minerals, and lacking metallic Fe. It is a matter of some controversy whether they once had chondrules and refractory inclusions that were later destroyed during formation of hydrous minerals, or they never had chondrules in the first place. CI chondrites are notable because their chemical compositions closely resemble that of the solar photosphere, neglecting the hydrogen and helium. Thus, they have the most "primitive" compositions of any meteorites and are often used as a standard for assessing the degree of chemical fractionation experienced by materials formed throughout the solar system. - CO (Ornans type) and CM (Mighei type) chondrites are two related groups that contain very small chondrules, mostly 0.1 to 0.3 mm in diameter; refractory inclusions are quite abundant and have similar sizes to chondrules. - CM chondrites are composed of about 70% fine-grained material (matrix), and most have experienced extensive aqueous alteration. The much studied Murchison meteorite, which fell in Australia in 1969, is the best known member of this group. - CO chondrites have only about 30% matrix and have experienced very little aqueous alteration. Most have experienced small degrees of thermal metamorphism. - CR (Renazzo type), CB (Bencubbin type), and CH (high metal) carbonaceous chondrites are three groups that seem to be related by their chemical and oxygen isotopic compositions. All are rich in metallic Fe-Ni, with CH and especially CB chondrites having a higher proportion of metal than all other chondrite groups. Although CR chondrites are clearly similar in most ways to other chondrite groups, the origins of CH and CB chondrites are somewhat controversial. Some workers conclude that many of the chondrules and metal grains in these chondrites may have formed by impact processes after "normal" chondrules had already formed, and thus they may not be "true" chondrites. - CR chondrites have chondrules that are similar in size to those in ordinary chondrites (near 1 mm), few refractory inclusions, and matrix comprises nearly half the rock. Many CR chondrites have experienced extensive aqueous alteration, but some have mostly escaped this process. - CH chondrites are remarkable for their very tiny chondrules, typically only about 0.02 mm (20 micrometers) in diameter. They have a small proportion of equally tiny refractory inclusions. Dusty material occurs as discrete clasts, rather than as a true matrix. CH chondrites are also distinguished by extreme depletions in volatile elements. - CB chondrites occur in two types, both of which are similar to CH chondrites in that they are very depleted in volatile elements and rich in metal. CBa (subgroup a) chondrites are coarse grained, with large, often cm-sized chondrules and metal grains and almost no refractory inclusions. Chondrules have unusual textures compared to most other chondrites. As in CH chondrites, dusty material only occurs in discrete clasts and there is no fine-grained matrix. CBb (subgroup b) chondrites contain much smaller (mm-sized) chondrules and do contain refractory inclusions. - CV (Vigarano type) chondrites are characterized by mm-sized chondrules and abundant refractory inclusions set in a dark matrix that comprises about half the rock. CV chondrites are noted for spectacular refractory inclusions, some of which reach centimeter sizes, and they are the only group to contain a distinctive type of large, once-molten inclusions. Chemically, CV chondrites have the highest abundances of refractory lithophile elements of any chondrite group. The CV group includes the remarkable Allende fall in Mexico in 1969, which became one of the most widely distributed and, certainly, the best-studied meteorite in history. - CK (Karoonda type) chondrites are chemically and texturally similar to CV chondrites. However, they contain far fewer refractory inclusions than CV, they are much more oxidized rocks, and most of them have experienced considerable amounts of thermal metamorphism (compared to CV and all other groups of carbonaceous chondrites). - Ungrouped carbonaceous chondrites: A number of chondrites are clearly members of the carbonaceous chondrite class, but do not fit into any of the groups. These include: the Tagish Lake meteorite, which fell in Canada in 2000 and is intermediate between CI and CM chondrites; Coolidge and Loongana 001, which form a grouplet that may be related to CV chondrites; and Acfer 094, an extremely primitive chondrite that shares properties with both CM and CO groups. , which comprise only 2% of the chondrites that fall on Earth, are among the most chemically reduced rocks known. Unlike in most other chondrites, the minerals in enstatite chondrites contain almost no iron oxide; metallic Fe-Ni and Fe-bearing sulfide minerals contain nearly all of the Fe. Enstatite chondrites contain a variety of unusual minerals that can only form in extremely reducing conditions, including oldhamite (Fe-Ni silicide), and alkali sulfides (e.g., djerfisherite ). All enstatite chondrites are dominantly composed of enstatite -rich chondrules plus abundant grains of metal and sulfide minerals. Dusty matrix material is uncommon and refractory inclusions are very rare. Chemically, enstatite chondrites are very low in refractory lithophile elements. Their oxygen isotopic compositions are intermediate between ordinary and carbonaceous chondrites, and are similar to rocks found on the Earth and Moon. Most enstatite chondrites have experienced thermal metamorphism on the parent asteroids. They are divided into two groups: - EH (high metal) chondrites contain small chondrules (~0.2 mm) and high ratios of siderophile elements to Si. Somewhat more than 10% of the rock is composed of metal grains. A diagnostic feature of EH chondrites is that the Fe-Ni metal contains ~3 wt% elemental silicon. - EL (low metal) chondrites contain larger chondrules (>0.5 mm), and low ratios of siderophile elements to Si. Fe-Ni metal contains ~1 wt% Si. R (Rumuruti type) chondrites are a very rare group, with only one documented fall out of almost 900 documented chondrite falls. They have a number of properties in common with ordinary chondrites, including similar types of chondrules, few refractory inclusions, similar chemical composition for most elements, and the fact that 17 O ratios are anomalously high compared to Earth rocks. However, there are significant differences between R chondrites and ordinary chondrites: R chondrites have much more dusty matrix material (about 50% of the rock); they are much more oxidized, containing little metallic Fe-Ni; and their enrichments in 17 O are higher than those of ordinary chondrites. Three chondrites form what is known as the K (Kakangari type) grouplet, characterized by large amounts of dusty matrix and oxygen isotope compositions similar to carbonaceous chondrites, highly reduced mineral compositions and high metal abundances that are most like enstatite chondrites, and concentrations of refractory lithophile elements that are most like ordinary chondrites. Because chondrites accumulated from material that formed very early in the history of the solar system, and because chondritic asteroids did not melt, they have very primitive compositions. "Primitive," in this sense, means that the abundances of most chemical elements do not differ greatly from that those that are measured by spectroscopic methods in the photosphere of the sun, which in turn should be well-representative of the entire solar system (note: to make such a comparison between a gaseous object like the sun and a rock like a chondrite, scientists choose one rock-forming element, such as silicon, to use as a reference point, and then compare ratios. Thus, the atomic ratio of Mg/Si measured in the sun (1.07) is identical to that measured in CI chondrites ). Although all chondrite compositions can be considered primitive, there is variation among the different groups, as discussed above. CI chondrites seem to be nearly identical in composition to the sun for all but the gas-forming elements (e.g., hydrogen, carbon, nitrogen, and noble gases). Other chondrite groups deviate from the solar composition (i.e., they are fractionated) in highly systematic ways: - At some point during the formation of many chondrites, particles of metal became partially separated from particles of silicate minerals. As a result, chondrites coming from asteroids that did not accrete with their full complement of metal (e.g., L, LL, and EL chondrites) are depleted in all siderophile elements, whereas those that accreted too much metal (e.g., CH, CB, and EH chondrites) are enriched in these elements compared to the sun. - In a similar manner, although the exact process is not very well understood, highly refractory elements like Ca and Al became separated from less refractory elements like Mg and Si, and were not uniformly sampled by each asteroid. The parent bodies of many groups of carbonaceous chondrites over-sampled grains rich in refractory elements, whereas those of ordinary and enstatite chondrites were deficient in them. - No chondrites except the CI group formed with a full, solar complement of volatile elements. In general, the level of depletion corresponds to the degree of volatility, where the most volatile elements are most depleted. A chondrite's group is determined by its primary chemical, mineralogical, and isotopic characteristics (above). The degree to which it has been affected by the secondary processes of thermal metamorphism and aqueous alteration on the parent asteroid is indicated by its petrologic type , which appears as a number following the group name (e.g., an LL5 chondrite belongs to the LL group and has a petrologic type of 5). The current scheme for describing petrologic types was devised by Van Schmus and Wood in 1967. The petrologic-type scheme originated by Van Schmus and Wood is really two separate schemes, one describing aqueous alteration (types 1-2) and one describing thermal metamorphism (types 3-6). The alteration part of the system works as follows: - Type 1 was originally used to designate chondrites that lacked chondrules and contained large amounts of water and carbon. Current usage of type 1 is simply to indicate meteorites that have experienced extensive aqueous alteration, to the point that most of their olivine and pyroxene have been altered to hydrous phases. This alteration took place at temperatures of 50 to 150°C, so type 1 chondrites were warm, but not hot enough to experience thermal metamorphism. The members of the CI group, plus a few highly altered carbonaceous chondrites of other groups, are the only instances of type 1 chondrites. - Type 2 chondrites are those which have experienced extensive aqueous alteration, but still contain recognizable chondrules as well as primary, unaltered olivine and/or pyroxene. The fine-grained matrix is generally fully hydrated and minerals inside chondrules may show variable degrees of hydration. This alteration probably occurred at temperatures below 20°C, and again, these meteorites are not thermally metamorphosed. Almost all CM and CR chondrites are petrologic type 2; with the exception of some ungrouped carbonaceous chondrites, no other chondrites are type 2. The thermal metamorphism part of the scheme describes a continuous sequence of changes to mineralogy and texture that accompany increasing metamorphic temperatures. These chondrites show little evidence of the effects of aqueous alteration: - Type 3 chondrites show low degrees of metamorphism. They are often referred to as unequilibrated chondrites because minerals such as olivine and pyroxene show a wide range of compositions, reflecting formation under a wide variety of conditions in the solar nebula. (Type 1 and 2 chondrites are also unequilibrated.) Chondrites that remain in nearly pristine condition, with all components (chondrules, matrix, etc.) having nearly the same composition and mineralogy as when they accreted to the parent asteroid, are designated type 3.0. As petrologic type increases from type 3.1 through 3.9, profound mineralogical changes occur, starting in the dusty matrix, and then increasingly affecting the coarser-grained components like chondrules. Type 3.9 chondrites still look superficially unchanged because chondrules retain their original appearances, but all of the minerals have been affected, mostly due to diffusion of elements between grains of different composition. - Types 4, 5, and 6 chondrites have been increasingly altered by thermal metamorphism. These are equilibrated chondrites, in which the compositions of most minerals have become quite homogeneous due to high temperatures. By type 4, the matrix has thoroughly recrystallized and coarsened in grain size. By type 5, chondrules begin to become indistinct and matrix cannot be discerned. In type 6 chondrites, chondrules begin to integrate with what was once matrix, and small chondrules may no longer be recognizable. As metamorphism proceeds, many minerals coarsen and new, metamorphic minerals such as feldspar form. Some workers have extended the Van Schmus and Wood metamorphic scheme to include a type 7, although there is not consensus on whether this is necessary. Type 7 chondrites have experienced the highest temperatures possible, short of that required to produce melting. Should the onset of melting occur the meteorite would probably be classified as a primitive achondrite instead of a chondrite. All groups of ordinary and enstatite chondrites, as well as R and CK chondrites, show the complete metamorphic range from type 3 to 6. CO chondrites comprise only type 3 members, although these span a range of petrologic types from 3.0 to 3.8.

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Lesson: Sticks & Stones Objective: To design ways to address bullying behaviors Grade Level: Kindergarten and up [Based partly on a lesson plan by Teaching Tolerance called Breaking Down The Walls Of Intolerance http://www.tolerance.org/teach/printar.jsp?p=0&ar=970&pi=apg ] Explain to students that an estimated 5.7 million young people in the United States have identified themselves as a bully, admit to being bullied, or both. Bullying can be verbal or non-verbal, physical or non-physical. Bullying can be direct, like hitting, teasing, or making threats. It can also be indirect, like rumors, manipulation, isolation and exclusion. A bully might be one person acting out independently, or a clique or group of people picking on someone out of a need to increase their popularity or to seem more cool. 1. Ask students what the think the saying “Sticks and stones can break my bones, but names can really hurt me.” Has anyone heard another version of this saying? Which is truer? Ask students to take a moment to reflect on their experiences. Have they ever had someone say something to them that hurt their feelings. Has someone ever hurt them physically or tried to scare them? Have they ever hurt someone by something they said or did? 2. Teachers might want to provide students with their own personal example of a time they were a victim or a witness to bullying or they hurt someone’s feelings. If students feel comfortable, allow them a few moments to share their experiences aloud. And/Or read a book about bullying like This is Our House, Hey, Little Ant, Mr. Lincoln’s Way, Say Something, or Simon’s Hook. 3. Give each student a light gray paper “stone.” Have students write a behavior that could hurt someone or make them feel bad such as calling someone an ethnic name, or tripping someone. Younger children can draw a picture. 4. Have them wrinkle up the "stone" and then try to smooth it out. Explain that once someone has been hurt, it is never forgotten. You cannot remove the hurt. The wrinkles will always be there. 5. Hang stones on wall to create a wall of intolerance or have students sit in a circle and pile the rocks up in the middle. Ask students to think about ways to prevent these things from happening. Create a class list of ideas. 6. In turn, have each student select someone else’s stone off the wall or from the pile. Read your stone and imagine that this happened to yourself or a friend of yours. What could you do about it? Pair and share your ideas. 7. Together as a class make a poster or some other product (PowerPoint, video, letter to newspaper) explaining something positive everyone could do about bullying. Home * Issues * Groups * Activities * Contact Us* About Us All materials on this site copyrighted by TeachPeaceNow 2007

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